Patent Publication Number: US-2020278241-A1

Title: Vibration determination device, vibration determination method, and program

Description:
TECHNICAL FIELD 
     The present disclosure relates to a technique for analyzing a vibration, and particularly, relates to a technique for analyzing a vibration of a structure. 
     BACKGROUND ART 
     A vibration characteristic of a structure such as a case and a printed board of a personal computer, or a frame of an automobile is effective for design, evaluation, and the like of structural units thereof. The vibration characteristic for use in design and evaluation of the structural units is, for example, a natural vibration frequency and a damping rate in a particular natural vibration mode of the structure. A vibration of the structure is measured by, for example, a sensor such as a displacement, speed, or acceleration sensor arranged on a surface or the like of the structure. The natural vibration mode indicates how a vibration appears in an object vibrating at the natural vibration frequency. How a vibration appears, that is, the natural vibration mode is represented by, for example, a spatial distribution of vibration amplitude of the object vibrating at the natural vibration frequency. For example, when a plurality of sensors are arranged on a surface of the structure and a vibration is measured by those sensors, the vibration of the structure is represented by, for example, a vector including, as an element, amplitude of the vibration measured by those sensors. In general, a structure has a plurality of natural vibration modes. The vibration of the structure is represented by superposition of the plurality of natural vibration modes. When a distribution of positions of vibration amplitude indicating the natural vibration modes of the structure is represented by vectors, a vector representing the vibration of the structure is represented by a linear sum of the vectors representing the natural vibration modes of the structure. The natural vibration frequency of the vibration of the structure is an eigenvalue. The vector representing the natural vibration mode of the structure at the natural vibration frequency is an eigenvector related to the natural vibration frequency of the vibration of the structure. As described above, the eigenvector represents a distribution of positions of vibration amplitude of a natural vibration indicated by the natural vibration mode. As described above, the vibration characteristic of the structure can be represented by the eigenvector, the natural vibration frequency, and the damping rate. 
     An actual vibration of the structure has various vibration modes. In design and evaluation of the structure, it is difficult to evaluate the vibration characteristic unless the vibration modes of the structure are the same. 
     PTL 1 discloses one example of a determination method of determining whether a vibration mode of a structure is the same as a vibration mode of interest. The method in PTL 1 determines whether a vibration mode to be determined is the vibration mode of interest, by using a mode correlation coefficient between an eigenvector of the vibration mode of interest and an eigenvector of the vibration mode to be determined. 
     CITATION LIST 
     Patent Literature 
     [PTL 1] Japanese Patent No. 4626351 
     SUMMARY OF INVENTION 
     Technical Problem 
     As described above, a vibration of a structure is measured by, for example, a sensor attached to a surface of the structure. When the sensor has an abnormality such as, for example, deterioration or failure, and when a place to which the sensor is attached has an abnormality such as, for example, cracking, it is impossible to acquire a normal measurement value as a vibration measurement value by using the sensor. The normal measurement value is a measurement value when, for example, the sensor is normal and the place to which the sensor is attached is normal. An abnormal measurement value will be hereinafter denoted as an abnormal value. When measurement values measured in a vibration mode to be determined include an abnormal value, the above-described mode correlation coefficient decreases due to the abnormal value, in comparison with a case in which the measurement values include no abnormal value, even when the vibration mode to be determined of the structure is a vibration mode of interest. Even when the vibration mode to be determined is the vibration mode of interest, the vibration mode to be determined may not be determined as the vibration mode of interest. 
     One object of the present disclosure is to provide a vibration determination device and the like which can improve vibration determination performance when measurement values of a vibration include an abnormality. 
     Solution to Problem 
     A vibration determination device according to an exemplary aspect of the present invention includes: determination means for determining, based on a plurality of feature values representing features of a vibration of a structure, whether the vibration of the structure is a standard vibration; and detection means for detecting, when it is not determined that the vibration of the structure is the standard vibration, an outlier included in the plurality of feature values, wherein the determination means further determines, based on the plurality of feature values other than the detected outlier, whether the vibration of the structure is the standard vibration, and the vibration determination device further comprises output means for outputting whether the vibration of the structure is the standard vibration. 
     A vibration determination method according to an exemplary aspect of the present invention includes: determining, based on a plurality of feature values representing features of a vibration of a structure, whether the vibration of the structure is a standard vibration; detecting, when it is not determined that the vibration of the structure is the standard vibration, an outlier included in the plurality of feature values; determining, based on the plurality of feature values other than the detected outlier, whether the vibration of the structure is the standard vibration; and outputting whether the vibration of the structure is the standard vibration. 
     A storage medium according to an exemplary aspect of the present invention stores a program causing a computer to execute: determination processing of determining, based on a plurality of feature values representing features of a vibration of a structure, whether the vibration of the structure is a standard vibration; and detection processing of detecting, when it is not determined that the vibration of the structure is the standard vibration, an outlier included in the plurality of feature values, wherein the determination processing further determines, based on the plurality of feature values other than the detected outlier, whether the vibration of the structure is the standard vibration, and the program further causes a computer to execute output processing of outputting whether the vibration of the structure is the standard vibration. An exemplary aspect of the present invention can be achieved by the program stored in the storage medium described above. 
     Advantageous Effects of Invention 
     The present disclosure has an advantageous effect of enabling improving vibration determination performance when measurement values of a vibration include an abnormality. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a block diagram representing an example of a configuration of a vibration determination device according to a first example embodiment of the present disclosure. 
         FIG. 2  is a block diagram representing an example of a configuration of a vibration determination system according to the first example embodiment of the present disclosure. 
         FIG. 3  is a diagram schematically illustrating an example of a structure having a plurality of sensors attached thereto and having no damage such as peeling. 
         FIG. 4  is a diagram schematically representing amplitude of a vibration based on measurement data acquired when the structure having no damage such as peeling is vibrated. 
         FIG. 5  is a diagram schematically illustrating an example of a structure having a plurality of sensors attached thereto and having peeling. 
         FIG. 6  is a diagram schematically representing amplitude of a vibration based on measurement data acquired when the structure having peeling is vibrated. 
         FIG. 7  is a flowchart representing an example of an operation of the vibration determination device according to the first example embodiment of the present disclosure. 
         FIG. 8  is a flowchart representing an example of an operation of the vibration determination device according to the first example embodiment of the present disclosure. 
         FIG. 9  is a flowchart representing an example of an operation of determination processing performed by the vibration determination device according to the first example embodiment of the present disclosure. 
         FIG. 10  is a block diagram representing an example of a configuration of a vibration determination device according to a second example embodiment of the present disclosure. 
         FIG. 11  is a flowchart representing an example of an operation of the vibration determination device according to the second example embodiment of the present disclosure. 
         FIG. 12  is a flowchart representing an example of an overall operation of the vibration determination device according to the second example embodiment of the present disclosure. 
         FIG. 13  is a block diagram representing a configuration of a vibration determination device according to a third example embodiment of the present disclosure. 
         FIG. 14  is a flowchart representing an example of an operation of the vibration determination device according to the third example embodiment of the present disclosure. 
         FIG. 15  is a diagram representing one example of a hardware configuration of a computer that can achieve the vibration determination device according to the example embodiments of the present disclosure. 
     
    
    
     EXAMPLE EMBODIMENT 
     Hereinafter, example embodiments of the present disclosure will be described in detail with reference to the drawings. 
     First Example Embodiment 
     [Description of Configuration] 
       FIG. 1  is a block diagram representing an example of a configuration of a vibration determination device according to a first example embodiment of the present disclosure. A vibration determination device  100  illustrated in  FIG. 1  includes a reception unit  101 , a calculation unit  102 , a comparison unit  103 , a determination unit  104 , a detection unit  105 , an update unit  106 , an extraction unit  107 , and an output unit  108 . 
