Abstract:
A diagnostic device for an exhaust gas purification system that has a diesel oxidation catalyst (DOC), a diesel particulate filter, and an exhaust pipe injection device. The device includes a sensor for detecting a temperature of the DOC, a first calculation unit for converting an integration time of the detected temperature between regeneration intervals into a thermal history time with respect to a predetermined set temperature, and calculating a degree of degradation of the DOC based on this thermal history time, a second calculation unit for calculating a quantity of heat generated in the DOC based on the detected temperature during a forced regeneration execution period, and calculating another degree of degradation of the DOC based on the quantity of heat generated; and a diagnosis unit for diagnosing a degradation state of the DOC based on the degrees of degradation entered from the first and second calculation units.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a U.S. National Stage Application, which claims the benefit under 35 U.S.C. §371 of PCT International Patent Application No. PCT/JP2014/076408, filed Oct. 2, 2014, which claims the foreign priority benefit under 35 U.S.C. §119 of Japanese Patent Application No. 2013-208918, filed Oct. 4, 2013, the contents of which are incorporated herein by reference. 
     TECHNICAL FIELD 
     The present invention relates to a diagnostic device, and in particular to diagnosis of degradation of an exhaust gas purifying catalyst arranged in an exhaust system of an internal combustion engine. 
     BACKGROUND ART 
     As an exhaust gas purifying catalyst to be arranged in an exhaust system of a diesel engine or the like, an oxidation catalyst (Diesel Oxidation Catalyst: DOC) for oxidizing hydrocarbons (HC), carbon monoxide (CO), and nitrogen monoxide (NO) contained in exhaust gas is known. In addition, a diesel particulate filter (DPF) for collecting particulate matter (PM) contained in the exhaust gas and other filtering devices are also known. 
     If a capability of the DOC to oxidize HC is degraded, a portion of HC which is supplied to the DOC by an exhaust pipe injection (in-pipe injection) or the like at the time of a forced regeneration of the DPF will experience a slip to the DPF on the downstream side without being oxidized by the DOC. Because the DPF also has a capability to oxidize HC, the portion of HC which has experienced a slip through the DOC may be oxidized and purified by the DPF. However, if HC oxidation performance of the DPF is also degraded, unburned HC which has experienced a slip through the DOC may pass through the DPF and released to the atmosphere. This may worsen undesired emissions. Thus, there is a demand to diagnose the capabilities of the DOC and the DPF to oxidize HC when the DOC and the DPF are on board (see, forexample, Patent Literature Document 1). 
     LISTING OF REFERENCES 
     Patent Literature Document 1: Japanese Patent Application Laid-Open Publication No. 2003-106140 
     Examples of techniques to diagnose the HC oxidation performance of the DOC and the DPF include a method of estimating HC heat generation rates of the DOC and the DPF at the time of the forced regeneration on the basis of detection values of exhaust gas temperature sensors arranged in front of and behind the DOC and the DPF, and comparing the HC heat generation rates to reference values. In particular, when a diagnosis as to the DPF is made, a slip amount of HC passing through the DOC at the time of a current forced regeneration needs to be estimated on the basis of an HC heat generation rate of the DOC which has been estimated at the time of an immediately previous forced regeneration. However, such a method, which gives consideration only to the HC heat generation rates in forced regeneration periods, does not take into account a thermal degradation of the DOC which occurs during a regeneration interval (i.e., a period from an end of a forced regeneration to a start of a next forced regeneration), and therefore may not be able to make a highly precise diagnosis. 
     SUMMARY OF THE INVENTION 
     A diagnostic device disclosed herein has an object to perform highly precise diagnoses as to the DOC and the DPF by taking into account the thermal degradation of the DOC which occurs during the regeneration interval. 
     A diagnostic device disclosed herein is a diagnostic device for an exhaust purification system including an oxidation catalyst arranged to oxidize hydrocarbons contained in exhaust gas, a filter arranged downstream of the oxidation catalyst with respect to an exhaust gas flowing direction to collect particulate matter contained in the exhaust gas, and a forced regeneration unit for performing a forced regeneration, i.e., supplying hydrocarbons to the oxidation catalyst and burning and removing particulate matter accumulated in the filter. The diagnostic device includes: a first temperature detecting unit for detecting a temperature of the oxidation catalyst; a first degradation degree calculation unit for converting a cumulative time of the temperature entered from the first temperature detecting unit to a thermal history time for a specified set temperature, and calculating a degradation degree of the oxidation catalyst on the basis of the thermal history time, in a period from an end of a forced regeneration to a start of a next forced regeneration; a second degradation degree calculation unit for calculating a quantity of heat generated in the oxidation catalyst on the basis of the temperature entered from the first temperature detecting unit in a forced regeneration period, and calculating the degradation degree of the oxidation catalyst on the basis of the quantity of heat generated; and a first diagnosis unit for performing a diagnosis as to degradation of the oxidation catalyst on the basis of at least one of the degradation degree introduced from the first degradation degree calculation unit and the degradation degree introduced from the second degradation degree calculation unit. 
     The diagnostic device disclosed herein is able to perform highly precise diagnoses as to a DOC and a DPF by taking into account a thermal degradation of the DOC which occurs during a regeneration interval. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic overall configuration diagram illustrating an intake and exhaust system of an engine to which a diagnostic device according to an embodiment of the present invention is applied. 
         FIG. 2  is a functional block diagram of an electronic control unit according to an embodiment of the present invention. 
         FIG. 3  is a graphic representation of the relationship between a generated heat quantity (calorific value) ratio and time. 
         FIG. 4  shows a graph created by an Arrhenius plot. 
         FIG. 5  is a graphic representation of cumulative times of temperature frequencies in a regeneration interval. 
         FIG. 6  shows a graphic representation obtained by converting the graph of  FIG. 5  to a graph of a thermal history time for an arbitrary set temperature. 
         FIG. 7  is a schematic diagram useful to describe conservation of energy generated by oxidation of HC supplied to a DOC at the time of a forced regeneration and by oxidation of a portion of HC which has experienced a slip to a DPF through the DOC. 
