Patent Publication Number: US-2021181057-A1

Title: Estimating device, estimating method, and program storing medium

Description:
TECHNICAL FIELD 
     The present invention relates to a technique of estimating strength of a pipe. 
     BACKGROUND ART 
     There is a case where a pipe constituting a piping network for transporting a resource such as water, petroleum, or gas is used beyond a service life. Therefore, problems such as leakage of fluid due to deterioration of a pipe, and rapture accident of a pipe are caused. In order to prevent these problems, a method of inspecting or estimating strength of a pipe is developed. 
     PTL 1 describes a buried-pipe inspection method of inspecting, with high accuracy, a degree of deterioration of a buried pipe such as a buried pipe and a ceramic pipe forming a sewer pipeline, an agricultural water pipeline, and the like, by performing an impact elastic wave test. 
     CITATION LIST 
     Patent Literature 
     [PTL 1] Japanese Unexamined Patent Application Publication No. 2012-118047 
     SUMMARY OF INVENTION 
     Technical Problem 
     The inspection method of a buried pipe described in PTL 1 is a method in which a deterioration state of a buried pipe is inspected from an inside of the pipe. However, in a pipe (hereinafter, referred to as a “water-filled pipe”) like a water supply pipe in which the inside of the pipe is filled with a fluid such as water, it is not easy to inspect a deterioration state from the inside of the pipe. 
     The present invention is made for solving the above-described problem, and a main object of the present invention is to provide an estimating device and the like that are capable of easily estimating strength of a water-filled pipe. 
     Solution to Problem 
     An estimating device according to one aspect of the present invention includes: a frequency response calculating unit for calculating a frequency response function of a pipe on the basis of an excitation force when the pipe is excited and a vibration response propagating through the pipe; a pipe rigidity variable estimating unit for estimating a parameter relating to rigidity of the pipe on the basis of a frequency response function model being a model representing a frequency response of the pipe, and the frequency response function; and a strength estimating unit for estimating strength of the pipe on the basis of a relation between the parameter and the strength of the pipe. 
     An estimating method according to one aspect of the present invention includes: calculating a frequency response function of a pipe on the basis of an excitation force when the pipe is excited and a vibration response propagating through the pipe; estimating a parameter relating to rigidity of the pipe on the basis of a frequency response function model being a model representing a frequency response of the pipe, and the frequency response function; and estimating strength of the pipe on the basis of a relation between the parameter and the strength of the pipe. 
     A program storing medium according to one aspect of the present invention stores a computer program causing a computer to execute: processing of calculating a frequency response function of a pipe on the basis of an excitation force when the pipe is excited and a vibration response propagating through the pipe; processing of estimating a parameter relating to rigidity of the pipe on the basis of a frequency response function model being a model representing a frequency response of the pipe, and the frequency response function; and processing of estimating strength of the pipe on the basis of a relation between the parameter and the strength of the pipe. 
     Advantageous Effects of Invention 
     According to the present invention, an estimating device and the like that are able to estimate strength of a water-filled pipe with ease can be provided. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a diagram illustrating a configuration of an estimating device according to an example embodiment of the present invention. 
         FIG. 2  is a diagram illustrating a configuration when tensile strength of a pipe is estimated by use of the estimating device according to the example embodiment of the present invention. 
         FIG. 3A  is a diagram used for describing a frequency response function model used by a pipe rigidity variable estimating unit. 
         FIG. 3B  is another diagram used for describing the frequency response function model used by the pipe rigidity variable estimating unit. 
         FIG. 4  is a diagram illustrating an example of the frequency response function model assumed in the pipe rigidity variable estimating unit. 
         FIG. 5  is a diagram illustrating one example of a relation between an elasticity modulus of a pipe used in a strength estimating unit and strength of the pipe. 
         FIG. 6  is a flowchart illustrating an operation of the estimating device according to the example embodiment of the present invention. 
         FIG. 7  is a diagram illustrating one example of a response time waveform being response data measured by a measuring instrument. 
         FIG. 8  is a diagram illustrating one example of a response spectrum acquired for the response time waveform. 
         FIG. 9  is a diagram illustrating one example of an information processing device achieving the estimating device according to the example embodiment of the present invention. 
     