     The acceptance unit  101  accepts, for example, measurement data acquired by measuring a vibration with a plurality of sensors installed at different places on a structure, and representing transition of the vibration of the structure. The structure is an object that may vibrate, such as a case or a printed board of a personal computer, or a frame of an automobile. The structure may be an architectural structure such as a bridge. The structure is not limited to the above-described examples. The sensor is, for example, a displacement sensor, a speed sensor, an acceleration sensor, or the like. The measurement data are, for example, data representing transition of the vibration of the structure and being represented by displacement, speed, acceleration, or the like of a place on the vibrated structure to which the sensor is attached, the displacement, speed, acceleration, or the like is measured by the above-described sensor at a predetermined period. The post-vibration transition of the vibration of the vibrated structure is called a vibration response. The measurement data are, for example, a row of measurement values measured by the sensor, the measurement values being arranged in order of measurement time of each sensor. In the following description, the measurement data will be also denoted as a series of measurement values and time-history waveform data. A set of measurement data acquired by the plurality of sensors will be also denoted as a measurement dataset. In this case, the measurement dataset is a plurality of series of measurement values. The measurement dataset includes data representing the vibration response. 
     The acceptance unit  101  may be connected with the sensor, and may receive a signal indicating transition of a measurement value from the sensor. The acceptance unit  101  may transform the received signal into the above-described time-history waveform data. The acceptance unit  101  may be connected with a device such as a data logger that stores the measurement dataset measured by the sensor, and may receive the measurement dataset from the device such as a data logger. 
       FIG. 2  is a block diagram representing an example of a configuration of a vibration determination system according to the first example embodiment of the present disclosure. A vibration determination system  1  illustrated in  FIG. 2  includes the vibration determination device  100 , a data logger  200 , and a terminal device  300 . The vibration determination device  100  is communicably connected with the data logger  200  and the terminal device  300 . 
     The data logger  200  includes a reception unit  201 , a storage unit  202 , and a transmission unit  203 . The reception unit  201  receives, for example, a signal indicating transition of a measurement value from the sensor attached to the structure. The signal may be a digital signal or an analog signal. The reception unit  201  transforms the received signal into, for example, data of the above-described time-history waveform data in a computer-treatable format, and stores the transformed data in the storage unit  202 . The storage unit  202  stores the time-history waveform data. The transmission unit  203  reads out, for example, in response to a request from the vibration determination device  100 , the time-history waveform data stored in the storage unit  202 , and transmits the read-out time-history waveform data to the vibration determination device  100 . 
     The terminal device  300  receives information (for example, a vibration characteristic of the structure, as will be described later) from the vibration determination device  100 , and outputs the received information. The terminal device  300  is, for example, a computer including a communication interface, a display unit such as a display, an input unit such as a keyboard, and the like. The terminal device  300  displays, for example, on the display unit, for example, the information received from the vibration determination device  100  via the communication interface. 
     An operator of the vibration determination system  1  may apply a vibration to the structure ascertained as having no damage or deterioration such as peeling or cracking. The operator may measure the structure vibrating due to the applied vibration, with a sensor ascertained as having no failure or attachment fault. A method of applying a vibration to the structure by an operator may be a method set in such a way that the structure vibrates in a natural vibration mode by which, for example, a vibration characteristic for use in design and evaluation of the structure can be acquired, among a plurality of natural vibration modes of the structure. The operator may record a measured measurement dataset by using a data logger. Such a measurement dataset will be hereinafter denoted as a standard dataset. Measurement data included in the standard dataset will be also denoted as standard data. A measurement value included in the standard data will be also denoted as a standard measurement value. The standard data are a series of standard measurement values. The standard dataset is a set of a plurality of pieces of standard data, that is, a plurality of series of standard measurement values. The standard dataset represents transition of the vibration in a standard natural vibration mode of the structure. A vibration mode of the structure when the measurement data in the standard dataset are measured will be denoted as a standard natural vibration mode. The reception unit  201  may receive a signal indicating a standard dataset, may transform the received signal into the standard dataset, and may store the acquired standard dataset in the storage unit  202 . The transmission unit  203  may read out the standard dataset from the storage unit  202 , and may transmit the read-out standard dataset to the vibration determination device  100 . The transmission unit  203  may transmit, in response to a request of the standard dataset from the vibration determination device  100 , the standard dataset to the vibration determination device  100 . The structure on which measurement of the standard dataset is performed may be a structure of the same quality and the same shape as the structure on which the above-described measurement of the measurement dataset is performed. The structure on which measurement of the standard dataset is performed may be a structure before occurrence of a change in a state such as failure of the sensor or damage or deterioration of the structure, on which the above-described measurement of the measurement dataset is performed. 
     The acceptance unit  101  further accepts the standard dataset. The acceptance unit  101  may request, for example, the data logger  200  for the standard dataset, when the vibration determination device  100  starts an operation. 
     The calculation unit  102  calculates a feature (for example, an eigenvector to be described later) of the vibration of the structure, from data (that is, the measurement dataset) representing transition of the vibration of the structure. The calculation unit  102  sends the calculated feature of the vibration of the structure to the comparison unit  103 . The calculation unit  102  may preliminarily calculate a feature (for example, a standard eigenvector to be described later) of the vibration in the standard natural vibration mode of the structure, from data (that is, the standard dataset) representing transition of the vibration in the standard natural vibration mode of the structure. The calculation unit  102  may send the calculated feature of the vibration in the standard natural vibration mode of the structure to the comparison unit  103 . 
     Specifically, the calculation unit  102  specifies a section (hereinafter, denoted as a damped section) representing a portion where the vibration of the structure caused by the applied vibration is damped, among a row of measurement values included in the time-history waveform data received by the acceptance unit  101 . In other words, the calculation unit  102  specifies a portion representing the vibration response. The calculation unit  102  may specify, for example, a section of a predetermined length representing the vibration response, among a row of measurement values. The calculation unit  102  may specify a peak of amplitude in a row of measurement values, and may specify, as the portion representing the vibration response, a predetermined number of values successive from a value measured a predetermined period of time after a value of the specified peak is measured. The calculation unit  102  transforms the measurement data of the damped section into frequency-domain data for each sensor used in measurement, by performing, for example, Fourier transform in relation to time for each sensor. The calculation unit  102  may perform, for example, fast Fourier transform on the measurement data of the damped section, that is, on a row of measurement values. The calculation unit  102  may transform the measurement data into frequency-domain data by using, for example, another transform such as Z-transform or Hilbert transform. The calculation unit  102  detects a peak of a frequency spectrum in the post-transform frequency-domain data. The calculation unit  102  may detect, for example, a frequency at which magnitude of a vector including, as an element, an amplitude value for an identical frequency of each sensor reaches a peak. A range of the frequency for which the calculation unit  102  calculates a peak may be preliminarily determined. The calculation unit  102  may calculate, as an eigenvector, a normalized vector of the above-described vector at the detected frequency. The calculation unit  102  sends the calculated eigenvector to the comparison unit  103 . 
     For example, description will be given of a vibration when the structure is a beam of a length L extending in an x-axis direction, both ends of the beam are fixed, and a free damping vibration is generated in the beam by applying a vibration to the beam. A time-history waveform of z-direction deflective displacement acquired from the displacement sensor installed at a position on the structure indicated by a coordinate x (0&lt;x&lt;L) can be approximated by the following expression. 
