JP2005242581A - Parameter estimation method, state monitoring method, parameter estimation apparatus, state monitoring apparatus and computer program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a parameter estimation method that quickly estimates a time series of parameters indicating the state of a monitored object, a state monitoring method that can monitor the state of a monitored object with external input, a parameter estimation apparatus, a state monitoring apparatus, and a computer program. <P>SOLUTION: The state monitoring apparatus (parameter estimation apparatus) stores an estimate θ<SB>N</SB>of a parameter in the case of application to an ARX model of a first sample time series of N pieces of data acquired from a monitored object and a first input time series of N pieces of data input into the monitored object. When a second sample time series and a second input time series each of L data are received (S4), an estimate θ<SB>N+L</SB>of the parameter in the case of the application to the ARX model of a third sample time series and a third input time series each of N+L data is calculated by approximate calculation using θ<SB>N</SB>(S8), and the state of the monitored object is determined according to the value θ<SB>N+L</SB>(S10). <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a method for estimating a time-series parameter composed of a plurality of data obtained from a monitoring target, a method for monitoring the state of a monitoring target based on the estimated parameter, a parameter estimation device, a state monitoring device, and a computer program About.

  As a method of maintaining various facilities such as production facilities used in factories or public facilities used in public facilities in order to prevent the occurrence of failures, a method of regularly checking and maintaining facilities (TBM: Time Based preventive) Maintenance) has been used in the past. In addition to the TBM, there is known a method (CBM: Condition Based preventive Maintenance) that constantly monitors the state of the equipment and performs maintenance when the state of the equipment has deteriorated to a predetermined standard. CBM has advantages such as being able to avoid initial failures after maintenance due to TBM, and being easier to control maintenance costs than TBM. Yes.

  In order to realize the CBM, a state monitoring method that acquires data such as the number of operations, temperature, or vibration indicating the state of the equipment, monitors the state of the equipment, and catches an abnormality sign as soon as possible. It is desirable to establish Since the data indicating the state of the facility differs depending on the field of the facility, various state monitoring methods have been proposed conventionally. For example, in the field of vibrating bodies, a method using an RMS (Root Mean Square) value that is a square root of a value obtained by squaring the amplitude of vibration is known. In the state monitoring method using the RMS value, the vibration amplitude is acquired as data, the RMS value that is the square root of the squared average of the acquired amplitude is calculated, and the calculated RMS value becomes larger than the reference Furthermore, since the amplitude of vibration is large, it can be determined that the equipment is in an abnormal state.

  As another status monitoring method, the time series of data acquired from the monitored equipment is applied to a discrete-time linear model for analysis, parameters indicating the relationship between the data are estimated, and the estimated parameters change significantly There is a method for determining that the equipment is abnormal. As an example of this method, a parameter is estimated for a time series composed of N data, and a parameter is estimated for a time series composed of N + 1 data when the (N + 1) th data is acquired. A method has been conventionally used in which parameter estimation is repeated each time a parameter is acquired, parameters are sequentially estimated, and changes in parameters are examined. As the discrete-time linear model, an AR (Autoregressive: Autoregressive) model or an ARMA (Autoregressive Moving Average) model is used.

  Generally, when CBM is performed in a factory, each facility is equipped with a sensor, and data acquired by the sensor is stored online by a computing device such as a personal computer (PC), microcomputer, minicomputer, or process computer. The processed data is processed and the equipment is monitored. Because the behavior of equipment in the factory is high-speed, in the method of estimating the parameters of the discrete-time linear model each time data is acquired, when using a computing device with low computing capacity, the data is compared to the processing speed of the computing device. The speed at which is accumulated is faster. For this reason, there is a possibility that the detection of the equipment abnormality will be failed, or the equipment abnormality detection delay may occur even if it is not a failure. Further, there is a problem that it is difficult to determine a change in the state of the equipment because the parameter hardly changes when only one data is added to a lot of data.

Therefore, the inventors of the present application, in Non-Patent Document 1, when a plurality of new data collected to some extent is obtained, a plurality of data is accumulated by estimating parameters for a time series to which the new data is added. A method has been proposed that makes it possible to perform a parameter estimation process at a sufficiently high speed compared to the speed to be performed. In this method, since the parameter changes greatly compared to the case where one data is added by examining the change in the parameter when a plurality of data is added, it is possible to determine the change in the state of the monitoring target. It becomes easy.
Takeyasu, Amemiya, Iino, Masuda, “About Multiple Data Processing Methods for Online Parameter Estimation”, Journal of Signal Processing, Signal Processing Society of Japan, May 2002, Vol. 6, No. 3, p. 189-198

  In the parameter estimation method proposed in Non-Patent Document 1, an AR model is used as a discrete-time linear model. In the AR model, the value of one data included in the time series of data is determined from the value of past data and noise. However, in reality, the value of data obtained from the equipment is often influenced by input such as the input voltage or forced external force to the equipment, and there is a problem that the AR model cannot cope with the actual problem.

  The present invention has been made in view of such circumstances, and the object of the present invention is to deal with more practical problems by using a model that takes into account external input. A parameter estimation method, a state monitoring method, a parameter estimation device, a state monitoring device, and a computer program are provided.

