CN114970686B - Multi-anomaly-mode-oriented partial information observable equipment fault detection method - Google Patents

Abstract

The invention discloses a fault detection method of part of information observable equipment facing to a multi-anomaly mode, which comprises the steps of firstly establishing a vector autoregressive model of a data stable part and calculating a data integral residual error according to multi-element degradation data acquired offline; secondly, establishing a hidden Markov degradation model capable of reflecting the multi-anomaly mode of the equipment based on residual data, and estimating degradation model parameters by adopting an expectation maximization algorithm; then, using Bayesian theorem to construct Bayesian posterior probability of the equipment in each abnormal mode, and alarming the equipment according to the posterior probability control threshold value and performing comprehensive fault detection; finally, with the aim of minimizing the running cost of the equipment, optimizing the control threshold value of fault detection through an algorithm based on a half Markov decision process to obtain an optimal control threshold value. The invention can screen the abnormal mode of the equipment according to the control threshold value and alarm so as to achieve the purpose of fault detection.

Description

A partial information observable device fault detection method for multiple abnormal patterns

Technical Field

The present invention belongs to the field of fault detection of partial information observable equipment, and in particular relates to a fault detection method for partial information observable equipment in a multi-abnormal mode.

Background technique

As modern equipment develops towards diversified functions and complex structures, it is increasingly difficult to directly observe the internal status of the equipment. The real health status of the equipment can only be evaluated through partial or indirect status information obtained by sensors. Such equipment is called partially observable equipment. Such equipment generally has multiple abnormal modes. If potential abnormalities are not identified and prevented in time, serious failure consequences will result, resulting in irreparable production losses.

Fault detection of partially observable devices is usually based on the use of indirect monitoring information to achieve its detection purpose. Existing methods often target one or several independent abnormal modes, ignoring the correlation between multiple abnormal modes, such as degradation-type abnormalities (wear and tear) or penetration-type abnormalities (water leakage, oil leakage) in the operation of wind turbines. Under different abnormal modes, the degradation process of the same equipment will show significantly different degradation characteristics, which makes fault detection based on partial monitoring information more challenging. In addition, the existing fault detection methods have the disadvantage of high false detection rate for partially observable devices, and their applicability in engineering is relatively low. Therefore, how to effectively detect the faults of partially observable devices under multiple abnormal modes to improve the operational reliability of the equipment is an urgent problem to be solved.

Summary of the invention

The present invention provides a partial information observable device fault detection method for multiple abnormal modes, which can make full use of partial observation information of the device for early fault detection in multiple abnormal modes. By effectively processing partial information, the health index of the device under multiple abnormal modes is constructed, and the possible faults of the device are detected according to the Bayesian posterior probability under each abnormal mode, and economical maintenance measures are provided.

The present invention can be solved by the following technical solutions:

A method for detecting partial information observable device faults in multiple abnormal modes, comprising the following steps:

(1) Data preprocessing process of partially observable equipment: collect multivariate degradation data of the equipment, select the stable part of the data history to establish a vector autoregression model, and calculate the residual of the entire data set so that the preprocessed data meets the multivariate normality;

(2) State modeling and parameter optimization of partially observable equipment: Based on the obtained residual sequence, a continuous-time hidden Markov process ( _Xt : t∈R ₊ ) is established with the healthy state as 0, the abnormal state as 1,…,M, and the fault state as M+1. The state transition probability of the equipment is _Pij (t)＝P( _Xt ＝ _jX0 ＝i), and its transition rate _λ00 ,…,λMM ₊₁ is estimated using the expectation maximization algorithm;

(3) Fault detection method for multiple abnormal modes: Establish the posterior probability of the device being in abnormal state 1, ..., M respectively As an indicator reflecting the health status of the equipment, the Bayesian theorem is used to update the posterior probability of each abnormal state when obtaining the observation value of the new sampling period. The high-risk posterior probability is screened out according to the control threshold and an alarm is issued to achieve the purpose of fault detection. With the goal of minimizing the long-term expected average cost of the equipment, the optimal control threshold of the fault detection method is solved through the calculation algorithm under the semi-Markov decision process.