     
       
         
           
             
               
                 
                   
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     Herein, the function w(x,t) is deflective displacement at a time t and a position x. The function ϕ n (x) is an eigenfunction representing a n-th natural vibration mode. The value A n  is initial vibration amplitude. The value λ n  is a damping rate of the n-th natural vibration mode. The value ω n  is a natural angular frequency of the n-th natural vibration mode. The value Φ n  is an initial phase of the n-th natural vibration mode. A natural vibration frequency is a value acquired by dividing a natural angular frequency by 2π. An eigenvector is generated by aligning values of eigenfunctions at a plurality of positions. For example, k sensor positions when k displacement sensors are attached on the x-axis set for the structure being the beam are denoted by x 1 , x 2 , . . . , x k . In this case, an eigenvector |ϕ n &gt; in the case of the n-th natural vibration mode is denoted by |ϕ n &gt;= t ((ϕ n (x 1 ), ϕ n (x 2 ), . . . , ϕ n (x k )). The function acquired by performing Fourier transform with time t on the time-history waveform w(x,t) of the deflective displacement is denoted by F(f,x). 
     The natural vibration frequency is a frequency at which a frequency spectrum acquired by performing Fourier transform on the function w(x,t) representing the time-history waveform of the deflective displacement reaches a peak. 
     When f is regarded as a constant, F(f,x) is represented by a linear combination of eigenfunctions ϕ n (x). Thus, the eigenvector representing amplitude of a natural vibration at a plurality of positions can be acquired by normalizing a vector including, as elements, values at the plurality of positions of the function acquired by performing Fourier transform on the function w(x,t). 
     For example, when positions of the k displacement sensors attached on the x-axis set for the beam are denoted by x 1 , x 2 , . . . , x k , the eigenvector (|ϕ n &gt;) representing a natural vibration at a position of a displacement sensor in the case of the n-th natural vibration mode is |ϕ n&gt;= 1/Z  t(F(ω   n ,x 1 ), F(ω n ,x 2 ), . . . , F(ω n ,x k )). Z is a normalization factor, and is set in such a way that an inner product &lt;ϕ n |ϕ n &gt; becomes &lt;ϕ n |ϕ n &gt;=1. 
     The function w(x,t) indicated in Math.  1  is an example in the case of the beam of the structure, and an expression indicating a vibration of another structure is different from the expression indicated in Math. 1. According to the present example embodiment, the above-described measurement dataset is equivalent to the function w(x,t). The frequency-domain data acquired by transforming, by using Fourier transform or the like, the measurement data included in the measurement dataset and measured by a plurality of sensors are equivalent to the function F(f,x). 
     When the structure is a board, the calculation unit  102  may calculate the eigenfunction, the natural vibration frequency, and the eigenvector according to, for example, a method described in Document “Yoshio ADACHI, ‘Dynamic Response in Infrasonic Frequency Range of Highway Bridge Deck Slabs’, Journal of Japan Society of Civil Engineers, vol. 330, February 1983, Japan Society of Civil Engineers”, regarding the eigenfunction or the natural vibration frequency. The above description is merely an example. The calculation unit  102  may calculate the eigenvector of the structure according to another method. 
     When the acceptance unit  101  receives a standard dataset, the calculation unit  102  similarly calculates an eigenvector from the received standard dataset. The eigenvector calculated from the standard dataset will be denoted as a standard eigenvector. When, for example, a model of the structure represented by the expression indicated in Math. 1 is known, the calculation unit  102  may calculate the standard eigenvector by numerical computation on the basis of the model of the structure. In this case, an operator of the vibration determination system  1  may preliminarily input data representing positions of sensors, to the vibration determination device  100  via, for example, the terminal device  300 . The calculation unit  102  sends the calculated standard eigenvector to the comparison unit  103 . 
       FIG. 3  is a diagram schematically illustrating an example of a structure having a plurality of sensors attached thereto and having no damage such as peeling. In the example illustrated in  FIG. 3 , five sensors (a sensor S 1 , a sensor S 2 , a sensor S 3 , a sensor S 4 , and a sensor S 5 ) are attached to the structure. 
       FIG. 4  is a diagram schematically representing amplitude of a vibration based on measurement data acquired when the structure illustrated in  FIG. 3  having no damage such as peeling is vibrated. X 1  to X 5  illustrated in  FIG. 4  respectively represent positions to which the sensors S 1  to S 5  are attached. The vertical axis in  FIG. 4  represents magnitude of amplitude. The black dots illustrated in  FIG. 4  respectively represent amplitude of a vibration measured by the sensors S 1  to S 5 . The standard eigenvector of the structure illustrated in  FIG. 3  is, for example, a vector including, as elements, values of amplitude indicated by the black dots illustrated in  FIG. 4 . 
       FIG. 5  is a diagram schematically illustrating an example of a structure having a plurality of sensors attached thereto and having peeling. Also in the example illustrated in  FIG. 5 , five sensors (a sensor S 1 , a sensor S 2 , a sensor S 3 , a sensor S 4 , and a sensor S 5 ) are attached to the structure. In the example illustrated in  FIG. 5 , a place to which the sensor S 2  is attached has peeling. The structure illustrated in  FIG. 5  is equal to the structure illustrated in  FIG. 3 , except for presence of the peeling. When the structure illustrated in  FIG. 5  is vibrated, a vibration equal to a vibration generated when the structure illustrated in  FIG. 3  is vibrated is generated in the structure illustrated in  FIG. 5 , except for the place of the peeling. 
       FIG. 6  is a diagram schematically representing amplitude of a vibration based on measurement data acquired when the structure illustrated in  FIG. 5  having peeling is vibrated. X 1  to X 5  illustrated in  FIG. 6  respectively represent positions to which the sensors S 1  to S 5  are attached. The vertical axis in  FIG. 6  represents magnitude of amplitude. 
     The black dots drawn in  FIG. 6  respectively represent amplitude of a vibration measured by the sensors S 1  to S 5 . In the example illustrated in  FIG. 6 , the amplitude of the vibration at the place indicated by X 2  is 0. Even when the structure is vibrated, the place indicated by X 2 , to which the sensor S 2  is attached, does not vibrate due to the peeling. The amplitude of the vibration at the places indicated by X 1 , X 3 , X 4 , and X 5  is equal to the amplitude of the vibration at the places indicated by X 1 , X 3 , X 4 , and X 5  illustrated in  FIG. 4 . The standard eigenvector of the structure illustrated in  FIG. 5  is, for example, a vector including, as elements, values of amplitude indicated by the black dots illustrated in  FIG. 6 . The amplitude may be complex amplitude including phase information. 
     The comparison unit  103  receives a feature (specifically, for example, the above-described standard eigenvector) of the vibration in the standard natural vibration mode of the structure from the calculation unit  102 , and stores the received feature (for example, the standard eigenvector) of the vibration in the standard natural vibration mode of the structure. The comparison unit  103  further receives a feature (specifically, for example, the eigenvector) of the measured vibration of the structure from the calculation unit  102 . The comparison unit  103  compares the feature of the measured vibration of the structure with the feature of the vibration in the standard natural vibration mode of the structure. Specifically, the comparison unit  103  compares the received target eigenvector with the standard eigenvector. Hereinafter, the eigenvector to be compared with the standard eigenvector will be denoted as a target eigenvector. More specifically, the comparison unit  103  calculates a value indicating a correlation between the standard eigenvector and the target eigenvector. The value indicating the correlation is, for example, a modal assurance criterion (MAC). 
     The MAC is represented by the following expression. In the following expression, |ϕ&gt; represents the standard eigenvector, and |ψ&gt; represents the target eigenvector. 
     
       
         
           
             
               
                 
                   
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     The comparison unit  103  sends, to the determination unit  104 , a result of comparison of the feature of the measured vibration of the structure with the feature of the vibration in the standard natural vibration mode of the structure. Specifically, the comparison unit  103  may send the above-described MAC to the determination unit  104 . 
     The determination unit  104  determines, on the basis of the result of comparison of the feature of the measured vibration of the structure with the feature of the vibration in the standard natural vibration mode of the structure, whether the measured vibration of the structure has the feature of the vibration in the standard natural vibration mode of the structure. 
