Patent Publication Number: US-2022213825-A1

Title: Prediction device, prediction method, and work vehicle

Description:
TECHNICAL FIELD 
     The present invention relates to a prediction device, a prediction method, and a work vehicle. 
     Priority is claimed on Japanese Patent Application No. 2019-133069, filed Jul. 18, 2019, the content of which is incorporated herein by reference. 
     BACKGROUND ART 
     In an exhaust gas regulation Tier 4 Final generation construction machine, a diesel exhaust fluid (DEF) (AUS32 JIS K2247) is used as a reducing agent for selective catalytic reduction (SCR). The DEF is stored in an in-vehicle tank, but in a cold region, for example, there is a problem in that the DEF freezes while an engine of the construction machine is stopped. When the engine of the construction machine is started, a thawing device, such as a heater for thawing mounted in the tank, is activated, and the frozen DEF can be thawed, but thawing takes time. Therefore, for example, when the engine is started, an output is limited, a work by the construction machine is limited, and waiting time occurs. 
     Patent Document 1 discloses a system that decides a change rate of a coolant temperature based on a coolant temperature of an engine and an ambient temperature of a reducing agent tank, predicts thawing time of a filling valve of the reducing agent tank based on the change rate and notifies an operator that filling of a reducing agent is prepared when the thawing prediction time is completed. 
     CITATION LIST 
     Patent Document 
     [Patent Document 1] 
     