Furthermore, the implementation process of step (1) is as follows:

First, the stationary part of the collected multivariate monitoring data is expressed as Then assume that the data in the stationary part follows a stationary vector autoregressive process:

Where p∈N is the order of the model; δ ₀ ∈R ² is the process mean of the stationary part; Φ _r ∈R ^2×2 is the autocorrelation matrix; ε _n is the error term that obeys the normal distribution N ₂ (0,Ω). The least squares method can be used to estimate the parameters of the model as Substituting the parameters into the model, the residual of the monitoring data can be calculated as

Furthermore, the implementation process of step (2) is as follows:

The state process of the equipment is established as a continuous-time hidden Markov process with M+2 states ( _Xt : t∈R ₊ ), where the healthy state is 0, the fault state is M+1, and there are M abnormal states in the middle, representing M abnormal modes. The state space is defined as S={0,...,M+1}; the state transition probability of the equipment is _Pij (t)=P( _Xt =j| _X0 =i), and its transfer rate _λ00 ,...,λMM ₊₁ is estimated by the expectation maximization algorithm. The calculated state transition probability matrix can be expressed as:

During the observation process, each observation vector is conditionally independent and obeys the multivariate normal distribution N _m (μ _m ,Σ _m ), m∈{0,...,M} under its corresponding state. Therefore, the probability density function of the residual under abnormal state m can be expressed as:

Furthermore, the implementation process of step (3) is as follows:

Calculate the posterior probability that the device is in abnormal mode m respectively Where m∈{1,...,M}, under the condition of collecting the observation sequence Y ₁ ,...,Y _n-1 , the posterior probability of the device at the n-1th sampling time can be calculated as:

According to Bayesian theorem and the obtained state transition probability matrix P(t) = [P _ij (t)] _i,j∈S , the posterior probability that the device is in abnormal mode m at the nth sampling time is Can be updated to:

And, the conditional reliability function can be calculated as:

By monitoring the posterior probability of the device being in each abnormal mode Whether it exceeds the corresponding control threshold W ¹ ,...,W ^M to detect faults. If the indicator is lower than the threshold, it means that the equipment operation risk is low and continues to be monitored. Once any An alarm is triggered and the equipment is shut down for inspection. If the detected fault matches the identified abnormal pattern, it is judged as a true alarm and preventive maintenance is provided to restore the equipment to its original condition. Otherwise, it is a false alarm and minor adjustments are made to restore the equipment to its original condition.

Furthermore, after calculating the posterior probability of the device being in each abnormal mode, it is necessary to determine the optimal control threshold of the posterior probability of the device in each abnormal mode. According to the cost minimization criterion, the control threshold is optimized through the policy iteration algorithm under the SMDP framework.

The fault detection scheme proposed in this invention aims to achieve the minimum long-term expected average cost per unit time. TC is defined as the total operation and maintenance cost of the equipment in a cycle, CL is defined as the time length of the equipment in a cycle, and the control threshold is defined as W ¹ ,...,W ^M ∈(0,1). According to the update theory, this problem is equivalent to finding the optimal control threshold So that:

This problem is solved using a policy iteration algorithm based on the SMDP framework.

Furthermore, the establishment of the SMDP framework requires the determination of its state space. First, the interval [0,1] of the posterior probability is divided into L equal parts. Assume that the posterior probability of the device being in abnormal mode m is obtained at the nth sampling. When it is in the interval [(i-1)/L,i/L), SMDP is defined at state (i,m). The state set is represented as L ₁ ={(i,m)|i=1,...,W ^m L}, where the first element is the state value of the posterior probability interval and the second element is the abnormal mode number of the device. When it exceeds the corresponding control threshold W ^m , the equipment is stopped and a comprehensive inspection is carried out. If the detected fault is consistent with the abnormal mode m, it is proved to be a true alarm, and the SMDP state is defined in state I ₁ to provide corresponding preventive maintenance measures to restore the equipment to the initial state (0, m); if the detected fault is inconsistent with the abnormal mode m or the equipment is fault-free, the SMDP state is defined in state I ₀ , and fine-tuning is carried out to restore the equipment to a new state (0, m); if a random fault occurs during operation, the SMDP state is defined in F, and fault maintenance is provided to restore the equipment to a new state (0, m).

