JP7634036B2 - Information processing device, information processing program, and information processing method - Google Patents

Description

This disclosure relates to an anomaly detection device that detects the occurrence of an anomaly that differs from normal times in a time series of observation data observed by a sensor.

Seismometers, which perform immediate damage estimation immediately after an earthquake occurs and prevent damage before it occurs, need to detect the seismic motion caused by an earthquake in real time. In particular, when estimating the location of the epicenter to estimate damage, it is necessary to detect the exact arrival timing of the P-waves from the seismic motion.

In response to this, the technology disclosed in Non-Patent Document 1 discloses a method called the STA/LTA method, which detects a sudden rise in amplitude, as a method for detecting the arrival timing of P waves, which are the earliest seismic waves that reach a seismometer.

Naoyasu Iwata, Shunroku Yamamoto, Shunta Noda, Masahiro Korenaga. Algorithms for estimating earthquake parameters and identifying noise for early earthquake warning. Journal of the Japan Society of Civil Engineers, Proceedings A1 (Structural and Earthquake Engineering). 2016, Vol. 72, No. 1, pp. 133-147.

However, in subduction-zone earthquakes such as the 2011 Tohoku Pacific Ocean earthquake, the rise in seismic amplitude is slow, which can result in the detection of P-waves being delayed or even impossible.
In addition, if miscellaneous vibrations from vehicles or the like are observed immediately before an earthquake, the background level of vibration (LTA) increases, making it impossible to detect subsequent P waves.
In addition, when coda waves from a preceding earthquake such as a foreshock are observed, the background level of vibration (LTA) rises, making it impossible to detect subsequent P waves.

The present disclosure aims to provide an information processing device that can accurately detect the timing of arrival of P waves even in cases where the rise in the amplitude of seismic motion is gradual, where miscellaneous vibrations of vehicles, etc. are observed immediately before seismic motion, or where coda waves from an earthquake immediately before a foreshock, etc. are observed.

The information processing device according to the present disclosure includes:
an amplitude calculation unit that calculates an amplitude that changes over time from observation data of an event observed by a sensor;
a frequency analysis unit that calculates a frequency characteristic from the amplitude in real time using an autoregressive model;
Equipped with.

The information processing device according to the present disclosure is equipped with a frequency analysis unit. Therefore, the information processing device according to the present disclosure can accurately detect the arrival timing of the P wave by detecting the frequency components specific to the seismic motion, even in the case of an earthquake in which the rise in the amplitude of the seismic motion is slow when all frequency components are included, or even in the case of an earthquake in which miscellaneous vibrations of a vehicle or the like are observed immediately before the seismic motion.

FIG. 1 is a system configuration diagram of an abnormality detection device 30 according to a first embodiment. FIG. 1 is a functional block diagram of an information processing device 20 according to a first embodiment. FIG. 11 is a flowchart showing an abnormality detection process of the information processing device 20 according to the first embodiment. FIG. 11 is a flowchart showing the abnormality end determination process of the information processing device 20 according to the first embodiment. FIG. 1 is a diagram of the first embodiment, showing the seismic motion of the 2011 Tohoku Pacific Ocean Earthquake. FIG. 1 is a diagram of the first embodiment, showing the seismic motion of the 2009 Suruga Bay offshore earthquake. FIG. 2 is a diagram showing the hardware configuration of an information processing device 20 according to the first embodiment.

In the description of the embodiments and in the drawings, the same elements and corresponding elements are given the same reference numerals. Descriptions of elements given the same reference numerals are omitted or simplified as appropriate. In the following embodiments, "part" may be read as "circuit," "process," "step," "processing," or "circuitry" as appropriate.

The symbols used in the first embodiment are summarized below. In the following descriptions other than those in Formula 1 to Formula 37, the lowercase letter l of L will be written as l ^* to distinguish it from the number 1.

<Index and transmitted data>
(1) l ^* : l ^* is a counter that counts up with each sampling.
(2) m: m is the index of the AR model.
(3) f: f is frequency (Hz).
(4) Dg(l ^* ): Dg(l ^* ) is the observed digital data.
(5) x(l ^* ): x(l ^* ) is the amplitude data in physical units.
(6) PS(l ^* ,f): PS(l ^* ,f) is the running spectrum based on the AR model (short-term average).
(7) PL(l ^* ,f): PL(l ^* ,f) is the running spectrum based on the AR model (long-term average).
(8) SLa(l ^* ): SLa(l ^* ) is an index value for anomaly detection.
(9) l ^* t: l ^* t is the abnormality detection timing.
(10) SLb(l ^* ): SLb(l ^* ) is an index value for determining the termination of an abnormality.
(11) l ^* e: l ^* e is the timing of abnormal termination.

<Internal variables>
(1) μS(l ^* ): μS(l ^* ) is the average according to the AR model (short-term average).
(2) CS _m (l ^* ): CS m (l ^* ) is the covariance function based on the AR model (short-term average) (m=0, . . . , M).
(3) φS _m (l ^* ): φS _m (l ^* ) is the AR coefficient of the AR model (short-term average) (m=1, . . . , M).
(4) xS(l ^* ): xS(l ^* ) is an estimate of the amplitude data by the AR model (short-term averaging).
(5) σS ² (l ^* ): σS ² (l ^* ) is the variance of the estimation error of the amplitude data by the AR model (short-term average).
(6) μL(l ^* ): μL(l ^* ) is the average according to the AR model (long-term average).
(7) CL _m (l ^* ): CL _m (l ^* ) is the covariance function according to the AR model (long-term average) (m = 0,...,M).
(8) φL _m (l ^* ): φL _m (l ^* ) is the AR coefficient of the AR model (long-term average) (m=1, . . . , M).
(9) xL(l ^* ): xL(l ^* ) is the estimated value of the amplitude data by the AR model (long-term average).
(10) σL ² (l ^* ): σL ² (l ^* ) is the variance of the estimation error of the amplitude data by the AR model (long-term average).

<Parameter>
(1) fs: fs is the sampling frequency (Hz) of the observed digital data.
(2) Cf: Cf is a physical value conversion coefficient.
(3) M: M is the order of the AR model.
(4) rS: rS is the forgetting factor of the AR model (short-time averaging). It is a coefficient that determines the window size for smoothing the running spectrum. The larger rS is, the smaller the window size becomes, resulting in a short-time average.
(5) rL: rL is the forgetting factor of the AR model (long-term average). It is a coefficient that determines the window size for smoothing the running spectrum. The smaller rL is, the larger the window size becomes, resulting in a long-term average.
(6) fsl ^* 1: fsl ^* 1 is the lower limit of the frequency (Hz) for calculating the index value for abnormality detection and the index value for abnormality termination determination.
(7) fsl ^* 2: fsl ^* 2 is the upper limit of the frequency (Hz) for calculating the index value for abnormality detection and the index value for abnormality termination determination.
(8) ETL: ETL is a threshold for detecting anomalies.
(9) EEL: EEL is a threshold value for determining the end of an abnormality.

