Patent Publication Number: US-2021164829-A1

Title: Information processing system, information processing apparatus, program, and information processing method

Description:
TECHNICAL FIELD 
     The present disclosure relates to an information processing system, an information processing apparatus, a program, and an information processing method. 
     BACKGROUND 
     Techniques of estimating the state of a device using data from a sensor are conventionally known. For example, JP 2012-100434 A (PTL 1) discloses an railroad vehicle anomaly diagnosis system that diagnoses an anomaly caused by degradation or the like in components of a railroad vehicle based on the acceleration, velocity, and current position of the railroad vehicle. JP 2012-251858 A (PTL 2) discloses a structure that, in an angle detector using a ball bearing as a bearing, provides an accelerometer on a bearing fixing plate on which the bearing is installed and detects vibration which occurs when rotation operation fails. 
     CITATION LIST 
     Patent Literature 
     PTL 1: JP 2012-100434 A 
     PTL 2: JP 2012-251858 A 
     SUMMARY 
     Technical Problem 
     Methods of estimating the state of a device based on whether the magnitude of the vibration of the device exceeds a predetermined threshold are conventionally known. With such methods, however, the accuracy of estimating the state of the device is not always sufficient, because the magnitude of the vibration of the device also varies due to, for example, the load of the device. To accurately estimate the state of the device, frequency analysis on the vibration of the device is commonly performed. For the frequency analysis, it is necessary to detect the vibration of the device by a sensor having relatively high sampling frequency (e.g. about 80 kHz), and process, by a calculator having relatively high computing power, a large amount of data output from the sensor. Accordingly, a sensor having relatively low sampling frequency (e.g. about several hundred Hz) and a calculator having relatively low computing power cannot be used. Thus, the convenience of the techniques of estimating the state of a device using data from a sensor is not always high. 
     It could therefore be helpful to provide an information processing system, an information processing apparatus, a program, and an information processing method that can improve the convenience of the techniques of estimating the state of a device using data from a sensor. 
     Solution to Problem 
     An information processing system according to one of the disclosed embodiments is an information processing system comprising: an acquisition means configured to acquire vibration of a device that vibrates during operation, as time-series data of a physical quantity A indicated by a plurality of axis components in a three-dimensional coordinate system; a calculation means configured to calculate a first evaluation value E indicating a degree of bias of the vibration of the device between axes, based on the time-series data of the physical quantity A; and an estimation means configured to estimate a degradation level G of the device based on the first evaluation value E. 
     An information processing apparatus according to one of the disclosed embodiments is an information processing apparatus comprising: an acquisition means configured to acquire vibration of a device that vibrates during operation, as time-series data of a physical quantity A indicated by a plurality of axis components in a three-dimensional coordinate system; a calculation means configured to calculate a first evaluation value E indicating a degree of bias of the vibration of the device between axes, based on the time-series data of the physical quantity A; and an estimation means configured to estimate a degradation level G of the device based on the first evaluation value E. 
     An information processing apparatus according to one of the disclosed embodiments is an information processing apparatus in an information processing system that includes: an acquisition means configured to acquire vibration of a device that vibrates during operation, as time-series data of a physical quantity A indicated by a plurality of axis components in a three-dimensional coordinate system; a calculation means configured to calculate a first evaluation value E indicating a degree of bias of the vibration of the device between axes, based on the time-series data of the physical quantity A; and an estimation means configured to estimate a degradation level G of the device based on the first evaluation value E, the information processing apparatus comprising at least one of the acquisition means, the calculation means, and the estimation means. 
     A program according to one of the disclosed embodiments is a program for causing an information processing apparatus to function as: an acquisition means configured to acquire vibration of a device that vibrates during operation, as time-series data of a physical quantity A indicated by a plurality of axis components in a three-dimensional coordinate system; a calculation means configured to calculate a first evaluation value E indicating a degree of bias of the vibration of the device between axes, based on the time-series data of the physical quantity A; and an estimation means configured to estimate a degradation level G of the device based on the first evaluation value E. 
     A program according to one of the disclosed embodiments is a program for causing, in an information processing system that is composed of a plurality of information processing apparatuses communicably connected to each other and includes: an acquisition means configured to acquire vibration of a device that vibrates during operation, as time-series data of a physical quantity A indicated by a plurality of axis components in a three-dimensional coordinate system; a calculation means configured to calculate a first evaluation value E indicating a degree of bias of the vibration of the device between axes, based on the time-series data of the physical quantity A; and an estimation means configured to estimate a degradation level G of the device based on the first evaluation value E, one of the plurality of information processing apparatuses to function as at least one of the acquisition means, the calculation means, and the estimation means. 
     An information processing method according to one of the disclosed embodiments is an information processing method comprising: acquiring vibration of a device that vibrates during operation, as time-series data of a physical quantity A indicated by a plurality of axis components in a three-dimensional coordinate system; calculating a first evaluation value E indicating a degree of bias of the vibration of the device between axes, based on the time-series data of the physical quantity A; and estimating a degradation level G of the device based on the first evaluation value E. 
     Advantageous Effect 
     It is therefore possible to provide an information processing system, an information processing apparatus, a program, and an information processing method that can improve the convenience of the techniques of estimating the state of a device using data from a sensor. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the accompanying drawings: 
         FIG. 1  is a block diagram illustrating a schematic structure of an information processing system according to one of the disclosed embodiments; 
         FIG. 2  is a block diagram illustrating a schematic structure of an information processing apparatus; 
         FIG. 3  is a flowchart illustrating an example of operation of a detection apparatus; 
         FIG. 4  is a flowchart illustrating an example of operation of the information processing apparatus; 
         FIG. 5  is a diagram illustrating an example of the correspondence relationship between each axis component Ci of a proportion C and each axis component Di of a second index D; 
         FIG. 6  is a flowchart illustrating an example of operation of a server; and 
         FIG. 7  is a flowchart illustrating an example of operation of a terminal apparatus. 
     