     As described above, the feature of the measured vibration of the structure is represented by, for example, the target eigenvector indicating the natural vibration mode of the measured vibration of the structure. The feature of the vibration in the standard natural vibration mode of the structure is represented by, for example, the standard eigenvector representing the standard natural vibration mode. A matter that the measured vibration of the structure has the feature of the vibration in the standard natural vibration mode of the structure indicates that the vibration of the structure is the vibration in the standard natural vibration mode. The result of comparison of the feature of the measured vibration of the structure with the feature of the vibration in the standard natural vibration mode of the structure is, specifically, the value (for example, the MAC) representing the correlation between the target eigenvector and the standard eigenvector. 
     For example, when the correlation between the target eigenvector and the standard eigenvector is higher than a predetermined criterion, the target eigenvector can be regarded as the standard eigenvector, that is, the vibration of the structure can be regarded as the vibration in the standard natural vibration mode. When the correlation between the target eigenvector and the standard eigenvector is higher than a predetermined criterion, the determination unit  104  determines that the vibration of the structure is the vibration in the standard natural vibration mode, that is, the measured vibration of the structure has the feature of the vibration in the standard natural vibration mode of the structure. Specifically, when the correlation value (for example, the above-described MAC) representing the correlation between the target eigenvector and the standard eigenvector is equal to or greater than a predetermined threshold value C, the determination unit  104  determines that the vibration of the structure is the vibration in the standard natural vibration mode. The threshold value C may be, for example, 0.8. The threshold value C may be, for example, 0.9. The value of the threshold value C is not limited to the above examples. The value of the threshold value C may be set, for example, according to a purpose. 
     The determination unit  104  may include the comparison unit  103 . The vibration determination device  100  does not need to include the comparison unit  103 , and the determination unit  104  may operate as the comparison unit  103 . According to the present example embodiment, the comparison unit  103  and the determination unit  104  are described as separate units. 
     When it is determined that the measured vibration of the structure does not have the feature of the vibration in the standard natural vibration mode of the structure, that is, when the correlation value is smaller than the threshold value C, there is a possibility that the measured vibration of the structure is the vibration in the standard natural vibration mode of the structure, but some pieces of measurement data may be abnormal. Abnormal measurement data refers to, for example, measurement data in which the vibration of the structure is not reflected. For example, when a sensor has failure, it is impossible to acquire data such as accurate displacement at a portion to which the sensor is attached. For example, when a place to which a sensor is attached on the structure has an abnormality such as peeling, the sensor is unable to acquire measurement data consistent with measurement data acquired by a sensor attached to a place having no abnormality. Among the features of the vibration of the structure, the feature based on abnormal measurement data will be denoted as an outlier. When measurement data include an abnormal value and the feature of the vibration of the structure is represented by the above-described eigenvector, any of the elements of the eigenvector is an outlier. 
     When it is determined that the measured vibration of the structure does not have the feature of the vibration in the standard natural vibration mode of the structure, the detection unit  105  detects an outlier included in the feature of the measured vibration of the structure, by using the feature of the vibration in the standard natural vibration mode of the structure. Specifically, when the correlation value is smaller than the threshold value C, the detection unit  105  detects the outlier in the elements of the target eigenvector by using the target eigenvector and the standard eigenvector. The outlier in the elements of the target eigenvector is, for example, an element having a larger difference between the element of the target eigenvector and the element of the standard eigenvector of the same number than a difference in the elements of another number. The detection unit  105  may detect the outlier in the elements of the target eigenvector by using cross comparison to be described below specifically. 
     The detection unit  105  may calculate a MAC for two vectors excluding one element of the same order from the target eigenvector and the standard eigenvector, while varying the elements to be excluded from the first element to the last element. In the following description, the MAC for two vectors excluding the i-th (i=1, k) element will be denoted by MAC i . A natural number k is the number of sensors attached to the structure, that is, the number of elements of the target eigenvector and the standard eigenvector. The detection unit  105  may detect, among MAC 1  to MAC k , a MAC (hereinafter, denoted by MAC m  (1≤m≤k)) being maximum and having another MAC being smaller than a predetermined threshold value (hereinafter, denoted as a threshold value C2). The threshold value C2 may be the same as the threshold value C. The detection unit  105  may simply detect the maximum MAC among MAC 1  to MAC k . The detection unit  105  detects, as an outlier, a target eigenvector element excluded when the detected MAC k  is calculated. The detection unit  105  detects, as abnormal measurement data, measurement data in which the element specified as the outlier is calculated. 
     Specifically, the detection unit  105  first generates, from the standard eigenvector |ϕ&gt;= t (a 1 , a 2 , . . . , a i−1 , a i , a i+1 , . . . , a k ), a new standard eigenvector including elements other than the i-th element of the standard eigenvector in the same order as the order in the original standard eigenvector. The generated standard eigenvector |ϕ i &gt; from which the i-th element a i  is excluded is |ϕ i &gt;= t (a 1 , a 2 , . . . , a i−1 , a i+1 , . . . , a k ). 
     The detection unit  105  generates, from the target eigenvector |ψ&gt;= t (b 1 , b 2 , . . . , b i−1 , b i , b i+1 , . . . , b k ), a new target eigenvector including elements other than the i-th element of the target eigenvector in the same order as the order in the original target eigenvector. The generated target eigenvector |ψ i &gt; from which the i-th element b, is excluded is |ψ i &gt;= t (b 1 , b 2 , . . . , b i−1 , b i+1 , . . . , b k ). A natural number k is the number of elements of the eigenvector. A natural number i is equal to or less than k. 
     The detection unit  105  calculates a correlation MAC i  between the updated standard eigenvector |ϕ i &gt; and the updated target eigenvector. The detection unit  105  repeats an operation of excluding the i-th element from the original target eigenvector and the original standard eigenvector and calculating MAC i  until i becomes the number k of elements of the eigenvector from 1, while incrementing i by one. 
     The number of elements to be excluded from each of the target eigenvector and the standard eigenvector is not limited to one. The detection unit  105  may exclude two or more elements, which is sufficiently smaller than the number k of elements of the eigenvector, from each of the target eigenvector and the standard eigenvector. The detection unit  105  may calculate a MAC between the target eigenvector and the standard eigenvector from which those elements are excluded. For example, when the number of elements to be excluded is two, the detection unit  105  calculates  k C 2  ways of MACs. 
     The detection unit  105  detects an element being an outlier, by using the calculated k MAC i  (i=1, 2, . . . , n). When, for example, MAC m  is maximum among MAC 1  to MAC k  and each of MAC j  (j≠m) is equal to or less than the preliminarily determined threshold value C2, the detection unit  105  detects the m-th element as the outlier. 
     The detection unit  105  generates, from the standard eigenvector, an updated standard eigenvector from which the m-th element is excluded. The update unit  106  generates, from the target eigenvector, an updated target eigenvector from which the m-th element detected as the outlier is excluded. 
     In the examples illustrated in  FIGS. 4 and 6 , when the MAC is smaller than a threshold value, for example, the element of the value indicated by the black dot at X 2  is equivalent to the outlier. In other words, the measurement data acquired by the sensor S 2  are determined as the outlier. 
     The detection unit  105  may estimate the eigenfunction, for example, from the values of each element of the standard eigenvector by using, for example, maximum likelihood estimation. When a value of an element of the target eigenvector is not included within a margin of error for a value, at any of the positions of the elements of the standard eigenvector, of the estimated eigenfunction, the detection unit  105  may detect, as the outlier, the element whose value is not included within the margin of error. 
     The method of detecting an outlier described above is an example. The detection unit  105  may detect an outlier by using another method such as, for example, a Hoteling&#39;s method, and a method based on difference in a distribution of the elements of the eigenvector. 