Embodiment 1.
The anomaly detection device 30 of the first embodiment will be described with reference to Figs. 1 to 7. In the following first embodiment, a seismometer is assumed as the anomaly detection device 30. The sensor described below is assumed to be a sensor that detects seismic motion, and the anomaly detection unit 23 is assumed to be a P-wave detection unit that detects P-waves (primary waves) as anomalies. However, the anomaly detection device 30 is not limited to a seismometer. The anomaly detection device 30 may also be an observation device that observes natural phenomena, such as a rain gauge or an anemometer. In a rain gauge, the observed data is the amount of rain, and in an anemometer, the observed data is the wind speed.

In the following embodiment 1, abnormality detection will be described as detection of P waves.

***Configuration Description***
1 is a system configuration diagram of an abnormality detection device 30. The abnormality detection device 30 includes a sensor 10 and an information processing device 20. The abnormality detection device 30 is capable of communicating with an external device 40 via a network 50.

2 is a block diagram of the information processing device 20. The information processing device 20 includes, as functional elements, an amplitude calculation unit 21, a frequency analysis unit 22, an abnormality detection unit 23, and an abnormality termination determination unit 24.
(1) The amplitude calculation unit 21 calculates the amplitude x(l ^* ) that changes with the passage of the counter l ^* from the observation data of the event observed by the sensor 10. The observation data is observed digital data Dg(l ^* ). The counter l ^* corresponds to time, and its interval is the reciprocal of the sampling frequency fs (fs) ^-1 . The event in the first embodiment is an earthquake.
(2) The frequency analysis unit 22 calculates the frequency characteristics in real time from the amplitude x(l ^* ) using an autoregressive model.
In addition, as described in Equation 18 and subsequent paragraphs, the frequency analysis unit 22 analyzes a first frequency characteristic (PS(l ^* , f)) in real time from the amplitude x(l ^* ) using a first time window, and also analyzes a second frequency characteristic (PL(l ^* , f)) in real time using a second time window that is longer than the first time window.
The frequency analysis unit 22 calculates a running spectrum in real time from the amplitude x(l ^* ) using an autoregressive model, and the running spectrum is an example of a frequency characteristic.
(3) The anomaly detection unit 23 detects anomalies in the observation data based on the running spectrum.
(4) The abnormality end determination unit 24 determines the end of the abnormality when an abnormality is detected. The abnormality end determination unit determines the end of the abnormality by comparing the running spectrum immediately before the occurrence of the abnormality with the current running spectrum.

*** Operation Description ***
3 and 4, the operation of the information processing device 20 will be described. The operation of the information processing device 20 corresponds to an information processing method. The operation of the information processing method corresponds to processing by an information processing program 231, which will be described later.
The information processing device 20 can be in a normal state or an abnormal state. The state of the information processing device 20 is the "normal state" when the power is turned on. When the information processing device 20 determines that the formula 15 described below is satisfied, the state of the information processing device 20 is the "abnormal state". When the information processing device 20 determines that the formula 17 described below is satisfied, the state of the information processing device 20 is the "normal state".
3 is a flowchart for explaining the operation of the abnormality detection process by the information processing device 20. The abnormality detection corresponds to the P-wave detection. FIG. 3 is executed when the information processing device 20 is in the "normal state."
Fig. 4 is a flowchart for explaining the operation of the abnormality end determination process by the information processing device 20. The abnormality end corresponds to the end of earthquake motion including P waves. Fig. 4 is executed when the information processing device 20 is in an "abnormal state".

In the following description, anomaly detection will be described as P-wave detection. In FIG. 3, the operation of the information processing device 20 is shown as process P201 to process P204. The information processing device 20 acquires ground motion as observed digital data from the sensor 10 at a time interval of the inverse of the sampling frequency fs (fs) ^-1 . Ground motion is vibration of the earth, and among ground motions, ground motion resulting from an earthquake is called "earthquake motion". Ground motions other than earthquake motion include miscellaneous vibrations caused by vehicles, background vibrations (continuous microtremors), noise, etc. Hereinafter, the inverse (fs) ^-1 will be referred to as the sampling interval. In a normal state, the information processing device 20 performs anomaly detection processing for each sampling.

ｘ（ｌ^＊）：振幅データ
Ｄｇ（ｌ^＊）：観測デジタルデータ
Ｃｆ：物理値換算係数。 <Process P201: Calculate the amplitude of observed data>
(1) The amplitude calculation unit 21 acquires, from the sensor 10, observed digital data Dg(l ^* ) observed by the sensor 10. The observed digital data Dg(l ^* ) is ground motion.
(2) The amplitude calculation unit 21 calculates the amplitude data x(l ^* ) based on the acquired observed digital data Dg(l ^* ) using Equation 1.

x(l ^* ): Amplitude data Dg(l ^* ): Observed digital data Cf: Physical value conversion coefficient.

<Process P202: Calculate running spectrum>
The frequency analysis unit 22 calculates a first running spectrum corresponding to a first time using a first time window. The first time window is a window for calculating a short-term average running spectrum. The first running spectrum is a short-term average running spectrum. The frequency analysis unit 22 also calculates a second running spectrum corresponding to the second time window using a second time window that is longer than the first time window. The second time window is a window for calculating a long-term average running spectrum. The second running spectrum is a long-term average running spectrum. The first running spectrum and the second running spectrum are used for anomaly detection by the anomaly detection unit 23. This will be specifically described below.