The initial state set, inspection state set and fault repair state set are represented as: L ₀ ={(0,m)}, L ₂ ={I ₀ ,I ₁ } and L ₃ ={F} respectively, so the state space of SMDP is L =L ₀ ∪L ₁ ∪L ₂ ∪L ₃ .

According to the defined SMDP state space, the necessary elements of SMDP need to be derived before optimization: transition probability, average residence time and average cost, which are defined as follows:

P _k,r : the probability that the current device is in state k∈L and changes to state r∈L at the next decision moment;

T _k : the expected dwell time of the device in state k∈L from the current decision moment to the next decision moment;

C _k : the expected cost of the device in state k∈L from the current decision moment to the next decision moment;

For a given control threshold W ¹ ,...,W ^M , the equipment operation cost g(W ¹ ,...,W ^M ) can be obtained by solving the following linear equations:

Where (i,m)∈L;

u _(s,m) = 0 for any (s,m)∈L.

The calculation formula of SMDP element is as follows:

Transition probability:

_PF,(0,m) = 1

Expected residence time

τ _F = _TF

Among them, _TI , T _Pr , _TF and are the time spent on comprehensive inspection, preventive maintenance and corrective maintenance respectively.

Expected costs

C _(i,m) = C _S ,(i,m)∈L ₁

_CI0 = _CI

C _I1 = C _I + C _Pr

_CF = _CF

Among them, _CS , _CI , C _Pr , _CF and are the costs of sampling, comprehensive inspection, preventive maintenance and corrective maintenance respectively.

The beneficial effects of the present invention are embodied in:

Based on the acquired multivariate monitoring data, a partial information observable equipment degradation model under multiple abnormal modes is established, and the expectation maximization algorithm is used to estimate the model parameters. The posterior probability of the equipment in multiple abnormal modes is constructed to reflect the operating risk of the equipment. The high-risk posterior probability is screened out according to the control threshold and an alarm is issued to achieve the purpose of fault detection. The present invention better solves the fault detection problem of partial information observable equipment with multiple abnormal modes, improves the accuracy and efficiency of equipment fault detection, and ensures the performance and safety of the equipment.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart of the present invention.

Figure 2 Real multivariate measurements of pump history data #1

Figure 3. Real multivariate measurements of pump history data #2

Figure 4 Residual distribution under two abnormal modes

Figure 5 Residuals of two historical data after data preprocessing

Figure 6 Fault detection process for abnormal mode 1 (historical data #1)

Figure 7 Fault detection process for abnormal mode 2 (historical data #1)

Figure 8 Fault detection process for abnormal mode 1 (historical data #2)

Figure 9 Fault detection process for abnormal mode 2 (historical data #2)

Detailed ways

The following describes the implementation of the present invention through specific embodiments. Those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification.

Referring to FIG. 1 , a method for detecting a partial information observable device fault in multiple abnormal modes according to the present invention specifically includes the following steps:

Step 1: Build an offline model: The present invention uses the actual diagnostic data of a pneumatic diaphragm pump for case verification. The device is a partially observable device whose internal degradation is not directly observable, and is used to pump corrosive and flammable liquids driven by compressed air. Different abnormal modes of the pump will lead to different degradation trends. For example, abnormal valve core wear will lead to increased pump operating frequency and output pressure; abnormal inlet blockage will lead to increased pump operating frequency and decreased output pressure. Therefore, the real state of the pump equipment can be indirectly reflected by monitoring the output pressure and operating frequency of the pump.

The operating frequency and pressure are sampled every 10 hours as multivariate observations through the magnetic induction of the diaphragm drive shaft and the pressure sensor respectively. Through monitoring, the pump has two modes: valve core abnormality (abnormal mode 1) and air inlet abnormality (abnormal mode 1). A total of 27 sets of multivariate degradation data of the pump were collected in the experiment, including U=12 sets of valve core failure data and V=15 sets of air inlet failure data. Figures 2 and 3 show two historical data of the pump respectively. In the first line, the observation value is relatively stable from the 1st to the 13th moment, which is regarded as the observation value of the stable/healthy part. After the 14th sampling moment, the observation value becomes unstable and shows a positively correlated upward trend, which is regarded as the observation value under abnormal mode 1. In the second line, the observation values from the 1st to the 15th moment all belong to the healthy part. After the 16th sampling moment, the observation value becomes unstable and the two signals show a negative correlation, which is regarded as the observation value under abnormal mode 2. Select the stable part of all historical data Then assume that the data in the stationary part follows a stationary vector autoregressive process:

The model best estimate is obtained by the least squares method. It can be calculated that:

And the residual for the entire data set can be calculated as:

The residual distributions under the two abnormal modes are shown in Figure 4. Among them, ‘○’ is the binary residual of the healthy part, ‘*’ is the binary residual under abnormal mode 1, and ‘△’ is the binary residual under abnormal mode 2.