    
    
     EXAMPLE EMBODIMENT 
     Each example embodiment of the present invention is described with reference to the accompanying drawings. First, a first example embodiment of the present invention is described.  FIG. 1  is a diagram illustrating an estimating device according to the first example embodiment of the present invention. 
     As illustrated in  FIG. 1 , an estimating device  100  according to the first example embodiment of the present invention includes a frequency response calculating unit  110 , a pipe rigidity variable estimating unit  120 , and a strength estimating unit  130 . The frequency response calculating unit  110  calculates, based on an excitation force when a pipe is excited and a vibration response propagating through the pipe, a frequency response function of the pipe. The pipe rigidity variable estimating unit  120  estimates, based on a frequency response function model representing a frequency response of the pipe, and the calculated frequency response function, a parameter relating to rigidity of the pipe. The strength estimating unit  130  estimates, based on a relation between the estimated parameter and strength of the pipe, strength of the pipe. 
     One example of a case in which strength of a pipe is estimated by using the estimating device  100  is described with reference to  FIG. 2 .  FIG. 2  is an example of a case in which strength of a pipe  301  being a part of a water-supply network is estimated. Specifically, in the example illustrated in  FIG. 2 , the estimating device  100  estimates strength of the pipe  301 . Note that, in the following example embodiment, a case in which the estimating device  100  estimates strength of a pipe configuring a water pipe is described as an example. Further, the pipe  301  is assumed to be the water-filled pipe described above. Specifically, a case in which the inside of the pipe  301  is filled with water by applying pressure to the water, or the water flowing into the pipe due to gravity is assumed. A main target of strength estimation by the estimating device  100  is a water-filled pipe. 
     In the example illustrated in  FIG. 2 , the pipe  301  is buried underground. Specifically, in the example illustrated in  FIG. 2 , the pipe  301  is assumed to be disposed in such a way that visual observation and contact of the pipe  301  is difficult in a normal condition. Further, accessories  302 - 1  and  302 - 2  are installed on the pipe  301 . Each of the accessories  302 - 1  and  302 - 2  is, for example, a fire hydrant, an air valve, or a gate valve, but may be another equipment attached to the pipe. Each of the accessories  302 - 1  and  302 - 2  is installed in a manhole. Specifically, in the example illustrated in  FIG. 2 , each of the accessories  302 - 1  and  302 - 2  is assumed to be disposed at a position where a contact can be made in a normal condition. 
     As illustrated in  FIG. 2 , an instrument for acquiring data required when strength of the pipe  301  is estimated by the estimating device  100  is installed on each of the accessories  302 - 1  and  302 - 2 . 
     An exciter  161  is installed on the accessory  302 - 1 . The exciter  161  excites, for example, the accessory  302 - 1 . With the excitation by the exciter  161 , an elastic wave is excited in the fluid such as water filled inside the pipe  301 . The elastic wave is also excited in the pipe  301 . 
     As the exciter  161 , a mechanism that is capable of exciting a vibration of a broad bandwidth is desirably used. As the exciter  161 , for example, an impulse hammer, a hydraulic actuator, a pneumatic actuator, or a water-releasing pressure-variation generator is used, but another mechanism may be used as the exciter  161 . 
     Further, the exciter  161  records an excitation force, which is magnitude of force when the accessory  302 - 1  is excited. Excitation force data, which are data recording the excitation force, are sent to, for example, the frequency response calculating unit  110  of the estimating device  100  via a wired or wireless communication network or another mechanism for data transmission. 
     A measuring instrument  162  is installed on the accessory  302 - 2 . The measuring instrument  162  measures an elastic wave propagating through the fluid such as water inside the pipe  301  and the pipe  301 . The measuring instrument  162  mainly measures an elastic wave generated by excitation by the exciter  161  and propagating through the fluid such as water inside the pipe  301  and the pipe  301 . 
     As the measuring instrument  162 , a sensor for measuring a vibration of a solid body is used. Examples of the measuring instrument  162  include a piezoelectric type acceleration sensor, a capacitive type acceleration sensor, an optical velocity sensor, a dynamic strain sensor, an eddy-current displacement sensor, a dial gauge, a digital image correlation measuring device, an optical fiber type strain gauge, a contact type displacement sensor, and a speckle light interferometer. However, another instrument may be used as the measuring instrument  162 . 
     A measurement result by the measuring instrument  162  is sent to, for example, the frequency response calculating unit  110  of the estimating device  100  via a wired or wireless communication network or another mechanism for data transmission. With a time point at which the exciter  161  performs excitation as a reference, the measuring instrument  162  may send a result of a measurement performed for a time period from before to after the time point to each component of the estimating device  100 . In the case described above, a length of the time period from before to after the reference time point at which the exciter  161  performs the excitation may be determined according to a time required for an elastic wave generated by the excitation to the accessory  302 - 1  by the exciter  161  to propagate to the measuring instrument  162 . 
     Note that, as described above, the pipe  301  is assumed to be buried underground, and visual observation and contact of the pipe  301  is assumed to be difficult. Therefore, the exciter  161  and the measuring instrument  162  are exemplified in such a way as to be attached to the accessories  302 . However, when it is possible to make contact with the pipe  301 , each of the exciter  161  and the measuring instrument  162  may be directly installed on, for example, the pipe  301 . 
     Further, in the example illustrated in  FIG. 2 , the pipe rigidity variable estimating unit  120  of the estimating device  100  is connected to an accessory information storing unit  151 . Specifically, when estimating a parameter that relates to rigidity of a pipe, the pipe rigidity variable estimating unit  120  may use information stored in the accessory information storing unit  151  as necessary. 
     Similarly, in the example illustrated in  FIG. 2 , the strength estimating unit  130  of the estimating device  100  is connected to a strength information storing unit  152 . Specifically, when estimating strength of a pipe, the strength estimating unit  130  may use information stored in the strength information storing unit  152  as necessary. 
     Next, each component of the estimating device  100  according to the present example embodiment is described. Note that, in each example embodiment of the present invention, each component of the estimating device  100  represents a block of a function unit. Some or all of each component of each device is achieved by, for example, any combination of an information processing device  500  and a program, such as illustrated in  FIG. 9 . The information processing device  500  includes, as one example, a configuration as follows.
         A central processing unit (CPU)  501     A read only memory (ROM)  502     A random access memory (RAM)  503     A program  504  loaded on the RAM  503     A storing device  505  storing the program  504     A drive device  507  performing reading and writing of a recording medium  506     A communication interface  508  connected to a communication network  509     An input/output interface  510  performing input and output of data   A bus  511  connecting each component       