μＳ（ｌ^＊）：ＡＲモデル（短時間平均）による平均
ｒＳ：ＡＲモデル（短時間平均）の忘却係数
ｘ（ｌ^＊）：振幅データ
（２）周波数解析部２２は、式３で、ＡＲモデル（短時間平均）による共分散関数ＣＳ_ｍ（ｌ^＊）を計算する。

ＣＳ_ｍ（ｌ^＊）ＡＲモデル（短時間平均）による共分散関数
ｒＳ：ＡＲモデル（短時間平均）の忘却係数
ｘ（ｌ^＊）：振幅データ
μＳ（ｌ^＊）：ＡＲモデル（短時間平均）による平均
（３）周波数解析部２２は、式４のＭ次連立方程式（ユールウォーカー方程式）を解いて、ＡＲモデル（短時間平均）のＡＲ係数φＳ_ｍ（ｌ^＊）を計算する。

ＣＳ_ｍ（ｌ^＊）：ＡＲモデル（短時間平均）による共分散関数
φＳ_ｍ（ｌ^＊）：ＡＲモデル（短時間平均）のＡＲ係数
Ｍ：ＡＲモデルの次数
（４）周波数解析部２２は、式５および式６で、ＡＲモデル（短時間平均）による振幅データの推定値ｘＳ（ｌ^＊）およびＡＲモデル（短時間平均）による振幅データの推定誤差の分散σＳ^２（ｌ^＊）を計算する。

ｘ（ｌ^＊）：振幅データ
μＳ（ｌ^＊）：ＡＲモデル（短時間平均）による平均
φＳ_ｍ（ｌ^＊）：ＡＲモデル（短時間平均）のＡＲ係数
ｘＳ（ｌ^＊）：ＡＲモデル（短時間平均）による振幅データの推定値
σＳ^２（ｌ^＊）：ＡＲモデル（短時間平均）による振幅データの推定誤差の分散
Ｍ：ＡＲモデルの次数
ｒＳ：ＡＲモデル（短時間平均）の忘却係数
（５）周波数解析部２２は、式７で、ＡＲモデル（短時間平均）によるランニングスペクトルＰＳ（ｌ^＊，ｆ）を計算する。

ＰＳ（ｌ^＊，ｆ）：ＡＲモデル（短時間平均）によるランニングスペクトル
σＳ^２（ｌ^＊）：ＡＲモデル（短時間平均）による振幅データの推定誤差の分散
φＳ_ｍ（ｌ^＊）：ＡＲモデル（短時間平均）のＡＲ係数
ｆ：周波数
ｆｓ：サンプリング周波数
Ｍ：ＡＲモデルの次数
（６）周波数解析部２２は、長時間平均の場合も、短時間平均の式２から式７のそれぞれに対応する以下の式８から式１３を計算する。

The frequency analysis unit 22 first performs smoothing by time averaging on the time series of the amplitude data x(l ^* ). Next, it calculates a time-averaged running spectrum of the amplitude data by expressing it as an autoregressive model. In this case, two types of running spectra are calculated using two types of methods, short-term averaging and long-term averaging, which have different smoothing window sizes. Hereinafter, the autoregressive model is referred to as an AR model.
(1) The frequency analysis unit 22 calculates the average μS(l ^* ) by the AR model (short-term average) using Equation 2.

μS(l ^* ): Average by AR model (short-time average) rS: Forgetting factor of AR model (short-time average) x(l ^* ): Amplitude data (2) The frequency analysis unit 22 calculates the covariance function CS _m (l ^* ) by the AR model (short-time average) using Equation 3.

CS _m (l ^* ) Covariance function by AR model (short-time average) rS: forgetting coefficient of AR model (short-time average) x(l ^* ): amplitude data μS(l ^* ): average by AR model (short-time average) (3) The frequency analysis unit 22 solves the Mth simultaneous equation (Yule-Walker equation) of Equation 4 to calculate the AR coefficient φS _m (l ^* ) of the AR model (short-time average).

CS _m (l ^* ): Covariance function based on the AR model (short-time average) φS _m (l ^* ): AR coefficient of the AR model (short-time average) M: Order of the AR model (4) The frequency analysis unit 22 calculates the estimated value xS(l ^* ) of the amplitude data based on the AR model (short-time average) and the variance σS ² (l ^* ) of the estimation error of the amplitude data based on the AR model (short-time average) using equations 5 and 6.

x(l ^* ): amplitude data μS(l ^* ): average by AR model (short-time average) φS _m (l ^* ): AR coefficient of AR model (short-time average) xS(l ^* ): estimated value of amplitude data by AR model (short-time average) σS ² (l ^* ): variance of estimated error of amplitude data by AR model (short-time average) M: order of AR model rS: forgetting coefficient of AR model (short-time average) (5) The frequency analysis unit 22 calculates the running spectrum PS(l ^* , f) by the AR model (short-time average) using equation 7.

PS(l ^* ,f): running spectrum by AR model (short-time average) ^σS2 (l ^* ): variance of estimation error of amplitude data by AR model (short-time average) _φSm (l ^* ): AR coefficient of AR model (short-time average) f: frequency fs: sampling frequency M: order of AR model (6) In the case of long-term average, the frequency analysis unit 22 calculates the following equations 8 to 13, which correspond to equations 2 to 7 of the short-term average, respectively.

ＳＬａ（ｌ^＊）：異常検出の指標値
ｆ：周波数
ｆｓｌ^＊１：周波数の下限（Ｈｚ）
ｆｓｌ^＊２：周波数の上限（Ｈｚ）
ＰＳ（ｌ^＊，ｆ）：ＡＲモデル（短時間平均）によるランニングスペクトル
ＰＬ（ｌ^＊，ｆ）：ＡＲモデル（長時間平均）によるランニングスペクトル <Process P203: Calculate index value of anomaly detection>
The anomaly detection unit 23 detects anomalies from the observed digital data by comparing the first running spectrum with the second running spectrum. The anomaly detection unit 23, which is a P-wave detection unit, calculates an anomaly detection index value SLa(l ^* ) using Equation 14. Here, the anomaly detection is P-wave detection. The anomaly detection index value SLa(l ^* ) means the frequency average of the ratio between the running spectrum PS(l ^* ,f) based on the AR model (short-time average) and the running spectrum PL(l ^* ,f) based on the AR model (long-time average). PS(l ^* ,f)/PL(l ^* ,f) corresponds to performing the STA/LTA method for each frequency component.

SLa(l ^* ): Index value for abnormality detection f: Frequency fsl ^* 1: Lower limit of frequency (Hz)
fsl ^* 2: Upper frequency limit (Hz)
PS(l ^* ,f): Running spectrum by AR model (short-term average) PL(l ^* ,f): Running spectrum by AR model (long-term average)

ＳＬａ（ｌ^＊）：異常検出の指標値
ＥＴＬ：閾値
（１）異常検出の指標値ＳＬａ（ｌ^＊）が式１５を満たす場合、異常検出部２３（Ｐ波検出部）は、異常が検出されたと判断する。すなわち異常検出部２３はＰ波を検出したと判断する（プロセスＰ２０４でＹＥＳ）。この場合、情報処理装置２０の状態は「異常状態」に遷移する。異常検出部２３（Ｐ波検出部）による異常検出の事象を「異常検出」といい、このときのｌ^＊を異常検出タイミングｌ^＊ｔとする。異常検出部２３は、異常検出タイミングｌ^＊ｔを、外部装置４０へ出力する。
（２）異常検出の指標値ＳＬａ（ｌ^＊）が式１５を満たさない場合、処理はプロセスＰ２０１に戻る。プロセスＰ２０１では、次のカウンタｌ^＊について処理が行われる。 <Process P204: Abnormality detected>
The anomaly detection unit 23 determines whether the index value SLa(l ^* ) of the anomaly detection satisfies Expression 15.