     The update unit  106  updates the feature of the measured vibration of the structure in such a way as to become the feature of the vibration represented by the measurement dataset excluding the abnormal measurement data detected from the received measurement dataset. The update unit  106  further updates the feature in the standard natural vibration mode of the structure in such a way as to become the feature of the vibration represented by the standard dataset excluding, from the standard dataset, data at a place where the detected abnormal measurement data are acquired. 
     Specifically, the update unit  106  performs updating of excluding the detected outlier, from the elements of the target eigenvector. The update unit  106  further performs updating of excluding the element of the same order as the outlier, from the elements of the standard eigenvector. More specifically, the update unit  106  generates the target eigenvector from which the element being the outlier is excluded, and the standard eigenvector from which the element of the same number as the number of the element being the outlier is excluded. The update unit  106  may normalize the generated target eigenvector and the generated standard eigenvector. The update unit  106  may normalize each of the updated target eigenvector and the updated standard eigenvector. The update unit  106  sends the updated target eigenvector and the updated standard eigenvector to the comparison unit  103 . Note that, when the detection unit  105  detects an outlier by using a MAC calculated from the target eigenvector and the standard eigenvector from which the element is excluded, the update unit  106  may be absent. In this case, the detection unit  105  may transmit, to the determination unit  104 , the MAC calculated from the target eigenvector and the standard eigenvector from which the detected outlier is excluded. 
     When the comparison unit  103  receives the updated target eigenvector and the updated standard eigenvector from the update unit  106 , the comparison unit  103  calculates a MAC between the received target eigenvector and the received standard eigenvector. The comparison unit  103  sends the calculated MAC to the determination unit  104 . 
     In the above description, the update unit  106  generates the target eigenvector and the standard eigenvector from which the outlier is excluded. However, the update unit  106  may generate outlier data (for example, a list of numbers of elements determined as outliers) indicating an element being the outlier, and may transmit the generated outlier data to the comparison unit  103 . In this case, the comparison unit  103  may calculate a correlation value such as a MAC by using elements other than the element indicated by the outlier data. 
     The determination unit  104  determines, on the basis of a result of comparison of the feature of the measured vibration of the structure based on the measurement dataset other than the abnormal measurement data, with the feature of the vibration in the standard natural vibration mode of the structure, whether the measured vibration of the structure has the feature of the vibration in the standard natural vibration mode of the structure. Specifically, when the correlation value (for example, the MAC) calculated by using elements other than the element indicated by the outlier data is greater than the predetermined threshold value C, the determination unit  104  determines that the vibration of the structure is the vibration in the standard natural vibration mode. When the correlation value (for example, the MAC) calculated by using elements other than the element indicated by the outlier data is equal to or less than the predetermined threshold value C, the determination unit  104  determines that the vibration of the structure is not the vibration in the standard natural vibration mode. 
     In the examples illustrated in  FIGS. 4 and 6 , the target eigenvector and the standard eigenvector from which the element of the value indicated by the black dot at the position indicated by X 2  is excluded are generated. When the MAC representing the correlation between these vectors is greater than a predetermined value, it is determined that the vibration of the structure illustrated in  FIG. 5  is the vibration in the standard natural vibration mode. 
     When it is determined that the measured vibration of the structure has the feature of the vibration in the standard natural vibration mode of the structure, that is, when it is determined that the vibration of the structure is the vibration in the standard natural vibration mode, the extraction unit  107  extracts another vibration characteristic in the natural vibration mode of the structure. The vibration characteristic is, for example, an eigenvector, a natural vibration frequency, and a damping rate. In this case, the another vibration characteristic is a natural vibration frequency and a damping rate. Specifically, the extraction unit  107  may extract, as a natural angular frequency, a value acquired by multiplying a peak frequency of a frequency spectrum in the measurement dataset by 2π. The frequency spectrum in the measurement dataset is frequency-domain data that can be acquired by transforming each piece of measurement data in the measurement dataset by performing Fourier transform in relation to time t. The extraction unit  107  may calculate, as a damping rate, a half width at half maximum of a peak value of the frequency spectrum in the measurement dataset. The extraction unit  107  may extract the vibration characteristic by using another method such as a method using linear predictive analysis. 
     When it is determined that the measured vibration of the structure does not have the feature of the vibration in the standard natural vibration mode of the structure, that is, when it is determined that the vibration of the structure is not the vibration in the standard natural vibration mode, the extraction unit  107  does not need to extract another vibration characteristic. 
     When it is determined that the vibration of the structure is the vibration in the standard natural vibration mode, that is, when another vibration characteristic of the structure is extracted, the output unit  108  may output the extracted vibration characteristic of the structure to, for example, the terminal device  300 . The vibration characteristic of the structure is, for example, an eigenvector, a natural vibration frequency, and a damping rate. In this case, the output unit  108  may output, for example, to the terminal device  300 , a message indicating that the vibration of the structure is the vibration in the standard natural vibration mode. 
     When it is determined that the vibration of the structure is not the vibration in the standard natural vibration mode, that is, when another vibration characteristic of the structure is not extracted, the output unit  108  does not need to output any vibration characteristic. In this case, the output unit  108  may output, for example, to the terminal device  300 , a message indicating that the vibration of the structure is not the vibration in the standard natural vibration mode. 
     [Description of Operation] 
     Next, an operation of the vibration determination device  100  according to the present example embodiment will be described in detail with reference to the drawings. 
     First, a preparation operation of the vibration determination device  100  will be described. 
       FIG. 7  is a flowchart representing an example of an operation of the vibration determination device  100  according to the present example embodiment. The operation illustrated in  FIG. 7  represents an operation of calculating a feature (that is, a standard eigenvector) of a vibration in a standard natural vibration mode from a plurality of series of standard data (that is, the above-described standard dataset). 
     First, the acceptance unit  101  accepts a standard dataset, that is, a plurality of series of standard measurement values (Step S 101 ). Then, the calculation unit  102  calculates, from the standard dataset, a feature (that is, a standard eigenvector) of a vibration in a standard natural vibration mode (Step S 102 ). The comparison unit  103  stores the calculated feature (that is, the standard eigenvector) of the vibration in the standard natural vibration mode (Step S 103 ). 
     Next, an overall operation of the vibration determination device  100  will be described. 
       FIG. 8  is a flowchart representing an example of an operation of the vibration determination device  100  according to the present example embodiment. 
     First, the acceptance unit  101  accepts a plurality of series of measurement data (that is, a measurement dataset) (Step S 111 ). The calculation unit  102  calculates, from the plurality of series of measurement data (that is, the measurement dataset), a feature (that is, a target eigenvector) of a vibration of a structure (Step S 112 ). 
     Then, the vibration determination device  100  performs determination processing (Step S 113 ). The operation of determination processing in Step S 113  will be described later in detail. The vibration determination device  100  determines, through the operation of determination processing in Step S 113 , whether the vibration of the structure for which the accepted plurality of series of measurement data have been acquired is a standard natural vibration, that is, whether the vibration of the structure is a vibration in a standard natural vibration mode. 
     When it is determined that the vibration is the standard natural vibration (YES in Step S 114 ), the extraction unit  107  extracts a vibration characteristic (Step S 115 ). Then, the output unit  108  outputs the vibration characteristic (Step S 116 ). In Step S 116 , the output unit  108  may output, as a result of determination, a message or the like indicating that the vibration is the standard natural vibration. 
     When it is not determined that the vibration is the standard natural vibration (NO in Step S 114 ), the vibration determination device  100  ends the operation illustrated in  FIG. 8 . Before the end of the operation illustrated in  FIG. 8 , the output unit  108  may output, as a result of determination, a message or the like indicating that the vibration is not the standard natural vibration. 