         
         Specification of United States Patent Application, Publication No. 2016/0282167 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
     With the system disclosed in Patent Document 1, the thawing time of the filling valve into the reducing agent tank is predicted, and the operator is notified that the predicted thawing time is completed. However, the system disclosed in Patent Document 1 does not predict the time for freezing or the time required for thawing in a case in which the reducing agent stored in the reducing agent tank may freeze or in a case in which the reducing agent freezes. For example, when the time for freezing or the time required for thawing can be predicted in advance, it is possible to formulate a work plan in anticipation of the time or take measures such as moving a chassis to a position having low freezing possibility. 
     The present invention has been made in view of the above circumstances, and an object of the present invention is to provide a prediction device, a prediction method, and a work vehicle, which can predict the time for the reducing agent to freeze or the time required for thawing the reducing agent. 
     Solution to Problem 
     In order to achieve the object described above, an aspect of the present invention relates to a prediction device that predicts time for a reducing agent accommodated in a container mounted on a work vehicle to freeze, the device including a remaining amount information acquisition unit configured to acquire remaining amount information indicating a remaining amount of the reducing agent accommodated in the container, a wall surface temperature acquisition unit configured to acquire a wall surface temperature detection value that is a detection result of a wall surface temperature of the container, a reducing agent temperature acquisition unit configured to acquire a reducing agent temperature detection value that is a detection result of a temperature of the reducing agent, and a time calculation unit configured to calculate the time for the reducing agent to freeze based on the wall surface temperature detection value, the reducing agent temperature detection value, and the remaining amount information. 
     Advantageous Effects of Invention 
     According to the aspect described above, it is possible to predict the time for the reducing agent to freeze or the time required for thawing the reducing agent. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a side view showing a work vehicle according to the present embodiment. 
         FIG. 2  is a system configuration diagram related to a controller  6  shown in  FIG. 1 . 
         FIG. 3  is a block diagram showing a configuration example of the controller  6  shown in  FIGS. 1 and 2 . 
         FIG. 4  is a schematic diagram showing a configuration example of a shape characteristic table  68  shown in  FIG. 3 . 
         FIG. 5  is a flowchart showing an operation example of the controller  6  shown in  FIG. 3 . 
         FIG. 6  is a flowchart showing another operation example of the controller  6  shown in  FIG. 3 . 
         FIG. 7  is a schematic diagram for describing an operation example of the controller  6  shown in  FIG. 3 . 
         FIG. 8  is a block diagram showing another configuration example of a server  11  and the controller  6  (controller  6   a  in  FIG. 8 ) shown in  FIGS. 1 and 2 . 
         FIG. 9  is a flowchart showing an operation example of the server  11  shown in  FIG. 8 . 
         FIG. 10  is a flowchart showing another operation example of the server  11  shown in  FIG. 8 . 
         FIG. 11  is a flowchart showing still another operation example of the controller  6  shown in  FIG. 3 . 
         FIG. 12  is a schematic diagram for describing an operation example of the controller  6  shown in  FIG. 11 . 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Embodiments of the present invention will be described below with reference to drawings. In addition, in each drawing, the same reference numerals are used for the same or corresponding configurations, and the description thereof will be omitted as appropriate. 
     First Embodiment 
       FIG. 1  is a side view showing a work vehicle according to a first embodiment of the present invention. In an example shown in  FIG. 1 , the work vehicle according to the first embodiment is a dump truck  100 . In the present embodiment, the dump truck  100  is a manned dump truck operated by a driver (operator) getting on a cab (driver&#39;s cab)  108 , but is not limited to this, and may be an unmanned dump truck. Further, in the present embodiment, for example, the dump truck  100  is a rigid type dump truck  100 , but is not limited to this, and may be a transport vehicle such as an articulated type dump truck. 
     The dump truck  100  includes a vehicle body  102  and a dump body  103  provided on the vehicle body  102 . The vehicle body  102  includes a travel device  104  and a chassis  105  supported by the travel device  104 . The travel device  104  includes wheels  106  and axles  107  that rotatably support the wheels  106 . 
     In addition, the chassis  105  includes a power generation device  110 . The power generation device  110  generates power to drive the travel device  104 . The power generation device  110  includes an engine  12 . In the present embodiment, the engine  12  is a diesel engine. The engine  12  includes an exhaust pipe  12 C. The exhaust pipe  12 C is connected to a diesel particulate filter (DPF) device  131  of an exhaust gas aftertreatment device  130 . 
     The exhaust gas aftertreatment device  130  includes the DPF device  131 , a mixing device  132 , and a selective catalytic reduction (SCR) device  133 . The DPF device  131  removes fine particles such as soot in an exhaust gas. The mixing device  132  mixes the exhaust gas discharged from the DPF device  131  with urea water as a reducing agent and delivers the mixture to the SCR device  133 . The mixed urea water is hydrolyzed to generate ammonia in the mixing device  132 . The exhaust gas and the generated ammonia are delivered to the SCR device  133 . The mixing device  132  includes a supply pipe and an injector, which are not shown, connected to a reducing agent tank  3 . The reducing agent tank  3  stores the urea water to be supplied to the mixing device  132 . The reducing agent tank  3  mounted on the work vehicle is a container that accommodates the urea water as the reducing agent. In addition, in the present embodiment, the exhaust gas aftertreatment device  130  of the dump truck  100  as the work vehicle is equipped with both the DPF device  131  and the SCR device  133 , but the exhaust gas aftertreatment device  130  may be equipped with the SCR device  133  without the DPF device  131 . 
     The SCR device  133  includes a reducing catalyst, and the reducing catalyst causes a catalytic reaction between nitrogen oxide (NOx) contained in the exhaust gas and the ammonia generated in the mixing device  132 . As the reducing catalyst, for example, a vanadium-based catalyst, a zeolite-based catalyst, or the like is used. The NOx contained in the exhaust gas is converted into nitrogen and water by the catalytic reaction with the ammonia, which is the reducing agent. In addition, in the present embodiment, both the urea water and the ammonia are referred to as the reducing agent. 
     The cab  108  includes a controller  6  and a monitor  8 . The controller  6  is a prediction device that predicts time for the urea water (reducing agent) accommodated in the reducing agent tank  3  of the dump truck  100  to freeze or predicts time for the urea water to be heated and thawed by a heater tube (heating unit) installed in the reducing agent tank  3  in a case in which the urea water accommodated in the reducing agent tank  3  freezes. The monitor  8  displays a prediction result by the controller  6 . For example, the monitor  8  displays the time for the urea water to freeze or a temporal change of a temperature of the urea water or displays the time for the urea water to be thawed or the temporal change of the temperature of the urea water. 
     Next, a configuration related to the input and output of the controller  6  will be described with reference to  FIG. 2 .  FIG. 2  is a system configuration diagram related to the controller  6  shown in  FIG. 1 . In addition, in an example shown in  FIG. 2 , a heater tube  1  and a sensor module  4  are installed inside the reducing agent tank  3  that accommodates urea water  2  (hereinafter referred to as a reducing agent  2 ). A coolant (warm water) of the engine  12  circulates in the heater tube  1  to heat the reducing agent  2 . The sensor module  4  includes a concentration sensor  41 , a remaining amount sensor  42 , and a reducing agent temperature sensor  43 . The concentration sensor  41  detects a concentration of the reducing agent  2  and outputs a detection result to the controller  6 . The remaining amount sensor  42  detects a remaining amount of the reducing agent  2  (for example, a ratio (%) with respect to a full tank) and outputs a detection result to the controller  6 . The reducing agent temperature sensor  43  detects a temperature of the reducing agent  2  and outputs a detection result to the controller  6 . In addition, the reducing agent tank  3  is covered with a tank cover  7 . In addition, a wall surface temperature sensor  5  is provided in the tank cover  7 . The wall surface temperature sensor  5  detects a wall surface temperature of the reducing agent tank  3  and outputs a detection result to the controller  6 . As the wall surface temperature sensor  5 , a thermocouple sensor can be used, and a heat flow sensor may also be used. The heat flow sensor is a sensor that outputs an electric signal in response to an amount and a direction of a heat flow, and is, for example, configured by using a thermopile. 
     The concentration sensor  41 , the remaining amount sensor  42 , the reducing agent temperature sensor  43 , the wall surface temperature sensor  5 , the monitor  8 , an antenna  10 , an outside air temperature sensor  13 , and a control unit of the engine  12  (not shown) are connected to the controller  6 . The outside air temperature sensor  13  is installed at a predetermined position of the vehicle body  102 , which is not easily affected by a heat source such as the engine  12 , detects an outside air temperature, and outputs a detection result to the controller  6 . The monitor  8  is a display device. Alternatively, the monitor  8  may be an input display device such as a touch panel including a display surface and an operation surface. The antenna  10  is used for performing wireless communication with a server  11  installed at a position away from the dump truck  100 . The server  11  is a control device in which an administrator or the like monitors (manages) an operation state of each unit of the dump truck  100  and performs a remote operation. 
     Hereinafter, a configuration example of the controller  6  shown in  FIGS. 1 and 2  will be described with reference to  FIG. 3 . The controller  6  shown in  FIGS. 1 and 2  is configured by a computer and peripheral devices thereof (input device, voice output device, and the like).  FIG. 3  is a block diagram showing the configuration example of the controller  6  shown in  FIGS. 1 and 2 , and shows, in blocks, functional components configured by a combination of a hardware such as the computer and the peripheral devices thereof which configure the controller  6  and a software such as a program executed by the computer. 
     In an example shown in  FIG. 3 , the controller  6  includes an outside air temperature acquisition unit  61 , a remaining amount information acquisition unit  62 , a wall surface temperature acquisition unit  63 , a reducing agent temperature acquisition unit  64 , a time calculation unit  65 , an output unit  66 , and a storage unit  67 . The outside air temperature acquisition unit  61  inputs an output signal of the outside air temperature sensor  13  and acquires the outside air temperature. In addition, the outside air temperature acquisition unit  61  executes a process of comparing the acquired outside air temperature with a freezing point of the reducing agent  2 . The remaining amount information acquisition unit  62  inputs an output signal of the remaining amount sensor  42  and acquires the remaining amount (remaining amount information) of the reducing agent in the reducing agent tank  3 . In addition, the remaining amount information acquisition unit  62  may input the output signal of the remaining amount sensor  42 , may refer to a table or the like in which the output signal of the remaining amount sensor  42  stored in the storage unit  67  and the remaining amount (volume) of the reducing agent are associated with each other, and may acquire the remaining amount information of the reducing agent in the reducing agent tank  3 . The wall surface temperature acquisition unit  63  inputs an output signal of the wall surface temperature sensor  5  and acquires the wall surface temperature (wall surface temperature detection value) of the reducing agent tank  3 . The reducing agent temperature acquisition unit  64  inputs the output signal of the reducing agent temperature sensor  43  and acquires the reducing agent temperature (reducing agent temperature detection value). The time calculation unit  65  calculates the time for the reducing agent to freeze or calculates the time for the reducing agent to be thawed based on the wall surface temperature detection value, the reducing agent temperature detection value, and the remaining amount information. The output unit  66  outputs the time for the reducing agent to freeze, which is calculated by the time calculation unit  65  or the time for the reducing agent to be thawed, and the temporal change of the temperature of the reducing agent to the monitor  8  or the like. The storage unit  67  stores a shape characteristic table  68 , characteristic information (freezing point temperature, specific heat, latent heat, density, and the like of the reducing agent  2 ) (not shown) of the reducing agent  2 , characteristic information (mass, specific heat, surface area, and the like of the reducing agent tank  3 ) of the reducing agent tank  3 , and the like. In addition, for example, the specific heat of the reducing agent  2  depends on the concentration and the temperature of the reducing agent  2 , and thus the specific heat of the reducing agent  2  can be represented by an array (table) including the concentration and the temperature as elements. In addition, the freezing point temperature of the reducing agent  2  depends on the concentration of the reducing agent  2 , and thus the freezing point temperature of the reducing agent  2  can be represented by an array (table) including the concentration of the reducing agent  2  as an element. 
     Here, a configuration example of the shape characteristic table  68  shown in  FIG. 3  will be described with reference to  FIG. 4 .  FIG. 4  is a schematic diagram showing a configuration example of the shape characteristic table  68  shown in  FIG. 3 . The shape characteristic table  68  shown in  FIG. 4  is configured by an array indicating a correspondence between the remaining amount (%) of the reducing agent, the mass (kg) of the reducing agent, a contact surface area (m 2 ) of the tank, and a contact surface area (m 2 ) of the heater tube. The contact surface area (m 2 ) of the tank is an area of a surface of the reducing agent tank  3  with which the reducing agent  2  comes into contact. The contact surface area (m 2 ) of the heater tube is an area of a surface of the heater tube  1  with which the reducing agent  2  comes into contact. The correspondence between the remaining amount (%) of the reducing agent, the mass (kg) of the reducing agent, the contact surface area (m 2 ) of the tank, and the contact surface area (m 2 ) of the heater tube is decided by a shape of the reducing agent tank  3 , a shape of the heater tube  1 , and an attachment method to the reducing agent tank  3 . By referring to the shape characteristic cable  68  shown in  FIG. 4 , each value corresponding to the remaining amount (%) of the reducing agent (the mass (kg) of the reducing agent, the contact surface area (m 2 ) of the tank, and the contact surface area (m 2 ) of the heater tube) can be acquired. 
     Next, an operation example of the controller  6  will be described with reference to  FIG. 5 .  FIG. 5  is a flowchart showing the operation example in a case in which the controller  6  shown in  FIG. 3  predicts freezing time. A process shown in  FIG. 5  is started in a case in which, for example, the operator performs a predetermined input operation with respect to the controller  6  in a state in which the coolant (warm water) does not circulate in the heater tube  1 . In addition, in a case in which the dump truck  100  is an unmanned dump truck, for example, the controller  6  may be operated by the controller  6  receiving a signal for providing an instruction for the prediction of the freezing time from the server  11  via the antenna  10  by the wireless communication. 
     In the controller  6 , when the process shown in  FIG. 5  is started, first, the outside air temperature acquisition unit  61  inputs the output signal of the outside air temperature sensor  13  to acquire the outside air temperature and compares the outside air temperature and the freezing point temperature of the reducing agent  2  (step S 11 ). On the other hand, in a case in which the outside air temperature is not equal to or lower than the freezing point temperature of the reducing agent  2  (in a case of “NO” in step S 11 ), the outside air temperature acquisition unit  61  displays that fact on, for example, the monitor  8 , and terminates the process shown in  FIG. 5 . 
     On the other hand, in a case in which the outside air temperature is equal to or lower than the freezing point temperature of the reducing agent  2  (in a case of “YES” in step S 11 ), the reducing agent temperature acquisition unit  64  inputs the output signal of the reducing agent temperature sensor  43  to acquire the reducing agent temperature (reducing agent temperature detection value) and the remaining amount information acquisition unit  62  inputs the output signal of the remaining amount sensor  42  to acquire the remaining amount (remaining amount information) of the reducing agent in the reducing agent tank  3  (step S 12 ). 
     Then, the wall surface temperature acquisition unit  63  inputs the output signal of the wall surface temperature sensor  5  a plurality of times (at least twice) at predetermined time intervals to acquire the wall surface temperature (wall surface temperature detection value) of the reducing agent tank  3  (step S 13 ). 
     Next, the time calculation unit  65  calculates freezing prediction time of the reducing agent  2  as follows (step S 14 ). 
     First, the time calculation unit  65  calculates a tank heat flux, which is the amount of heat that crosses a unit area of the reducing agent tank  3  in a unit time, by the following expression (A1). In addition, in a case in which the heat flow sensor is used as the wall surface temperature sensor  5 , the value itself detected by the heat flow sensor can be used as the tank heat flux shown on the left side of the following expression (A1). 
     