SLa(l ^* ): index value of abnormality detection ETL: threshold value (1) When the index value of abnormality detection SLa(l ^* ) satisfies the formula 15, the abnormality detection unit 23 (P wave detection unit) judges that an abnormality has been detected. That is, the abnormality detection unit 23 judges that a P wave has been detected (YES in process P204). In this case, the state of the information processing device 20 transitions to an "abnormal state". An event of abnormality detection by the abnormality detection unit 23 (P wave detection unit) is called "abnormality detection", and l ^* at this time is the abnormality detection timing l ^* t. The abnormality detection unit 23 outputs the abnormality detection timing l ^* t to the external device 40.
(2) If the index value SLa(l ^* ) of anomaly detection does not satisfy Expression 15, the process returns to process P201, where the next counter l ^* is processed.

Highly accurate anomaly detection is possible according to the flowchart in Figure 3. In particular, highly accurate anomaly detection is possible by the processing of formula 14 in the anomaly detection unit 23.

The operation of the abnormality termination determination process in the abnormality detection device 30 will be described with reference to Figure 4. The process in Figure 4 is executed when the information processing device 20 is in an "abnormal state."

<Processes P201-1, P202-1>
The information processing device 20 acquires ground motion, which is observed digital data, from the sensor 10 at a sampling interval that is the reciprocal of the sampling frequency fs. When the information processing device 20 is in an abnormal state, the information processing device 20 performs an abnormality end determination process for each counter l ^* . The contents of process P201-1 and process P202-1 are the same as those of process P201 and process P202, respectively.

ＳＬｂ（ｌ^＊）：異常終息判定の指標値
ｆ：周波数
ｆｓｌ^＊１：周波数の下限（Ｈｚ）
ｆｓｌ^＊２：周波数の上限（Ｈｚ）
ＰＳ（ｌ^＊，ｆ）：ＡＲモデル（短時間平均）によるランニングスペクトル
ＰＬ（ｌ^＊ｔ－１，ｆ）：ＡＲモデル（長時間平均）によるランニングスペクトル <Process P205: Calculate index value for abnormal termination judgment>
The abnormality end determination unit 24 calculates the index value SLb(l ^* ) for abnormality end determination using Equation 16. The index value SLb(l ^* ) for abnormality end determination is the frequency average of the ratio between the short-time average running spectrum in the AR model at the current time (l ^* ) and the long-time average running spectrum in the AR model immediately before the abnormality detection timing (l ^* t). The index value SLb(l ^* ) for abnormality end determination is an index value for whether the running spectrum has returned to the state before the abnormality was detected, for each frequency component.

SLb(l ^* ): Index value for determining abnormality termination f: Frequency fsl ^* 1: Lower limit of frequency (Hz)
fsl ^* 2: Upper frequency limit (Hz)
PS(l ^* ,f): Running spectrum by AR model (short-time average) PL(l ^* t-1,f): Running spectrum by AR model (long-time average)

ＳＬｂ（ｌ^＊）：異常終息判定の指標値
ＥＥＬ：閾値
（１）異常終息判定の指標値ＳＬｂ（ｌ^＊）が式１７を満たす場合、異常終息判定部２４は、異常検出の前に戻ったと判断する。すなわち、異常終息判定部２４は、現在の状態がＰ波検出前の状態に戻ったと判断する（プロセスＰ２０６でＹＥＳ）。この場合、情報処理装置２０の状態は「通常状態」に遷移する。異常終息判定部２４による異常終息判定の事象を「異常終息」といい、このときのｌ^＊を異常終息タイミングｌ^＊ｅとする。異常終息判定部２４は、異常終息タイミングｌ^＊ｅを、外部装置４０へ出力する。
（２）異常終息判定の指標値ＳＬｂ（ｌ^＊）が式１７を満たさない場合、処理はプロセスＰ２０１－１に戻る。プロセスＰ２０１－１では、次のカウンタｌ^＊について処理が行われる。 <Process P206: Determining abnormal termination>
The abnormality end determination unit 24 determines whether the index value SLb(l ^* ) for determining the abnormality end satisfies Expression 17.

SLb(l ^* ): index value for abnormality termination judgment EEL: threshold value (1) When the index value for abnormality termination judgment SLb(l ^* ) satisfies formula 17, the abnormality termination judgment unit 24 judges that the state has returned to the state before the abnormality was detected. That is, the abnormality termination judgment unit 24 judges that the current state has returned to the state before the P wave was detected (YES in process P206). In this case, the state of the information processing device 20 transitions to a "normal state". The event of abnormality termination judgment by the abnormality termination judgment unit 24 is called "abnormal termination", and l ^* at this time is the abnormality termination timing l ^* e. The abnormality termination judgment unit 24 outputs the abnormality termination timing l ^* e to the external device 40.
(2) If the index value SLb(l ^* ) for determining the end of the abnormality does not satisfy Expression 17, the process returns to process P201-1, where the process is performed on the next counter l ^* .

The frequency analysis unit 22 can be summarized as follows. The information processing device 20 of the first embodiment includes the frequency analysis unit 22. The frequency analysis unit 22 calculates a running spectrum using an autoregressive model. Compared to FFT, the method of calculating a running spectrum using an autoregressive model has the following advantages (1) to (7).
(1) High time resolution since no taper is required.
(2) The AR model allows for natural smoothing of the spectrum.
(3) Since the AR coefficients are calculated sequentially, the calculation time does not depend on the window size, and high-speed calculation is possible.
(4) Since the AR coefficients are discrete values, it is possible to reduce the dimensions of the data, which is suitable for application to machine learning.
(5) By converting the observed digital data into multi-channel data, it is also possible to measure the cross-correlation between channels.
(6) The window width can be easily adjusted by simply changing the forgetting factor.
(7) By calculating the Akaike Information Criterion (described later), the degree of fit of the AR model to the amplitude data can be evaluated, making it possible to set the optimal AR order.

FIG. 5 shows P-wave detection (anomaly detection) by the information processing device 20 in response to seismic motion from the 2011 Tohoku Pacific Coast Earthquake.
Fig. 6 shows P-wave detection (anomaly detection) by the information processing device 20 for seismic motion from the 2009 Suruga Bay earthquake. The horizontal axis in Fig. 5 and Fig. 6 represents time, and the vertical axis represents the amplitude value of the amplitude data and the index value of anomaly detection (index value of P-wave detection).