    
    
     DETAILED DESCRIPTION 
     One of the disclosed embodiments will be described below. 
     An information processing system  1  according to one of the disclosed embodiments will be described below, with reference to  FIG. 1 . In this embodiment, the information processing system  1  includes a detection apparatus  20 , an information processing apparatus  30 , a server  40 , and a terminal apparatus  50 . The information processing apparatus  30 , the server  40 , and the terminal apparatus  50  are communicably connected with a network  60  such as the Internet. 
     The information processing system  1  is a system that estimates the degree of degradation of a device  10  and presents the estimated degree of degradation to a user. The device  10  is a rotator as an example, but may be any device that vibrates during operation. As an overview, the information processing system  1  detects vibration of the device  10  that vibrates during operation, by the detection apparatus  20 . The information processing system  1  estimates the degradation level G of the device  10  by the information processing apparatus  30 , based on the output of the detection apparatus  20 . The information processing system  1  accumulates the degradation level G of the device  10  in the server  40 . The information processing system  1  transmits the degradation level G of the device  10  accumulated in the server  40 , to the terminal apparatus  50  used by the user. The information processing system  1  then presents the degradation level G of the device  10  to the user by the terminal apparatus  50 . 
     (Hardware Structure of Detection Apparatus) 
     The hardware structure of the detection apparatus  20  will be described below. The detection apparatus  20  is an apparatus that includes a sensor used in a state of being attached to the device  10 , and an output interface that outputs data detected by the sensor. Non-limiting examples of the sensor included in the detection apparatus  20  include a three-axis accelerometer and a three-axis gyroscope sensor. As the sensor included in the detection apparatus  20 , a sensor having a sampling frequency of several hundred Hz (e.g. about 170 Hz) can be used, as described later. 
     (Hardware Structure of Information Processing Apparatus) 
     The hardware structure of the information processing apparatus  30  will be described below, with reference to  FIG. 2 . The information processing apparatus  30  includes a communication unit  31 , a storage unit  32 , and a controller  33 . 
     The communication unit  31  includes one or more communication interfaces that perform wireless or wired communication with external apparatuses. In this embodiment, the communication unit  31  includes a communication interface that communicates with the detection apparatus  20  and a communication interface that communicates with the network  60 . 
     The storage unit  32  includes one or more memories. The one or more memories may each be any memory, and non-limiting examples include a semiconductor memory, a magnetic memory, and an optical memory. The storage unit  32  functions, for example, as a primary storage or a secondary storage. As an example, the storage unit  32  is contained in the information processing apparatus  30 . Alternatively, the storage unit  32  may be externally connected to the information processing apparatus  30  via any interface. 
     The controller  33  includes one or more processors. In this embodiment, the controller  33  is a microcontroller. The controller  33  is, however, not limited to such, and may be any processor such as a general-purpose processor or a special-purpose processor dedicated to specific processing. The controller  33  controls the operation of the whole information processing apparatus  30 . 
     (Hardware Structure of Server) 
     The hardware structure of the server  40  illustrated in  FIG. 1  will be described below. The server  40  is one server apparatus or a plurality of server apparatuses communicable with each other. The server  40  includes a communication interface that communicates with the network  60 , one or more memories, and one or more processors. The server  40  is, however, not limited to such, and may have any hardware. 
