CN111027719B

CN111027719B - Multi-component system state opportunity maintenance optimization method

Info

Publication number: CN111027719B
Application number: CN201911111521.3A
Authority: CN
Inventors: 肖雷; 汤俊萱; 鲍劲松
Original assignee: Donghua University
Current assignee: Donghua University
Priority date: 2019-11-14
Filing date: 2019-11-14
Publication date: 2023-06-20
Anticipated expiration: 2039-11-14
Also published as: CN111027719A

Abstract

The invention relates to a multi-component system state opportunity maintenance optimization method. When the equipment maintenance strategy is formulated, not only the current state of the equipment, but also the future degradation trend and failure probability of the equipment are considered. Only if the future degradation trend of the equipment is accurately known, the maintenance strategy can be formulated better. According to the situation, the invention compares various prediction algorithms, establishes equipment degradation prediction and residual life prediction models aiming at a single individual on the basis of analyzing the state monitoring signals of the equipment, and establishes an opportunity state maintenance model of the multi-component equipment under a long task period by considering the structure of the system and the length of the task period. The invention uses advanced signal acquisition technology and signal processing technology, realizes the implementation detection and real-time prediction of the system, and expands the theory and method of the maintenance of the equipment opportunity based on the state.

Description

Multi-component system state opportunity maintenance optimization method

Technical Field

The invention relates to a maintenance scheme optimization technology based on states of a multi-component system. Specifically, considering the characteristics of different products, combining engineering practice conditions, establishing an individual life prediction model of the equipment under the condition of no failure data and tail cutting data, applying the model to a multi-component system, and establishing a maintenance optimization model of the equipment in the multi-component system based on states.

Background

In engineering practice, reasonable maintenance of equipment is often an important means of improving the reliability of the equipment. The multi-component system is often maintained by an individual maintenance or group maintenance method, and the two maintenance modes cause frequent shutdown and startup or waste of component service life. When maintenance is implemented, equipment is often required to be stopped, so that the equipment maintenance can occupy the production and processing time of the equipment, and further the completion time of processing tasks is delayed. Therefore, in order to schedule the production process tasks, it is necessary to consider the influence of maintenance of the equipment on the production tasks in addition to the information on the process tasks themselves. In addition, when the maintenance strategy of the equipment is formulated, not only the current state of the equipment is considered, but also the future degradation trend and failure probability of the equipment are considered. A more scientific and reasonable maintenance strategy is often obtained on the basis of accurate state evaluation and predictive analysis. Conventional event data methods often require a large amount of failure data or tail-biting data. However, for new products and new devices, the state monitoring data of the same products are less, and sometimes, the failure data is less due to the safety and reliability. In this case, it is particularly important how to build a predictive model of the device, and thus a state maintenance model of its device.

Disclosure of Invention

The purpose of the invention is that: considering the characteristics of different prediction methods, combining engineering practice conditions, establishing an individual life prediction model of the equipment under the condition of no failure data and tail cutting data, applying the model to a multi-component system, and establishing a maintenance optimization model of the equipment in the multi-component system based on states.

In order to achieve the above purpose, the technical scheme of the invention is to provide a multi-component system state opportunity maintenance optimization method, which is characterized by comprising the following steps:

the first step, single component degradation prediction is carried out, and the method comprises the following steps of;

step 1, performing state monitoring on a part, extracting degradation characteristics capable of reflecting degradation conditions of the part, and representing a degradation characteristic vector of a component i at a time t as D _i,t ；