***Advantages of First Embodiment***
Compared with the STA/LTA method disclosed in Non-Patent Document 1, which detects a sudden rise in amplitude, the information processing device 20 of the first embodiment detects a sudden rise in amplitude for each frequency component. Therefore, even in the case of an earthquake with a gradual rise in the amplitude of seismic motion, when miscellaneous vibrations of a vehicle or the like are observed immediately before the seismic motion, or when coda waves from an earthquake immediately before a foreshock or the like overlap, the P-wave arrival timing can be accurately detected.
In addition, by adjusting the parameters fsl ^* 1 and fsl ^* 2 in Equation 14, it is possible to focus only on the target frequency band. Therefore, it is possible to detect earthquake motion while avoiding known frequency bands such as those caused by train vibration.
In addition, frequency characteristics such as a running spectrum can be obtained when an anomaly is detected (detection of P waves), which can be used to distinguish whether the detected anomaly is due to an earthquake or noise.

φＳ_ｍ（ｌ^＊）：ＡＲモデル（短時間平均）のＡＲ係数
ｚＳ_ｑ（ｌ^＊）：ＡＲモデル（短時間平均）の特性根
Ｍ：ＡＲモデルの次数
（２）次に、周波数解析部２２は、式１９から式２２でＡＲモデル（短時間平均）によるランニングスペクトルのピーク周波数ｆＳ_ｑ（ｌ^＊）とその場合のスペクトルのピーク値ＰＳ_ｑ（ｌ^＊）を計算する。

ｚＳ_ｑ（ｌ^＊）：ＡＲモデル（短時間平均）の特性根
ｆＳ_ｑ（ｌ^＊）：ＡＲモデル（短時間平均）によるランニングスペクトルのピーク周波数ｆｓ：サンプリング周波数

ＰＳ_ｑ（ｌ^＊）：ＡＲモデル（短時間平均）によるランニングスペクトルのピーク値
σＳ^２（ｌ^＊）：ＡＲモデル（短時間平均）による振幅データの推定誤差の分散
φＳ_ｍ（ｌ^＊）：ＡＲモデル（短時間平均）のＡＲ係数
ｆＳ_ｑ（ｌ^＊）：ＡＲモデル（短時間平均）によるランニングスペクトルのピーク周波数Ｍ：ＡＲモデルの次数
ｆｓ：サンプリング周波数

ＬｏｓｓＳ（ｌ^＊）：ＡＲモデル（短時間平均）による損失関数
ｘ（ｌ^＊）：振幅データ
ｘＳ（ｌ^＊）：ＡＲモデル（短時間平均）による振幅データの推定値
σＳ^２（ｌ^＊）：ＡＲモデル（短時間平均）による振幅データの推定誤差の分散

ＡｉｃＳ（ｌ^＊）：ＡＲモデル（短時間平均）による赤池情報量規準
ＬｏｓｓＳ（ｌ^＊）：ＡＲモデル（短時間平均）による損失関数
Ｍ：ＡＲモデルの次数
（３）周波数解析部２２は、長時間平均の場合も、短時間平均の式１８から式２２のそれぞれに対応する以下の式２３から式２７を計算する。

（４）異常検出部２３は、式２８から式３３のうちの何れかから、異常検出の指標値ＳＬａ（ｌ^＊）を計算する。

ＳＬａ（ｌ^＊）：異常検出の指標値
ｚＳ_ｑ（ｌ^＊）：ＡＲモデル（短時間平均）の特性根
ｚＬ_ｑ（ｌ^＊）：ＡＲモデル（長時間平均）の特性根

ＳＬａ（ｌ^＊）：異常検出の指標値
ｆＳ_ｑ（ｌ^＊）：ＡＲモデル（短時間平均）によるランニングスペクトルのピーク周波数ｆＬ_ｑ（ｌ^＊）：ＡＲモデル（長時間平均）によるランニングスペクトルのピーク周波数

ＳＬａ（ｌ^＊）：異常検出の指標値
ＰＳ_ｑ（ｌ^＊）：ＡＲモデル（短時間平均）によるランニングスペクトルのピーク値
ＰＬ_ｑ（ｌ^＊）：ＡＲモデル（長時間平均）によるランニングスペクトルのピーク値

ＳＬａ（ｌ^＊）：異常検出の指標値
ｆＳｑ’（ｌ^＊）：ＡＲモデル（短時間平均）によるランニングスペクトルの卓越周波数であり、ｑ’は式２０で計算されるＡＲモデル（短時間平均）によるランニングスペクトルのピーク値ＰＳｑ（ｌ^＊）が最大となるｑ
ｆＬｑ’’（ｌ^＊）：ＡＲモデル（長時間平均）によるランニングスペクトルの卓越周波数であり、ｑ’’は式２５で計算されるＡＲモデル（長時間平均）によるランニングスペクトルのピーク値ＰＬｑ（ｌ^＊）が最大となるｑ

ＳＬａ（ｌ^＊）：異常検出の指標値
ＬｏｓｓＳ（ｌ^＊）：ＡＲモデル（短時間平均）による損失関数
ＬｏｓｓＬ（ｌ^＊）：ＡＲモデル（長時間平均）による損失関数

ＳＬａ（ｌ^＊）：異常検出の指標値
ＡｉｃＳ（ｌ^＊）：ＡＲモデル（短時間平均）による赤池情報量規準
ＡｉｃＬ（ｌ^＊）：ＡＲモデル（長時間平均）による赤池情報量規準
以上のように異常検出の指標値ＳＬａ（ｌ^＊）を計算することで、式１４のように多くの周波数ｆについてスペクトルの値を計算することなく、ランニングスペクトルの急激な変化を検出することができるので、計算時間を短縮することが可能である。 In the above, it is assumed that the frequency analysis unit 22 calculates a running spectrum in real time and detects an anomaly using the index value SLa(l ^* ) for anomaly detection shown in Equation 14.
However, the abnormality detection index value SLa(l ^* ) can be defined in various other ways as an index of the distance between the running spectrum PS(l ^* ,f) based on the AR model (short-time average) and the running spectrum PL(l ^* ,f) based on the AR model (long-time average). For example, the following embodiment is possible.
(1) In the case of short-term average, the frequency analysis unit 22 solves an M-th order polynomial (characteristic equation) for the complex number z shown in Equation 18, and defines the solutions whose imaginary parts are 0 or positive as the characteristic roots _zSq (l ^* ) of the AR model (short-term average) (q is a consecutive number, q = 1, ..., Q).