     (Hardware structure of terminal apparatus) 
     The hardware structure of the terminal apparatus  50  will be described below. The terminal apparatus  50  is, for example, a personal computer, a smartphone, or a tablet terminal. The terminal apparatus  50  is, however, not limited to such, and may be any apparatus used by the user. The terminal apparatus  50  includes a communication interface that communicates with the network  60 , one or more memories, one or more processors, and a user interface that presents information to the user by video output or audio output. The terminal apparatus  50  is, however, not limited to such, and may have any hardware. 
     (Software Structure of Information Processing Apparatus) 
     The software structure of the information processing apparatus  30  will be described below, with reference to  FIG. 2 . One or more programs used to control the operation of the information processing apparatus  30  are stored in the storage unit  32 . When the one or more programs are read by the controller  33 , the one or more programs cause the controller  33  to function as a storage means  331 , an acquisition means  332 , a calculation means  333 , an estimation means  334 , and a transmission means  335 . 
     An overview of each means will be given below. The storage means  331  is a means that stores information in the storage unit  32 . The acquisition means  332  is a means that acquires information from the storage unit  32 . The calculation means  333  is a means that calculates a first evaluation value E indicating the bias of vibration of the device  10  using data input from the detection apparatus  20 , as described later. The estimation means  334  is a means that estimates the degradation level G of the device  10  based on the first evaluation value E, as described later. The transmission means  335  is a means that transmits the degradation level G to the server  40  via the communication unit  31  and the network  60 . Detailed operation of each means will be described later. 
     (Operation of Information Processing System) 
     The operation of the information processing system  1  estimating the degradation level G of the device  10  will be described below, with reference to  FIGS. 3 to 7 . First, the detection apparatus  20  performs steps S 100  to S 101  illustrated in  FIG. 3 . 
     Step S 100 : The detection apparatus  20  detects vibration of the device  10  that vibrates during operation, as time-series data of a physical quantity A=(Ax, Ay, Az) indicated by three-axis (x-axis, y-axis, z-axis) components in a three-dimensional coordinate system. Non-limiting examples of the physical quantity A include acceleration, velocity, angular acceleration, angular velocity, and displacement. 
     Step S 101 : The detection apparatus  20  outputs the time-series data of the physical quantity A detected in step S 100  to the information processing apparatus  30 . 
     Next, the information processing apparatus  30  performs steps S 200  to S 211  illustrated in  FIG. 4 . 
     Step S 200 : The storage means  331  stores the time-series data of the physical quantity A received from the detection apparatus  20  via the communication unit  31 , in the storage unit  32 . Here, suppose the time-series data of the physical quantity A in n periods T 1  to Tn (where n is an integer greater than or equal to 2) is stored, as described later. 
     Step S 201 : The calculation means  333  sets a variable m to 1. 
     Step S 202 : The acquisition means  332  acquires time-series data in the period Tm from among the time-series data of the physical quantity A stored in the storage unit  32 . 
     Step S 203 : The calculation means  333  calculates the variance or standard deviation for each axis component of the time-series data of the physical quantity A acquired in step S 202 , as a first index B=(Bx, By, Bz). For example, in the case where the variance of the time-series data of the physical quantity A for each axis component is the first index B, the first index B is calculated according to the following Formula (1): 
     