     Each component of each device according to each example embodiment is achieved by the CPU  501  acquiring and executing the program  504  achieving a function of each component. The program  504  achieving a function of each component of each device is, for example, previously stored in the storing device  505  or the RAM  503 , and read out by the CPU  501  as necessary. Note that, the program  504  may be provided to the CPU  501  via the communication network  509 , or may be previously stored in the recording medium  506 , read out by the drive device  507 , and thereby provided to the CPU  501 . 
     There are various modification examples of a method of achieving each device. For example, each device may be achieved by any combination of the information processing device  500  that is separated for each component and a program. Further, a plurality of components included in each device may be achieved by any combination of one information processing device  500  and a program. 
     Some or all of each component of each device is achieved by a dedicated or general-purpose circuit including a processor and the like, or a combination thereof. The dedicated or general-purpose circuit may be configured by a single chip, or may be configured by a plurality of chips connected to each other via a bus. Some or all of each component of each device may be achieved by a combination of the above-described circuit and the like and a program. 
     When some or all of each component of each device is achieved by a plurality of information processing devices and circuits and the like, the plurality of information processing devices and circuits and the like may be concentratedly or distributedly disposed. For example, the information processing devices and circuits and the like may be achieved as a form, such as a client-and-sever system and a cloud computing system, in which each of the information processing devices and circuits and the like is connected via a communication network. 
     Among the components of the estimating device  100 , the frequency response calculating unit  110  is described first. The frequency response calculating unit  110  calculates, based on an excitation force when a pipe is excited and a vibration response propagating through the pipe, a frequency response function of the pipe. The frequency response function of the pipe is a function expressed in a frequency domain as a ratio of magnitude of the vibration response to the excitation force applied to the pipe. 
     The excitation force indicates, in a case where a pipe is excited, a temporal change in magnitude of force applied to the pipe. As one example, the excitation force indicates a temporal change in magnitude of force applied to the pipe  301  by the exciter  161  illustrated in  FIG. 2 . In the example illustrated in  FIG. 2 , the excitation force is assumed to be recorded at a time of excitation performed by the exciter  161 . Excitation force data indicating the recorded excitation force are sent to the frequency response calculating unit  110  via a wired or wireless communication network or another means, as appropriate. 
     The vibration response is a response of the pipe or the fluid such as water inside the pipe to the excitation performed by the exciter  161 . In the example illustrated in  FIG. 2 , the vibration response is acquired by the measuring instrument  162  measuring a temporal change of the elastic wave, which is generated by the excitation by the exciter  161  and propagating through the fluid such as water inside the pipe  301  and the pipe  301 . In the example illustrated in  FIG. 2 , measured data indicating the vibration response measured by the measuring instrument  162  are sent to the frequency response calculating unit  110  via a wired or wireless communication network or another means, as appropriate. 
     The frequency response calculating unit  110  acquires, as one example, a frequency response function of the pipe as follows. First, let excitation force data be f(t), and response data be x(t). Further, let functions in a frequency domain into which f(t) and x(t) are Fourier transformed be F(ω) and X(ω), respectively. The frequency response calculating unit  110  acquires F(ω) and X(ω) with respect to f(t) and x(t), respectively. ω represents an angular frequency. 
     Then, the frequency response calculating unit  110  acquires, by using the following expression (1), a frequency response function H exp (ω). 
     