     Next, an operation of determination processing performed by the vibration determination device  100  will be described. 
       FIG. 9  is a flowchart representing an example of an operation of determination processing performed by the vibration determination device  100  according to the present example embodiment. 
     The comparison unit  103  and the determination unit  104  determine whether the vibration is a standard natural vibration on the basis of the feature (that is, the target eigenvector) of the vibration (Step S 121 ). Specifically, the comparison unit  103  calculates a correlation value (for example, the above-described MAC) between the eigenvector and the standard eigenvector. When the calculated correlation value is greater than a predetermined threshold value C, the determination unit  104  determines that the vibration is the standard natural vibration. When the calculated correlation value is equal to or less than the predetermined threshold value C, the determination unit  104  does not determine that the vibration is the standard natural vibration. 
     When it is determined that the vibration is the standard natural vibration (YES in Step S 122 ), the vibration determination device  100  ends the operation illustrated in  FIG. 9 . 
     When it is not determined that the vibration is the standard natural vibration (NO in Step S 122 ), the detection unit  105  detects an abnormal value of the feature of the vibration (Step S 123 ). Specifically, the detection unit  105  detects, as the abnormal value of the feature of the vibration, an outlier in elements of the target eigenvector, as described above. When the abnormal value of the feature of the vibration is absent (NO in Step S 124 ), that is, when no abnormal value of the feature of the vibration is detected, the determination unit  104  determines that the vibration is not the standard natural vibration (Step S 128 ). 
     When the abnormal value of the feature of the vibration is present (YES in Step S 124 ), that is, when the abnormal value of the feature of the vibration is detected, the update unit  106  updates the feature of the vibration in such a way that the feature of the vibration does not include the detected abnormal value (Step S 125 ). Specifically, the update unit  106  generates, for example, an eigenvector that includes the elements of the pre-update eigenvector other than the element being the outlier in the same order as the order in the pre-update eigenvector, and that does not include the element being the outlier. In Step S 125 , the update unit  106  further updates the feature of the standard natural vibration in such a way as not to include a value calculated from a measurement value measured by a sensor that has measured the measurement value for which the detected abnormal value is calculated. Specifically, the update unit  106  generates, for example, a standard eigenvector that includes the elements of the pre-update standard eigenvector other than the element of the same number as the element being the outlier in the same order as the order in the pre-update standard eigenvector, and that does not include the element of the same number as the element being the outlier. 
     The comparison unit  103  and the determination unit  104  determine, on the basis of the updated feature (that is, the target eigenvector) of the vibration, whether the vibration is the standard natural vibration (Step S 126 ). Specifically, the comparison unit  103  calculates a correlation value (for example, the above-described MAC) between the post-update eigenvector and the post-update standard eigenvector. When the calculated correlation value is greater than the predetermined threshold value C, the determination unit  104  determines that the vibration is the standard natural vibration. 
     When it is determined that the vibration is the standard natural vibration (YES in Step S 127 ), the vibration determination device  100  ends the operation of determination processing illustrated in  FIG. 9 . 
     When the calculated correlation value is equal to or less than the predetermined threshold value C, that is, when it is not determined that the vibration is the standard natural vibration (NO in Step S 127 ), the determination unit  104  determines that the vibration is not the standard natural vibration (Step S 128 ). Then, the vibration determination device  100  ends the operation of determination processing illustrated in  FIG. 9 . 
     [Description of Advantageous Effect] 
     Next, an advantageous effect of the present example embodiment will be described. 
     The present example embodiment has an advantageous effect of improving vibration determination performance when measurement values of a vibration include an abnormality. The reason is that, when it is not determined that a vibration of a structure is a standard natural vibration, the detection unit  105  detects an abnormal value in a feature of the vibration of the structure. The determination unit  104  determines whether the vibration of the structure is the standard natural vibration on the basis of the feature of the vibration of the structure excluding the detected abnormal value. Thus, a possibility is reduced that the vibration of the structure is determined as not being the standard natural vibration because the feature of the vibration includes an abnormal value caused by an abnormality of a sensor or a place to which the sensor is attached, although the vibration of the structure is the standard natural vibration. In other words, vibration determination performance when measurement values of a vibration include an abnormality is improved. 
     Second Example Embodiment 
     Next, a second example embodiment according to the present disclosure will be described in detail with reference to the drawings. 
       FIG. 10  is a block diagram representing an example of a configuration of a vibration determination device  100 A according to the present example embodiment. The vibration determination device  100 A illustrated in  FIG. 10  includes an acceptance unit  101 , a calculation unit  102 , a comparison unit  103 , a determination unit  104 , a detection unit  105 , an update unit  106 , an extraction unit  107 , an output unit  108 , a sensor information storage unit  109 , and a generation unit  110 . 
     The acceptance unit  101 , the calculation unit  102 , the comparison unit  103 , the determination unit  104 , the detection unit  105 , the update unit  106 , the extraction unit  107 , and the output unit  108  perform the same operations as the operations of the units assigned with the same names according to the first example embodiment, except for a difference described below. 
     The acceptance unit  101  further receives information on a position to which a sensor is attached. The acceptance unit  101  may receive, as the information on the position to which the sensor is attached, for example, information representing the shape of a structure and information on the position of the sensor on the structure. The information representing the shape of the structure may be, for example, a three-dimensional model of the structure. The information representing the shape of the structure may be an image on which the shape of the structure is projected. The acceptance unit  101  stores, in the sensor information storage unit  109 , the received information on the position to which the sensor is attached. 
     The sensor information storage unit  109  stores the information on the position to which the sensor is attached. 
     The detection unit  105  may further detect, as abnormal measurement data, measurement data included in a measurement dataset and from which an outlier in a feature of a vibration of the structure is derived. The abnormal measurement data represent the measurement data from which the outlier in the feature of the vibration of the structure is derived. Specifically, the detection unit  105  may specify, as the abnormal measurement data, measurement data from which an element detected as the outlier of the above-described target eigenvector is derived. The detection unit  105  may further specify, as an abnormal sensor, a sensor that has acquired the abnormal measurement data. The detection unit  105  may send, for example, to the determination unit  104 , information specifying the measurement data detected as the abnormal measurement data. The detection unit  105  may send, for example, to the determination unit  104 , information specifying the sensor specified as the abnormal sensor. The information specifying the abnormal sensor may be the information specifying the measurement data detected as the abnormal measurement data. 
     When it is determined that the vibration of the structure is a vibration in a standard natural vibration mode, and also an abnormal value of the feature of the vibration is detected, the determination unit  104  may send the measurement data detected as the abnormal measurement data to the output unit  108 , for example, via the extraction unit  107 . When it is determined that the vibration of the structure is a vibration in a standard natural vibration mode, and when an abnormal value of the feature of the vibration is detected, the determination unit  104  may send the information specifying the abnormal sensor to the generation unit  110 . 
     The generation unit  110  receives the information specifying the abnormal sensor, for example, from the determination unit  104 . The generation unit  110  generates, on the basis of the information specifying the abnormal sensor, and the information representing the position to which the sensor is attached, which is stored in the sensor information storage unit  109 , information specifying a place where the abnormal measurement data that are measured by the abnormal sensor are measured. The generation unit  110  may generate, as the information specifying the place where the abnormal measurement data are measured, information representing a place to which the abnormal sensor is attached. The information specifying the place where the abnormal measurement data are measured may be, for example, the information specifying the abnormal sensor. The information representing the place to which the abnormal sensor is attached is, for example, an image of the structure, with a mark indicating the place to which the abnormal sensor is attached being superimposed on a position equivalent to the place to which the abnormal sensor is attached. The mark indicating the place to which the abnormal sensor is attached will be also denoted as a mark indicating the abnormal sensor. The mark may be, for example, a circle, a polygon such as a triangle or a square, an arrow, or another shape. The mark may be a + mark, an X mark, a character, or a character string. The mark may be a combination of a shape and one or a plurality of characters. The mark is not limited to the above examples. The mark may be flickering. The generation unit  110  may superimpose, on the image of the structure, the mark indicating a sensor not detected as the abnormal sensor. In this case, the generation unit  110  may superimpose, on the image of the structure, the mark indicating the abnormal sensor, in a display format different in at least any of color, size, and motion from a display format of the mark indicating the sensor not detected as the abnormal sensor. 