The parameter estimation method according to the first aspect of the present invention is the first sample time series {x _n : n = 1, each consisting of N pieces of data (where N is a natural number), using a computer having a storage unit and a calculation unit. , 2,..., N} and the first input time series {u _n : n = 1, 2,..., N}, each of which is composed of L pieces of data (where L is a natural number and L <N). When the two-sample time series {x _n : n = N + 1, N + 2,..., N + L} and the second input time series {u _n : n = N + 1, N + 2,..., N + L} are added, the first sample time series is added. The third sample time series to which the second sample time series is added and the third input time series to which the second input time series is added to the first input time series are (p, p) order (where p is a natural number) method for estimating a parameter when applied to an ARX model, wherein the first sample time series and the first An input time series (p, p) storing the first estimate theta _N of the estimated value of the parameter when fitted on to the next ARX model expressed in a matrix of 2p rows and one column in the storage unit, the following formula A matrix A to be defined is stored in the storage unit;

  The second sample time series and the second input time series are stored in the storage unit, and the matrices B and D defined by the following equations are calculated in the calculation unit,

A second estimated value θ _{N +} expressing the estimated value of the parameter as a 2p × 1 matrix when the third sample time series and the third input time series are applied to the (p, p) -order ARX model. _L is calculated by the calculation unit using the following equation (a) or (b): θ _{N + L} = θ _N − (L / N) A ⁻¹ D− (L / N) A ⁻¹ Bθ _N ... (a)
θ _{N + L} = θ _N − (L / N) A ⁻¹ D− (L / N) A ⁻¹ Bθ _N
+ (L / N) ² (A ⁻¹ B) ² θ _N + (L / N) ² A ⁻¹ BA ⁻¹ D (b)
It is characterized by.

A state monitoring method according to a second aspect of the present invention is a computer including a storage unit and a calculation unit, and a sample time series composed of a plurality of data obtained from a monitoring target that accepts data input and a plurality of data input to the monitoring target In the method of monitoring the state of the monitoring target based on the parameters when the input time series consisting of the above data is applied to the ARX model, it consists of N pieces (where N is a natural number) obtained from the monitoring target. A first input time series {u _n : n = 1, 2,..., Consisting of a first sample time series {x _n : n = 1, 2,..., N} and N pieces of data input to the monitoring target. N} is a (p, p) -order (where p is a natural number) ARX model, and the first estimated value θ _N expressing the estimated value of the parameter as a 2p × 1 matrix is stored in the storage unit. Store the matrix A defined by the following equation Store in the storage unit,

A second sample time series {x _n : n = N + 1, N + 2,..., N + L} consisting of L pieces of data (L is a natural number and L <N) obtained from the monitoring target and the monitoring target. The second input time series {u _n : n = N + 1, N + 2,..., N + L} composed of L pieces of data is stored in the storage unit, and the matrices B and D defined by the following equations are calculated in the calculation unit. And

A third sample time series in which the second sample time series is added to the first sample time series and a third input time series in which the second input time series is added to the first input time series (p, p) The second estimated value θ _{N + L in} which the estimated value of the parameter when applied to the next ARX model is expressed by a matrix of 2p rows and 1 column is calculated using the following equation (a) or (b): Calculated in part
θ _{N + L} = θ _N − (L / N) A ⁻¹ D− (L / N) A ⁻¹ Bθ _N (a)
θ _{N + L} = θ _N − (L / N) A ⁻¹ D− (L / N) A ⁻¹ Bθ _N
+ (L / N) ² (A ⁻¹ B) ² θ _N + (L / N) ² A ⁻¹ BA ⁻¹ D (b)
The state of the monitoring target is determined by the arithmetic unit based on the second estimated value θ _{N + L} calculated by the arithmetic unit.

The parameter estimation apparatus according to the third aspect of the present invention includes a first sample time series {x _n : n = 1, 2,..., N} each composed of N pieces (where N is a natural number) and a first input time series. {U _n : second sample time series {x _n : n = N + 1, N + 2} each consisting of L pieces of data (where L is a natural number and L <N) for n = 1, 2,..., N} ,..., N + L} and the second input time series {u _n : n = N + 1, N + 2,..., N + L} are added, the second sample time series is added to the first sample time series. When a three-sample time series and a third input time series obtained by adding the second input time series to the first input time series are applied to a (p, p) -order (where p is a natural number) ARX model An apparatus for estimating a parameter, wherein the first sample time series and the first input time series are converted into a (p, p) -order ARX model. Means for storing a first estimated value theta _N representing the estimated value of the parameter matrix of 2p rows and one column when fitted Te, means for storing the matrix A defined by the following formula,

  Means for storing the second sample time series and the second input time series; means for calculating matrices B and D defined by the following equations;

A second estimated value θ _{N +} expressing the estimated value of the parameter as a 2p × 1 matrix when the third sample time series and the third input time series are applied to the (p, p) -order ARX model. _L to the following formula (a) or (b) means for calculating using the equation _{θ N + L = θ N -} (L / N) a -1 D- (L / N) a -1 Bθ N ... ( a)
θ _{N + L} = θ _N − (L / N) A ⁻¹ D− (L / N) A ⁻¹ Bθ _N
+ (L / N) ² (A ⁻¹ B) ² θ _N + (L / N) ² A ⁻¹ BA ⁻¹ D (b)
It is characterized by providing.

According to a fourth aspect of the present invention, a state monitoring apparatus applies a sample time series composed of a plurality of data obtained from a monitoring target that receives data input and an input time series composed of a plurality of data input to the monitoring target to an ARX model. The first sample time series {x _n : n = 1, which consists of N pieces of data (where N is a natural number) obtained from the monitoring object 2, ..., the first input time series {u _n of n data input to the monitoring target n}: n = 1, 2, ..., a n} (p, p) follows (however, means for storing a first estimated value θ _{N in} which an estimated value of a parameter when applied to an ARX model (p is a natural number) is expressed by a matrix of 2p rows and 1 column, and means for storing a matrix A defined by the following equation When,

A second sample time series {x _n : n = N + 1, N + 2,..., N + L} consisting of L pieces of data (L is a natural number and L <N) obtained from the monitoring target and the monitoring target. Means for storing a second input time series {u _n : n = N + 1, N + 2,..., N + L} consisting of L data, means for calculating matrices B and D defined by the following equations,

A third sample time series in which the second sample time series is added to the first sample time series and a third input time series in which the second input time series is added to the first input time series (p, p) A second estimated value θ _{N + L in} which the estimated value of the parameter when applied to the next ARX model is expressed by a matrix of 2p rows and 1 column is calculated using the following equation (a) or (b): Means,
θ _{N + L} = θ _N − (L / N) A ⁻¹ D− (L / N) A ⁻¹ Bθ _N (a)
θ _{N + L} = θ _N − (L / N) A ⁻¹ D− (L / N) A ⁻¹ Bθ _N
+ (L / N) ² (A ⁻¹ B) ² θ _N + (L / N) ² A ⁻¹ BA ⁻¹ D (b)
Means for determining the state of the monitoring target based on the second estimated value θ _{N + L} calculated by the means.