φS _m (l ^* ): AR coefficient of the AR model (short-time average) zS _q (l ^* ): characteristic root of the AR model (short-time average) M: order of the AR model (2) Next, the frequency analysis unit 22 calculates the peak frequency fS _q (l ^* ) of the running spectrum based on the AR model (short-time average) and the peak value PS _q (l ^* ) of the spectrum in that case using equations 19 to 22.

_zSq (l ^* ): characteristic root of the AR model (short-time average) _fSq (l ^* ): peak frequency of the running spectrum by the AR model (short-time average) fs: sampling frequency

PS _q (l ^* ): Peak value of the running spectrum by the AR model (short-time average) σ S ² (l ^* ): Variance of the estimation error of the amplitude data by the AR model (short-time average) φ S _m (l ^* ): AR coefficient of the AR model (short-time average) f S _q (l ^* ): Peak frequency of the running spectrum by the AR model (short-time average) M: Order of the AR model fs: Sampling frequency

LossS(l ^* ): Loss function by AR model (short-time average) x(l ^* ): Amplitude data xS(l ^* ): Estimated value of amplitude data by AR model (short-time average) σS ² (l ^* ): Variance of estimated error of amplitude data by AR model (short-time average)

AicS(l ^* ): Akaike Information Criterion based on AR model (short-time average)LossS(l ^* ): Loss function based on AR model (short-time average)M: Order of the AR model (3) In the case of long-term average, the frequency analysis unit 22 calculates the following equations 23 to 27 corresponding to equations 18 to 22 for the short-term average, respectively.

(4) The anomaly detection unit 23 calculates the anomaly detection index value SLa(l ^* ) using any one of Equations 28 to 33.

SLa(l ^* ): Index value of anomaly detection zS _q (l ^* ): Characteristic root of AR model (short-term average) zL _q (l ^* ): Characteristic root of AR model (long-term average)

SLa(l ^* ): Index value of anomaly detection _fSq (l ^* ): Peak frequency of running spectrum by AR model (short-time average) _fLq (l ^* ): Peak frequency of running spectrum by AR model (long-time average)

SLa(l ^* ): Index value of abnormality detection _PSq (l ^* ): Peak value of running spectrum by AR model (short-time average) _PLq (l ^* ): Peak value of running spectrum by AR model (long-time average)

SLa(l ^* ): index value of anomaly detection fSq'(l ^* ): dominant frequency of the running spectrum by the AR model (short-time average), q' is the q at which the peak value PSq(l ^* ) of the running spectrum by the AR model (short-time average) calculated by Equation 20 is maximized
fLq″(l ^* ): the dominant frequency of the running spectrum by the AR model (long-term average), and q″ is the q at which the peak value PLq(l ^* ) of the running spectrum by the AR model (long-term average) calculated by Equation 25 is maximized.

SLa(l ^* ): Index value of anomaly detection LossS(l ^* ): Loss function by AR model (short-time average) LossL(l ^* ): Loss function by AR model (long-time average)

SLa(l ^* ): index value for anomaly detection AicS(l ^* ): Akaike Information Criterion based on AR model (short-term average) AicL(l ^* ): Akaike Information Criterion based on AR model (long-term average) By calculating the index value for anomaly detection SLa(l ^* ) as described above, it is possible to detect sudden changes in the running spectrum without having to calculate spectral values for many frequencies f as in Equation 14, thereby shortening the calculation time.

As an index of the distance between the running spectrum PS(l ^* ,f) based on the AR model (short-term average) and the running spectrum PL(l ^* ,f) based on the AR model (long-term average), other possible embodiments include the chi-squared kernel, positive definite chi-squared kernel, histogram intersection kernel, Hellinger kernel, correlation function, etc.

In addition, an embodiment is possible in which all or part of PS(l ^* ,f) and PL(l ^* ,f) calculated using Equations 7 and 13 are used in machine learning such as deep learning to learn the characteristics of anomalies, thereby enabling highly accurate anomaly detection.

Furthermore, zS _q (l ^* ), fS q(l ^* ), PS _q (l*), zL _q (l ^* ), fL _q (l ^* ) and PL _q (l ^* ) calculated using equations 18 to 20 and equations ₂₃ to ²⁵ are equivalent to the dimensionality reduction of the running spectrum across all frequencies f, so that all or part of these can be used in machine learning such as deep learning to effectively learn the characteristics of anomalies, enabling an embodiment to perform highly accurate anomaly detection.

In the first embodiment, the amplitude data x(l ^* ) is assumed to be one of the three spatial components, but it is also possible to use a plurality of spatial components simultaneously, or to use a function value calculated from a plurality of spatial components. For example, it is possible to use particle motion (particle trajectory) calculated from the displacement data of the three spatial components.

ＳＬａ（ｌ^＊）：異常検出の指標値
ｆＳ_ｑ’（ｌ^＊）：ＡＲモデル（短時間平均）によるランニングスペクトルの卓越周波数であり、ｑ’は式２０で計算されるＡＲモデル（短時間平均）によるランニングスペクトルのピーク値ＰＳ_ｑ（ｌ^＊）が最大となるｑである。

ＳＬａ（ｌ^＊）：異常検出の指標値
ＬｏｓｓＳ（ｌ^＊）：ＡＲモデル（短時間平均）による損失関数

ＳＬａ（ｌ^＊）：異常検出の指標値
ＡｉｃＳ（ｌ^＊）：ＡＲモデル（短時間平均）による赤池情報量規準 In addition, in embodiment 1, in the anomaly detection unit 23, the anomaly detection index value SLa(l ^* ) is defined using the ratio of the running spectrum PS(l ^* ,f) based on the AR model (short-time average) to the running spectrum PL(l ^* ,f) based on the AR model (long-term average) as shown in equation 14. However, embodiments that simply use the dominant frequency itself as shown in equation 34, embodiments that simply use the loss function itself based on the AR model (short-time average) as shown in equation 35, and embodiments that simply use the Akaike Information Criterion itself based on the AR model (short-time average) as shown in equation 36 are also possible.

SLa(l ^* ): index value fS for abnormality detection; _q' (l ^* ): dominant frequency of the running spectrum based on the AR model (short-term average), and q' is the q at which the peak value _PSq (l ^* ) of the running spectrum based on the AR model (short-term average) calculated by Equation 20 is maximized.