After calculation, the residual calculation results of the two historical data of Figures 2 and 3 are shown in Figure 5. The solid line represents the pressure measurement value, and the dotted line represents the frequency measurement value.

After data preprocessing, this case uses the residuals to establish a hidden Markov model with four states to describe the degradation process of the pump, where the healthy state is 0, the fault state is 3, and there are two abnormal states in the middle, 1 and 2 (corresponding to the valve core wear abnormality and the air inlet blockage abnormality, respectively). In addition, only the fault state is observable, and the other states are unobservable. The state space is defined as S = {0,1,2,3}. The state process ( _Xt : t∈R ₊ ) is represented as a multivariate continuous-time hidden Markov chain, where _Xt∈S .

The expectation maximization algorithm is used to estimate the model parameters. The partial information can be used to observe the optimal parameters of the equipment degradation model. and The estimation process is shown in Table 1.

Table 1 Hidden Markov model parameters estimated using the EM algorithm

Schedule

The estimated state parameters Substituting into the Kolmogorov backward differential equation, the state transition probability matrix can be calculated:

The estimated observation parameters Substituting into the probability density function of the residual, we can get:

Step 2: Development and optimization of fault detection schemes: Establish the a posteriori probability of the device being in two abnormal modes respectively and Then, using Bayes’ theorem, after obtaining the new observation value _Yn, and To update:

The control threshold of the fault detection scheme is defined as W ¹ ,W ² ∈(0,1). According to the update theory, the problem of minimizing the long-term expected average cost of the equipment is equivalent to finding the optimal control threshold So that:

To calculate the optimal control threshold You need to define the SMDP framework first. Discretize into L = 20 finite states. Secondly, define fixed cost parameters _CS = 5, _CI = 100, C _Pr = 300, _CF = 1500 and time parameters _TI = 1, _TPr = 1, _TF = 8. Through calculation, the following three elements in the SMDP framework can be obtained.

Transition probability:

P _F,0 ＝1

Expected residence time

τ _F = _TF

Expected costs

C _(i,m) = C _S ,(i,m)∈L ₁

_CF = _CF

For given control limits W ¹ , W ² , the long-term expected average cost g(W ¹ , W ² ) can be obtained by solving the following linear equations:

Where (i,m)∈L;

u _(s,m) = 0 for any (s,m)∈L.

After iterative calculation, the optimal control threshold is obtained as The corresponding minimum long-term expected average cost is

Step 3 Online monitoring: After obtaining the optimal control threshold of this solution, the pneumatic diaphragm pump can be fault detected. The case provides the fault detection process of two historical data of the pump equipment, as shown in Figures 6, 7, 8 and 9.

In Figures 6 and 7, the device first starts running from a new state and is monitored at a constant sampling interval. In the first 13 moments, the posterior probability of the device being in the two abnormal modes is lower than the respective control thresholds. At the 14th sampling moment, the posterior probability of the device being in abnormal mode 1 is updated to 0.2695, which is higher than the set control threshold. The device actively alarms. At this time, the posterior probability that the device is in abnormal mode 2 is still lower than the threshold Therefore, the fault detection result provided by the method is: the equipment has abnormal mode 1 which may cause valve core failure. After a comprehensive shutdown inspection, it is found that the equipment valve core is severely worn and there is a fault, so the alarm signal generated by the proposed method is determined to be true.