The computer program according to the fifth aspect of the present invention includes a first sample time series {x _n : n = 1, 2,..., N} each consisting of N pieces of data (where N is a natural number) and a first input time series { u _n : n = 1, 2,..., N} and the (p, p) -order (where p is a natural number) ARX model represents the estimated parameter values as a 2p-by-1 matrix. A first estimated value θ _N , a matrix A defined by

A second sample time series {x _n : n = N + 1, N + 2,..., N + L} consisting of L pieces of data (where L is a natural number and L <N), and a second input time series {L} u _n : a computer storing n = N + 1, N + 2,..., N + L}, a third sample time series in which the second sample time series is added to the first sample time series, and the first input time series A computer program for estimating a parameter when a third input time series to which a second input time series is added is applied to a (p, p) order (where p is a natural number) ARX model, A procedure for calculating the matrices B and D defined by the following equations;

A second estimated value representing an estimated value of a parameter in a 2p × 1 matrix when the computer applies the third sample time series and the third input time series to a (p, p) -order ARX model. theta _{N + L} to the following formula (a) or (b) a procedure for calculating using the equation _{θ N + L = θ N -} (L / N) a -1 D- (L / N) a -1 Bθ _N ... (a)
θ _{N + L} = θ _N − (L / N) A ⁻¹ D− (L / N) A ⁻¹ Bθ _N
+ (L / N) ² (A ⁻¹ B) ² θ _N + (L / N) ² A ⁻¹ BA ⁻¹ D (b)
It is characterized by including.

The computer program according to the sixth aspect of the present invention is a first sample time series {x _n : n = 1, 2,..., Consisting of N pieces (where N is a natural number) obtained from a monitoring target that accepts data input. N} and the first input time series {u _n : n = 1, 2,..., N} composed of N pieces of data input to the monitoring target (p, p) order (where p is a natural number) A first estimated value θ _N representing an estimated value of a parameter when applied to the ARX model of the above in a 2p × 1 matrix, a matrix A defined by the following equation,

A second sample time series {x _n : n = N + 1, N + 2,..., N + L} consisting of L pieces of data obtained from the monitoring target (where L is a natural number and L <N), and input to the monitoring target has been the L comprising data of the second input time series _{{u n: n = n +} 1, n + 2, ..., n + L} in the computer for storing a computer program for monitoring the state of the monitored object, the computer, A procedure for calculating the matrices B and D defined by the following equations;

The computer includes a third sample time series in which the second sample time series is added to the first sample time series and a third input time series in which the second input time series is added to the first input time series. The second estimated value θ _{N + L in} which the estimated value of the parameter when applied to the (p, p) next ARX model is expressed by a matrix of 2p rows and 1 column is expressed by the following equation (a) or (b): Procedure to calculate
θ _{N + L} = θ _N − (L / N) A ⁻¹ D− (L / N) A ⁻¹ Bθ _N (a)
θ _{N + L} = θ _N − (L / N) A ⁻¹ D− (L / N) A ⁻¹ Bθ _N
+ (L / N) ² (A ⁻¹ B) ² θ _N + (L / N) ² A ⁻¹ BA ⁻¹ D (b)
And a procedure for causing the computer to determine the state of the monitoring target based on the calculated second estimated value θ _{N + L.}

In the present invention, an ARX (Autoregressive with exogenous input: exogenous input autoregressive) model is used as a discrete-time linear model, and L data is added to a sample time series composed of N data obtained from a monitoring target. Calculate the parameters when. If the sample time series {x _n : n = 1, 2,..., N,...} Composed of N pieces of data obtained from the monitoring target is the sample time series of the steady ergodic normal process x (t), The (p, m) next ARX model is expressed by the following equation (1).

Here, {e _n } is normal noise with an average value of 0 and variance σ _e ² , and {u _n } is an input time series for the monitoring target. {A _i : i = 1, 2,..., P} and {c _i : i = 1, 2,..., M} are parameters of the ARX model. Further, it is assumed that the equation (1) satisfies a steady condition. In modern control theory, it is well known that m ≦ p. In the following, the discussion proceeds with m = p for simplicity.

Vector Z _n and vector θ are defined as follows.
Z _n = [-x _n-1 , ...,-x _np , u _n-1 , ..., u _np ] ^T
_{θ = [a 1, a 2} , ..., a p, c 1, c 2, ..., c p] T
When the formula (1) is rewritten into the formula for x _n , the formula (1) can be expressed by the following formula (2).
x _n = θ ^T Z _n + e _n (2)

When a sample time series {x _n : n = 1, 2,..., N} and an input time series {u _n : n = 1, 2,. In order to obtain from the time series by the least square method, θ that minimizes the right side of the following equation (3) obtained from equation (2) may be obtained.

Therefore, the right side of the equation (3) is partially differentiated by θ and equal to 0, so that the vector θ estimated from the sample time series {x _n } and the input time series {u _n } consisting of N data is obtained. The estimated value θ _N is given by the following equation (4).