       
         
           
             
               
                 
                   
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                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
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                     Tank 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     heat 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
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                       ⁢ 
                       
                           
                       
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                             ⁢ 
                             amount 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
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                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             wall 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             surface 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
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                               ⁡ 
                               
                                 [ 
                                 
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                             × 
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   
                                     Mass 
                                     ⁢ 
                                     
                                         
                                     
                                     [ 
                                     kg 
                                     ] 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   of 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
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                                   × 
                                 
                               
                             
                             
                               
                                 
                                   Specific 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     heat 
                                     ⁢ 
                                     
                                         
                                     
                                     [ 
                                     
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                                       / 
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                                     ] 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   of 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   tank 
                                 
                               
                             
                           
                         
                       
                     
                     
                       Surface 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         area 
                         ⁢ 
                         
                             
                         
                         [ 
                         
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                           2 
                         
                         ] 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       of 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       tank 
                     
                   
                 
               
               
                 
                   ( 
                   
                     A 
                     ⁢ 
                     
                         
                     
                     ⁢ 
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     In the expression (A1), a change amount of the wall surface temperature is a temperature change per unit time and is calculated based on results of a plurality of measurements of the wall surface temperature of the reducing agent tank  3 , which is acquired in step S 13 . The mass of the tank, the specific heat of the tank, and the surface area of the tank, which are indicated by the expression (A1), are the mass, the specific heat, and the surface area of the reducing agent tank  3 . 
     Then, the time calculation unit  65  calculates a temperature change per time, which is the temperature change of the reducing agent  2  per unit time, by the following expression (A2). 
     
       
         
           
             
               
                 
                   
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                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
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                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     Temperature 
                     ⁢ 
                     
                         
                     
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                     charge 
                     ⁢ 
                     
                         
                     
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                     ⁢ 
                     
                         
                     
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                             Tank 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             heat 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               flux 
                               [ 
                               
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                                   ⁢ 
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                             × 
                           
                         
                       
                       
                         
                           
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                             ⁢ 
                             
                                 
                             
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                             ⁢ 
                             
                                 
                             
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                               ⁢ 
                               
                                   
                               
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                               ] 
                             
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                             of 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             tank 
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               Mass 
                               ⁢ 
                               
                                   
                               
                               [ 
                               kg 
                               ] 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             of 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             reducing 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
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                             × 
                           
                         
                       
                       
                         
                           
                             Specific 
                             ⁢ 
                             
                                 
                             
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                               ⁢ 
                               
                                   
                               
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                               ] 
                             
                             ⁢ 
                             
                                 
                             
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                             ⁢ 
                             
                                 
                             
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                   ( 
                   
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                     ⁢ 
                     
                         
                     
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     In the expression (A2), the contact surface area of the tank and the mass of the reducing agent are values obtained from the shape characteristic table  68  based on the remaining amount information. As the specific heat of the reducing agent, the specific heat of the reducing agent  2  stored in the storage unit  67  as the characteristic information is read out and used. As the tank heat flux, the tank heat flux obtained by the expression (A1) is used. 
     Then, the time calculation unit  65  calculates the freezing prediction time (liquid region), which is the time for the temperature of the liquid reducing agent  2  to drop to the freezing point temperature, by the following expression (A3-1). 
     