Step 2, calculating an initial degradation growth rate of the component i, which comprises the following steps:

an initial time window ws is given ₀ And a start prediction time point STP, assuming that all components are under the same state monitoring strategy, the degradation characteristic of component i within the time window is denoted as W _i,1 and W_i,2 ，W _i,1 and W_i,2 Is scaled by the initial time window ws ₀ And the feature extraction method is determined by:

in the formula ,D_i,STP Representing the degraded feature vector of component i at point in time STP. And has:

in the formula ,M_i,1 and M_i,2 Respectively W _i,1 and W_i,2 If M is the average value of _i,1 and M_i,2 Is multidimensional, one of which is selected as the main element for calculation,

and />

Is the corresponding mean value in the main element and is used for calculating the initial degradation growth rate;

initial degradation growth rate r _i,0 For the ratio of the average values in two adjacent time windows, there is

Step 3, the initial degradation growth rate r _i,0 If r, compared with the floating factor f _i,0 >(1+f) if the degradation speed is relatively high in a relatively short period of time, step 5 is executed to detect degradation abnormality. Otherwise, step 4 is performed, wherein the floating factor f is used to account for the stability of the trend of degradation and its acceptable range;

step 4, compressing the time window step by step, if the calculated degradation growth rate is smaller than (1+f), removing the leftmost two features in the left time window, at this timeAfter one compression, the time window becomes: ws (what is) ₁ ＝ws ₀ -1, recalculating the degradation growth rate in the corresponding compression time window by adopting the method of the step 2, and repeating the step 4 until the degradation growth rate is not less than (1+f), wherein after the k-step compression, the characteristics, the mean value and the degradation growth rate in the time window are shown as follows:

in the formula ,W_i,k1 and W_i,k2 Is a characteristic matrix after being compressed in k steps, ws _i,k For the corresponding time window size, M _i,k1 and M_i,k2 Is W _i,k1 and W_i,k2 Mean value of r _i,k Is the corresponding degradation growth rate;

step 5, if r _i,k >(1+f), degradation anomaly detection is performed: defining h as an alert value if the feature matrix W _i,k2 Exceeding h, a smaller time window ws _s For detecting degradation anomalies if in the time window ws _s The characteristics on the right side of the middle are all compared with W _i,k2 The remaining features in (a) are large, in which case degradation is considered abnormal, otherwise, degradation is considered stable;

step 6, determining a training sample:

if a degradation anomaly is detected in step 5, then in a time window ws _s Is used to train an ANN; if no degradation abnormality occurs, thenW _i,k1 and W_i,k2 The input samples and the output samples are used for training the ANN, and the number of neurons of the input layer and the output layer is the same;

step 7, executing prediction

When the degradation abnormality occurs and is detected, predicting by using a linear model, stopping prediction when the predicted value exceeds a preset failure threshold value, and if the extracted degradation characteristic is multidimensional, predicting by using a main element and comparing with the preset failure threshold value;

when the degradation abnormality does not occur, the ANN is used for prediction, and multi-step advanced prediction is performed; at each prediction there is ws _i,k The individual degradation characteristics are predicted. Rolling prediction is performed according to the following formula:

during the training process of the ANN,

and />

Is used as input and output of training samples, then the degradation characteristic->

For predicting degenerative characteristics->

In each prediction there is ws _i,k The individual degradation features are predicted;

step 8, performing failure risk assessment

The risk of failure of a component can be expressed by a degradation characteristic expressed in terms of:

WD _i ＝[D _i,1 ；D _i,2 ；…；D _i,STP ；WPD _i,P ]

the above formula includes two parts, one part is degradation characteristic extracted from state monitoring data, and the other part is predicted degradation characteristic, wherein WD _i Is the overall degradation characteristic of component i; d (D) _i,1 ；D _i,2 ；…；D _i,STP Is a known part; WPD (Wireless Power distribution) _i,P Including degradation features predicted from an ANN or linear model, all of which are normalized according to the following equation:

the failure risk calculation is then performed according to the following equation:

in the formula ,WDN_i For the normalized degenerate feature matrix of component i, cumsum represents the sum, FR _i To accumulate failure risk vectors, which monotonically increase between intervals (0, 1), FR _i ＝[F _i,1 ；F _i,2 ；......；F _i,T ]，F _i,T Is the failure risk of component i at time T, T being the predicted failure time;

and secondly, performing multi-component system opportunistic substitution modeling based on the single component degradation prediction result obtained in the first step, wherein the method comprises the following steps of:

during the mission period, the total cost of the system is expressed as:

C _Total ＝C _EF +C _EP +C _DA

in the formula ,C_Total Is the total cost, C _EF C for failure replacement of desired costs _EP To prevent replacement of desired costs, C _DA For total disassembly and installation costs;

for the problem of determining how many components need to be replaced simultaneously during each replacement, firstly defining a current cost rate function, assuming that N positions in the system are used for installing the key components, replacing N components together, replacing m components together, and replacing the rest components independently, wherein the corresponding current cost rate calculation formula is as follows:

t≥STP,n≤N.

t≥STP,m≤N.

t≥STP,l＝1,2,...,N-n-m.

in the formula ,C_Rscn Cost rate for n components to replace together, C _Rscm Cost rate for m components to replace together, C _Rscl Cost rate for component individual replacement, C _f To replace cost for one time failure, C _p To prevent replacement cost once, F _x,t 、F _y,t and F_l,t For component x, component y and component l at time t, c _DA For one disassembly and assembly cost, since the components may be replaced simultaneously, the disassembly and assembly costs may be shared by each component, for a total cost rate C _R The calculation formula is as follows:

in the formula ,

and />

Minimum cost rate for a group of replacement components, +.>

Minimum cost rate for an individually replaced component;

by analyzing all cases, the case with the minimum total cost rate is selected as the optimal replacement case, and assuming that the replacement case is the optimal replacement policy, the optimal replacement time of each sub-case is:

wherein ,

and />

Optimal replacement time for replacement of components in groups, +.>

For the optimal time of the individual replacement of the components, the corresponding optimal replacement time T _S,t The method comprises the following steps:

the theoretical optimal replacement time is

For the minimum value thereof, +.>

A first replacement time for the scenario; as the detection time advances, the predicted values of remaining life and failure risk also change, and therefore, the replacement strategy should also be dynamically adjusted:

defining a conservation time window to determine possible replacement time, wherein the conservation time window is positioned on the right side of the STP, if the STP is not smaller than the minimum value in the conservation time window, immediately replacing, after replacing, recalculating the current cost rate and the optimal replacement strategy, and repeatedly executing prediction-replacement until the task period is met.

Preferably, in step 6, if a degradation anomaly is detected in step 5, the degradation anomaly is detected in a time window ws _s The following simplified linear model is used for prediction:

d _i,t ＝a _i ×t+b _i +ε _i,t

in the formula ,a_i and b_i Is a parameter of the linear model; epsilon _i,t Is the measurement error of the component i at the time t; d, d _i,t Is the degenerate element selected for prediction.

Preferably, in step 7, after each prediction, the prediction result is processed according to the following formula:

the above formula is based on two assumptions: one assumption is that the degree of degradation of the component increases with time of service; another assumption is that since no degradation anomaly occurs, the degree of degradation is smooth, and the predicted termination condition is the following:

if PD _i,t' ×r _i,k ≥H,then RUL _i ＝t'-STP

if PD _i,t' ×r _i,k <H,then performing rolling prediction

in the formula ,ND_i,t' To normalize degradation characteristics of component i at any time t', PD _i,t' Is the predicted degradation characteristic after inverse normalization, H is a predetermined failure threshold, RUL _i Is the remaining life of component i

The invention has the following advantages:

1. the model provided by the invention is provided from the engineering practice angle by combining the theoretical significance of different methods, and is favorable for guiding the engineering practice, so that certain economic value can be brought to a factory or the safe operation of equipment can be ensured.

2. The degradation prediction and residual life prediction method adopted by the invention can achieve better prediction results by only using partial data instead of all state monitoring data.

Drawings

FIG. 1 is a comparison of time windows before and after a compression window;

fig. 2 is an illustration of alternative policy selection.