Assuming that R _j is an autocorrelation function of {x _n } whose lag is j, R _j and R _−j can be expressed by the following equations according to the definition of the autocorrelation function. Here, E [y _n ] is an expected value of the data string {y _n : n = 1, 2,.
R _j = E [x _n x _{n + j} ]
R _-j = R _j

The autocorrelation function S _j of {u _n} can be expressed similarly to the following equation.
S _j = E [u _n u _{n + j} ]
S _-j = S _j

Also, assuming that j is j ≧ 0, the cross-correlation function T _j between {u _n } and {x _n } can be expressed by the following equation.
T _j = E [u _nj x _n ]
Since u _{n + j} and x _n , which are future inputs from the time point _n , are uncorrelated, the following equation holds.

T _−j = E [u _{n + j} x _n ] = 0
When a sample time series {x _n : n = 1, 2,..., N} and an input time series {u _n : n = 1, 2,..., N} each consisting of N data are obtained, Estimated values R _{N, j} , T _{N, j} , S _{N, j} of R _j , T _j , S _j estimated from data of n = 1 to _N can be expressed by the following equation (5).

Next, consider the E [Z _n Z _n ^T] and E [Z _n x _n]. E [Z _n Z _n ^T] can be represented by the following equation (6).

  Here, the matrices R, T, and S are defined by the following equation (7).

Similarly, E [Z _n x _n ] can be expressed by the following equation (8).

  Here, the matrices r and t are defined by the following equation (9).

  Therefore, the parameter θ can be expressed by the following equation (10) from the equation (4).

By substituting the estimated values R _{N, j} , T _{N, j} , S _{N, j} of R _j , T _j , S _{j into} the equation (10), a sample time series (N 1 (Sample time series) {x _n : n = 1, 2,..., N} and input time series (first input time series) {u _n : n = 1, 2,. The estimated value (first estimated value) θ _N of the parameter θ can be calculated from the equation.

Next, a sample time series (second sample time series) {x _n : n = N + 1, N + 2,..., N + L} consisting of L data in addition to each N data and an input time series (second input time _{series) {u n: n = n} + 1, n + 2, ..., n + L} and were obtained. The estimated value R _{N + L, j} of the autocorrelation function R _j of {x _n } estimated from the data of n = 1 to _{N + L} can be expressed by the following equation (12). Note that the estimated value of the autocorrelation function R _j of {x _n } estimated from n = N + 1 to N + L data is R _{N / L, j} .

  Here, since the order p is generally often from several orders to several tens, it can be considered that N >> L >> p. Further, j ≦ p−1. Therefore, the expression (12) can be approximately expressed by the following expression (13).

  α and β are defined by the following equation (14).

From the equation (14), the equation (13) can be expressed by the following equation (15).
R _{N + L, j} = αR _{N, j} + βR _{N / L, j} (15)

n = 1~N + L T _j estimated from the data of the estimated value of _{S j T N + L, j} , S N + L, for even _{j, n = N + 1~N +} L T j estimated from the data of the S _j Using the estimated values T _{N / L, j} and S _{N / L, j,} they can be similarly expressed by the following equations (16) and (17).
T _{N + L, j} = αT _{N, j} + βT _{N / L, j} (16)
S _{N + L, j} = αS _{N, j} + βS _{N / L, j} (17)

The estimated values R _{N / L, j} , T _{N / L, j} and S _{N / L, j} of R _j , T _j and S _j estimated from the data of n = N + 1 to N + L are expressed by the following equation (18). Can be obtained.

Accordingly, the sample time series {x _n : n = 1, 2,..., N} and the input time series {u _n : n = 1, 2,. Parameter θ when a sample time series {x _n : n = N + 1, N + 2,..., N + L} and an input time series {u _n : n = N + 1, N + 2,. The estimated value (second estimated value) θ _{N + L} can be expressed by the following expression (19) using the expressions (11) and (15) to (17).

  In order to simplify the equation (19), the matrices A, B, C, and D are defined by the following equation (20).

Using the matrices A, B, C, and D, the equation (19) can be expressed by the following equation (21).
θ _{N + L} = − (αA + βB) ⁻¹ (αC + βD) (21)
The equation (11) can be expressed as θ _N = −A ⁻¹ C.

Further, the following formula that holds between the square matrices Q and P and the unit matrix I is applied to the equation (21).
[Q + P] ⁻¹ = Q ⁻¹ −Q ⁻¹ P [I + Q ⁻¹ P] ⁻¹ Q ⁻¹
[I + Q] ⁻¹ = I− [I + Q] ⁻¹ Q
At this time, the equation (21) can be expressed by the following equation (22).
θ _{N + L} = − (αA) ⁻¹ (αC) − (αA) ⁻¹ (βD)
+ (ΑA) ⁻¹ (βB) [I + (αA) ⁻¹ βB] ⁻¹ (αA) ⁻¹ (αC + βD)
= Θ _N- (L / N) A ^-1 D- (L / N) A ^-1 Bθ _N
+ (L / N) ² (A ⁻¹ B) ² θ _N + (L / N) ² A ⁻¹ BA ⁻¹ D
− (L / N) ³ A ⁻¹ B [I + (L / N) A ⁻¹ B] ⁻¹ (A ⁻¹ B) ² θ _N
-(L / N) ³ (A ^-1 B) ² A ^-1 D
+ (L / N) ⁴ A ^-1 B [I + (L / N) A ^-1 B] ^-1 (A ^-1 B) ² A ^-1 D
... (22)

From Equation (22), assuming that N >> L, and taking a linear approximation of (L / N), θ _{N + L} can be expressed by Equation (23) below.
θ _{N + L} = θ _N − (L / N) A ⁻¹ D− (L / N) A ⁻¹ Bθ _N (23)
Further, when taking a quadratic approximation of (L / N), θ _{N + L} can be expressed by the following equation (24).
θ _{N + L} = θ _N − (L / N) A ⁻¹ D− (L / N) A ⁻¹ Bθ _N
+ (L / N) ² (A ⁻¹ B) ² θ _N + (L / N) ² A ⁻¹ BA ⁻¹ D (24)

Θ _{N + L} that can be calculated using the equation (23) or the equation (24) is a sample time series (third sample time series) consisting of N + L data respectively {x _n : n = 1, 2,... N + L} and the input time series (third input time series) {u _n : n = 1, 2,..., N + L} are estimated values of the parameter θ when applied to ARX. Therefore, by using the equation (23) or the equation (24), a sample time series and input time series consisting of L pieces of data are obtained in addition to the sample time series consisting of N pieces of data and the input time series. The estimated value of the parameter θ can be easily obtained.