       
         
           
             
               
                 
                   
                     
                       H 
                       exp 
                     
                      
                     
                       ( 
                       ω 
                       ) 
                     
                   
                   = 
                   
                     
                       X 
                        
                       
                         ( 
                         ω 
                         ) 
                       
                     
                     
                       F 
                        
                       
                         ( 
                         ω 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     Note that, the frequency response calculating unit  110  may perform processing for improving a signal-to-noise ratio, as necessary. For example, the frequency response calculating unit  110  may perform averaging processing for acquiring an average value of frequency response functions acquired by a plurality of times of excitation and measurement of a response. 
     The pipe rigidity variable estimating unit  120  estimates a parameter relating to rigidity of the pipe, on the basis of the frequency response function model representing the frequency response of the pipe, and the frequency response function. As the frequency response function, H exp (ω) acquired by the frequency response calculating unit  110  is used. 
     In the pipe rigidity variable estimating unit  120 , an expression of the frequency response function model is determined in advance, according to a characteristic of the pipe being a target and H exp (ω) acquired by the frequency response calculating unit  110 . A frequency response function model specifically representing a frequency response of a pipe being a target is acquired by approximating an expression of the frequency response function model to a frequency response function that is actually measured. Therefore, the parameter relating to the rigidity of the pipe is acquired by approximating the frequency response function model to the frequency response function. 
     The pipe rigidity variable estimating unit  120  estimates the parameter relating to the rigidity of the pipe by acquiring such a parameter that the expression of the frequency response function model approximates the frequency response function H exp (ω) acquired by the frequency response calculating unit  110 . 
     Prior to a description of the parameter acquired by the pipe rigidity variable estimating unit  120 , the expression of the frequency response function model used in the pipe rigidity variable estimating unit  120  is described. In the following description, the pipe is assumed to be a water-filled pipe whose inside is filled with water. 
     First, when it is assumed that a weight is applied from both sides of the pipe as illustrated in  FIGS. 3A and 3B , displacement w in a radius-direction of the pipe, which is generated when a weight P is applied from both sides of the pipe, is expressed as the following expression (2). 
     