Detailed Description

The invention will be further illustrated with reference to specific examples. It is to be understood that these examples are illustrative of the present invention and are not intended to limit the scope of the present invention. Further, it is understood that various changes and modifications may be made by those skilled in the art after reading the teachings of the present invention, and such equivalents are intended to fall within the scope of the claims appended hereto.

The invention provides a multi-component system state opportunity maintenance optimization method, which comprises the following steps:

the method of the invention is part 1: single component degradation prediction method

And 1, performing state monitoring on the parts, and extracting degradation characteristics capable of reflecting degradation conditions of the parts. In this section, component i is at time tThe degraded eigenvector is denoted as D _i,t . D is to be noted _i,t Either one-dimensional or multi-dimensional. Its dimensions are affected by the feature extraction method. For example, if the peak is extracted as a degradation feature, it is one-dimensional. If wavelet packet analysis is used, db4 is wavelet base and the number of decomposition layers is three, then it is eight-dimensional.

And 2, calculating the initial degradation growth rate of the component i. First, an initial time window ws is given ₀ And a start prediction time point STP. Herein, ws ₀ And STP is not related to component i. Because it is assumed that all components are under the same state monitoring policy. The degradation characteristic of component i over the time window is denoted as W _i,1 and W_i,2 ，W _i,1 and W_i,2 Is of the scale of ws ₀ And feature extraction method decisions. Wherein STP, ws ₀ 、W _i,1 and W_i,2 The relationship of (2) is shown in FIG. 1.

In the formulas (2) and (3), M _i,1 and M_i,2 Respectively W _i,1 and W_i,2 Is a mean value of (c). And W is equal to _i,1 and W_i,2 Similarly, M _i,1 and M_i,2 It may also be multidimensional. If M _i,1 and M_i,2 Is multidimensional. One of the dimensions is selected as the primary element for computation.

and />

Is the corresponding mean value in the main element for calculating the initial degradation growth rate r _i,0 . As shown in equation (3), the degradation growth rate is the ratio of the average values over two adjacent time windows.

The mean can reflect the overall degradation information over a time window. The degree of degradation of a component increases as its length of service increases. As the degradation features extracted from the condition monitoring tend to increase in volatility due to workload or other factors, it is difficult to obtain a monotonically increasing trend to reflect the degradation of the component. Thus, the ratio of the mean values is used to account for the degradation trend over the time window.

And 3, comparing the initial degradation growth rate with a floating factor. The floating factor f is the stability used to illustrate the tendency of degradation and its acceptable range. In general, f is set in the interval [0,0.1 ]]Between them. If r _i,0 >(1+f) if the degradation speed is relatively high in a relatively short period of time, step 5 is executed to detect degradation abnormality. Otherwise, step 4 is executed.

And 4, compressing the time window step by step. The compression direction is shown in fig. 1. If the calculated degradation growth rate is less than (1+f), the leftmost two features within the left time window are removed. At this time, after one compression, the time window becomes: ws (what is) ₁ ＝ws ₀ -1, the degradation growth rate in the corresponding compression time window is recalculated. This step is repeated until the degradation growth rate is not less than (1+f). After the compression of k steps, the characteristics, the mean value and the degradation growth rate in the time window are shown in the formulas (4) to (6).

In the formulae (4) to (6), W _i,k1 and W_i,k2 Is a characteristic matrix after being compressed in k steps, ws _i,k For a corresponding time window size. M is M _i,k1 and M_i,k2 Is W _i,k1 and W_i,k2 Mean value of r _i,k Is the corresponding degradation growth rate.

Step 5 if r _i,k >(1+f), degradation abnormality detection is performed. Define h as an alert value. If at W _i,k2 Exceeding h, a smaller time window ws _s For degradation anomaly detection. If at ws _s The characteristics on the right side of the middle are all compared with W _i,k2 The remaining features in (a) are large, in which case degradation is considered abnormal, otherwise, degradation is considered stable. W is illustrated in FIG. 1 _i,k1 and ws_s Is a relationship of (3).