       
         
           
             
               
                 
                   
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                     Freezing 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     prediction 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     time 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           liquid 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           region 
                         
                         ) 
                       
                       ⁢ 
                       
                           
                       
                       [ 
                       s 
                       ] 
                     
                   
                   = 
                   
                     
                       
                         
                           
                             
                               Reducing 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               agent 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 temperature 
                                 ⁢ 
                                 
                                     
                                 
                                 [ 
                                 K 
                                 ] 
                               
                             
                             - 
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   Freezing 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   point 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     temperature 
                                     ⁢ 
                                     
                                         
                                     
                                     [ 
                                     K 
                                     ] 
                                   
                                 
                               
                             
                             
                               
                                 
                                   of 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   reducing 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   agent 
                                 
                               
                             
                           
                         
                       
                     
                     
                       Temperature 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       change 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       per 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         time 
                         ⁢ 
                         
                             
                         
                         [ 
                         
                           K 
                           / 
                           s 
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     A3 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
           
         
       
     
     In the expression (A3-1), the reducing agent temperature is the value acquired in step S 12 . In addition, the time calculation unit  65  can calculate a temperature drop curve of the reducing agent  2  in the liquid region by an expression {reducing agent temperature at freely-selected time=initial value of reducing agent temperature−(temperature change per time×freely-selected time)}.  FIG. 7  shows an example of a prediction value and a measurement value of a temperature drop curve of the reducing agent  2 .  FIG. 7  is a schematic diagram for describing an operation example of the controller  6  shown in  FIG. 3 , and a horizontal axis represents the time and a vertical axis represents the temperature of the reducing agent  2 , which indicate the temperature change of the reducing agent  2 . In an example shown in  FIG. 7 , the freezing point temperature of the reducing agent  2  is −11° C. 
     Then, the time calculation unit  65  calculates the freezing prediction time (solid-liquid coexistence region), which is the time during which the reducing agent  2  dropped to the freezing point temperature is maintained in the solid-liquid coexistence region, by the following expression (A3-2). Note that, in the solid-liquid coexistence region, the reducing agent temperature is fixed at the freezing point temperature. As the latent heat of the reducing agent, the latent heat of the reducing agent  2  stored in the storage unit  67  as the characteristic information is read out and used. As the tank heat flux, the tank heat flux obtained by the expression (A1) is used. 
     
       
         
           
             
               
                 
                   
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                       Expression 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       4 
                     
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                     Freezing 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     prediction 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     time 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           solid 
                           ⁢ 
                           
                             - 
                           
                           ⁢ 
                           liquid 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           coexistence 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           region 
                         
                         ) 
                       
                       ⁢ 
                       
                           
                       
                       [ 
                       s 
                       ] 
                     
                   
                   = 
                   
                     
                       
                         
                           
                             
                               Mass 
                               ⁢ 
                               
                                   
                               
                               [ 
                               kg 
                               ] 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             of 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             reducing 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             agent 
                             × 
                           
                         
                       
                       
                         
                           
                             Latent 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               heat 
                               ⁢ 
                               
                                   
                               
                               [ 
                               
                                 J 
                                 / 
                                 kg 
                               
                               ] 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             of 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             reducing 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             agent 
                           
                         
                       
                     
                     
                       
                         
                           
                             Tank 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             heat 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               flux 
                               ⁢ 
                               
                                   
                               
                               [ 
                               
                                 J 
                                 
                                   
                                     m 
                                     s 
                                   
                                   ⁢ 
                                   s 
                                 
                               
                               ] 
                             
                             × 
                           
                         
                       
                       
                         
                           
                             Contact 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             surface 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               area 
                               ⁢ 
                               
                                   
                               
                               [ 
                               
                                 m 
                                 2 
                               
                               ] 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             of 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             tank 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     A 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     Then, the time calculation unit  65  calculates the freezing prediction time (solid region), which is the time required for the temperature of the solid reducing agent  2  to drop to an any reducing agent temperature, by the following expression (A3-3). 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       Expression 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       5 
                     
                     ] 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     Tank 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     heat 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       flux 
                       ⁢ 
                       
                           
                       
                       [ 
                       
                         J 
                         
                           
                             m 
                             2 
                           
                           ⁢ 
                           s 
                         
                       
                       ] 
                     
                   
                   = 
                   
                     
                       
                         
                           
                             Change 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             amount 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             of 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             wall 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             surface 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               temperature 
                               ⁡ 
                               
                                 [ 
                                 
                                   K 
                                   s 
                                 
                                 ] 
                               
                             
                             × 
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   
                                     Mass 
                                     ⁢ 
                                     
                                         
                                     
                                     [ 
                                     kg 
                                     ] 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   of 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   tank 
                                   × 
                                 
                               
                             
                             
                               
                                 
                                   Specific 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     heat 
                                     ⁢ 
                                     
                                         
                                     
                                     [ 
                                     
                                       J 
                                       / 
                                       kgK 
                                     
                                     ] 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   of 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   tank 
                                 
                               
                             
                           
                         
                       
                     
                     
                       Surface 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         area 
                         ⁢ 
                         
                             
                         
                         [ 
                         
                           m 
                           2 
                         
                         ] 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       of 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       tank 
                     
                   
                 
               
               
                 
                   ( 
                   
                     A 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
               
             
           
         
       