     The output unit  108  may receive the information specifying the measurement data detected as the abnormal data, from the determination unit  104 , for example, via the extraction unit  107 . The output unit  108  may output, for example, to the terminal device  300  or the like, the information specifying the measurement data detected as the abnormal measurement data. 
     The output unit  108  may receive, from the generation unit  110 , the information specifying the place where the abnormal measurement data are measured, and may output, for example, to the terminal device  300  or the like, the received information specifying the place where the abnormal measurement data are measured. 
     [Description of Operation] 
     Next, an operation of the vibration determination device  100 A according to the present example embodiment will be described in detail with reference to the drawings. 
       FIG. 11  is a flowchart representing an example of an operation of the vibration determination device  100 A according to the present example embodiment. The operation illustrated in  FIG. 11  represents an initial operation of the vibration determination device  100 A. In the operation illustrated in  FIG. 11 , the vibration determination device  100 A accepts information on a position of a sensor, as well as calculating a feature (that is, a standard eigenvector) of a vibration in a standard natural vibration mode from a plurality of series of standard data (that is, the above-described standard dataset). 
     The operations from Step S 101  to Step S 103  in  FIG. 11  are the same as the operations from Step S 101  to Step S 103  according to the first example embodiment, which are illustrated in  FIG. 7 . 
     Then, the acceptance unit  101  accepts information on a position of a sensor (Step S 204 ). The acceptance unit  101  stores, in the sensor information storage unit  109 , the accepted information on the position of the sensor (Step S 205 ). 
       FIG. 12  is a flowchart representing an example of an overall operation of the vibration determination device  100 A according to the present example embodiment. The operations from Step S 111  to Step S 116  in  FIG. 12  are the same as the operations from Step S 111  to Step S 116 , respectively, which are illustrated in  FIG. 8 . 
     When it is determined that the vibration of the structure is a standard natural vibration and, further, an outlier is detected in the feature of the vibration of the structure (YES in Step S 217 ), the output unit  218  outputs information relating to an abnormal value from which the outlier is derived. The information relating to the abnormal value from which the outlier is derived may be, for example, the above-described information specifying the abnormal measurement data. The information relating to the abnormal value from which the outlier is derived may be, for example, the information specifying the abnormal sensor. The information relating to the abnormal value from which the outlier is derived may be information relating to a place where the abnormal value from which the outlier is derived is measured. The information relating to the place where the abnormal value from which the outlier is derived is measured may be information relating to a place to which the abnormal sensor is attached. The information relating to the place to which the abnormal sensor is attached may be an image of the structure on which a mark indicating a place of the abnormal sensor is superimposed. 
     When the outlier is detected in the feature of the vibration of the structure (NO in Step S 217 ), the vibration determination device  100 A ends the operation illustrated in  FIG. 12 . 
     [Description of Advantageous Effect] 
     The present example embodiment has the same advantageous effect as the advantageous effect of the first example embodiment. The reason is the same as the reason why the advantageous effect of the first example embodiment is produced. 
     The present example embodiment further has an advantageous effect of making it easy to find an abnormality occurring in a sensor and a structure. The reason is that the generation unit  110  generates information specifying measurement data detected as abnormal data. The information specifying the measurement data detected as the abnormal data is output by the output unit  108 . 
     Third Example Embodiment 
       FIG. 13  is a block diagram representing a configuration of a vibration determination device  100 B according to a third example embodiment of the present disclosure. 
     The vibration determination device  100 B illustrated in  FIG. 13  includes a determination unit  104 , a detection unit  105 , and an output unit  108 . 
     The determination unit  104  determines, on the basis of a plurality of feature values representing features of a vibration of a structure, whether the vibration of the structure is a standard vibration. The plurality of feature values representing the features of the vibration of the structure are, for example, the above-described eigenvector (that is, a plurality of elements of the above-described eigenvector). The standard vibration is a vibration in the above-described standard natural vibration mode. The determination unit  104  may determine whether the vibration of the structure is the standard vibration, according to the same method as the method used by the determination unit  104  according to the first example embodiment and the second example embodiment. 
     When it is not determined that the vibration of the structure is the standard vibration, the detection unit  105  detects an outlier included in the plurality of feature values. The detection unit  105  may detect the outlier according to the same method as the method used by the detection unit  105  according to the first example embodiment and the second example embodiment. 
     The determination unit  104  further determines, on the basis of feature values other than the detected outlier among the plurality of feature values, whether the above-described vibration of the structure is the standard vibration. 
     The output unit  108  outputs whether the vibration of the structure is the standard vibration. In other words, the output unit  108  outputs information indicating whether the vibration of the structure is the standard vibration. In still other words, when it is determined in any of Steps S 302  and S 304  that the vibration is the standard vibration, the output unit  108  outputs information indicating that the vibration of the structure is the standard vibration. The information indicating that the vibration of the structure is the standard vibration may be a text message. The information indicating that the vibration of the structure is the standard vibration may be a preliminarily determined value. When it is not determined in Step S 304  that the vibration of the structure is the standard vibration, the output unit  108  outputs information indicating that the vibration of the structure is not the standard vibration. The information indicating that the vibration of the structure is not the standard vibration may be a text message. The information indicating that the vibration of the structure is not the standard vibration may be a preliminarily determined value different from the value indicating that the vibration of the structure is the standard vibration. 
     [Description of Operation] 
       FIG. 14  is a flowchart representing an example of an operation of the vibration determination device  100 B according to the present example embodiment. 
     First, the determination unit  104  determines, on the basis of a plurality of feature values representing features of a vibration of a structure, whether the vibration of the structure is a standard vibration (Step S 301 ). When it is determined that the vibration is the standard vibration (YES in Step S 302 ), the vibration determination device  100 B then performs the operation of Step S 305 . When it is not determined that the vibration is the standard vibration (NO in Step S 302 ), the detection unit  105  detects an outlier from the plurality of feature values (Step S 303 ). The determination unit  104  further determines, on the basis of the plurality of feature values excluding the detected outlier, whether the vibration of the structure is the standard vibration (Step S 304 ). 
     Then, the output unit  108  outputs whether the vibration of the structure is the standard vibration (Step S 305 ). 
     [Description of Advantageous Effect] 
     The present example embodiment has the same advantageous effect as the advantageous effect of the first example embodiment. The reason is the same as the reason why the advantageous effect of the first example embodiment is produced. 
     Another Example Embodiment 
     The vibration determination device according to the above-described example embodiments can be achieved by a computer that includes a memory on which a program read out from a storage medium is loaded and a processor executing the program. The vibration determination device according to the above-described example embodiments can be also achieved by dedicated hardware. The vibration determination device according to the above-described example embodiments can be also achieved by a combination of the above-described computer and the above-described dedicated hardware. 