In the first, third and fifth inventions, the second sample consisting of L data in addition to the first sample time series {x _n } consisting of N data and the first input time series {u _n }. When the time series {x _n } and the second input time series {u _n } are obtained, the third sample time series {x _n } and the third input time series {u _n } each including N + L data are obtained. The second estimated value θ _{N + L} of the parameter θ when applied to the ARX model is calculated using the equation (23) or (24).

In the second, fourth and sixth inventions, the first sample time series {x _n } composed of N pieces of data obtained from the monitoring object and the first input time comprising N data inputted to the monitoring object If the sequence {u _n} second sample time series consisting of L data in addition to {x _n} and the second input time series {u _n} is obtained, the third consisting of each n + L data The second estimated value θ _{N + L} of the parameter θ when the sample time series {x _n } and the third input time series {u _n } are applied to the ARX model is calculated using the formula (23) or the formula (24). Then, the state of the monitoring target is determined based on the calculated value of θ _{N + L.}

In the first, third and fifth inventions, the sample time series {x _n } consisting of L data in addition to the sample time series {x _n } consisting of N data and the input time series {u _n }. _n } and the input time series {u _n }, when the sample time series {x _n } and the input time series {u _n } each consisting of N + L data are applied to the ARX model, the parameter θ By calculating the estimated value θ _{N + L} using an approximate expression, θ _{N + L} can be calculated in a short time.

In the second, fourth and sixth inventions, since the state of the monitoring target is determined based on the estimated value θ _{N + L} of the parameter θ calculated using the approximate expression, it is compared with the speed at which data is accumulated. It is possible to determine the state of the monitoring target at a sufficiently high speed, and to perform state monitoring that immediately corresponds to the state of the monitoring target without causing failure or delay in the abnormality detection of the monitoring target. Further, by using an ARX model in which the value of data obtained from the monitoring target is determined from the past data value, noise, and the input to the monitoring target as a discrete-time linear model, an external voltage such as input voltage or forced external force is used. Even when the status of the monitoring target is affected by the input, it is possible to determine the status of the monitoring target, so that it becomes possible to monitor the status of the monitoring target such as equipment in the factory under more realistic conditions, etc. The present invention has an excellent effect.

Hereinafter, the present invention will be specifically described with reference to the drawings showing embodiments thereof.
FIG. 1 is a block diagram showing the configuration of the state monitoring apparatus of the present invention. The state monitoring device 1 of the present invention is operated to monitor the state of a facility (monitoring target) (not shown) installed in a factory and to issue an alarm when an abnormality occurs in the facility. The equipment is provided with an output sensor 31 for measuring data output from the equipment such as vibration, temperature or output voltage. Further, the equipment is provided with an input sensor 33 for measuring data input to the equipment such as an input voltage or a forced external force. The output sensor 31 and the input sensor 33 are connected to the data acquisition device 32 and are configured to input measurement data to the data acquisition device 32. The data acquisition device 32 samples the measurement data input from the output sensor 31 and the input sensor 33 at a predetermined period, and from the sample time series composed of a plurality of data obtained from the facility and the plurality of data input to the facility. It has a function to acquire the input time series. The data acquisition device 32 is connected to the communication network N, and the communication network N is connected to the state monitoring device 1 of the present invention. The data acquisition device 32 is configured to transmit the acquired data to the state monitoring device 1 via the communication network N.

  The state monitoring device 1 also has a function as a parameter estimation device of the present invention, and is configured using a general-purpose computer. The state monitoring device 1 includes a CPU (arithmetic unit) 11 that performs computation, a RAM (storage unit) 12 that stores temporary information generated along with the computation, an external storage device 13 such as a CD-ROM drive, And an internal storage device 14 such as a hard disk. The CPU 11 reads the computer program 20 of the present invention from the recording medium 2 such as a CD-ROM by the external storage device 13 and stores the read computer program 20 in the internal storage device 14. The computer program 20 is loaded from the internal storage device 14 to the RAM 12 as necessary, and the CPU 11 executes processing necessary for the state monitoring device 1 based on the loaded computer program 20.

  The CPU 11 is connected to an input unit 15 (accepting unit) connected to the communication network N. The CPU 11 receives the data transmitted from the data acquisition device 32 via the communication network N at the input unit 15. The CPU 11 is connected to an output unit 16 that outputs information to the outside.

Further, the internal storage device 14 has a sample time series (first sample time series) {x _n : n = 1, 2,..., N} composed of N pieces of data obtained from the equipment and N inputted to the equipment. An input time series (first input time series) {u _n : n = 1, 2,..., N} composed of individual data is stored. Further, the internal storage device 14 estimates the parameter θ when the sample time series {x _n } composed of N pieces of data and the input time series {u _n } are applied to the (p, p) -order ARX model. _N and a matrix A defined by the equation (20) calculated from the sample time series {x _n } and the input time series {u _n } are stored. Further, the internal storage device 14 stores the order p of the (p, p) -order ARX model.