     
     For example, when the reducing agent temperature of the expression (A3-3) is the outside air temperature, the time for the reducing agent temperature to drop to the outside air temperature (time for thermal equilibrium with the outside air) can be obtained by the expression (A3-3). In addition, in the time calculation unit  65  can calculate a temperature drop curve of the reducing agent  2  in the solid region by an expression {reducing agent temperature at freely-selected time=freezing point temperature of reducing agent temperature−(temperature change per time×freely-selected time)}. 
     As shown in  FIG. 7 , the freezing prediction time calculated in the present embodiment is a value roughly close to an actual measurement value in the liquid region, the solid-liquid coexistence region, and the solid region. 
     Next, the output unit  66  outputs the freezing prediction time calculated in step S 14  to the monitor  8 , and terminates the process shown in  FIG. 5  (step S 15 ). The freezing prediction time to be output may be, for example, only the freezing prediction time (liquid region), or may be all or part of the freezing prediction time (liquid region), the freezing prediction time (solid-liquid coexistence region), and the freezing prediction time (solid region). 
     Next, another operation example of the controller  6  will be described with reference to  FIG. 6 .  FIG. 6  is a flowchart showing an operation example in a case in which the controller  6  shown in  FIG. 3  predicts thawing time. A process shown in  FIG. 6  is started in a case in which, for example, the operator performs a predetermined input operation with respect to the controller  6  in a state in which the circulation of the coolant (warm water) in the heater tube  1  is started. 
     In the controller  6 , when the process shown in  FIG. 6  is started, first, the reducing agent temperature acquisition unit  64  determines whether or not freezing of the reducing agent tank  3  is detected and the circulation of the coolant (warm water) in the heater tube  1  is started, based on, for example, the information obtained from the control unit and the like of the engine  12  (step S 21 ). On the other hand, in a case in which freezing of the reducing agent tank  3  is not detected or the circulation of the coolant (warm water) in the heater tube  1  is not started (in a case of “NO” in step S 21 ), for example, the reducing agent temperature acquisition unit  64  displays that fact on, for example, the monitor  8 , and terminates the process shown in  FIG. 6 . 
     On the other hand, in a case in which freezing of the reducing agent tank  3  is detected and the circulation of the coolant (warm water) in the heater tube  1  is started (in a case of “YES” in step S 21 ), the reducing agent temperature acquisition unit  64  inputs the output signal of the reducing agent temperature sensor  43  to acquire the reducing agent temperature (reducing agent temperature detection value) and the remaining amount information acquisition unit  62  inputs the output signal of the remaining amount sensor  42  to acquire the remaining amount (remaining amount information) of the reducing agent in the reducing agent tank  3  (step S 22 ). 
     Then, the wall surface temperature acquisition unit  63  inputs the output signal of the wall surface temperature sensor  5  a plurality of times (at least twice) at predetermined time intervals to acquire the wall surface temperature (wall surface temperature detection value) of the reducing agent tank  3  (step S 23 ). 
     Next, the time calculation unit  65  calculates thawing prediction time of the reducing agent  2  as follows (step S 24 ). 
     First, the time calculation unit  65  calculates the tank heat flux, which is the amount of heat that crosses the unit area of the reducing agent tank  3  in a unit time, by the following expression (B1). In addition, in a case in which the heat flow sensor is used as the wall surface temperature sensor  5 , the value itself detected by the heat flow sensor can be used as the tank heat flux shown on the left side of the following expression (B1). 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       Expression 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       6 
                     
                     ] 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     Tank 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     heat 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       flux 
                       ⁢ 
                       
                           
                       
                       [ 
                       
                         J 
                         
                           
                             m 
                             2 
                           
                           ⁢ 
                           s 
                         
                       
                       ] 
                     
                   
                   = 
                   
                     
                       
                         
                           
                             Change 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             amount 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             of 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             wall 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             surface 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               temperature 
                               ⁡ 
                               
                                 [ 
                                 
                                   K 
                                   s 
                                 
                                 ] 
                               
                             
                             × 
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   
                                     Mass 
                                     ⁢ 
                                     
                                         
                                     
                                     [ 
                                     kg 
                                     ] 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   of 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   tank 
                                   × 
                                 
                               
                             
                             
                               
                                 
                                   Specific 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     heat 
                                     ⁢ 
                                     
                                         
                                     
                                     [ 
                                     
                                       J 
                                       / 
                                       kgK 
                                     
                                     ] 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   of 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   tank 
                                 
                               
                             
                           
                         
                       
                     
                     
                       Surface 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         area 
                         ⁢ 
                         
                             
                         
                         [ 
                         
                           m 
                           2 
                         
                         ] 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       of 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       tank 
                     
                   
                 
               
               
                 
                   ( 
                   B1 
                   ) 
                 
               
             
           
         
       
     
     In the expression (B1), the change amount of the wall surface temperature is the temperature change per unit time and is calculated based on the results of a plurality of measurements of the wall surface temperature of the reducing agent tank  3 , which is acquired in step S 23 . The mass of the tank, the specific heat of the tank, and the surface area of the tank, which are indicated by the expression (B1), are the mass, the specific heat, and the surface area of the reducing agent tank  3 . 
     Then, the time calculation unit  65  calculates the temperature change per time, which is the temperature change of the reducing agent  2  per unit time, by the following expression (B2). 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       Expression 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       7 
                     
                     ⁢ 
                     
                         
                     
                     ] 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     Temperature 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     change 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     per 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       time 
                       ⁢ 
                       
                           
                       
                       [ 
                       
                         K 
                         / 
                         s 
                       
                       ] 
                     
                   
                   = 
                   
                     
                       { 
                       
                         
                           ( 
                           
                             HT 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             heat 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               flux 
                               ⁢ 
                               
                                   
                               
                               [ 
                               
                                 J 
                                 
                                   
                                     m 
                                     2 
                                   
                                   ⁢ 
                                   s 
                                 
                               
                               ] 
                             
                             × 
                             Contact 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             surface 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               area 
                               ⁢ 
                               
                                   
                               
                               [ 
                               
                                 m 
                                 2 
                               
                               ] 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             of 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             HT 
                           
                           ) 
                         
                         - 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             Tank 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             heat 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               flux 
                               ⁢ 
                               
                                   
                               
                               [ 
                               
                                 J 
                                 
                                   
                                     m 
                                     2 
                                   
                                   ⁢ 
                                   s 
                                 
                               
                               ] 
                             
                             × 
                             Contact 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             surface 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               area 
                               ⁢ 
                               
                                   
                               
                               [ 
                               
                                 m 
                                 2 
                               
                               ] 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             of 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             tank 
                           
                           ) 
                         
                       
                       } 
                     
                     ÷ 
                     
                       ( 
                       
                           
                       
                       ⁢ 
                       
                         
                           
                             
                               
                                 
                                   
                                     Mass 
                                     ⁢ 
                                     
                                         
                                     
                                     [ 
                                     kg 
                                     ] 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   of 
                                 
                                 ⁢ 
                                 
                                     
                                 
                               
                             
                           
                           
                             
                               
                                 reducing 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 agent 
                               
                             
                           
                         
                         × 
                         
                           
                             
                               
                                 Specific 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   heat 
                                   ⁢ 
                                   
                                       
                                   
                                   [ 
                                   
                                     J 
                                     / 
                                     kgK 
                                   
                                   ] 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 of 
                               
                             
                           
                           
                             
                               
                                 reducing 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 agent 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   B2 
                   ) 
                 
               
             
           
         
       
     
     In the expression (B2), the contact surface area of the tank, the mass of the reducing agent, and the contact surface area of the heater tube (HT) are values obtained from the shape characteristic table  68  based on the remaining amount information. The heat flux of the heater tube (HT) can be decided, for example, by using an empirical expression or a table set experimentally or by simulation calculation with parameters such as the reducing agent temperature, the coolant temperature, and the coolant flow rate. In addition, as the specific heat of the reducing agent, the specific heat of the reducing agent  2  stored in the storage unit  67  as the characteristic information is read out and used. As the tank heat flux, the tank heat flux obtained by the expression (B1) is used. 
     Then, the time calculation unit  65  calculates the thawing prediction time (solid region), which is the time required for the temperature of the reducing agent  2  in the solid region to rise by a predetermined reducing agent temperature, by the following expression (B3-1). 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       Expression 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       8 
                     
                     ] 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     Thawing 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     prediction 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     time 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           solid 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           region 
                         