Two possibilities need to be considered, step 4 and step 5, one is that at step 4, no feature is left after compression. If this occurs, no degradation prediction is necessary, as degradation is deemed slow, and the defect takes a long time to degrade to failure. Another situation is that in step 4 there are few features left when the end condition is reached. These remaining features are introduced into step 5 and abnormal degradation detection is performed. If an anomaly occurs, the linear model in step 6 is used for prediction, otherwise, no prediction is performed, because the amount of data is too small, and ANN cannot predict well.

And 6, determining a training sample. Consider two cases, one is that if a degradation anomaly is detected in step 5, then at ws _s Is used for prediction, not at W _i,k1 And all of the features in (a). Due to at ws _s The number of features in the model is small, and a simplified linear model is adopted as formula (7):

d _i,t ＝a _i ×t+b _i +ε _i,t (7)

in the formula (7), a _i and b_i Is a parameter of the linear model. Epsilon _i,t Is the measurement error of component i at time t. Herein, falseThe error terms are set independently of each other. The parameter a can be estimated by Least Squares (LSM) _i and b_i . D in consideration of feature extraction method _i,t May be multidimensional. If D _i,t Is multidimensional, then the main degenerate element d _i,t Is selected for prediction.

Another scenario is that no degradation anomaly occurs. Then W is _i,k1 and W_i,k2 Is used as an input sample and an output sample for training the ANN. The number of input layer and output layer neurons is the same.

And 7, executing prediction. Consider two cases. First, degradation anomalies occur and are detected, so linear models are used for prediction. When the predicted value exceeds a predetermined failure threshold, the prediction is stopped. If the extracted degradation features are multidimensional, then a principal element is used for prediction and comparison to a predetermined failure threshold. Another situation, the degradation anomaly, does not occur. Then ANN is used for prediction. Multi-step early prediction is performed. At each prediction there is ws _i,k The individual degradation characteristics are predicted. The rolling prediction is performed according to equation (8). During the training process of the ANN,

and />

Is used as the input and output of training samples. Then, degeneration feature->

For predicting degradation characteristics

In each prediction there is ws _i,k The individual degradation characteristics are predicted.

It should be noted that, due to the requirement of ANN, the degradation features need to be normalized and then predicted. Further, after each prediction, the prediction result is processed according to the formula (9). Equation (9) is based on two assumptions. One assumption is that the degree of degradation of the component increases with time of service; another assumption is that the degree of degradation is smooth since no degradation anomaly occurs. The prediction termination condition is formula (10).

in the formula ,ND_i,t' To normalize degradation characteristics of component i at any time t', PD _i,t' Is the predicted degradation characteristic after inverse normalization, H is a predetermined failure threshold, RUL _i Is the remaining life of component i. And D _i,t Similarly, PD _i,t' Is also a vector. PD (potential difference) device _i,t' Is determined by the feature extraction method, and D _i,t The same applies. Similarly, if PD _i,t' Is multidimensional, and selects one principal element from the dimensions for calculation and comparison. The selected principal element should be equal to D _i,t And consistent.

And 8, performing failure risk assessment. The risk of failure of one component may be represented by a degradation characteristic. The degradation characteristic can be expressed according to formula (11). Equation (11) includes two parts, one part is degradation characteristics extracted from the state monitoring data, and the other part is predicted degradation characteristics.