       
         
           
             
               
                 
                   w 
                   = 
                   
                     
                       
                         PR 
                         3 
                       
                       
                         4 
                          
                         EI 
                       
                     
                      
                     
                       ( 
                       
                         
                           cos 
                            
                           
                               
                           
                            
                           θ 
                         
                         + 
                         
                           θ 
                            
                           
                               
                           
                            
                           sin 
                            
                           
                               
                           
                            
                           θ 
                         
                         - 
                         
                           4 
                           π 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     In the expression (2), R is a radius of the pipe, E is an elasticity modulus of the pipe, I is a second moment of area of the pipe, and θ is an angle of a position at which the displacement w is considered with respect to a reference direction. In the expression (2), one of the directions perpendicular to a direction in which the weight is applied is assumed to be the above-described reference direction, and θ is determined thereby. 
     Then, a pipe rigidity, which is the rigidity of the pipe, is defined by transforming the expression (2) and expressing the expression (2) in a form of the Hooke&#39;s law. Specifically, a pipe rigidity K is expressed as the following expression (3). 
     
       
         
           
             
               
                 
                   K 
                   = 
                   
                     
                       P 
                       w 
                     
                     = 
                     
                       
                         4 
                          
                         EI 
                       
                       
                         
                           R 
                           3 
                         
                          
                         
                           ( 
                           
                             
                               cos 
                                
                               
                                   
                               
                                
                               θ 
                             
                             + 
                             
                               θ 
                                
                               
                                   
                               
                                
                               sin 
                                
                               
                                   
                               
                                
                               θ 
                             
                             - 
                             
                               4 
                               π 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     In the expressions (2) and (3), when a wall thickness of the pipe is assumed to be t, and a unit length of the pipe is assumed to be L, the second moment of area I is expressed as I=Lt 3 /12. Specifically, the pipe rigidity K is determined by the elasticity modulus E of the pipe, the wall thickness t, and the radius R of the pipe. Among those variables, the radius R of the pipe can be generally known from a drawing and the like of the pipe. Further, the elasticity modulus E and the wall thickness t of the pipe may change with deterioration of the pipe. Thus, in the present example embodiment, the pipe rigidity variable estimating unit  120  estimates, as one example of the parameter relating to the rigidity of the pipe, either one or both of the elasticity modulus E of the pipe or/and a value of the wall thickness t of the pipe. The parameter acquired by the pipe rigidity variable estimating unit  120  may be appropriately determined according to a relation and the like used in the strength estimating unit  130  to be described later. 
     The expression of the frequency response function model is expressed as H(ω|θ M , θ F ), as a function of an angular frequency ω, a pipe rigidity variable θ M , and an accessory parameter θ F . The pipe rigidity variable θ M  is a parameter relating to the rigidity of the pipe, and is defined as θ M =[E, t, R]. The accessory parameter θ F  is a parameter relating to a structure of an accessory such as the accessories  302  illustrated in  FIG. 2 , and is defined as θ F =[m, k, c]. E t, and R included in the pipe rigidity variable θ M  indicate, as described above, the elasticity modulus, the wall thickness of the pipe, and the radius of the pipe, respectively. The radius R is acquired from a drawing of the pipe, a description of configuration information of the pipe, and the like. The elasticity modulus E and the wall thickness t are estimated by the pipe rigidity variable estimating unit  120 . Regarding the accessory parameter θ F , m, k, and c respectively indicate an equivalent mass, an equivalent rigidity, and an equivalent damping coefficient when the accessory is modeled. Each parameter included in the accessory parameter θ F  is previously determined according to actual values of the accessories  302  to which the exciter  161  and the measuring instrument  162  are attached. Those values are acquired from, for example, a drawing of the pipe or a description of configuration information of the pipe, a result of an actual measurement, and the like. 
     A frequency response function model with respect to an example illustrated in  FIG. 4 , in which a spring, a mass, and a damper are connected to a ring is assumed. In the example illustrated in  FIG. 4 , a ring unit corresponds to the pipe  301  illustrated in  FIG. 2 , and accessories correspond to the accessories  302  illustrated in  FIG. 2 . The expression H(ω|θ M , θ F ) of the frequency response function model with respect to the example is expressed by the following expressions (4) and (5). 
     