                         ) 
                       
                       ⁢ 
                       
                           
                       
                       [ 
                       s 
                       ] 
                     
                   
                   = 
                   
                     
                       Reducung 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       agent 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         temperature 
                         ⁢ 
                         
                             
                         
                         [ 
                         K 
                         ] 
                       
                     
                     
                       Temperature 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       change 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       per 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         time 
                         ⁢ 
                         
                             
                         
                         [ 
                         
                           K 
                           / 
                           s 
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     B3 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
           
         
       
     
     For example, when the reducing agent temperature of the expression (B3-1) is a temperature corresponding to a difference between the current reducing agent temperature and the freezing point temperature, the time required for the temperature to rise to the freezing point temperature can be obtained by the expression (B3-1). In addition, in the time calculation unit  65  can calculate a temperature rise curve of the reducing agent  2  in the solid region by an expression {reducing agent temperature at freely-selected time=reducing agent temperature (initial value)+(temperature change per time×freely-selected time)}. 
     Then, the time calculation unit  65  calculates the thawing prediction time (solid-liquid coexistence region), which is the time during which the reducing agent  2  rising to the freezing point temperature is maintained in the solid-liquid coexistence region, by the following expression (B3-2). As the tank heat flux, the tank heat flux obtained by the expression (B1) is used. As the latent heat of the reducing agent, the latent heat of the reducing agent  2  stored as characteristic information in the storage unit  67  is read out and used. In addition, in the solid-liquid coexistence region, the reducing agent temperature is assumed to be fixed at the freezing point temperature. 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       Expression 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       9 
                     
                     ] 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     Thawing 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     prediction 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     time 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           solid 
                           ⁢ 
                           
                             - 
                           
                           ⁢ 
                           liquid 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           coexistence 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           region 
                         
                         ) 
                       
                       ⁢ 
                       
                           
                       
                       [ 
                       s 
                       ] 
                     
                   
                   = 
                   
                     
                       
                         
                           
                             
                               Mass 
                               ⁢ 
                               
                                   
                               
                               [ 
                               kg 
                               ] 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             of 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             reducing 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             agent 
                             × 
                           
                         
                       
                       
                         
                           
                             Latent 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               heat 
                               ⁢ 
                               
                                   
                               
                               [ 
                               
                                 J 
                                 / 
                                 kg 
                               
                               ] 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             of 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             reducing 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             agent 
                           
                         
                       
                     
                     
                       
                         
                           
                             Tank 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             heat 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               flux 
                               ⁢ 
                               
                                   
                               
                               [ 
                               
                                 J 
                                 
                                   
                                     m 
                                     s 
                                   
                                   ⁢ 
                                   s 
                                 
                               
                               ] 
                             
                             × 
                           
                         
                       
                       
                         
                           
                             Contact 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             surface 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               area 
                               ⁢ 
                               
                                   
                               
                               [ 
                               
                                 m 
                                 2 
                               
                               ] 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             of 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             tank 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     B 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     Then, the time calculation unit  65  calculates the thawing prediction time (liquid region), which is the time for the temperature of the liquid reducing agent  2  to rise to a predetermined reducing agent temperature, by the following expression (B3-3). 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       Expression 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       10 
                     
                     ] 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     Thawing 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     prediction 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     time 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           liquid 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           region 
                         
                         ) 
                       
                       ⁢ 
                       
                           
                       
                       [ 
                       s 
                       ] 
                     
                   
                   = 
                   
                     
                       
                         
                           
                             Reducing 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             agent 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               temperature 
                               ⁢ 
                               
                                   
                               
                               [ 
                               K 
                               ] 
                             
                             * 
                           
                         
                       
                       
                         
                           
                             Freezing 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             point 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               temperature 
                               ⁢ 
                               
                                   
                               
                               [ 
                               K 
                               ] 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             of 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             reducing 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             agent 
                           
                         
                       
                     
                     
                       Temperature 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       change 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       per 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         time 
                         ⁢ 
                         
                             
                         
                         [ 
                         
                           K 
                           / 
                           s 
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     B 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
               
             
           
         
       