SLa(l ^* ): Index value of anomaly detection LossS(l ^* ): Loss function by AR model (short-time average)

SLa(l ^* ): Index value of anomaly detection AicS(l ^* ): Akaike information criterion by AR model (short-term average)

ＳＬａ（ｌ^＊）：異常検出の指標値
ＥＰＬ：閾値 Moreover, a modification in which (1) in the explanation of formula 15 in the first embodiment is changed to the following (1) is also possible.
(1) When the index value SLa(l ^* ) of abnormality detection satisfies the formula 15, the abnormality detection unit 23 (P wave detection unit) judges that an abnormality has been detected. That is, the abnormality detection unit 23 judges that a P wave has been detected (YES in process P204). In this case, the state of the information processing device 20 transitions to an "abnormal state". An event of abnormality detection by the abnormality detection unit 23 (P wave detection unit) is called "abnormality detection". Next, the timing at which the counter l ^* is counted back and the maximum l ^* that satisfies the formula 37 is added by 1 is set as the abnormality detection timing l ^* t. The abnormality detection unit 23 outputs the abnormality detection timing l ^* t to the external device 40.

SLa(l ^* ): Index value for abnormality detection EPL: Threshold value

In addition, in the first embodiment, the order of the AR model (short-term average) and the AR model (long-term average) is a common M, but there are also embodiments in which the orders of the two are different from each other.

In addition, in the first embodiment, an autoregressive model is used to calculate the running spectrum in the frequency analysis unit 22, but other embodiments are also possible in which the running spectrum is calculated using other methods, such as FFT (Fast Fourier Transform).

In addition, in the first embodiment, a device for observing natural phenomena, such as a seismometer, is assumed as the abnormality detection device. However, the abnormality detection device may also be a self-diagnosis device for machinery, or a structural health monitoring device that monitors damage caused by earthquakes to structures such as bridges. In the case of a self-diagnosis device, the observation data may be self-diagnosis data from a sensor attached to the machinery, and in the case of a structural health monitoring device, the observation data may be microtremor measurement data attached to the structure.

(Hardware Supplement)
7 shows a hardware configuration of the information processing device 20. The hardware configuration of the information processing device 20 is shown. The information processing device 20 is a computer. The information processing device 20 includes a processor 210. The information processing device 20 includes, as hardware components, the processor 210, a main storage device 220, an auxiliary storage device 230, and a communication interface 240. The processor 210 is connected to other hardware via a signal line 250 and controls the other hardware.

The information processing device 20 includes an amplitude calculation unit 21, a frequency analysis unit 22, an abnormality detection unit 23, and an abnormality termination determination unit 24. These functions are realized by an information processing program 231.

The processor 210 is a device that executes the information processing program 231. When the processor 210 executes the information processing program 231, the functions of the amplitude calculation unit 21, the frequency analysis unit 22, the abnormality detection unit 23, and the abnormality termination determination unit 24 are realized. The processor 210 is an integrated circuit (IC) that performs arithmetic processing.

A specific example of the main memory 220 is a static random access memory (SRAM).
The main memory 220 stores the results of operations performed by the processor 210.

The auxiliary storage device 230 is a storage device that stores data in a non-volatile manner. A specific example of the auxiliary storage device 230 is a hard disk drive (HDD). The auxiliary storage device 230 may be a portable recording medium. The auxiliary storage device 230 stores an information processing program 231.

The communication interface 240 is a communication port through which the processor 210 communicates with other devices. The communication interface 240 is connected to the network 50.

The processor 210 loads the information processing program 231 from the auxiliary storage device 230 into the main storage device 220. The processor 210 reads the loaded information processing program 231 from the main storage device 220 and executes it.

The information processing program 231 is a program that causes a computer to execute each process, procedure, or step of the amplitude calculation unit 21, the frequency analysis unit 22, the abnormality detection unit 23, and the abnormality termination determination unit 24, where "part" is replaced with "process," "procedure," or "step."

The method performed by the information processing device 20, which is a computer, executing the information processing program 231 is an information processing method. The information processing program 231 may be provided by being stored in a computer-readable recording medium, or may be provided as a program product.

Various aspects of the present disclosure are summarized below as appendices.
(Appendix 1)
an amplitude calculation unit that calculates an amplitude that changes over time from observation data of an event observed by a sensor;
a frequency analysis unit that calculates a frequency characteristic from the amplitude in real time using an autoregressive model;
An information processing device comprising:
(Appendix 2)
an amplitude calculation unit that calculates an amplitude that changes over time from observation data of an event observed by a sensor;
Analyzing a first frequency characteristic corresponding to the first time window in real time from the amplitude using a first time window;
a frequency analysis unit that analyzes in real time a second frequency characteristic corresponding to a second time window, the second time window being longer than the first time window, from the amplitude;
An information processing device comprising:
(Appendix 3)
The frequency analysis unit is
3. The information processing device according to claim 2, further comprising: an autoregressive model for analyzing the first frequency characteristic and the second frequency characteristic in real time.
(Appendix 4)
The information processing device further includes:
4. The information processing device according to claim 2, further comprising an anomaly detection unit configured to detect an anomaly from the observation data by using the first frequency characteristic and the second frequency characteristic.
(Appendix 5)
The abnormality detection unit
5. The information processing device according to claim 4, further comprising: a processor for detecting an anomaly from the observation data by comparing the first frequency characteristic with the second frequency characteristic.
(Appendix 6)
The information processing device further includes:
6. The information processing device according to claim 4, further comprising an abnormality end determination unit that determines an end of the abnormality when the abnormality is detected.
(Appendix 7)
The abnormality termination determination unit is
7. The information processing device according to claim 6, wherein the end of the abnormality is determined by comparing the second frequency characteristic immediately before the occurrence of the abnormality with the current first frequency characteristic.
(Appendix 8)
On the computer,
an amplitude calculation process for calculating an amplitude that changes over time from the observation data of the event observed by the sensor;
A frequency analysis process for calculating a frequency characteristic from the amplitude in real time using an autoregressive model;
The information processing program to be executed.
(Appendix 9)
On the computer,
an amplitude calculation process for calculating an amplitude that changes over time from the observation data of the event observed by the sensor;
a frequency analysis process for analyzing, in real time, a first frequency characteristic corresponding to the first time window from the amplitude using a first time window, and analyzing, in real time, a second frequency characteristic corresponding to the second time window from the amplitude using a second time window that is longer than the first time window;
An information processing program that executes the above.
(Appendix 10)
The frequency analysis process includes:
10. The information processing program according to claim 9, further comprising: analyzing the first frequency characteristic and the second frequency characteristic in real time by using an autoregressive model.
(Appendix 11)
The information processing program further comprises:
11. The information processing program according to claim 9 or 10, further comprising an anomaly detection process for detecting an anomaly from the observation data by using the first frequency characteristic and the second frequency characteristic.
(Appendix 12)
The abnormality detection process includes:
12. The information processing program according to claim 11, further comprising: detecting an anomaly from the observation data by comparing the first frequency characteristic with the second frequency characteristic.
(Appendix 13)
The information processing program further comprises:
13. The information processing program according to claim 11, further comprising an abnormality end determination process for determining an end of the abnormality when the abnormality is detected.
(Appendix 14)
The abnormality termination determination process includes:
14. The information processing program according to claim 13, further comprising: determining whether the abnormality has ended by comparing the second frequency characteristic immediately before the occurrence of the abnormality with the current first frequency characteristic.
(Appendix 15)
The computer
Calculate the amplitude that changes over time from the observation data of the event observed by the sensor,
An information processing method for calculating frequency characteristics in real time from the amplitude using an autoregressive model.
(Appendix 16)
The computer
Calculate the amplitude that changes over time from the observation data of the event observed by the sensor,
an information processing method for analyzing, in real time, a first frequency characteristic corresponding to a first time window from the amplitude using a first time window, and analyzing, in real time, a second frequency characteristic corresponding to the second time window from the amplitude using a second time window that is longer than the first time window.