       
         
           
             
               
                 
                   
                     
                       
                         B 
                         = 
                           
                          
                         
                           ( 
                           
                             Bx 
                             , 
                             By 
                             , 
                             Bz 
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             { 
                             
                               
                                 
                                   1 
                                   k 
                                 
                                  
                                 
                                   
                                     ∑ 
                                     
                                       i 
                                       = 
                                       1 
                                     
                                     k 
                                   
                                    
                                   
                                     
                                       ( 
                                       
                                         Axj 
                                         - 
                                         
                                           Ax 
                                           _ 
                                         
                                       
                                       ) 
                                     
                                     2 
                                   
                                 
                               
                               , 
                               
                                 
                                   1 
                                   k 
                                 
                                  
                                 
                                   
                                     ∑ 
                                     
                                       j 
                                       = 
                                       1 
                                     
                                     k 
                                   
                                    
                                   
                                     
                                       ( 
                                       
                                         Ayj 
                                         - 
                                         
                                           Ay 
                                           _ 
                                         
                                       
                                       ) 
                                     
                                     2 
                                   
                                 
                               
                               , 
                               
                                 
                                   ∑ 
                                   
                                     j 
                                     = 
                                     1 
                                   
                                   k 
                                 
                                  
                                 
                                   
                                     ( 
                                     
                                       Azj 
                                       - 
                                       
                                         Az 
                                         _ 
                                       
                                     
                                     ) 
                                   
                                   2 
                                 
                               
                             
                             } 
                           
                           . 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     In Formula (1), k is the number of pieces of data of each axis component included in the time-series data of the physical quantity A (where k is an integer greater than or equal to 2). The first index B is a parameter indicating the degree of variation of the physical quantity A for each axis component. 
     Step S 204 : The calculation means  333  calculates a proportion C=(Cx, Cy, Cz) of each axis component Bi (where i is x, y, or z) of the first index B to the total of the axis components Bi. Specifically, the calculation means  333  calculates the proportion C using the first index B according to the following Formula (2): 
     
       
         
           
             
               
                 
                   
                     
                       
                         C 
                         = 
                           
                          
                         
                           ( 
                           
                             Cx 
                             , 
                             Cy 
                             , 
                             Cz 
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             { 
                             
                               
                                 Bx 
                                 / 
                                 
                                   ( 
                                   
                                     Bx 
                                     + 
                                     By 
                                     + 
                                     Bz 
                                   
                                   ) 
                                 
                               
                               , 
                               
                                 By 
                                 / 
                                 
                                   ( 
                                   
                                     Bx 
                                     + 
                                     By 
                                     + 
                                     Bz 
                                   
                                   ) 
                                 
                               
                               , 
                               
                                 Bz 
                                 / 
                                 
                                   ( 
                                   
                                     Bx 
                                     + 
                                     By 
                                     + 
                                     Bz 
                                   
                                   ) 
                                 
                               
                             
                             } 
                           
                           . 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     The proportion C is a parameter indicating the balance (evenness) of the first index B (the degree of variation of the physical quantity A for each axis component) between the three axes. For example, when Cx=Cy=Cz=⅓, the balance of the first index B between the three axes is even. 
     Step S 205 : The calculation means  333  converts each axis component Ci of the proportion C using a predetermined conversion function f(Ci), to calculate a second index D=(Dx, Dy, Dz) that is minimum (e.g. 0) when the axis component Ci is ⅓ and is maximum (e.g. 1) when the axis component Ci is 0 or 1. Specifically, the calculation means  333  calculates the second index D using the proportion C according to the following Formula (3): 
         D =( Dx,Dy,Dz )={ f ( Cx ), f ( Cy ), f ( Cz )}  (3).
 