     
     In the expression (B3-3), the reducing agent temperature is a predetermined temperature. By using the expression (B3-3), for example, the time for the liquid reducing agent  2  to be maintained at a fixed temperature (time for an amount of heat obtained from the coolant and an amount of heat taken by the outside air) can be obtained. In addition, in the time calculation unit  65  can calculate the temperature rise curve of the reducing agent  2  in the liquid region by an expression {reducing agent temperature at freely-selected time=freezing point temperature+(temperature change per time×freely-selected time)}. 
     Next, the output unit  66  outputs the thawing prediction time calculated in step S 24  to the monitor  8 , and terminates the process shown in  FIG. 6  (step S 25 ). The thawing prediction time to be output may be, for example, only the thawing prediction time (solid region), or may be all or part of the thawing prediction time (solid region), the thawing prediction time (solid-liquid coexistence region), and the thawing prediction time (liquid region). 
     As described above, according to the present embodiment, the time for freezing or the time required for thawing can be predicted in a case in which the reducing agent  2  stored in the reducing agent tank  3  may freeze or in a case in which the reducing agent freezes. Therefore, according to the present embodiment, for example, by predicting the time for freezing or the time required for thawing in advance, it is possible to formulate an operation plan of the work vehicle in anticipation of the time or take measures such as moving the work vehicle to a position having low freezing possibility before the work vehicle is stopped. 
     Second Embodiment 
     Hereinafter, a second embodiment of the present invention will be described with reference to  FIGS. 8 to 10 .  FIG. 8  is a block diagram showing another configuration example (configuration example according to the second embodiment) of the server  11  and the controller  6  shown in  FIGS. 1 and 2  (shown as a controller  6   a  in  FIG. 8 ).  FIG. 9  is a flowchart showing an operation example of the server  11  shown in  FIG. 8 .  FIG. 10  is a flowchart showing another operation example of the server  11  shown in  FIG. 8 . 
     In the first embodiment, the controller  6  mounted on the dump truck  100  calculates the freezing prediction time and the thawing prediction time, whereas in the second embodiment, the server  11  calculates the freezing prediction time and the thawing prediction time. The second embodiment will be described below focusing on a difference from the first embodiment. 
     First, the configuration examples of the server  11  and the controller  6  shown in  FIGS. 1 and 2  in the second embodiment (controller  6   a ) will be described with reference to  FIG. 8 . The server  11  shown in  FIGS. 1 and 2  is configured by a computer and peripheral devices thereof (input device, voice output device, and the like), in the same manner as the controller  6  (controller  6   a ).  FIG. 8  is a block diagram showing the configuration examples of the server  11  and the controller  6   a  shown in  FIGS. 1 and 2 , and shows, in blocks, functional components configured by a combination of a hardware such as the computer and the peripheral devices thereof which configure the server  11  and the controller  6   a  and a software such as a program executed by the computer. 
     The controller  6   a  shown in  FIG. 8 , the time calculation unit  65  and the storage unit  67  are removed and a communication unit  69  is newly provided with respect to the controller  6  shown in  FIG. 3 . The communication unit  69  transmits the information acquired by the outside air temperature acquisition unit  61 , the remaining amount information acquisition unit  62 , the wall surface temperature acquisition unit  63 , and the reducing agent temperature acquisition unit  64  to the server  11 , transmits the information (for example, information indicating whether or not thawing of the warm water is started) acquired from the control unit of the engine  12  to the server  11 , or displays the information received from the server  11  on the monitor  8  via the output unit  66 . 
     The server  11  shown in  FIG. 8  includes a thawed state reception unit  111 , an outside air temperature reception unit  112 , a remaining amount information reception unit  113 , a wall surface temperature reception unit  114 , a reducing agent temperature reception unit  115 , and a time calculation unit  116 , a transmission unit  117 , and a storage unit  118 . 
     The thawed state reception unit  111  receives the information indicating whether or not thawing of warm water is started from the control unit of the engine  12  via the communication unit  69  (or from the control unit of the engine  12  via a predetermined communication unit without using the communication unit  69 ). The outside air temperature reception unit  112  receives information on the outside air temperature acquired by the outside air temperature acquisition unit  61  from the communication unit  69 . The remaining amount information reception unit  113  receives the remaining amount (remaining amount information) of the reducing agent in the reducing agent tank  3 , which is acquired by the remaining amount information acquisition unit  62  from the communication unit  69 . The wall surface temperature reception unit  114  receives the wall surface temperature (wall surface temperature detection value) of the reducing agent tank  3 , which is acquired by the wall surface temperature acquisition unit  63  from the communication unit  69 . The reducing agent temperature reception unit  115  receives the reducing agent temperature (reducing agent temperature detection value) acquired by the reducing agent temperature acquisition unit  64  from the communication unit  69 . Similar to the time calculation unit  65  according to the first embodiment shown in  FIG. 3 , the time calculation unit  116  calculates the time for the reducing agent to freeze or calculates the time for the reducing agent to be thawed based on the wall surface temperature detection value, the reducing agent temperature detection value, and the remaining amount information. The transmission unit  117  transmits the time for the reducing agent to freeze or the time for the reducing agent to be thawed, and the temporal change of the temperature of the reducing agent calculated by the time calculation unit  116  to the communication unit  69  of the controller  6   a . Similar to the storage unit  67  shown in  FIG. 3 , the storage unit  118  stores the shape characteristic table  68 , the characteristic information (freezing point temperature, specific heat, latent heat, density, and the like of the reducing agent  2 ) (not shown) of the reducing agent  2 , the characteristic information (mass, specific heat, surface area, and the like of the reducing agent tank  3 ) of the reducing agent tank  3 , and the like. In addition, for example, the specific heat of the reducing agent  2  depends on the concentration and the temperature of the reducing agent  2 , and thus the specific heat of the reducing agent  2  can be represented by the array (table) including the concentration and the temperature as the elements. In addition, the freezing point temperature of the reducing agent  2  depends on the concentration of the reducing agent  2 , and thus the freezing point temperature of the reducing agent  2  can be represented by the array (table) including the concentration of the reducing agent  2  as the element. 
     Next, the operation example of the server  11  shown in  FIG. 8  will be described with reference to  FIG. 9 .  FIG. 9  is a flowchart showing the operation example in a case in which the server  11  shown in  FIG. 8  predicts the freezing time. A process shown in  FIG. 9  is started in a case in which, for example, the operator of the server  11 , such as the administrator, performs a predetermined input operation with respect to the server  11  in a state in which the coolant (warm water) does not circulate in the heater tube  1 . 
     In the server  11 , when the process shown in  FIG. 9  is started, first, the outside air temperature reception unit  112  receives the outside air temperature acquired by the outside air temperature acquisition unit  61  (step S 31 ). Then, for example, the outside air temperature reception unit  112  compares the outside air temperature with the freezing point temperature of the reducing agent  2  (step S 32 ). On the other hand, in a case in which the outside air temperature is not equal to or lower than the freezing point temperature of the reducing agent  2  (in a case of “NO” in step S 32 ), the outside air temperature reception unit  112  displays that fact on, for example, a predetermined monitor of the server  11 , and terminates the process shown in  FIG. 9 . 
     On the other hand, in a case in which the outside air temperature is equal to or lower than the freezing point temperature of the reducing agent  2  (in a case of “YES” in step S 32 ), the reducing agent temperature reception unit  115  receives the reducing agent temperature (reducing agent temperature detection value) acquired by the reducing agent temperature acquisition unit  64 , and the remaining amount information reception unit  113  receives the remaining amount (remaining amount information) of the reducing agent in the reducing agent tank  3 , which is acquired by the remaining amount information acquisition unit  62  (step S 33 ). 
     Then, the wall surface temperature reception unit  114  receives the wall surface temperature (wall surface temperature detection value) of the reducing agent tank  3 , which is acquired a plurality of times (at least twice) at predetermined time intervals by the wall surface temperature acquisition unit  63  (step S 34 ). 
     Next, the time calculation unit  116  calculates the freezing prediction time of the reducing agent  2  in the same manner as the time calculation unit  65  according to the first embodiment (step S 35 ). 