  Further, the state monitoring device 1 includes an output unit 16, and the alarm device 4 is connected to the output unit 16. The alarm device 4 includes any one or a combination of a buzzer, a lamp, a display unit that displays the content of the alarm, and the like. The CPU 11 transmits information indicating an abnormality of the facility from the output unit 16 to the alarm device 4, and the alarm device 4 notifies the abnormality of the facility according to the information received from the state monitoring device 1.

  The computer program 20 may be loaded from the external server device (not shown) connected to the communication network N to the state monitoring device 1 according to the present invention and stored in the internal storage device 14.

FIG. 2 is a flowchart showing operations performed by the state monitoring device 1 and the data acquisition device 32 of the present invention. The CPU 11 of the state monitoring device 1 performs the following processing according to the computer program 20 loaded into the RAM 12. The output sensor 31 measures data such as vibration output as the equipment is operated, and the input sensor 33 measures data such as input voltage inputted to the equipment. The data acquisition device 32 samples the measurement data input from the output sensor 31 and the input sensor 33 at a predetermined period (S1), and obtains the data obtained from the monitoring target equipment and the data input to the monitoring target equipment. get. The data acquisition device 32 determines whether or not a predetermined number L pieces of data obtained from the facility and data input to the facility to be monitored are accumulated (S2). When L pieces of data are not accumulated (S2: NO), the data acquisition device 32 returns the process to step S1 and continues sampling. When L pieces of data are accumulated (S2: YES), the data acquisition device 32 obtains a sample time series (second sample time series) {x _n consisting of L pieces of data obtained from the equipment to be monitored. : n = n + 1, n + 2, ..., n + L} and the input time series (second input time series) consisting of L pieces of data entered into the equipment monitored _{{u n: n = n +} 1, n + 2, ..., n + L} Is transmitted to the state monitoring apparatus 1 via the communication network N (S3).

The state monitoring device 1 receives the sample time series {x _n } and the input time series {u _n } each consisting of L pieces of data transmitted from the data acquisition device 32 (S4). From the received sample time series {x _n } and input time series {u _n }, the CPU 11 of the state monitoring device 1 determines R _{N / L, j} , which is defined by Equation (18) as j = 0 to p−1. T _{N / L, j} and S _{N / L, j} are calculated (S5). Next, the CPU 11 uses the calculated R _{N / L, j} , T _{N / L, j} and S _{N / L, j} as elements to generate matrices B and D defined by the equation (20) ( S6), θ _N and matrix A stored in the internal storage device 14 are read out to the RAM 12 (S7). Next, the CPU 11 samples N + L samples (third sample time series) {x _n : n = 1, 2,..., N + L} and input time series (second input time series) {u _n : Estimated value (second estimated value) θ _{N + L} of parameter θ when n = 1, 2,..., N + L} is applied to the (p, p) order ARX model, θ _N , A, B , D using the equation (23) (S8). In addition, since it is possible to calculate θ _{N + L} faster by using the equation (23) among the equations (23) and (24), usually θ _{N + L} is calculated using the equation (23). However, if it is desired to monitor the state of the equipment more accurately, θ _{N + L} may be calculated using the equation (24).

Next, the CPU 11 calculates J = | θ _{N + L} −θ _N | ² (S9), and determines whether or not the calculated value of J is larger than a predetermined value (S10). When the value of J is larger than the predetermined value (S10: YES), the CPU 11 determines that an abnormality has occurred in the monitored equipment because the estimated value of the parameter θ has changed greatly, and the equipment Abnormal information indicating abnormality is transmitted to the alarm device 4 by the output unit 16 (S14), and the process is terminated. In accordance with the abnormality information received from the state monitoring device 1, the alarm device 4 notifies an abnormality of the facility by sounding a buzzer, turning on a lamp, displaying the content of the abnormality information on the display unit, or the like. As a result, measures such as manually stopping the equipment determined to be abnormal are taken. The abnormality information is information indicating the degree of abnormality according to the value of J, and the alarm device 4 may be configured to perform processing according to the content of the abnormality information. Moreover, the form which performs the process which controls the state of an installation according to abnormality information may be sufficient.

If the value of J is less than or equal to the predetermined value in step S10 (S10: NO), the equipment to be monitored is normal, so the CPU 11 is a sample composed of the latest N pieces of data among N + L pieces of data. The time series {x _n } and the input time series {u _n } are stored in the internal storage device 14 (S11). Next, the CPU 11 calculates a new matrix A and an estimated value θ _N of the parameter θ from the sample time series {x _n } and the input time series {u _n } composed of the latest N pieces of data (S12), The calculated A and θ _N are stored in the internal storage device 14 (S13), and the process ends. In addition, the form which performs the process which accumulate | stores a sample time series and an input time series as N + L-> N may be sufficient. It may also be in the form for storing A and theta _N state unchanged without calculating a new A and theta _N.

As described above in detail, in the present invention, the sample time series {x _n } composed of N pieces of data obtained from the equipment to be monitored and the input time series {u _n comprising N pieces of data input to the equipment. }, An estimated value θ _N of the parameter θ of the ARX model is calculated, and when a new sample time series {x _n } and input time series {u _n } each including L data are obtained, An estimated value θ _{N + L} of the parameter θ is calculated when the sample time series and the input time series each consisting of N + L data are applied to the ARX model. By calculating θ _{N + L} using the approximate expression (23) or (24), θ _{N + L} can be calculated in a short time. In addition, since the status of the monitored equipment is determined based on the calculated parameter estimated value θ _{N + L} , it is possible to determine the status of the monitored target sufficiently faster than the speed at which data is accumulated. It becomes. Therefore, it is possible to perform state monitoring that immediately responds to the state of the facility without causing failure or delay in the facility abnormality detection.

  In the present invention, the ARX model in which the value of the data obtained from the monitoring target is determined from the past data value, noise, and the input to the monitoring target is used as the discrete-time linear model. Even when the state of the monitoring target is affected by an external input such as forced external force, the state of the monitoring target can be determined. Therefore, it is possible to monitor the state of the monitoring target such as equipment in the factory under more practical conditions.