       FIG. 5  is a graph illustrating an example of the conversion function Di=f(Ci). In the example illustrated in  FIG. 5 , the axis component Di of the second index D increases as the axis component Ci of the proportion C separates from ⅓. The conversion function Di=f(Ci) is, however, not limited to the example illustrated in  FIG. 5 . For example, there may be a range of the axis component Ci of the proportion C in which the axis component Di of the second index D decreases as the axis component Ci of the proportion C separates from ⅓. There may be a range of the axis component Ci of the proportion C in which the axis component Di of the second index D is unchanged even when the axis component Ci of the proportion C changes. 
     Step S 206 : The calculation means  333  calculates the product of the axis components Di of the second index D, as the first evaluation value E. Specifically, the calculation means  333  calculates the first evaluation value E using the second index D according to the following Formula (4): 
         E=Dx×Dy×Dz   (4).
 
     The first evaluation value E is a parameter indicating the degree of bias of the vibration of the device  10  between the three axes. In detail, the first evaluation value E is minimum when the balance of the first index B (the degree of variation of the physical quantity A for each axis component) between the three axes is even (Cx=Cy=Cz=⅓) (i.e. when there is no bias of the vibration of the device  10  between the three axes). When the balance of the first index B between the three axes is lost and is uneven (i.e. when the degree of bias of the vibration of the device  10  between the three axes increases), the first evaluation value E increases. 
     Typically, when the degradation of the rotator progresses, vibration of a specific frequency predominantly occurs in a direction of any of the x-axis, the y-axis, and the z-axis. For example, a method of estimating the degree of degradation of the rotator by frequency-analyzing the vibration and detecting the vibration of the specific frequency may be used. However, to perform the frequency analysis, a sensor having relatively high sampling frequency (e.g. about 80 kHz) needs to be used to detect the vibration of the rotator. This causes an increase in processing load. 
     It is considered that, as a result of the vibration of the specific frequency occurring in any of the axis directions, the degree of bias of the vibration of the device  10  between the three axes increases. It is therefore possible to estimate the degradation of the rotator based on the degree of bias of the vibration of the device  10  between the three axes. Hence, in this embodiment, the degradation level G of the device  10  is estimated based on the first evaluation value E indicating the degree of bias of the vibration in the below-described steps S 207  to S 210 . For example, another embodiment in which the first evaluation value E itself is set as the degradation level G may also be possible. In such a case, a higher degradation level G indicates that the device  10  degrades more. In this embodiment, however, the accuracy of estimating the degradation level G is improved as a result of the below-described steps S 207  to S 210 . The reason why the accuracy of estimating the degradation level G is improved will be given later. 
     Step S 207 : The calculation means  333  determines whether m=n. In the case where the calculation means  333  determines that m=n (step S 207 : Yes), the process advances to step S 209 . In the case where the calculation means  333  determines that m≠n (step S 207 : No), the process advances to step S 208 . 
     Step S 208 : The calculation means  333  increments m. The process then returns to step S 202 . Thus, steps S 202  to S 208  are repeated until n first evaluation values E (hereafter also referred to as “first evaluation values E 1  to En”) respectively corresponding to the n periods T 1  to Tn are calculated. 
     Step S 209 : In the case where the calculation means  333  determines that m=n in step S 207  (i.e. in the case where the n first evaluation values E 1  to En are calculated), the estimation means  334  calculates the variance or standard deviation of the n first evaluation values E 1  to En as a second evaluation value F. For example, in the case where the standard deviation of the n first evaluation values E 1  to En is the second evaluation value F, the second evaluation value F is calculated according to the following Formula (5): 
     
       
         
           
             
               
                 
                   F 
                   = 
                   
                     
                       
                         
                           1 
                           n 
                         
                          
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             n 
                           
                            
                           
                             
                               ( 
                               
                                 Ej 
                                 - 
                                 
                                   E 
                                   _ 
                                 
                               
                               ) 
                             