       
         
           
             
               
                 
                   
                     H 
                      
                     
                       ( 
                       
                         
                           ω 
                            
                           
                             θ 
                             M 
                           
                         
                         , 
                         
                           θ 
                           F 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       3 
                        
                       π 
                        
                       
                           
                       
                        
                       
                         ( 
                         
                           k 
                           + 
                           
                             jc 
                              
                             
                                 
                             
                              
                             ω 
                           
                         
                         ) 
                       
                     
                     
                       4 
                        
                       
                         D 
                          
                         
                           ( 
                           ω 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                     D 
                      
                     
                       ( 
                       ω 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         { 
                         
                           K 
                           + 
                           k 
                           - 
                           
                             M 
                              
                             
                                 
                             
                              
                             
                               ω 
                               2 
                             
                           
                           + 
                           
                             j 
                              
                             
                                 
                             
                              
                             
                               ω 
                                
                               
                                 ( 
                                 
                                   C 
                                   + 
                                   c 
                                 
                                 ) 
                               
                             
                           
                         
                         } 
                       
                        
                       
                           
                       
                        
                       
                         { 
                         
                           k 
                           - 
                           
                             m 
                              
                             
                                 
                             
                              
                             
                               ω 
                               2 
                             
                           
                           + 
                           
                             jc 
                              
                             
                                 
                             
                              
                             ω 
                           
                         
                         } 
                       
                     
                     - 
                     
                       
                         ( 
                         
                           k 
                           + 
                           
                             jc 
                              
                             
                                 
                             
                              
                             ω 
                           
                         
                         ) 
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     In the expression (5), M, K, and C respectively indicate an equivalent mass, an equivalent rigidity, and an equivalent damping coefficient when the ring unit illustrated in  FIG. 4  is represented by a simple model of the mass, the spring, and the damper. 
     Note that, the expression H(ω|θ M , θ F ) of the frequency response function model expressed by the expressions (4) and (5) is assumed in a case in which the exciter  161  and the measuring instrument  162  are attached to the accessories. However, as described above, a position to which the exciter  161  or the measuring instrument  162  is attached is not limited thereto, and in such a case, for example, each accessory parameter θ F  may be set to an appropriate value. 
     The pipe rigidity variable estimating unit  120  acquires an estimated value of the pipe rigidity variable by approximating the expression H(ω|θ M , θ F ) of the frequency response function model to the frequency response function H exp (ω) acquired by the frequency response calculating unit  110 . Specifically, the pipe rigidity variable estimating unit  120  acquires the estimated value of the pipe rigidity variable by approximating H(ω|θ M , θ F ) to H exp (ω) in such a way that a difference between H(ω|θ M , θ F ) and H exp (ω) is within a predetermined range. The pipe rigidity variable estimating unit  120  acquires the estimated value of the pipe rigidity variable by using the following expression (6), for example. 
     
       
         
           
             
               
                 
                   
                     
                       θ 
                       ^ 
                     
                     M 
                   
                   = 
                   
                     argmin 
                      
                     
                       [ 
                       
                         
                           ∑ 
                           i 
                           N 
                         
                          
                         
                           
                              
                             
                               
                                 H 
                                  
                                 
                                   ( 
                                   
                                     
                                       
                                         ω 
                                         i 
                                       
                                        
                                       
                                         θ 
                                         M 
                                       
                                     
                                     , 
                                     
                                       θ 
                                       F 
                                     
                                   
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   H 
                                   exp 
                                 
                                  
                                 
                                   ( 
                                   
                                     ω 
                                     i 
                                   
                                   ) 
                                 
                               
                             
                              
                           