         FIG. 8  is a schematic side view useful to describe a heat loss in the DOC and the DPF due to influences of forced convection. 
         FIG. 9  is a flowchart illustrating control performed by the diagnostic device according to the embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     A diagnostic device according to embodiments of the present invention will be described with reference to the accompanying drawings. Like parts are designated by like reference numerals, and such like parts have like names and functions. Accordingly, redundant detailed descriptions of such like parts will be omitted. 
     As shown in  FIG. 1 , a diesel engine (hereinafter referred to simply as “engine”)  10  has an intake manifold  10   a  and an exhaust manifold  10   b . An intake passage  11  for introducing fresh air is connected to the intake manifold  10   a , and an exhaust passage  12  for discharging exhaust gas to the atmosphere is connected to the exhaust manifold  10   b.    
     On the intake passage  11 , disposed are an air cleaner  30 , a mass air flow sensor  31 , a compressor  32   a  of a turbo charger, an intercooler  33 , and so on in this order from the upstream side with respect to an intake air flowing direction. On the exhaust passage  12 , disposed are a turbine  32   b  of the turbo charger, an exhaust gas after-treatment device  20 , and so on are arranged in this order from the upstream side with respect to an exhaust gas flowing direction. It should be noted that in  FIG. 1  reference numeral “ 36 ” denotes an outside air (ambient air) temperature sensor. The outside air temperature sensor  36  is a preferred example of a third temperature detecting unit according to the present invention. 
     The exhaust gas after-treatment device  20  includes a cylindrical catalyst casing  20   a , a DOC  21 , and a DPF  22 . The DOC  21  is disposed upstream of the DPF  22  in the catalyst casing  20   a . An exhaust pipe injection device  23  is arranged upstream of the DOC  21 , a DOC inlet temperature sensor  25  is arranged upstream of the DOC  21 , a DOC outlet temperature sensor  26  is arranged between the DOC  21  and the DPF  22 , and a DPF outlet temperature sensor  27  is arranged downstream of the DPF  22 . A differential pressure sensor  29 , which is used to detect (measure) a difference in pressure between the upstream and downstream sides of the DPF  22 , is arranged across the DPF  22 . 
     The exhaust pipe injection device  23  is an example of a forced regeneration unit according to the present invention, and injects unburned fuel (mainly HC) into the exhaust passage  12  in response to an instruction signal issued from an electronic control unit (hereinafter referred to as “ECU”)  40 . It should be noted that if post-injections by means of multiple injections of the engine  10  are employed, the exhaust pipe injection device  23  may be omitted. 
     The DOC  21  includes a ceramic support having, for example, a cordierite honeycomb structure, and catalytic components supported on a surface of the ceramic support. As HC is supplied to the DOC  21  by the exhaust pipe injection device  23  or the post-injections, the DOC  21  oxidizes HC to elevate the temperature of the exhaust gas. 
     The DPF  22  includes, for example, a large number of cells defined by porous partitions and arranged along the exhaust gas flowing direction, with the upstream and downstream sides of the cells being sealed or plugged alternately. In the DPF  22 , PM contained in the exhaust gas collects in pores of the partitions and on surfaces of the partitions. When an amount of accumulated PM reaches a predetermined amount, a so-called forced regeneration is carried out, i.e., the accumulated PM is burnt for removal. The forced regeneration is accomplished by supplying the unburned fuel (HC) into the DOC  21  through the exhaust pipe injection device  23  or the post-injections, and raising the temperature of the exhaust gas flowing into the DPF  22  up to a PM combustion temperature (for example, about 600 degrees C.). The DPF  22  has a capability to oxidize that portion of unburned HC which has experienced a slip through the DOC  21  without being oxidized by the upstream DOC  21 . 
     The DOC inlet temperature sensor  25  is an example of a first temperature detecting unit according to the present invention, and detects the temperature (hereinafter referred to as “DOC inlet exhaust gas temperature”) of the upstream exhaust gas flowing into the DOC  21 . The DOC outlet temperature sensor  26  is an example of the first or second temperature detecting unit according to the present invention, and detects the temperature (hereinafter referred to as “DOC outlet exhaust gas temperature” or “DPF inlet exhaust gas temperature”) of the downstream exhaust gas flowing out of the DOC  21 . The DPF outlet temperature sensor  27  is an example of the second temperature detecting unit according to the present invention, and detects the temperature (hereinafter referred to as “DPF outlet exhaust gas temperature”) of the downstream exhaust gas flowing out of the DPF  22 . Detection values of the temperature sensors  25  to  27  are introduced to the ECU  40 , which is electrically connected to the sensors  25  to  27 . 
     The ECU  40  performs various types of control, such as control over the engine  10 , the exhaust pipe injection device  23 , and so on. The ECU  40  includes a CPU, a ROM, a RAM, input ports, output ports, and other elements which are known in the art. 
     As shown in  FIG. 2 , the ECU  40  also includes first DOC degradation degree calculation unit  41 , second DOC degradation degree calculation unit  42 , a DOC failure diagnosis unit  43 , an HC slip amount calculation unit  44 , a DPF degradation degree calculation unit  45 , and a DPF failure diagnosis unit  46  as functional components thereof. It is assumed in the following description that all of these functional components are included in the ECU  40 , which is a single unified piece of hardware. Alternatively, one or more of these functional components may be included in a separate piece of hardware. 
     The first DOC degradation degree calculation unit  41  is an example of a first degradation degree calculation unit according to the present invention, and calculates the degree (hereinafter referred to as “DOC degradation degree D DOC int ”) of degradation of the DOC  21  in a period from an end of a forced regeneration of the DPF  22  to a start of a next forced regeneration of the DPF  22  (this period will be hereinafter referred to as “regeneration interval”). The DOC degradation degree D DOC int  is calculated on the basis of an HC generated heat quantity ratio of the DOC  21  in the regeneration interval. A procedure for calculating the HC generated heat quantity ratio will be described below. 
     Assuming that the ratio (hereinafter referred to as “HC generated heat quantity ratio” LN) of an amount (quantity) of heat generated in a DOC (for example, a new DOC) which has normal HC oxidation performance to a quantity of heat generated in a degraded DOC is linear with respect to time t as shown in  FIG. 3 , the generated heat quantity ratio LN is expressed by Equation 1, where k is a reaction rate constant.
 