10 Sensor, 20 Information processing device, 21 Amplitude calculation unit, 22 Frequency analysis unit, 23 Anomaly detection unit, 24 Anomaly termination determination unit, 30 Anomaly detection device, 40 External device, 50 Network, 210 Processor, 220 Main storage device, 230 Auxiliary storage device, 231 Information processing program, 240 Communication interface, 250 Signal line.

Claims (15)

an amplitude calculation unit that calculates an amplitude that changes over time from observation data of an event observed by a sensor;
a frequency analysis unit that analyzes, in real time, a first frequency characteristic corresponding to the first time window from the amplitude using a first time window, and analyzes, in real time, a second frequency characteristic corresponding to the second time window from the amplitude using a second time window that is longer than the first time window;
Equipped with
The frequency analysis unit is
An information processing apparatus that analyzes the first frequency characteristic and the second frequency characteristic in real time by using an autoregressive model,
The information processing device further includes:
an anomaly detection unit that detects an anomaly from the observation data by using the first frequency characteristic and the second frequency characteristic. The abnormality detection unit
The information processing apparatus according to claim 1 , wherein the first frequency characteristic is compared with the second frequency characteristic to detect an anomaly from the observation data. The information processing device further includes:
The information processing apparatus according to claim 1 , further comprising an abnormality end determination unit that determines an end of the abnormality when the abnormality is detected. The abnormality termination determination unit is
The information processing apparatus according to claim 3 , wherein the termination of the abnormality is determined by comparing the second frequency characteristic immediately before the occurrence of the abnormality with the current first frequency characteristic. On the computer,
an amplitude calculation process for calculating an amplitude that changes over time from the observation data of the event observed by the sensor;
a frequency analysis process for analyzing, in real time, a first frequency characteristic corresponding to the first time window from the amplitude using a first time window, and analyzing, in real time, a second frequency characteristic corresponding to the second time window from the amplitude using a second time window that is longer than the first time window;
An information processing program for executing
In the frequency analysis process,
Analyzing the first frequency characteristic and the second frequency characteristic in real time using an autoregressive model;
The information processing program further comprises:
An information processing program comprising an anomaly detection process for detecting an anomaly from the observation data by using the first frequency characteristic and the second frequency characteristic. The abnormality detection process includes:
The information processing program according to claim 5 , further comprising: detecting an anomaly from the observation data by comparing the first frequency characteristic with the second frequency characteristic. The information processing program further comprises:
7. The information processing program according to claim 5, further comprising an abnormality end determination process for determining an end of the abnormality when the abnormality is detected. The abnormality termination determination process includes:
8. The information processing program according to claim 7, wherein the termination of the abnormality is determined by comparing the second frequency characteristic immediately before the occurrence of the abnormality with the current first frequency characteristic. The computer
Calculate the amplitude that changes over time from the observation data of the event observed by the sensor,
an information processing method for analyzing, in real time, a first frequency characteristic corresponding to the first time window from the amplitude using a first time window, and analyzing, in real time, a second frequency characteristic corresponding to the second time window from the amplitude using a second time window that is longer than the first time window,
The computer includes:
Analyzing the first frequency characteristic and the second frequency characteristic in real time using an autoregressive model;
The computer includes:
An information processing method for detecting an anomaly from the observation data by using the first frequency characteristic and the second frequency characteristic. The computer includes:
The information processing method according to claim 9 , further comprising the step of: detecting an anomaly from the observation data by comparing the first frequency characteristic with the second frequency characteristic. The computer includes:
The information processing method according to claim 9 or 10, further comprising the step of determining whether the abnormality has ended when the abnormality is detected. The computer includes:
The information processing method according to claim 11 , further comprising the step of: determining whether the abnormality has ended by comparing the second frequency characteristic immediately before the occurrence of the abnormality with the current first frequency characteristic. an amplitude calculation unit that calculates an amplitude that changes over time from observation data of an event observed by a sensor;
a frequency analysis unit that analyzes, in real time, a first frequency characteristic corresponding to the first time window from the amplitude using a first time window, and analyzes, in real time, a second frequency characteristic corresponding to the second time window from the amplitude using a second time window that is longer than the first time window;
Equipped with
The frequency analysis unit is
An information processing apparatus that analyzes the first frequency characteristic and the second frequency characteristic in real time by using an autoregressive model,
The information processing device further includes:
An information processing apparatus comprising: an abnormality detection unit that compares the first frequency characteristic with the second frequency characteristic. On the computer,
an amplitude calculation process for calculating an amplitude that changes over time from the observation data of the event observed by the sensor;
a frequency analysis process for analyzing, in real time, a first frequency characteristic corresponding to the first time window from the amplitude using a first time window, and analyzing, in real time, a second frequency characteristic corresponding to the second time window from the amplitude using a second time window that is longer than the first time window;
An information processing program for executing
In the frequency analysis process,
Analyzing the first frequency characteristic and the second frequency characteristic in real time using an autoregressive model;
The information processing program further comprises:
An information processing program comprising an abnormality detection process for comparing the first frequency characteristic with the second frequency characteristic. The computer
Calculate the amplitude that changes over time from the observation data of the event observed by the sensor,
an information processing method for analyzing, in real time, a first frequency characteristic corresponding to the first time window from the amplitude using a first time window, and analyzing, in real time, a second frequency characteristic corresponding to the second time window from the amplitude using a second time window that is longer than the first time window,
The computer includes:
Analyzing the first frequency characteristic and the second frequency characteristic in real time using an autoregressive model;
The computer includes:
An information processing method for comparing the first frequency characteristic with the second frequency characteristic.

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