                           2 
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     Hereinafter, a left-side value of the expression (6) is referred to as “the estimated value of the pipe rigidity variable”. In the expression (6), argmin indicates a set of arguments that minimizes the function given in the brackets. Specifically, the pipe rigidity variable estimating unit  120  acquires the estimated value of the pipe rigidity variable in such a way that a sum of squares of an absolute value of the difference between H(ω|θ M , θ F ) and H exp (ω) is minimized. 
     The pipe rigidity variable estimating unit  120  acquires the estimated value of the pipe rigidity variable by using, for example, a nonlinear optimization method such as a Levenberg-Marquardt method. However, when acquiring the estimated value of the pipe rigidity variable, the pipe rigidity variable estimating unit  120  may use any other method of curve-fitting. 
     The strength estimating unit  130  estimates strength of the pipe, on the basis of a relation between the parameter estimated by the pipe rigidity variable estimating unit  120  and the strength of the pipe. The strength estimating unit  130  estimates, mainly as the strength of the pipe, tensile strength of the pipe. The tensile strength of the pipe may change with deterioration of the pipe. Specifically, a degree of deterioration of the pipe is estimated by acquiring the tensile strength of the pipe. 
     The strength estimating unit  130  estimates the strength of the pipe by using, for example, a relation, as illustrated in  FIG. 5 , between any one parameter relating to rigidity of the pipe and strength of the pipe, or a strength estimation equation generated from the relation illustrated in  FIG. 5 .  FIG. 5  is an example illustrating a relation between an elasticity modulus, which is one of parameters relating to the rigidity of the pipe, and strength of the pipe. Specifically, the strength estimating unit  130  estimates the strength of the pipe according to the parameter by applying some or all of the parameters estimated by the pipe rigidity variable estimating unit  120  to the above-described relation. 
     The relation illustrated in  FIG. 5  is acquired by, as one example, previously conducting an actual measurement by using a sample pipe. However, as the relation, a relation acquired by another means may be used. Further, the relation between the parameter relating to the rigidity of the pipe and the strength of the pipe is, for example, previously stored in the strength information storing unit  152 . The strength estimating unit  130  refers to, as one of operation examples, being previously stored in the strength information storing unit  152 , as appropriate, and estimates the strength of the pipe. Further, when a relation between any one of the parameters estimated by the pipe rigidity variable estimating unit  120  and strength of the pipe is acquired similarly to the relation and a relational expression illustrated in  FIG. 5 , strength other than tensile strength may be acquired by the strength estimating unit  130 . In this case, the strength estimating unit  130  acquires, for example, bending strength, compression strength, or yield stress. 
     The tensile strength, which is one of the strengths acquired by the strength estimating unit  130 , is related to deterioration of the pipe. Specifically, the tensile strength indicates a degree of deterioration of the pipe. Therefore, the degree of deterioration of the pipe can be estimated by estimating the tensile strength. 
     Next, an operation of the estimating device  100  according to the present example embodiment is described with reference to the flowchart illustrated in  FIG. 6 . 
     First, excitation of the pipe, and measurement of a vibration response of the pipe and the fluid inside the pipe to the excitation are performed (Step S 101 ). 
     In the configuration example illustrated in  FIG. 2 , the exciter  161  excites the accessory  302 - 1 . Thereby, an elastic wave is excited in a fluid inside the pipe  301 , and the pipe  301 . Further, the measuring instrument  162  measures, via the accessory  302 - 2 , vibration including the elastic wave generated by the excitation by the exciter  161 . Thereby, data representing an excitation force and a vibration response are acquired. The data representing the excitation force and the vibration response acquired in Step S 101  are sent to the frequency response calculating unit  110  via a communication network or another means. 
     Next, the frequency response calculating unit  110  acquires a frequency response function of the pipe, on the basis of the excitation force and the vibration response acquired in Step S 101 , (Step S 102 ). 
     Next, the pipe rigidity variable estimating unit  120  estimates a parameter, on the basis of the frequency response function model in which a frequency response of the pipe is modeled and the frequency response function of the pipe acquired in Step S 102  (Step S 103 ). As described above, the pipe rigidity variable estimating unit  120  estimates, as one example, the elasticity modulus E and the wall thickness t of the pipe, which are values each included in the pipe rigidity variable θ M . 