 LN=k·t    [Equation 1]
 
     The Arrhenius equation is expressed by Equation 2, where Ea is activation energy, T is a fluid temperature, R is a fluid constant, and A is a frequency factor. 
     
       
         
           
             
               
                 
                   k 
                   = 
                   
                     A 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       exp 
                       ⁡ 
                       
                         ( 
                         
                           
                             - 
                             Ea 
                           
                           RT 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   ] 
                 
               
             
           
         
       
     
     Taking the natural logarithm (LN) of Equation 2 yields Equation 3. 
     
       
         
           
             
               
                 
                   
                     LN 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     k 
                   
                   = 
                   
                     
                       LN 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       A 
                     
                     - 
                     
                       
                         Ea 
                         R 
                       
                       ⁢ 
                       
                         1 
                         T 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ] 
                 
               
             
           
         
       
     
     The reaction rate constants k are calculated in advance for various temperatures of the DOC  21  by experiments or the like, and an Arrhenius plot is prepared on the basis of Equation 3, with the vertical axis representing LNk and the horizontal axis representing the reciprocal of the temperature, 1/T, as shown in  FIG. 4 . Then, the activation energy Ea can be determined from the inclination of the Arrhenius plot, and the frequency factor A can be determined from the intercept of the Arrhenius plot. 
       FIG. 5  shows an example of a temperature frequency T n  of the DOC  21  in the regeneration interval integrated over time. A cumulative time t n  of the temperature frequency T n  can be converted to a thermal history time t heat  for an arbitrary set temperature T X  using Equation 4 (see  FIG. 6 ). It should be noted that the thermal history time t heat  refers to a heat load time which indicates how many hours the DOC  21  is supposed to have received a heat load during the regeneration interval if the temperature is fixed at the arbitrary set temperature T X  during the regeneration interval. The arbitrary set temperature T X  may be set appropriately in accordance with, for example, the volume of the DOC  21 . 
     
       
         
           
             
               
                 
                   
                     
                       
                         e 
                         
                           ( 
                           
                             - 
                             
                               Ea 
                               
                                 R 
                                 · 
                                 
                                   T 
                                   n 
                                 
                               
                             
                           
                           ) 
                         
                       
                       × 
                       
                         t 
                         n 
                       
                     
                     
                       e 
                       
                         ( 
                         
                           - 
                           
                             Ea 
                             
                               R 
                               · 
                               
                                 T 
                                 x 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                   = 
                   
                     t 
                     heat 
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ] 
                 
               
             
           
         
       
     
     Determining the activation energy Ea and the frequency factor A in Equation 3 on the basis of the Arrhenius plot (see  FIG. 4 ) and substituting the arbitrary set temperature T X  in Equation 3 yield the reaction rate constant k for the arbitrary set temperature T X . Substituting the reaction rate constant k and the thermal history time t heat  obtained by conversion using Equation 4 in Equation 5 yields the generated heat quantity ratio LN of the DOC  21  in the regeneration interval.
 