       FIG. 15  is a diagram representing one example of a hardware configuration of a computer  1000  that can achieve the vibration determination device according to the example embodiments of the present disclosure. Referring to  FIG. 15 , the computer  1000  includes a processor  1001 , a memory  1002 , a storage device  1003 , and an input/output (I/O) interface  1004 . The computer  1000  is able to access a storage medium  1005 . The memory  1002  and the storage device  1003  are, for example, a random access memory (RAM) and a storage device such as a hard disk. The storage medium  1005  is, for example, a RAM, a storage device such as a hard disk, a read only memory (ROM), or a portable storage medium. The storage device  1003  may be the storage medium  1005 . The processor  1001  is able to perform reading and writing of data or a program on the memory  1002  and the storage device  1003 . The processor  1001  is able to communicate with, for example, the data logger  200  and the terminal device  300  via the I/O interface  1004 . The processor  1001  is able to access the storage medium  1005 . The storage medium  1005  stores a program that causes the computer  1000  to operate as the vibration determination device  100 , the vibration determination device  100 A, or the vibration determination device  100 B. 
     The processor  1001  loads, on the memory  1002 , the program that is stored in the storage medium  1005  and causes the computer  1000  to operate as the vibration determination device  100 , the vibration determination device  100 A, or the vibration determination device  100 B. Then, when the processor  1001  executes the program loaded on the memory  1002 , the computer  1000  operates as the vibration determination device  100 , the vibration determination device  100 A, or the vibration determination device  100 B. 
     The acceptance unit  101 , the calculation unit  102 , the comparison unit  103 , the determination unit  104 , the detection unit  105 , the update unit  106 , the extraction unit  107 , and the output unit  108  can be achieved by, for example, the processor  1001  that executes a dedicated program loaded on the memory  1002 . The generation unit  110  can be also achieved by, for example, the processor  1001  that executes a dedicated program loaded on the memory  1002 . The sensor information storage unit  109  can be achieved by the memory  1002  or the storage device  1003  such as a hard disk device, which are included in the computer  1000 . Some or all of the acceptance unit  101 , the calculation unit  102 , the comparison unit  103 , the determination unit  104 , the detection unit  105 , the update unit  106 , the extraction unit  107 , and the output unit  108  can be also achieved by a dedicated circuit implementing functions of the units. Some or all of the sensor information storage unit  109  and the generation unit  110  can be also achieved by a dedicated circuit implementing the functions of the units. 
     Some or all of the above-described example embodiments can be also described as the following supplementary notes, but are not limited to the following. 
     (Supplementary Note 1) 
     A vibration determination device including: 
     determination means for determining, based on a plurality of feature values representing features of a vibration of a structure, whether the vibration of the structure is a standard vibration; and 
     detection means for detecting, when it is not determined that the vibration of the structure is the standard vibration, an outlier included in the plurality of feature values, wherein 
     the determination means further determines, based on the plurality of feature values other than the detected outlier, whether the vibration of the structure is the standard vibration, and 
     the vibration determination device further includes 
     output means for outputting whether the vibration of the structure is the standard vibration. 
     (Supplementary Note 2) 
     The vibration determination device according to Supplementary Note 1, wherein 
     each of the plurality of feature values represents a feature of a vibration measured at a different place on the structure, and 
     the output means further outputs information relating to a place where the feature of the vibration indicated by the feature value detected as the outlier is measured. 
     (Supplementary Note 3) 
     The vibration determination device according to Supplementary Note 2, wherein the output means outputs information specifying an abnormal sensor being a sensor installed at a place where the feature of the vibration indicated by the feature value detected as the outlier is measured. 
     (Supplementary Note 4) 
     The vibration determination device according to Supplementary Note 3, wherein 
     the output means outputs an image of the structure on which a mark indicating a place of the abnormal sensor attached to the structure is superimposed. 
     (Supplementary Note 5) 
     The vibration determination device according to any one of Supplementary Notes 1 to 4, wherein 
     the detection means detects the selected feature value as the outlier when it is determined, based on the plurality of feature values other than a selected feature value selected from the plurality of feature values, that the vibration of the structure is the standard vibration. 
     (Supplementary Note 6) 
     A vibration determination method including: 
     determining, based on a plurality of feature values representing features of a vibration of a structure, whether the vibration of the structure is a standard vibration; 
     detecting, when it is not determined that the vibration of the structure is the standard vibration, an outlier included in the plurality of feature values; 
     determining, based on the plurality of feature values other than the detected outlier, whether the vibration of the structure is the standard vibration; and 
     outputting whether the vibration of the structure is the standard vibration. 
     (Supplementary Note 7) 
     The vibration determination method according to Supplementary Note 6, wherein 
     each of the plurality of feature values represents a feature of a vibration measured at a different place on the structure, and the outputting further includes outputting information relating to a place where the feature of the vibration indicated by the feature value detected as the outlier is measured. 
     (Supplementary Note 8) 
     The vibration determination method according to Supplementary Note 7, including 
     outputting information specifying an abnormal sensor being a sensor installed at a place where the feature of the vibration indicated by the feature value detected as the outlier is measured. 
     (Supplementary Note 9) 
     The vibration determination method according to Supplementary Note 8, including 
     outputting an image of the structure on which a mark indicating a place of the abnormal sensor attached to the structure is superimposed. 
     (Supplementary Note 10) 
     The vibration determination method according to any one of Supplementary Notes 6 to 9, wherein 
     detecting the selected feature value as the outlier when it is determined, based on the plurality of feature values other than a selected feature value selected from the plurality of feature values, that the vibration of the structure is the standard vibration. 
     (Supplementary Note 11) 
     A storage medium storing a program causing a computer to execute: 
     determination processing of determining, based on a plurality of feature values representing features of a vibration of a structure, whether the vibration of the structure is a standard vibration; and 
     detection processing of detecting, when it is not determined that the vibration of the structure is the standard vibration, an outlier included in the plurality of feature values, wherein 
     the determination processing further determines, based on the plurality of feature values other than the detected outlier, whether the vibration of the structure is the standard vibration, and 
     the program further causes a computer to execute 
     output processing of outputting whether the vibration of the structure is the standard vibration. 
     (Supplementary Note 12) 
     The storage medium according to Supplementary Note 11, wherein 
     each of the plurality of feature values represents a feature of a vibration measured at a different place on the structure, and 
     the output processing further outputs information relating to a place where the feature of the vibration indicated by the feature value detected as the outlier is measured. 
     (Supplementary Note 13) 
     The storage medium according to Supplementary Note 12, wherein 
     the output processing outputs information specifying an abnormal sensor being a sensor installed at a place where the feature of the vibration indicated by the feature value detected as the outlier is measured. 
     (Supplementary Note 14) 
     The storage medium according to Supplementary Note 13, wherein 
     the output processing outputs an image of the structure on which a mark indicating a place of the abnormal sensor attached to the structure is superimposed. 
     (Supplementary Note 15) 
     The storage medium according to any one of Supplementary Notes 11 to 14, wherein 
     the detection processing detects the selected feature value as the outlier when it is determined, based on the plurality of feature values other than a selected feature value selected from the plurality of feature values, that the vibration of the structure is the standard vibration. 
     In the above, the present invention has been described with reference to the example embodiments. However, the present invention is not limited to the above-described example embodiments. Various modifications that can be understood by a person skilled in the art may be made in the configurations and details of the present invention within the scope of the present invention. 
     INDUSTRIAL APPLICABILITY 
     The present invention is applicable to mode determination and extraction of a structure such as a bridge. 
     REFERENCE SIGNS LIST 
       1  Vibration determination system 
       100  Vibration determination device 
       100 A Vibration determination device 
       100 B Vibration determination device 
       101  Acceptance unit 
       102  Calculation unit 
       103  Comparison unit 
       104  Determination unit 
       105  Detection unit 
       106  Update unit 
       107  Extraction unit 
       108  Output unit 
       109  Sensor information storage unit 
       110  Generation unit 
       200  Data logger 
       201  Reception unit 
       202  Storage unit 
       203  Transmission unit 
       300  Terminal device 
       1000  Computer 
       1001  Processor 
       1002  Memory 
       1003  Storage device 
       1004  I/O interface 
       1005  Storage medium