In Figures 8 and 9, the device operates well in the first 15 sampling moments, and the posterior probabilities of the two abnormal modes are lower than their corresponding control thresholds. At the 16th moment, the posterior probability of the device in abnormal mode 2 suddenly increases and exceeds the control threshold. The alarm is triggered, and the posterior probability that the device is in abnormal mode 1 is still lower than the threshold Therefore, the fault detection result provided by the method is: the equipment has abnormal mode 2 which may cause the air inlet fault. After a comprehensive shutdown inspection, it was found that there was a large amount of viscous liquid in the pump air inlet filter screen, indicating a fault, so the alarm signal generated by the proposed method was determined to be true.

Utilizing the above technical methods, the present invention designs a method for partially information observable equipment fault detection for multiple abnormal modes, which can perform data preprocessing on the acquired multivariate degradation data and perform state modeling for the multiple abnormal modes of partially information observable equipment. The equipment risk is revealed by monitoring the posterior probability of the equipment in each abnormal mode, and the high-risk posterior probability is screened out according to the control threshold obtained after optimization to perform fault detection. The method has been algorithmically verified and case-tested using real multivariate diagnostic data of pneumatic diaphragm pumps. The results show that the method can effectively identify the abnormal mode of the pump based on the multivariate degradation data monitored online, and can detect the potential faults of the pneumatic diaphragm pump. The method ensures the accuracy of fault detection and can take appropriate maintenance measures to prevent the occurrence of faults. While the performance and safety of the equipment are improved, the operation and maintenance costs are also saved.

The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims (7)

1. The fault detection method of the part of information observable equipment facing to the multi-anomaly mode is characterized by comprising the following steps of:

(1) Data preprocessing process of part of information observable equipment: fitting the acquired multi-element monitoring data by using a vector autoregressive model, and calculating residual errors between a predicted value of the vector autoregressive model and a true value of the data, wherein the obtained residual errors meet multi-element normalization;

(2) State modeling and parameter estimation of part of information observable equipment: establishing a continuous time hidden Markov process (X _t:t∈R₊) with the health state of 0, the abnormal state of 1, …, M and the fault state of M+1 according to the obtained residual sequence; the state transition probability of the device is P _ij(t)＝P(X_t＝j|X₀ =i), and the transition rate lambda ₀₀,...,λ_MM+1 is estimated by using a expectation maximization algorithm;

(3) The fault detection method for the multi-anomaly mode comprises the following steps: establishing a posterior probability under M, respectively, that the device is in an abnormal state 1 As an index reflecting the health condition of the equipment, using the bayesian theorem, updating posterior probability under various abnormal states when obtaining the observed value of a new sampling period, screening the posterior probability of high risk according to a control threshold value, alarming to achieve the purpose of fault detection, and solving the optimal control threshold value of the fault detection method through a half Markov decision process algorithm with the minimum equipment operation and maintenance cost as a target.

2. The method for detecting a failure of a part of information observable equipment facing a multi-anomaly mode according to claim 1, wherein the implementation process of the step (1) is as follows:

First, the stationary part of the acquired multivariate monitoring data is expressed as The stationary part of the data was fitted using a vector autoregressive process:

Wherein p ε N is the order of the model; Delta ₀∈R² is the plateau process mean; Φ _r∈R^2×2 is an autocorrelation matrix; epsilon _n is the error term that obeys the normal distribution N ₂ (0, Ω);

Finally, estimating the model parameters by using a least square method to obtain the model parameters as Substituting the parameters into the model to calculate residual error of the monitoring data as

3. The method for detecting a failure of a part of information observable equipment facing a multi-anomaly mode according to claim 1, wherein the implementation process of the step (2) is as follows:

the state process of the device is established as a continuous time hidden markov process (X _t:t∈R₊) with m+2 states, where the healthy state is 0, the faulty state is m+1, there are M abnormal states in between, representing M abnormal modes, and the state space is defined as s= { 0..a., m+1}; the state transition probability of the device is P _ij(t)＝P(X_t＝j|X₀ =i), the transition rate lambda ₀₀,...,λ_MM+1 is estimated by the expectation maximization algorithm, and the calculated state transition probability matrix can be expressed as:

During observation, each observation vector is independent of conditions and obeys the multivariate normal distribution N _m(μ_m,Σ_m under its corresponding state), M e {0,..m }, the probability density function of the residual in the abnormal state M can be expressed as:

4. The method for detecting a failure of a part of information observable equipment facing a multi-anomaly mode according to claim 1, wherein the implementation process of the step (3) is as follows:

When the observation sequence Y ₁,...,Y_n-1 is acquired, the posterior probability of the nth-1 sampling point device in the state corresponding to the mth abnormal mode can be expressed as follows:

According to the Bayesian theorem and the obtained state transition probability matrix P (t) = [ P _ij(t)]_i,j∈S ], posterior probability of the nth sampling point device in the state corresponding to the abnormal mode m The updating method can be updated as follows:

and, the conditional reliability function may be calculated as:

by monitoring the posterior probability of the device being in various abnormal modes Whether the corresponding control threshold W ¹,...,W^M is exceeded or not is used for fault detection, if the index is lower than the threshold, the running risk of the equipment is lower, the monitoring is continued, and once any one is detectedAnd alarming and carrying out equipment shutdown checking, if the checked faults are consistent with the identified abnormal modes, judging the equipment to be truly alarming and providing preventive maintenance to enable the equipment to be restored as new, otherwise, carrying out false alarming, and enabling the equipment to be restored as new after carrying out micro adjustment.

5. The multi-anomaly-oriented partial information observable equipment fault detection method of claim 4, wherein the objective of the fault detection method is to achieve a minimum operation and maintenance cost per unit time, which is equivalent to finding an optimal control threshold according to an update theorySuch that:

wherein TC and CL respectively represent the total operation and maintenance cost and the time length of the equipment in one period, and the fault detection method adopts an SMDP-based algorithm to solve the optimal control threshold and the minimum long-term expected average cost.

6. The multi-anomaly mode oriented partial information observable device failure detection method of claim 5, wherein the SMDP establishment requires determining its state space: firstly, dividing a value interval [0,1] of posterior probability into L equal parts, and supposing that posterior probability of the device in an abnormal mode m is obtained in nth samplingWhen the SMDP is positioned in the interval [ (i-1)/L, i/L), the SMDP is defined in a state (i, m), the state set is expressed as L ₁＝{(i,m)|i＝1,...,W^m L }, wherein the first element is a state value of a posterior probability interval, and the second element is an abnormal mode number of equipment; posterior probability whenWhen the detected fault exceeds the corresponding control threshold W ^m, stopping the equipment and performing comprehensive inspection, if the detected fault accords with the abnormal mode m, proving to be a true alarm, and defining the SMDP state in the state I ₁ to provide corresponding preventive maintenance measures to enable the equipment to be restored to the initial state (0, m); if the detected fault does not accord with the abnormal mode m or the equipment does not have the fault, defining the SMDP state in a state I ₀, and performing fine tuning to restore the equipment to a new state (0, m); if random faults are generated in the operation process, defining the SMDP state as F, and providing fault maintenance;

the initial state set, the inspection state set, and the trouble maintenance state set are expressed as: l ₀＝{(0,m)},L₂＝{I₀,I₁ and L ₃ = { F }, so the state space of SMDP is l=l ₀∪L₁∪L₂∪L₃.

7. The multi-anomaly mode oriented partial information observable device fault detection method of claim 6, wherein the SMDP based algorithm includes three elements, transition probability, expected residence time, and expected cost, defined as follows:

P _k,r: probability that the current device is in state k epsilon L and is converted into state r epsilon L at the next decision moment;

T _k: the device is in state k epsilon L, and the expected residence time from the current decision time to the next decision time;

C _k: the equipment is in a state k epsilon L, and the expected cost from the current decision time to the next decision time;

for a given control threshold W ¹,...,W^M, the running cost of the device g (W ¹,...,W^M) can be obtained by solving a system of linear equations:

Wherein (i, m) ε L;

u _(s,m) = 0 for any one (s, m) ∈l;

the calculation formula of the transition probability is as follows:

P_F,(0,m)＝1；

The expected residence time is calculated as follows:

τ_F＝T_F

wherein T _I、T_Pr、T_F and the time spent for the total inspection, preventive maintenance and corrective maintenance, respectively;

the expected cost is calculated as follows:

C_(i,m)＝C_S,(i,m)∈L₁

C_F＝C_F

Wherein C _S、C_I、C_Pr and C _F are costs spent for sampling, general inspection, preventive maintenance and corrective maintenance, respectively.