 LN=k·t   heat    [Equation 5]
 
     The reaction rate constant k for the arbitrary set temperature T X  calculated by the above-described procedure, Equation 4, and Equation 5 are stored in advance in the ECU  40  of this embodiment. The first DOC degradation degree calculation unit  41  converts the cumulative time t n  of the temperature frequency T n  of the DOC  21 , which is entered from the DOC inlet temperature sensor  25  in the regeneration interval, to the thermal history time t heat  for the arbitrary set temperature T X  on the basis of Equation 4. Then, the first DOC degradation degree calculation unit  41  calculates the DOC degradation degree D DOC int  (=1−LN) in the regeneration interval on the basis of the generated heat quantity ratio LN obtained by substituting the thermal history time t heat  in Equation 5. It should be noted that the cumulative time t n  of the temperature frequency T n  may be detected using a timer that is built in the ECU  40  or the like, for example. It should also be noted that the temperature frequency T n  may be obtained as the average of a detection value of the DOC inlet temperature sensor  25  and a detection value of the DOC outlet temperature sensor  26 . 
     The second DOC degradation degree calculation unit  42  is an example of a second degradation degree calculation unit according to the present invention, and calculates the degree (hereinafter referred to as “DOC degradation degree D DOC reg ”) of degradation of the DOC  21  in a forced regeneration period, i.e., a period during which the forced regeneration is applied to the DPF  22 . The DOC degradation degree D DOC reg  is calculated on the basis of an actual HC heat generation rate of the DOC  21  in the forced regeneration period. A procedure for calculating the actual HC heat generation rate of the DOC  21  at the time of the forced regeneration will be described below. 
     As shown in  FIG. 7 , the actual quantity C DOC act  of heat generated by HC supplied from the exhaust pipe injection device  23  into the DOC  21  at the time of the forced regeneration can be obtained by adding the quantity Q DOC lost  of heat loss, i.e., the quantity of heat dissipated from the DOC  21  to the outside air, to an exhaust gas energy difference between exhaust gas energy Q DOC in  on the upstream side of the DOC  21  and exhaust gas energy Q DOC out  on the downstream side of the DOC  21 . 
     The exhaust gas energy Q DOC in  on the upstream side is calculated on the basis of Equation 6, and the exhaust gas energy Q DOC out  on the downstream side is calculated on the basis of Equation 7.
 
 Q   Doc   _   in   =c   exh   ·m   exh   ·T   DOC   _   in    [Equation 6]
 
 Q   DOC   _   out   =c   exh   ·m   exh   ·T   DOC   _   out    [Equation 7]
 
     In Equations 6 and 7, c exh  denotes specific heat of the exhaust gas. m exh  denotes the flow rate of the exhaust gas, which is obtained from a detection value of the MAF sensor  31 , an amount of fuel injection by the engine  10 , and so on. It should be noted that the flow rate m exh  of the exhaust gas may be obtained directly from an exhaust gas flow rate sensor (not shown) or the like. T DOC in  denotes the DOC inlet exhaust gas temperature, which is obtained by the DOC inlet temperature sensor  25 . T DOC out  denotes the DOC outlet exhaust gas temperature, which is obtained by the DOC outlet temperature sensor  26 . 
     The quantity Q DOC lost  of heat loss can be assumed to be a sum of quantity Q DOC natural  of heat loss caused by natural convection and quantity Q DOC forced  of heat loss caused by forced convection (i.e., Q DOC lost =Q DOC natural +Q DOC forced ). 
     The quantity Q DOC natural  of heat loss caused by the natural convection is calculated on the basis of Equation 8.
 
Q DOC   _   natural   =h   n   _   DOC   ·A   s   _   DOC ·( T   DOC   _   brick   −T   ambient )   [Equation 8]
 
     In Equation 8, A s DOC  denotes the effective area of an outer circumferential surface of the DOC  21  (or an outer circumferential surface of that portion of the catalyst casing  20   a  in which the DOC  21  is arranged). T DOC brick  denotes the internal temperature of the DOC  21 , which is calculated as the average of the DOC inlet exhaust gas temperature T DOC in  and the DOC outlet exhaust gas temperature T DOC out . T ambient  denotes the temperature of the outside air (ambient air), which is obtained by the outside air temperature sensor  36 . h n DOC  denotes a heat transfer coefficient of natural convection, which is given by Equation 9. 
     
       
         
           
             
               
                 
                   
                     h 
                     
                       n 
                       ⁢ 
                       _ 
                       ⁢ 
                       DOC 
                     
                   
                   = 
                   
                     
                       
                         Nu 
                         
                           n 
                           ⁢ 
                           _ 
                           ⁢ 
                           DOC 
                         
                       
                       · 
                       k 
                     
                     
                       L 
                       
                         n 
                         ⁢ 
                         _ 
                         ⁢ 
                         DOC 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     9 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equation 9, k denotes thermal conductivity of air. L n DOC  denotes a characteristic length of the DOC  21 , which is determined appropriately in accordance with, for example, the volume of the DOC  21 . Nu n DOC  denotes a Nusselt number for natural convection. 
     The DOC  21  has a generally cylindrical shape, and the catalyst casing  20   a , in which the DOC  21  is housed, has a substantially cylindrical shape. Therefore, oxidation heat generated in the DOC  21  is presumably dissipated to the outside air through entire cylindrical outer circumferential surfaces of the DOC  21  and the catalyst casing  20   a . Assuming that heat dissipation by natural convection causes heat to transfer through the entire cylindrical outer circumferential surface with an axis of the cylindrical shape being horizontally oriented, the Nusselt number Nu n DOC  is given by Equation 10, where Gr is the Grashof number, and Pr is the Prandtl number.
 