     Next, the transmission unit  117  transmits the freezing prediction time calculated in step S 35  to the communication unit  69 , and terminates the process shown in  FIG. 9  (step S 36 ). On the other hand, the communication unit  69  of the controller  6   a  outputs the received information indicating the freezing prediction time on the monitor  8 . 
     Next, another operation example of the server  11  will be described with reference to  FIG. 10 .  FIG. 10  is a flowchart showing the operation example in a case in which the server  11  shown in  FIG. 8  predicts the thawing time. A process shown in  FIG. 10  is started in a case in which, for example, the operator of the server  11 , such as the administrator, performs a predetermined input operation with respect to the server  11  in a state in which the circulation of the coolant (warm water) in the heater tube  1  is started. 
     In the server  11 , when the process shown in  FIG. 10  is started, first, the reducing agent temperature reception unit  115  receives the reducing agent temperature (reducing agent temperature detection value) acquired by the reducing agent temperature acquisition unit  64  (step S 41 ). Then, the thawed state reception unit  111  receives information indicating whether or not the circulation of the coolant (warm water) in the heater tube  1  is started from the control unit of the engine  12  and the like (step S 42 ). 
     Next, for example, the thawed state reception unit  111  determines whether or not freezing of the reducing agent tank  3  is detected and the circulation of the coolant (warm water) in the heater tube  1  is started, based on the information acquired in step S 41  and step S 42  (step S 43 ). On the other hand, in a case in which freezing of the reducing agent tank  3  is not detected or the circulation of the coolant (warm water) in the heater tube  1  is not started (in a case of “NO” in step S 43 ), for example, the thawed state reception unit  111  displays that fact on, for example, the predetermined monitor of the server  11 , and terminates the process shown in  FIG. 10 . 
     On the other hand, in a case in which freezing of the reducing agent tank  3  is detected and the circulation of the coolant (warm water) in the heater tube  1  is started (in a case of “YES” in step S 43 ), the reducing agent temperature reception unit  115  receives the reducing agent temperature (reducing agent temperature detection value) acquired by the reducing agent temperature acquisition unit  64 , and the remaining amount information reception unit  113  receives the remaining amount (remaining amount information) of the reducing agent in the reducing agent tank  3 , which is acquired by the remaining amount information acquisition unit  62  (step S 44 ). 
     Then, the wall surface temperature reception unit  114  receives the wall surface temperature (wall surface temperature detection value) of the reducing agent tank  3 , which is acquired a plurality of times (at least twice) at predetermined time intervals by the wall surface temperature acquisition unit  63  (step S 45 ). 
     Next, the time calculation unit  116  calculates the thawing prediction time of the reducing agent  2  in the same manner as the time calculation unit  65  according to the first embodiment (step S 46 ). 
     Next, the transmission unit  117  transmits the thawing prediction time calculated in step S 46  to the communication unit  69 , and terminates the process shown in  FIG. 10  (step S 47 ). On the other hand, the communication unit  69  of the controller  6   a  outputs the received information indicating the thawing prediction time on the monitor  8 . 
     As described above, according to the second embodiment, the freezing prediction time or the thawing prediction time of the reducing agent  2  can be predicted on the server  11  side. 
     Third Embodiment 
     Hereinafter, a third embodiment of the present invention will be described with reference to  FIGS. 11 and 12 .  FIG. 11  is a flowchart showing still another operation example (operation example of the third embodiment) of the controller  6  shown in  FIGS. 1 and 2 .  FIG. 12  is a schematic diagram for describing still another operation example of the controller  6  shown in  FIGS. 1 and 2 . In addition, in the third embodiment, part of the operations of the controller  6  is different from that of the first embodiment. 
     The operation example of the controller  6  according to the third embodiment will be described with reference to  FIG. 11 .  FIG. 11  is a flowchart showing the operation example in a case in which the controller  6  shown in  FIG. 3  predicts the freezing time. A process shown in  FIG. 11  is started in a case in which, for example, the operator performs a predetermined input operation with respect to the controller  6  in a state in which the coolant (warm water) does not circulate in the heater tube  1 . 
     In the controller  6 , when the process shown in  FIG. 11  is started, first, the outside air temperature acquisition unit  61  inputs the output signal of the outside air temperature sensor  13  to acquire the outside air temperature and compares the outside air temperature and the freezing point temperature of the reducing agent  2  (step S 51 ). On the other hand, in a case in which the outside air temperature is not equal to or lower than the freezing point temperature of the reducing agent  2  (in a case of “NO” in step S 51 ), the outside air temperature acquisition unit  61  displays that fact on, for example, the monitor  8 , and terminates the process shown in  FIG. 11 . 
     On the other hand, in a case in which the outside air temperature is equal to or lower than the freezing point temperature of the reducing agent  2  (in a case of “YES” in step S 51 ), the reducing agent temperature acquisition unit  64  inputs the output signal of the reducing agent temperature sensor  43  to acquire the reducing agent temperature (reducing agent temperature detection value) and the remaining amount information acquisition unit  62  inputs the output signal of the remaining amount sensor  42  to acquire the remaining amount (remaining amount information) of the reducing agent in the reducing agent tank  3  (step S 52 ). 
     Then, the wall surface temperature acquisition unit  63  inputs the output signal of the wall surface temperature sensor  5  a plurality of times (at least twice) at predetermined time intervals to acquire the wall surface temperature (wall surface temperature detection value) of the reducing agent tank  3  (step S 53 ). 
     Next, the time calculation unit  65  calculates the freezing prediction time of the reducing agent  2  in the same manner as in step S 14  of  FIG. 5  and calculates the temperature change (information related to temperature drop prediction) of the reducing agent  2  as described above (step S 54 ). 
     Next, the output unit  66  outputs the freezing prediction time and the temperature drop curve (temporal change of temperature) calculated in step S 54  to the monitor  8 , for example, as shown in  FIG. 12 , and terminates the process shown in  FIG. 11  (step S 55 ). 
     According to the present embodiment, more detailed information related to the freezing prediction time can be provided to the operator of the work vehicle, the administrator of the work vehicle, or the administrator of a work site in which the work vehicle is operated. 
     In the above, the embodiments of the present invention have been described with reference to the drawings, but the specific configuration is not limited to the embodiments described above and includes design changes and the like without departing from the scope of the present invention. 
     For example, each acquisition unit  64  may be grasped as a functional component, which includes each sensor. In addition, the heat flux represented by the expression (A1) and the expression (B1) may be measured and obtained by the heat flow sensor. In addition, the change amount of the wall surface temperature may be obtained by using the table which decides the change amount of the wall surface temperature based on the outside air temperature, the wall surface temperature, the remaining amount of the reducing agent, the reducing agent temperature, and the like by an experiment or by simulation in advance. In addition, an output destination or a transmission destination to which the output unit  66  or the transmission unit  117  outputs or transmits the prediction result or the information indicating the temperature change is not limited to the monitor  8  or the like, but may be a voice output device, a portable terminal device, or the like. In addition, in a case in which the heater tube  1  (heating unit) is configured to heat a heating wire by using the electric power of a battery mounted on the work vehicle to heat the reducing agent  2  accommodated in the reducing agent tank  3 , thawing of the reducing agent  2  may be started by energizing the heating wire with the electric power of the battery in response to an instruction from the server  11 . The work vehicle is not limited to the dump truck  100  and can be, for example, a general vehicle including an SCR device. In addition, the work vehicle may include the SCR device and may be, for example, a vehicle such as a hydraulic excavator, a wheel loader, a bulldozer, or a motor grader. 
     INDUSTRIAL APPLICABILITY 
     According to the above disclosure of the present invention, it is possible to predict the time for the reducing agent to freeze or the time required for thawing the reducing agent. 
     REFERENCE SIGNS LIST 
     
         
           100 : dump truck 
           1 : heater tube 
           2 : reducing agent 
           3 : reducing agent tank 
           4 : sensor module 
           5 : wall surface temperature sensor 
           6 : controller 
           8 : monitor 
           11 : server 
           12 : engine 
           13 : outside air temperature sensor 
           41 : concentration sensor 
           42 : remaining amount sensor 
           43 : reducing agent temperature sensor 
           62 : remaining amount information acquisition unit 
           63 : wall surface temperature acquisition unit 
           64 : reducing agent temperature acquisition unit 
           65 : time calculation unit 
           66 : output unit 
           133 : SCR device