WD _i Is the overall degradation characteristic of component i. D (D) _i,1 ；D _i,2 ；…；D _i,STP Is a known part. WPD (Wireless Power distribution) _i,P Including degradation features predicted from an ANN or linear model. All degradation characteristics are according to the formula(12) Normalization is performed, and then failure risk calculation is performed according to equation (13). If the degradation characteristic is multidimensional, the main element is used for calculation in the formulas (12) and (13).

in the formula ,WDN_i Is the normalized degenerate feature matrix for component i. cumsum represents the sum of the accumulation. FR (FR) _i To accumulate the failure risk vector, it is monotonically increasing between intervals (0, 1). FR (FR) _i ＝[F _i,1 ；F _i,2 ；......；F _i,T ]，F _i,T Is the failure risk of component i at time T, which is the predicted failure time.

From equation (13), it can be seen that the risk of failure is and the degree of degradation is related to the length of service. This widely accepted assumption is that: if the degradation characteristic approaches the failure threshold, the component has a higher risk of failure; if the component is in service for a longer period of time, the component has a higher risk of failure. That is, the failure risk of a component is positively correlated with its degree of degradation and length of service. This assumption is also consistent with the results from equation (13).

The method of the invention is part 2: multi-component system opportunistic replacement modeling

During a mission period, the total cost of the system may be expressed according to equation (14):

C _Total ＝C _EF +C _EP +C _DA (14)

in the formula ,C_Total Is the total cost, C _EF C for failure replacement of desired costs _EP To prevent replacement of desired costs, C _DA For total disassembly and installation costs. As the condition monitoring data is updated, the prediction and failure risk assessment results change.

For determining how many components are at each replacementTo replace this problem at the same time, a current cost rate function is first defined. Assume that a total of N locations in the system install such critical components. Among the possible alternative combinations are: (1) All components individually replace S ₁ =1; (2) Two components are replaced together, the remaining components are replaced together or separately, S ₂ ＝C _N ² (3) three components are replaced together, and the remaining components are replaced together or individually with S ₃ ＝C _N ³ And so on. S is S ₂ ＝C _N ² 、S ₃ ＝C _N ³ Meaning of permutation and combination, N is subscript, and 2 and 3 are superscripts. Assume a scenario: n components are replaced together, the other m components are replaced together, and the remaining components are replaced individually. The corresponding current cost rate calculation formulas are formulas (15) to (17).

wherein ,C_Rscn Cost rate for n components to replace together, C _Rscm Cost rate for m components to replace together, C _Rscl Cost rate for component individual replacement, C _f To replace cost for one time failure, C _p To prevent replacement cost once, F _x,t 、F _y,t and F_l,t For component x, component y and component l, the failure risk at time t, which can be calculated according to equation (13), c _DA Is a cost of one-time disassembly and assembly. Since the components may be replaced simultaneously, the disassembly and installation costs may be shared by each component. The total cost rate is calculated as formula (18).

in the formula ,

and />

Minimum cost rate for a group of replacement components, +.>

Minimum cost rate for an individually replaced component.

By analyzing all cases, the case with the smallest total cost rate is selected as the optimal replacement case. Assuming that the above replacement scenario is an optimal replacement strategy, the optimal replacement time for each sub-scenario is:

wherein ,

and />

Optimal replacement time for replacement of components in groups, +.>

For optimal time for individual replacement of the components,

therefore, the corresponding optimal replacement time is:

equation (23) is the theoretical optimal replacement time,

is the minimum value thereof.

In the theory, the method is that,

for the first time in this scenario. As the detection time advances, the predicted values of remaining life and risk of failure also change. Therefore, the replacement policy should also be dynamically adjusted.

A conservative time window is defined to determine the possible replacement times. The conservative time window is located to the right of STP. As shown in fig. 2. If STP is not less than the minimum value within the conservative time window, then the substitution is made immediately. While the theoretical optimal replacement time may be greater than the replacement time within the conservation time window, if the maximum replacement time is reached, the component may fail before this.

After replacement, the current cost rate and the optimal replacement policy need to be recalculated due to the addition of the new component. The predict-replace is repeatedly performed until the task cycle is satisfied. A simple complexity analysis is performed here: because the prediction results change continuously with increasing detection time, the failure risk also changes, and the optimal replacement strategy changes dynamically. Especially as the number of components in the system increases, the number of alternative combinations will be more and the computational effort will be greater. Thus, the model has a certain complexity.