 Nu   n   _   DOC =0.53×( Gr·Pr ) 0.25    [Equation 10]
 
     The quantity Q DOC forced  of heat loss caused by forced convection is calculated on the basis of Equation 11.
 
 Q   DOC   _   forced   =h   f   _   DOC   ·A   f   _   DOC ·( T   DOC   _   brick   −T   ambient )   [Equation 11]
 
     In Equation 11, A f DOC  denotes the effective area of the outer circumferential surface of the DOC  21  (or the outer circumferential surface of that portion of the catalyst casing  20   a  in which the DOC  21  is arranged). h f DOC  denotes a heat transfer coefficient of forced convection, which is given by Equation 12. 
     
       
         
           
             
               
                 
                   
                     h 
                     
                       f 
                       ⁢ 
                       _ 
                       ⁢ 
                       DOC 
                     
                   
                   = 
                   
                     
                       
                         Nu 
                         
                           f 
                           ⁢ 
                           _ 
                           ⁢ 
                           DOC 
                         
                       
                       · 
                       k 
                     
                     
                       L 
                       
                         f 
                         ⁢ 
                         _ 
                         ⁢ 
                         DOC 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     12 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equation 12, L f DOC  denotes the characteristic length of the DOC  21 , which is determined appropriately in accordance with, for example, the volume of the DOC  21 . Nu f DOC  denotes a Nusselt number for forced convection. 
     As illustrated in  FIG. 8 , the catalyst casing  20   a , in which the DOC  21  is housed, is typically fixed to a lower portion of a chassis frame S of a vehicle body, and a transmission TM and other components are arranged in front of the catalyst casing  20   a . Accordingly, a wind which flows from in front of the vehicle body into a space below the vehicle body while the vehicle is running can be assumed to be a planar turbulent flow which influences only a lower surface portion of the DOC  21  (or of the catalyst casing  20   a ). Therefore, the Nusselt number Nu f DOC  for forced convection is given by Equation 13, which is derived by solving a heat transfer equation for planar turbulence.
 
 Nu   f   _   DOC =0.037× Re   0.8   ×Pr   0.33    [Equation 13]
 
     In Equation 13, Re denotes the Reynolds number. The Reynolds number Re is given by Equation 14, where v is the average velocity of air, ρ is air density, L f DOC  is the characteristic length of the DOC  21 , and μ is a dynamic viscosity coefficient. 
     
       
         
           
             
               
                 
                   Re 
                   = 
                   
                     
                       v 
                       · 
                       p 
                       · 
                       
                         L 
                         
                           f 
                           ⁢ 
                           _ 
                           ⁢ 
                           DOC 
                         
                       
                     
                     μ 
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     14 
                   
                   ] 
                 
               
             
           
         
       
     
     The second DOC degradation degree calculation unit  42  adds the quantity Q DOC lost  of heat loss, which is calculated on the basis of Equations 8 to 14, to the exhaust gas energy difference between the exhaust gas energy Q DOC in  on the upstream side, which is calculated on the basis of Equation 6, and the exhaust gas energy Q DOC out  on the downstream side, which is calculated on the basis of Equation 7, to calculate the actual quantity C DOC act  of heat generated by HC in the DOC  21  in the forced regeneration period. The second DOC degradation degree calculation unit  42  then divides the actual quantity C DOC act  of heat generated by HC by a theoretical quantity C DOC theo  of heat to be generated by an exhaust pipe injection (or post-injection) to calculate the actual HC heat generation rate C DOC act % . The second DOC degradation degree calculation unit  42  calculates the DOC degradation degree D DOC reg  (=1−C DOC act % ) in the forced regeneration period on the basis of the actual HC heat generation rate C DOC act % . It should be noted that the theoretical quantity C DOC theo  of heat to be generated is obtained by multiplying the amount HC inj qty  of the exhaust pipe injection (or the amount of the post-injection) by a theoretical HC heat generation rate C theo %  (i.e., C DOC theo =HC inj qty ×C theo % ). 
     The DOC failure diagnosis unit  43  is an example of a first diagnosis unit according to the present invention, and determines whether the DPF  22  is malfunctioning on the basis of the DOC degradation degree D DOC int , which is entered from the first DOC degradation degree calculation unit  41 , and the DOC degradation degree D DOC reg , which is entered from the second DOC degradation degree calculation unit  42 . For example, the DOC  21  is determined to be malfunctioning if the DOC degradation degree D DOC int  or the DOC degradation degree D DOC reg  is greater than a predetermined upper limit threshold value D DOC max , which indicates a degradation in HC oxidation performance. 
     The HC slip amount calculation unit  44  is an example of a slip amount calculation unit according to the present invention, and calculates the slip amount HC slp qty  of unburned HC flowing into the downstream DPF  22  without being oxidized by the DOC  21  on the basis of the DOC degradation degree D DOC int , which is entered from the first DOC degradation degree calculation unit  41 , and the DOC degradation degree D DOC reg , which is entered from the second DOC degradation degree calculation unit  42 . The slip amount HC slp qty  is calculated by multiplying the amount HC inj qty  of the exhaust pipe injection for a current forced regeneration by the sum of the DOC degradation degree D DOC reg  calculated in an immediately previous forced regeneration period and the DOC degradation degree D DOC int  calculated in an immediately previous regeneration interval (i.e., HC slp qty =HC inj qty ×(D DOC int +D DOC reg )). 
     The DPF degradation degree calculation unit  45  is an example of a third degradation degree calculation unit according to the present invention, and calculates the degree (hereinafter referred to as “DPF degradation degree D DPF reg ”) of degradation of the DPF  22  in the forced regeneration period. The DPF degradation degree D DPF reg  is calculated on the basis of an actual heat generation rate for that portion of HC which has flowed into the DPF  22  after experiencing a slip through the DOC  21  at the time of the forced regeneration. A procedure for calculating the actual HC heat generation rate at the time of the forced regeneration of the DPF  22  will be described below. 
     Referring to  FIG. 7 , the actual quantity C DPF act  of heat generated by that portion of HC which is oxidized by the DPF  22  after experiencing a slip through the DOC  21  can be obtained by adding the quantity Q DPF lost  of heat loss, i.e., the quantity of heat dissipated from the DPF  22  to the outside air, to an exhaust gas energy difference between energy Q DPF in  of the exhaust gas on the upstream side of the DPF  22  and energy Q DPF out  of the exhaust gas on the downstream side of the DPF  22 . 
     The energy Q DPF in  of the exhaust gas on the upstream side is calculated on the basis of Equation 15, and the energy Q DPF out  of the exhaust gas on the downstream side is calculated on the basis of Equation 16.
 