                             2 
                           
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     The second evaluation value F is a parameter indicating the degree of variation of the n first evaluation values E 1  to En (i.e. the temporal stability of the degree of bias of the vibration of the device  10  between the three axes). 
     Step S 210 : The estimation means  334  estimates the common logarithm of the second evaluation value F as the degradation level G. 
     The reason why the accuracy of estimating the degradation level G is improved as a result of steps S 207  to S 210  is as follows: When the degradation of the device  10  progresses, the degree of bias of the vibration of the device  10  between the three axes increases as mentioned above, and the first evaluation value E indicating the degree of bias of the vibration increases, too. However, for example, suppose the degree of bias of the vibration between the three axes increases due to a factor other than degradation. In such a case, the first evaluation value E increases despite the device  10  not degrading. Thus, for example in another embodiment in which the first evaluation value E itself is set as the degradation level G, the accuracy of estimating the degradation level G is not always sufficient. 
     When the degradation of the rotator progresses, the temporal change of the frequency spectrum of the vibration of the rotator increases. That is, when the degradation of the rotator progresses, the degree of bias of the vibration of the rotator between the three axes becomes unstable, i.e. increases/decreases, over time. Hence, the degradation of the rotator can be estimated based on whether the degree of bias of the vibration of the rotator between the three axes is stable over time. Accordingly, in this embodiment, the degradation level G is estimated based on the second evaluation value F indicating the degree of variation of then first evaluation values E 1  to En (i.e. the temporal stability of the degree of bias of the vibration of the device  10  between the three axes), as described above with regard to steps S 207  to S 210 . Although this embodiment describes the case where the common logarithm of the second evaluation value F is set as the degradation level G on the assumption that the number of digits of the second evaluation value F differs depending on the degree of degradation of the device  10 , another embodiment in which the second evaluation value F itself is set as the degradation level G is also possible. 
     Step S 211 : The transmission means  335  transmits the degradation level G of the device  10  to the server  40  via the communication unit  31  and the network  60 . 
     Next, the server  40  performs steps S 300  to S 301  illustrated in  FIG. 6 . 
     Step S 300 : The server  40  receives the degradation level G of the device  10  from the information processing apparatus  30  via the network  60 , and accumulates the degradation level G of the device  10  in the memory. 
     Step S 301 : The server  40  acquires the degradation level G of the device  10  from the memory, and transmits the degradation level G to the terminal apparatus  50  via the network  60 . For example, the degradation level G may be pull-distributed from the server  40  in response to a request from the terminal apparatus  50 , or push-distributed from the server  40 . 
     Next, the terminal apparatus  50  performs steps S 400  to S 401  illustrated in  FIG. 7 . 
     Step S 400 : The terminal apparatus  50  receives the degradation level G of the device  10  from the server  40  via the network  60 , and stores the degradation level G in the memory. 
     Step S 400 : The terminal apparatus  50 , for example automatically or according to user operation, acquires the degradation level G from the memory, and presents the degradation level G to the user by video output or audio output. Based on the degradation level G presented by the terminal apparatus  50 , the user can determine whether the device  10  needs maintenance, inspection, and the like, for example even when he or she is away from the device  10 . 
     As described above, the information processing system  1  according to one of the disclosed embodiments includes: the acquisition means  332  that acquires the vibration of the device  10  as the time-series data of the physical quantity A=(Ax, Ay, Az) indicated by the three-axis (x, y, z) components in the three-dimensional coordinate system; the calculation means  333  that calculates the first evaluation value E indicating the degree of bias of the vibration of the device  10  between the three axes, based on the time-series data of the physical quantity A; and the estimation means  3334  that estimates the degradation level G of the device  10  based on the first evaluation value E. With such a structure, there is no need to perform frequency analysis on the time-series data of the physical quantity A. Thus, a sensor having relatively low sampling frequency (e.g. about 170 Hz) can be used in the detection apparatus  20 . Moreover, a processor having relatively low computing power can be used in the information processing apparatus  30 . The convenience of the techniques of estimating the state of a device using data from a sensor is therefore improved. 
     Although the presently disclosed techniques have been described by way of the drawings and examples, various changes and modifications may be easily made by those of ordinary skill in the art based on the present disclosure. Such changes and modifications are therefore included in the scope of the present disclosure. For example, the functions included in the means, steps, etc. may be rearranged without logical inconsistency, and a plurality of means, steps, etc. may be combined into one means, step, etc. and a means, step, etc. may be divided into a plurality of means, steps, etc. 