The proposed model is validated using the simulation dataset as follows:

(1) Single component degradation prediction method validation

This simulation experiment produced 50 bearings with outer ring faults. Assuming that the failure times of these bearings obey a weibull distribution with a dimensional parameter of 3500 hours and a shape parameter of 5, a gaussian white noise signal is generated to represent the actual sensor sampling situation. These simulated bearings have the following parameters: the pitch diameter of the bearing is 39.04nm, the number of balls is 9, the diameter of the balls is 15.00nm, and the contact angle is 0. The rotational speed is assumed to be 1800rpm. The sampling interval was 1 second and the sampling frequency was 12kHz. And (3) extracting degradation characteristics by wavelet packet analysis, wherein the wavelet base is db4, and the decomposition layer number is 3. The wavelet packet factor energy is used as degradation characteristic, and the failure threshold is set to 14000Hz.

The input layer and the output layer of the artificial neural network are set to have 8 neurons, and the hidden layer has 10 neurons. The hyperbolic tangent function is an activation function of the hidden layer, and the activation function of the output layer is a linear function. The Levenberg-Marquardt algorithm is used to adjust weights in two neurons. Setting the maximum iteration number as 1000 generations, the learning rate as 0.05 and the error target as 1e ^-10 . The initial time window size is 100 and the floating factor is 0.02. The window size for anomaly detection is 10.

It is assumed that at the beginning of the mission period, all the dummy bearings are new, distributed independently and identically, but with different lifetimes. These bearings are mounted in a supporting position. These simulated signals can be regarded as real-time sensor data.

Through verification, the method provided by the invention has good prediction capability. The proposed failure risk model can obtain better results, which are similar to the true values.

(2) Multi-component system opportunistic replacement modeling method verification

Assume that four support seats are HA, HB, HC, and HD, respectively. These components are mounted on a support, for which possible alternative combinations are as follows: (1)

(2)/>

(3)/>

(4)/>

(5)/>

(6)/>

(7)/>

(8)

(9)/>

(10)/>

(11)/>

(12)/>

(13)/>

(14)/>

(15)/>

There are 15 alternative combinations in which the framed representations are replaced simultaneously.

Suppose C _f ＝20，C _p ＝14，C _DA =4. Disassembly and assembly time is omitted herein. The lead time of the spare parts is ignored, so long as the spare parts are required to be delivered in time. The conservative time window size set for substitution was 20 hours and the task cycle length was 5000 hours.

Based on the calculation, the system is shut down 3 times in total for replacement during the whole task period. The 1 st shutdown is 1211 hours, with C3 on HC replaced. The 2 nd shutdown was at 2324 hours, with C1, C2 and C4 on HA, HB and HD replaced. The 3 rd shutdown was at 4529 hours, with components on HA and HC replaced. A total of 6 spare parts are used. The expected system guarantee time is 5203 hours. The total replacement cost is 118.87. The cumulative maintenance cost rate was 0.0262.

Claims

1. A method for optimizing the maintenance of a multi-component system state opportunity, comprising the steps of:

an initial time window ws is given ₀ Start predictionAt time point STP, assuming that all components are under the same state monitoring strategy, the degradation characteristic of component i within the time window is denoted as W _i,1 and W_i,2 ，W _i,1 and W_i,2 Is scaled by the initial time window ws ₀ And the feature extraction method is determined by:

in the formula ,D_i,STP The degradation feature vector representing component i at time point STP, and has:

and />

Step 3, the initial degradation growth rate r _i,0 If r, compared with the floating factor f _i,0 >(1+f) description in a shorter timeExecuting the step 5 to detect degradation abnormality if the degradation speed is relatively high; otherwise, step 4 is performed, wherein the floating factor f is used to account for the stability of the trend of degradation and its acceptable range;