 Q   DPF   _   in   =c   exh   ·m   exh   ·T   DPF   _   in    [Equation 15]
 
 Q   DPF   _   out   =c   exh   ·m   exh   ·T   DPF   _   out    [Equation 16]
 
     In Equations 15 and 16, T DPF in  denotes the DPF inlet exhaust gas temperature, which is acquired by the DOC outlet temperature sensor  26 . T DPF out  denotes the DPF outlet exhaust gas temperature, which is acquired by the DPF outlet temperature sensor  27 . 
     The quantity Q DPF lost  of heat loss can be assumed to be a sum of the quantity Q DPF natural  of heat loss caused by natural convection and the quantity Q DPF forced  of heat loss caused by forced convection (i.e., Q DPF lost =Q DPF natural +Q DPF forced ). 
     The quantity Q DPF natural  of heat loss caused by natural convection is calculated on the basis of Equation 17.
 
 Q   DPF   _   natural   =h   n   _   DPF   ·A   s   _   DPF ·( T   DPF   _   brick   −T   ambient )   [Equation 17]
 
     In Equation 17, A s DPF  denotes the effective area of an outer circumferential surface of the DPF  22  (or an outer circumferential surface of that portion of the catalyst casing  20   a  in which the DPF  22  is arranged). T DPF brick  denotes the internal temperature of the DPF  22 , which is calculated as the average of the DPF inlet exhaust gas temperature T DPF in  and the DPF outlet exhaust gas temperature T DPF out . h n DPF  denotes a heat transfer coefficient of natural convection, which is given by Equation 18. 
     
       
         
           
             
               
                 
                   
                     h 
                     
                       n 
                       ⁢ 
                       _ 
                       ⁢ 
                       DPF 
                     
                   
                   = 
                   
                     
                       
                         Nu 
                         
                           n 
                           ⁢ 
                           _ 
                           ⁢ 
                           DPF 
                         
                       
                       · 
                       k 
                     
                     
                       L 
                       
                         n 
                         ⁢ 
                         _ 
                         ⁢ 
                         DPF 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     18 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equation 18, L n DPF  denotes a characteristic length of the DPF  22 , which is determined appropriately in accordance with, for example, the volume of the DPF  22 . Nu n DPF  denotes a Nusselt number for natural convection, which is given by Equation 19 on the assumption that heat is dissipated through the entire cylindrical outer circumferential surfaces of the DPF  22  and the catalyst casing  20   a , as is similarly the case with Equation 10.
 
 Nu   n   _   DPF =0.53×( Gr·Pr ) 0.25    [Equation 19]
 
     The quantity Q DPF forced  of heat loss caused by forced convection is calculated on the basis of Equation 20.
 
 Q   DPF   _   forced   =h   f   _   DPF   ·A   f   _   DPF ·( T   DPF   _   brick   −T   ambient )   [Equation 20]
 
     In Equation 20, A f DPF  denotes the effective area of the outer circumferential surface of the DPF  22  (or the outer circumferential surface of that portion of the catalyst casing  20   a  in which the DPF  22  is arranged), and h f DPF  denotes a heat transfer coefficient of forced convection, which is given by Equation 21. 
     