     Next, the strength estimating unit  130  estimates strength of the pipe, on the basis of the parameter relating to rigidity of the pipe acquired in Step S 103 , and a relation between, for example, the parameter and the strength of the pipe (Step S 104 ). As the relation between the parameter and the strength of the pipe, a relation stored in the strength information storing unit  152  is used. Further, as described above, tensile strength of the pipe is estimated as the strength of the pipe. The acquired strength of the pipe is output via any means including a display and a communication network, as appropriate. 
     As described above, the estimating device  100  according to the present example embodiment estimates the parameter relating to the rigidity of the pipe, on the basis of the frequency response function model representing the frequency response of the pipe, and the frequency response function calculated on the basis of an actually measured value. Then, the estimating device  100  according to the present example embodiment estimates the strength of the pipe including the tensile strength, on the basis of the relation between the estimated parameter and the strength of the pipe. 
     The estimating device  100  is further described in comparison with the method described in PTL 1, by using a more detailed example.  FIG. 7  is a measurement example of a response time waveform measured in a water-filled pipe filled with water inside the pipe. The response time waveform illustrated in  FIG. 7  is one of actual examples of response data. Further,  FIG. 8  is a response spectrum with respect to the response time waveform illustrated in  FIG. 7 . The response time waveform and its response spectrum illustrated in  FIGS. 7 and 8  are examples of a case where a measurement is performed when a distance between the accessory on which the exciter  161  is installed and the accessory on which the measuring instrument  162  is installed is about 100 m (meters). 
     Referring to  FIG. 8 , a resonance peak, which is a frequency component at which acceleration increases, appears in a domain of approximately 500 Hz (Hertz) or less. In the example illustrated in  FIG. 8 , the resonance peak is single. As in this example, generally, in a buried water-filled pipe such as a water pipe, an interval at which accessories are installed is often several tens of meters or more. Therefore, a high frequency component of an elastic wave excited by the exciter  161  and propagating through a fluid inside the pipe and the pipe is attenuated before being measured by the measuring instrument  162 . As a result, in the response spectrum with respect to the response data measured in the measuring instrument  162 , frequency of the resonance peak may be 500 Hz or less. 
     On the other hand, in the method described in PTL 1, an interval between a striking unit and a vibration receiving unit is assumed to be about several meters at most. Further, in the method described in PTL 1, a frequency domain of 0.5 kHz (kilohertz) to 7.0 kHz is assumed to be an entire frequency domain, and a frequency domain of 3.5 kHz to 7.0 kHz is assumed to be a high frequency domain. Then, strength of a pipe is estimated on the basis of an area ratio of the high frequency domain to the entire frequency domain. 
     However, it may be difficult to dispose the striking unit and the vibration receiving unit on a buried water-filled pipe at the interval assumed in PTL 1. Further, as described in  FIGS. 7 and 8 , in a vibration response measured in the buried water-filled pipe, an elastic wave in a frequency domain corresponding to the high frequency domain in PTL 1 is attenuated. Specifically, it may not be necessarily easy to apply the method described in PTL 1 to a buried water-filled pipe. 
     On the other hand, in the estimating device  100  according to the present example embodiment, the pipe rigidity variable M described above is acquired by using the frequency response function model according to a generation mechanism of a resonance peak in the response spectrum with respect to the response data. Specifically, in the estimating device  100  according to the present example embodiment, a parameter relating to the rigidity of the pipe is acquired by using an appropriate frequency response function model. Since the parameter relating to the rigidity of the pipe is acquired, strength of the pipe such as tensile strength is estimated in the estimating device  100 . Specifically, the estimating device  100  according to the present example embodiment can estimate the strength of the water-filled pipe with ease. 
     While the invention has been particularly shown and described with reference to exemplary embodiments thereof, the invention is not limited to these embodiments. It will be understood by those of ordinary skill in the art that various changes in form and details may be made therein without departing from the spirit and scope of the present invention as defined by the claims. Further, a configuration according to each example embodiment may be combined with each other without departing from the scope of the present invention. 
     This application is based upon and claims the benefit of priority from Japanese patent application No. 2017-215729 filed on Nov. 8, 2017, the disclosure of which is incorporated herein its entirety by reference. 
     REFERENCE SIGNS LIST 
     
         
           100  Estimating device 
           110  Frequency response calculating unit 
           120  Pipe rigidity variable estimating unit 
           130  Strength estimating unit 
           151  Accessory information storing unit 
           152  Strength information storing unit 
           161  Exciter 
           162  Measuring instrument 
           301  Pipe 
           302  Accessory