step 4, compressing the time window step by step, if the calculated degradation growth rate is smaller than (1+f), removing the leftmost two features in the left time window, and at this time, after one compression, changing the time window into: ws (what is) ₁ ＝ws ₀ -1, recalculating the degradation growth rate in the corresponding compression time window by adopting the method of the step 2, and repeating the step 4 until the degradation growth rate is not less than (1+f), wherein after the k-step compression, the characteristics, the mean value and the degradation growth rate in the time window are shown as follows:

step 5, if r _i,k >(1+f), degradation anomaly detection is performed: defining h as an alert value if the feature matrix W _i,k2 Exceeding h, a smaller time window ws _s For entering intoLine degradation anomaly detection if in time window ws _s The characteristics on the right side of the middle are all compared with W _i,k2 The remaining features in (a) are large, in which case degradation is considered abnormal, otherwise, degradation is considered stable;

step 6, determining a training sample:

if a degradation anomaly is detected in step 5, then in a time window ws _s Is used to train an ANN; if no degradation abnormality occurs, then W _i,k1 and W_i,k2 The input samples and the output samples are used for training the ANN, and the number of neurons of the input layer and the output layer is the same;

step 7, executing prediction

when the degradation abnormality does not occur, the ANN is used for prediction, and multi-step advanced prediction is performed; at each prediction there is ws _i,k The individual degradation characteristics are predicted, rolling prediction is performed according to the following equation:

during the training process of the ANN,

and />

…；D _i,STP Is used as input and output of training samples, then the degradation characteristic->

…；D _i,STP For predicting degradation characteristics D _i,STP+1 ；…；/>

step 8, performing failure risk assessment

WD _i ＝[D _i,1 ；D _i,2 ；…；D _i,STP ；WPD _i,P ]

where H is a predetermined failure threshold, WDN _i For the normalized degenerate feature matrix of component i, cumsum represents the sum, FR _i To accumulate failure risk vectors, which monotonically increase between intervals (0, 1), FR _i ＝[F _i,1 ；F _i,2 ；......；F _i,T ]，F _i,T Is the failure risk of component i at time T, T being the predicted failure time;

during the mission period, the total cost of the system is expressed as:

C _Total ＝C _EF +C _EP +C _DA

t≥STP,n≤N.

t≥STP,m≤N.

t≥STP,l＝1,2,...,N-n-m.

in the formula ,C_Rscn Cost rate for n components to replace together, C _Rscm Cost rate for m components to replace together, C _Rscl Cost rate for component individual replacement, C _f To replace cost for one time failure, C _p To prevent replacement cost once, F _x,t 、F _y,t and F_l,t Is component x, component y and componentRisk of failure at time t, c _DA For one disassembly and assembly cost, since the components may be replaced simultaneously, the disassembly and assembly costs may be shared by each component, for a total cost rate C _R The calculation formula is as follows:

in the formula ,

and />

Minimum cost rate for a group of replacement components, +.>

Minimum cost rate for an individually replaced component;

wherein ,

and />

Optimal replacement time for replacement of components in groups, +.>

the theoretical optimal replacement time is

For the minimum value thereof, +.>

2. The method of claim 1, wherein in step 6, if a degradation anomaly is detected in step 5, the degradation anomaly is detected in a time window ws _s The following simplified linear model is used for prediction:

d _i,t ＝a _i ×t+b _i +ε _i,t

3. The method of claim 1, wherein in step 7, after each prediction, the prediction result is processed according to the following formula:

if

then/>

if

then/>

if PD _i,t' ×r _i,k ≥H,then RUL _i ＝t'-STP

if PD _i,t' ×r _i,k <H,then performing rolling prediction

in the formula ,ND_i,t' To normalize degradation characteristics of component i at any time t', PD _i,t' Is the predicted degradation characteristic after inverse normalization, RUL _i Is the remaining life of component i.