       
         
           
             
               
                 
                   
                     h 
                     
                       f 
                       ⁢ 
                       _ 
                       ⁢ 
                       DPF 
                     
                   
                   = 
                   
                     
                       
                         Nu 
                         
                           f 
                           ⁢ 
                           _ 
                           ⁢ 
                           DPF 
                         
                       
                       · 
                       k 
                     
                     
                       L 
                       
                         f 
                         ⁢ 
                         _ 
                         ⁢ 
                         DPF 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     21 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equation 21, L f DPF  denotes the characteristic length of the DPF  22 , which is determined appropriately in accordance with, for example, the volume of the DPF  22 . Nu f DPF  denotes a Nusselt number for forced convection, which is given by Equation 22 on the assumption that the forced convection causes a planar turbulent flow which influences only a lower surface portion of the DPF  22  (or of the catalyst casing  20   a ), as is similarly the case with Equation 8.
 
 Nu   f   _   DPF =0.037× Re   0.9   ×Pr   0.33    [Equation 22]
 
     The Reynolds number Re in Equation 17 is given by Equation 23, where v is the average velocity of air, ρ is air density, L f DPF  is the characteristic length of the DPF  22 , and μ is a dynamic viscosity coefficient. 
     
       
         
           
             
               
                 
                   Re 
                   = 
                   
                     
                       v 
                       · 
                       p 
                       · 
                       
                         L 
                         
                           f 
                           ⁢ 
                           _ 
                           ⁢ 
                           DPF 
                         
                       
                     
                     μ 
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     23 
                   
                   ] 
                 
               
             
           
         
       
     