  In addition, in this Embodiment, although the form which monitors the state of an installation based on the data which the output sensor 31 and the input sensor 33 measured is not restricted to this, one installation or several Each of the facilities is provided with a plurality of output sensors 31 and input sensors 33, and each of the plurality of output sensors 31 and input sensors 33 is connected to the state monitoring device 1 via the data acquisition device 32 and the communication network N to output each of them. It is good also as a form which monitors the state of one or several installations based on each data which the sensor 31 and the input sensor 33 measured.

  Furthermore, in the present embodiment, a form for monitoring equipment in a factory is shown, but the present invention is not limited to this, and may be a form for monitoring the state of other general devices, It may be a form in which a phenomenon such as a change in the sales amount of a product or a change in a stock price is monitored. For example, in the case of monitoring stock price fluctuations, the value of the stock price at each time is set as a sample time series, and the transaction at each time is set as the input time series, so that the parameter is calculated and a more realistic stock price Predictions can be made.

It is a block diagram which shows the structure of the state monitoring apparatus of this invention. It is a flowchart which shows the operation | movement which the state monitoring apparatus and data acquisition apparatus of this invention perform.

Explanation of symbols

1 state monitoring device 11 CPU (calculation unit)
12 RAM (storage unit)
2 Recording medium 20 Computer program

Claims (6)

A first sample time series {x _n : n = 1, 2,..., N} each of which is composed of N pieces of data (where N is a natural number) and a first one using a computer having a storage unit and a calculation unit. A second sample time series {x _n : n = consisting of L pieces of data for each of the input time series {u _n : n = 1, 2,..., N} (where L is a natural number and L <N). n + 1, n + 2, ..., n + L} and the second input time series _{{u n: n = n +} 1, n + 2, ..., the second sample time series is added to the first sample time series when the n + L} was added The third sample time series and the third input time series obtained by adding the second input time series to the first input time series are applied to the (p, p) -order (where p is a natural number) ARX model. A method for estimating parameters of time,
A first estimated value θ _N representing a parameter estimated value when the first sample time series and the first input time series are applied to a (p, p) -order ARX model is expressed by a matrix of 2p rows and 1 column. Store in the storage unit,
A matrix A defined by the following equation is stored in the storage unit,

Storing the second sample time series and the second input time series in the storage unit;
The matrixes B and D defined by the following formula are calculated by the calculation unit,

A second estimated value θ _{N +} expressing the estimated value of the parameter as a 2p × 1 matrix when the third sample time series and the third input time series are applied to the (p, p) -order ARX model. _L is calculated by the calculation unit using the following equation (a) or (b): θ _{N + L} = θ _N − (L / N) A ⁻¹ D− (L / N) A ⁻¹ Bθ _N ... (a)
θ _{N + L} = θ _N − (L / N) A ⁻¹ D− (L / N) A ⁻¹ Bθ _N
+ (L / N) ² (A ⁻¹ B) ² θ _N + (L / N) ² A ⁻¹ BA ⁻¹ D (b)
A parameter estimation method characterized by Using a computer including a storage unit and a calculation unit, ARX includes a sample time series composed of a plurality of data obtained from a monitoring target that accepts data input and an input time series composed of a plurality of data input to the monitoring target In the method for monitoring the state of the monitoring target based on parameters when applied to a model,
A first sample time series {x _n : n = 1, 2,..., N} composed of N pieces of data (where N is a natural number) obtained from the monitoring target and N pieces of data input to the monitoring target 1p input time series {u _n : n = 1, 2,..., N} is applied to a (p, p) -order (where p is a natural number) ARX model, an estimated parameter value is 2p Storing the first estimated value θ _N expressed in a matrix of rows and columns in the storage unit;
A matrix A defined by the following equation is stored in the storage unit,

A second sample time series {x _n : n = N + 1, N + 2,..., N + L} consisting of L pieces of data (L is a natural number and L <N) obtained from the monitoring target and the monitoring target. A second input time series {u _n : n = N + 1, N + 2,..., N + L} composed of L pieces of data is stored in the storage unit,
The matrixes B and D defined by the following formula are calculated by the calculation unit,

A third sample time series in which the second sample time series is added to the first sample time series and a third input time series in which the second input time series is added to the first input time series (p, p) The second estimated value θ _{N + L in} which the estimated value of the parameter when applied to the next ARX model is expressed by a matrix of 2p rows and 1 column is calculated using the following equation (a) or (b): Calculated in part
θ _{N + L} = θ _N − (L / N) A ⁻¹ D− (L / N) A ⁻¹ Bθ _N (a)
θ _{N + L} = θ _N − (L / N) A ⁻¹ D− (L / N) A ⁻¹ Bθ _N
+ (L / N) ² (A ⁻¹ B) ² θ _N + (L / N) ² A ⁻¹ BA ⁻¹ D (b)
The state monitoring method, wherein the state of the monitoring target is determined by the arithmetic unit based on the second estimated value θ _{N + L} calculated by the arithmetic unit. A first sample time series {x _n : n = 1, 2,..., N} and a first input time series {u _n : n = 1, 2, each consisting of N pieces (where N is a natural number). .., N} is a second sample time series {x _n : n = N + 1, N + 2,..., N + L} and second input each consisting of L pieces of data (where L is a natural number and L <N). When the sequence {u _n : n = N + 1, N + 2,..., N + L} is added, the third sample time series in which the second sample time series is added to the first sample time series and the first input time An apparatus for estimating parameters when a third input time series obtained by adding the second input time series to a series is applied to a (p, p) order (where p is a natural number) ARX model,
A first estimated value θ _N representing a parameter estimated value when the first sample time series and the first input time series are applied to a (p, p) -order ARX model is expressed by a matrix of 2p rows and 1 column. Means for storing;
Means for storing a matrix A defined by:

Means for storing the second sample time series and the second input time series;
Means for calculating matrices B and D defined by:

A second estimated value θ _{N +} expressing the estimated value of the parameter as a 2p × 1 matrix when the third sample time series and the third input time series are applied to the (p, p) -order ARX model. _L to the following formula (a) or (b) means for calculating using the equation _{θ N + L = θ N -} (L / N) a -1 D- (L / N) a -1 Bθ N ... ( a)
θ _{N + L} = θ _N − (L / N) A ⁻¹ D− (L / N) A ⁻¹ Bθ _N
+ (L / N) ² (A ⁻¹ B) ² θ _N + (L / N) ² A ⁻¹ BA ⁻¹ D (b)
A parameter estimation device comprising: The monitoring target based on parameters when a sample time series composed of a plurality of data obtained from a monitoring target that accepts data input and an input time series composed of a plurality of data input to the monitoring target are applied to an ARX model In the device that monitors the state of
A first sample time series {x _n : n = 1, 2,..., N} composed of N pieces of data (where N is a natural number) obtained from the monitoring target and N pieces of data input to the monitoring target 1p input time series {u _n : n = 1, 2,..., N} is applied to a (p, p) -order (where p is a natural number) ARX model, an estimated parameter value is 2p Means for storing a first estimated value θ _N expressed in a matrix of rows and columns;
Means for storing a matrix A defined by:

A second sample time series {x _n : n = N + 1, N + 2,..., N + L} consisting of L pieces of data (L is a natural number and L <N) obtained from the monitoring target and the monitoring target. Means for storing a second input time series {u _n : n = N + 1, N + 2,..., N + L} comprising L pieces of data;
Means for calculating matrices B and D defined by:

A third sample time series in which the second sample time series is added to the first sample time series and a third input time series in which the second input time series is added to the first input time series (p, p) A second estimated value θ _{N + L in} which the estimated value of the parameter when applied to the next ARX model is expressed by a matrix of 2p rows and 1 column is calculated using the following equation (a) or (b): Means,
θ _{N + L} = θ _N − (L / N) A ⁻¹ D− (L / N) A ⁻¹ Bθ _N (a)
θ _{N + L} = θ _N − (L / N) A ⁻¹ D− (L / N) A ⁻¹ Bθ _N
+ (L / N) ² (A ⁻¹ B) ² θ _N + (L / N) ² A ⁻¹ BA ⁻¹ D (b)
Means for determining the state of the monitoring object based on the second estimated value θ _{N + L} calculated by the means. A first sample time series {x _n : n = 1, 2,..., N} and a first input time series {u _n : n = 1, 2, each consisting of N pieces (where N is a natural number). .., N} and a (p, p) -order (where p is a natural number) ARX model, a first estimated value θ _N representing an estimated value of a parameter as a 2p × 1 matrix, Matrix A defined by

A second sample time series {x _n : n = N + 1, N + 2,..., N + L} consisting of L pieces of data (where L is a natural number and L <N), and a second input time series {L} u _n : a computer storing n = N + 1, N + 2,..., N + L}, a third sample time series in which the second sample time series is added to the first sample time series, and the first input time series A computer program for estimating a parameter when a third input time series to which a second input time series is added is applied to a (p, p) order (where p is a natural number) ARX model,
A procedure for causing a computer to calculate matrices B and D defined by the following formulas:

A second estimated value representing an estimated value of a parameter in a 2p × 1 matrix when the computer applies the third sample time series and the third input time series to a (p, p) -order ARX model. theta _{N + L} to the following formula (a) or (b) a procedure for calculating using the equation _{θ N + L = θ N -} (L / N) a -1 D- (L / N) a -1 Bθ _N ... (a)
θ _{N + L} = θ _N − (L / N) A ⁻¹ D− (L / N) A ⁻¹ Bθ _N
+ (L / N) ² (A ⁻¹ B) ² θ _N + (L / N) ² A ⁻¹ BA ⁻¹ D (b)
A computer program comprising: A first sample time series {x _n : n = 1, 2,..., N} consisting of N pieces of data (where N is a natural number) obtained from a monitoring target that accepts data input is input to the monitoring target. Parameters when the first input time series { _n : n = 1, 2,..., N} composed of N pieces of data is applied to a (p, p) -order (where p is a natural number) ARX model. A first estimated value θ _N expressing the estimated value of the above in a 2p × 1 matrix, a matrix A defined by the following equation,

A second sample time series {x _n : n = N + 1, N + 2,..., N + L} consisting of L pieces of data obtained from the monitoring target (where L is a natural number and L <N), and input to the monitoring target has been the L comprising data of the second input time series _{{u n: n = n +} 1, n + 2, ..., n + L} in the computer for storing a computer program for monitoring the state of the monitored object,
A procedure for causing a computer to calculate matrices B and D defined by the following formulas:

The computer includes a third sample time series in which the second sample time series is added to the first sample time series and a third input time series in which the second input time series is added to the first input time series. The second estimated value θ _{N + L in} which the estimated value of the parameter when applied to the (p, p) next ARX model is expressed by a matrix of 2p rows and 1 column is expressed by the following equation (a) or (b): Procedure to calculate
θ _{N + L} = θ _N − (L / N) A ⁻¹ D− (L / N) A ⁻¹ Bθ _N (a)
θ _{N + L} = θ _N − (L / N) A ⁻¹ D− (L / N) A ⁻¹ Bθ _N
+ (L / N) ² (A ⁻¹ B) ² θ _N + (L / N) ² A ⁻¹ BA ⁻¹ D (b)
A computer program comprising: causing a computer to determine the state of the monitoring target based on the calculated second estimated value θ _{N + L.}

Images