     For example, the detection apparatus  20  and the information processing apparatus  30  according to the foregoing embodiment may be implemented as one apparatus. For example, all or part of the operation performed by the information processing apparatus  30  according to the foregoing embodiment may be performed by the server  40 . For example, the components or the means in the information processing apparatus  30  may be distributed between a plurality of information processing apparatuses. At least one of the plurality of information processing apparatuses may be, for example, a server connected to the network  60 . 
     The foregoing embodiment describes an example of the operation of the information processing system  1  with reference to  FIGS. 3, 4, 6, and 7 . However, part of the steps included in the foregoing operation or part of operation included in one step may be omitted without logical inconsistency. Moreover, a plurality of steps included in the foregoing operation may be replaced with each other in order without logical inconsistency. 
     The foregoing embodiment describes an example in which, regarding the proportion C indicating the balance (evenness) of the first index B (the degree of variation of the physical quantity A for each axis component) between the three axes, when Cx=Cy=Cz=⅓, the balance of the first index B between the three axes is even. In other words, in the foregoing embodiment, the normal value of each axis component of the proportion C calculated when the device  10  operates normally is ⅓. Each axis component Ci of the proportion C is then converted using the predetermined conversion function f(Ci) to calculate the second index D that is minimum (e.g. 0) when the axis component Ci is the normal value (⅓ in the foregoing embodiment). 
     However, there is a possibility that, even when the device  10  operates normally, the balance of the first index B between the three axes is uneven. In other words, the normal values of the respective axis components of the proportion C can be different from one another. One example is that the normal value of Cx is ⅖, the normal value of Cy is ⅖, and the normal value of Cz is ⅕. In view of this, in one of the disclosed embodiments, the normal value of each axis component of the proportion C may be determined beforehand by, for example, experiment or simulation. The normal value is greater than 0 and less than 1. Moreover, conversion functions fx(Cx), fy(Cy), and fz(Cz) may be determined beforehand for the respective axis components so as to yield a minimum value (e.g. 0) when the axis component Ci of the proportion C is the normal value and a maximum value (e.g. 1) when the axis component Ci is 0 or 1. In such a case, the calculation means  333  may convert the axis components Cx, Cy, and Cz of the proportion C respectively using the conversion functions fx(Cx), fy(Cy), and fz(Cz) to calculate the second index D=(Dx, Dy, Dz). 
     The foregoing embodiment describes a structure of estimating the degradation of the rotator based on the degree of bias of the vibration of the device  10  between the three axes on the assumption that, when the degradation of the rotator progresses, vibration of a specific frequency occurs in an axis direction of any of the three axes. However, depending on the rotator, there is a possibility that the normal values of the respective axis components are different from one another as mentioned above, or that, when the degradation of the rotator progresses, vibration of the specific frequency occurs substantially not in one axis direction but in any of the other two axis directions. In view of this, in one of the disclosed embodiments, the vibration of the device  10  may be detected and acquired as time-series data of the physical quantity A indicated by two-axis components in the three-dimensional coordinate system. In such a case, “three-axis components” and “between three axes” in the foregoing description can be respectively interpreted as “two-axis components” and “between two axes”. 
     The foregoing embodiment describes each means realized by the controller  33  in the information processing apparatus  30  as a software structure. However, at least one of these means may have a concept including a software resource and/or a hardware resource. For example, the storage means  331  may include one or more memories. 
     An apparatus such as a computer or a mobile phone may be used to function as the information processing apparatus  30  according to the foregoing embodiment. The apparatus can be implemented by storing, in a memory in the apparatus, a program describing processes for achieving the functions of the information processing apparatus  30  according to the foregoing embodiment and reading and executing the program by a processor in the apparatus. 
     REFERENCE SIGNS LIST 
     
         
         
           
               1  information processing system 
               10  device 
               20  detection apparatus 
               30  information processing apparatus 
               31  communication unit 
               32  storage unit 
               33  controller 
               331  storage means 
               332  acquisition means 
               333  calculation means 
               334  estimation means 
               335  transmission means 
               40  server 
               50  terminal apparatus 
               60  network