     The DPF degradation degree calculation unit  45  adds the quantity Q DPF lost  of heat loss, which is calculated on the basis of Equations 17 to 23, to the exhaust gas energy difference between the energy Q DPF in  of the exhaust gas on the upstream side, which is calculated on the basis of Equation 15, and the energy Q DPF out  of the exhaust gas on the downstream side, which is calculated on the basis of Equation 16, to calculate the actual quantity C DPF act  of heat generated by HC in the DPF  22  in the forced regeneration period. The DPF degradation degree calculation unit  45  then divides the actual quantity C DPF act  of heat generated by HC by a theoretical quantity C DPF theo  of heat to be generated by that portion of HC which has experienced a slip to calculate the actual HC heat generation rate C DPF act % , and calculates the DPF degradation degree D DPF reg  (=1−C DPF act % ) in the forced regeneration period on the basis of this actual HC heat generation rate C DPF act % . It should be noted that the theoretical quantity C DPF theo  of heat to be generated is obtained by multiplying the slip amount HC slp qty  by a theoretical HC heat generation rate C theo %  (i.e., C DPF theo =C slp qty ×C theo % ). 
     The DPF failure diagnosis unit  46  is an example of a second diagnosis unit according to the present invention, and determines whether the DPF  22  is malfunctioning on the basis of the DPF degradation degree D DPF reg , which is entered from the DPF degradation degree calculation unit  45 . For example, the DPF  22  is determined to be malfunctioning if the DPF degradation degree D DPF reg  is greater than a predetermined upper limit threshold value D DPF max , which indicates a degradation in HC oxidation performance. 
     Next, a control flow of the diagnostic device according to this embodiment will be described below with reference to  FIG. 9 . In a flowchart of  FIG. 9 , “F 1 ” denotes a flag to indicate a start of a forced regeneration of the DPF  22 . The flag is set to ON (i.e., F 1 =1) when the forced regeneration starts, and is set to OFF (i.e., F 1 =0) when the forced regeneration ends. A determination as to whether the forced regeneration has started is made on the basis of a detection value of the differential pressure sensors  29 , and a determination as to whether the forced regeneration has ended is made on the basis of a value calculated by the ECU  40 . 
     If a forced regeneration of the DPF  22  is started (i.e., F 1 =1) at step (hereinafter, “Step” will be denoted simply as “S”)  100 , a calculation of the DOC degradation degree D DOC reg  in the forced regeneration period is started at S 110 . 
     If a predetermined time elapses after the start of the forced regeneration, and the calculation of the DOC degradation degree D DOC reg  is finished, a determination as to whether the DOC  21  is malfunctioning in the forced regeneration period is performed at S 120 . If the DOC degradation degree D DOC reg  is greater than the upper limit threshold value D DOC max  (Yes), it means that a slip of HC to the downstream DPF  22  has occurred, and the control proceeds to S 200 , and the DOC  21  is determined to be malfunctioning. On the other hand, if the DOC degradation degree D DOC reg  is no greater than the upper limit threshold value D DOC max  (No), it means that a degradation in the HC oxidation performance has not occurred, and the control proceeds to S 130 . 
     If the forced regeneration of the DPF  22  ends (i.e., F 1 =0) at S 130 , a calculation of the DOC degradation degree D DOC int  in the regeneration interval is started at S 140 . 
     If a next forced regeneration is started (i.e., F 1 =1) at S 150 , the calculation of the DOC degradation degree D DOC int  is finished. Accordingly, at S 160 , a determination as to whether the DOC  21  is malfunctioning in the regeneration interval is performed. If the DOC degradation degree D DOC int  is greater than the upper limit threshold value D DOC max  (Yes), it means that a slip of HC to the downstream DPF  22  has occurred, and the control proceeds to S 200 . On the other hand, if the DOC degradation degree D DOC int  is equal to or less than the upper limit threshold value D DOC max  (No), it means that a degradation in the HC oxidation performance of the DOC  21  has not occurred (i.e., a slip of HC does not occur), and the control proceeds to S 300  to determine that the DOC  21  is functioning in a normal state. 
     At S 210 , a calculation of the DPF degradation degree D DPF reg  in the forced regeneration period is started. The slip amount of HC is calculated by multiplying the amount HC inj qty  of the exhaust pipe injection for the current forced regeneration by the sum of the DOC degradation degree D DOC reg  in the forced regeneration period calculated at S 110  and the DOC degradation degree D DOC int  in the regeneration interval calculated at S 140 . 
     If a predetermined time elapses after the start of the forced regeneration, and the calculation of the DPF degradation degree D DPF reg  is finished, a determination as to whether the DPF  22  is malfunctioning is made at S 220 . If the DPF degradation degree D DPF reg  is greater than the upper limit threshold value D DPF max  (Yes), it means that a slip of HC through the DPF  22  may occur to permit HC to be emitted to the atmosphere, and the control proceeds to S 230  to determine that the DPF  22  is malfunctioning. On the other hand, if the DPF degradation degree D DPF   _   regg  is equal to or less than the upper limit threshold value D DOC max  (No), it means that a degradation in the HC oxidation performance of the DPF  22  has not occurred (i.e., that portion of HC which has experienced a slip through the DOC  21  can be subjected to purification by the DPF  22 ), and the control proceeds to S 310  to determine that the DPF  22  (i.e., the exhaust gas after-treatment device  20 ) is functioning properly. Thereafter, the above-described control steps are repeatedly performed until an ignition key is turned off. 
     Next, beneficial effects of the diagnostic device according to the embodiments of the present invention will be described below. 
     Diagnoses as to degradation of the DOC  21  and the DPF  22  are typically made by estimating, for example, the HC heat generation rates of the DOC  21  and the DPF  22  at the time of the forced regeneration. In particular, when a diagnosis as to the degradation of the DPF  22  is made, a slip amount of HC at the time of a current forced regeneration needs to be estimated on the basis of an HC heat generation rate of the DOC  21  which has been estimated at the time of an immediately previous forced regeneration. Such a method, however, does not take into account a thermal degradation of the DOC  21  which occurs during the regeneration interval, and therefore may not be able to make a highly precise diagnosis. 
     On the contrary, the diagnostic device according to this embodiment calculates the thermal history time of the DOC  21  in the regeneration interval, and calculates the DOC degradation degree in the regeneration interval on the basis of the generated heat quantity ratio obtained from this thermal history time. Further, when a diagnosis as to the degradation of the DPF  22  is made, the diagnostic device of this embodiment calculates the slip amount of HC flowing from the DOC  21  into the DPF  22  while taking into account both the DOC degradation degree in the regeneration interval and the DOC degradation degree in the forced regeneration period. 
     Accordingly, the diagnostic device of this embodiment is able to calculate the slip amount of HC while taking into account the thermal degradation of the DOC  21  which occurs during the regeneration interval, and is therefore able to make highly precise diagnoses as to the degradation of the DOC  21  and the DPF  22 . 
     In addition, in the diagnostic device of this embodiment, the actual quantity of heat generated by HC supplied to the DOC  21  at the time of the forced regeneration is calculated on the basis of the exhaust gas energy difference between the energy of the exhaust gas on the upstream side of the DOC  21  and the energy of the exhaust gas on the downstream side of the DOC  21 , and the quantity of heat loss, i.e., the quantity of heat dissipated from the DOC  21  to the outside air. The actual quantity of heat generated by that portion of HC which is oxidized by the DPF  22  after experiencing a slip through the DOC  21  is calculated on the basis of the exhaust gas energy difference between the energy of the exhaust gas on the upstream side of the DPF  22  and the energy of the exhaust gas on the downstream side of the DPF  22 , and the quantity of heat loss, i.e., the quantity of heat dissipated from the DPF  22  to the outside air. 
     Therefore, as compared to a method of calculating the quantity of heat generated by HC in each of the DOC  21  and the DPF  22  at the time of the forced regeneration only on the basis of a difference between the temperature of the exhaust gas on the upstream side and the temperature of the exhaust gas on the downstream side, the diagnostic device of this embodiment is configured to provide a more precise calculation thereof by taking into account the quantity of heat loss to the outside air. Accordingly, the diagnostic device of this embodiment can achieve an effective improvement in precision of diagnosis that is applied to each of the DOC  21  and the DPF  22  at the time of the forced regeneration. 
     It should be noted that the present invention is not limited to the above-described embodiment, and that modifications can be made as appropriate without departing from the scope and spirit of the present invention. 
     For example, although it has been assumed in the foregoing description that a degradation diagnosis is performed to the DPF  22  when a slip of HC through the DOC  21  has occurred, the degradation diagnosis of the DPF  22  may be performed even when a degradation of the DOC  21  has not occurred. In this configuration, an amount of the exhaust pipe injection (or the amount of the post-injection) may be increased to intentionally cause a slip of HC through the DOC  21 . The engine  10  is not limited to the diesel engine, and embodiments of the present invention can be widely applied to other internal combustion engines, such as gasoline engines.