CN111027719A

CN111027719A - Maintenance optimization method for multi-component system state opportunity

Info

Publication number: CN111027719A
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: 2020-04-17
Anticipated expiration: 2039-11-14
Also published as: CN111027719B

Abstract

The invention relates to a maintenance optimization method for multi-component system state opportunities. 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 better established. According to the situation, the invention compares various prediction algorithms, establishes a model for predicting the degradation and the residual life of the single individual device on the basis of analyzing the state monitoring signal of the device, and establishes an opportunity state maintenance model of the multi-component device 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 maintenance of the equipment opportunity based on state.

Description

Maintenance optimization method for multi-component system state opportunity

Technical Field

The invention relates to a maintenance scheme optimization technology based on a state of a multi-component system. Specifically, the characteristics of different products are considered, a prediction model of the service life of an equipment unit under the condition of no failure data and truncated data is established by combining with engineering practice conditions, the model is applied to a multi-component system, and a maintenance optimization model of equipment opportunity in the multi-component system based on the state is established.

Background

In engineering practice, proper maintenance of equipment is often an important means to improve equipment reliability. The maintenance of the multi-component system is usually performed by an individual maintenance method or a group maintenance method, and the two maintenance methods either cause frequent shutdown and startup or waste of the service life of the components. During maintenance, equipment is often required to be stopped, so that the equipment maintenance may occupy the production and processing time of the equipment, and further the completion time of a processing task is delayed. Therefore, when scheduling a production job, it is necessary to consider not only information of the production job itself but also an influence of maintenance of equipment on the production job. In addition, when the equipment maintenance strategy is prepared, not only the current state of the equipment but also the future degradation trend and failure probability of the equipment are considered. More scientific and reasonable maintenance strategies are often obtained on the basis of accurate state assessment and predictive analysis. Conventional event data methods often require large amounts of failure data or truncation data. However, for new products and new equipment, the state monitoring data of the same type of products is less, and sometimes the failure data is less due to the safety and reliability. In this case, how to build a prediction model of the device, and thus a state maintenance model of the device, is particularly important.

Disclosure of Invention

The purpose of the invention is: and (3) considering the characteristics of different prediction methods, establishing an individual life prediction model for equipment under the condition of no failure data and truncated data by combining engineering practice conditions, applying the model to a multi-component system, and establishing a state-based maintenance optimization model for equipment opportunities in the multi-component system.

In order to achieve the above object, the technical solution of the present invention is to provide a method for maintaining and optimizing multi-component system state opportunities, which is characterized by comprising the following steps:

the method comprises the following steps of firstly, predicting degradation of a single component;

step 1, monitoring the state of the part, extracting degradation features capable of reflecting the degradation condition of the part, and representing the degradation feature vector of a component i at the time t as D_i,t；

Step 2, calculating the initial degradation growth rate of the component i, and comprising the following steps:

an initial time window ws is first given₀And a start prediction time point STP, the degradation characteristic of component i within the time window is denoted as W, assuming all components are under the same state monitoring strategy_i,1 and W_i,2，W_i,1 and W_i,2Is scaled by an initial time window ws₀And the feature extraction method, then:

in the formula ,D_i,STPRepresenting the degradation feature vector of component i at the time point STP. And has the following components:

in the formula ,M_i,1 and M_i,2Are respectively W_i,1 and W_i,2If M is the mean value of_i,1 and M_i,2Is multidimensional, one of the dimensions is selected as the main element for calculation,

and

is the corresponding mean value in the main element used for calculating the initial backThe growth rate is changed;

initial degradation growth rate r_i,0The ratio of the mean values in two adjacent time windows is

Step 3, increasing the initial degradation rate r_i,0If r is compared with the floating factor f_i,0>(1+ f), which shows that the degradation speed is relatively high in a relatively short time, step 5 is executed to perform degradation abnormality detection. Otherwise, step 4 is executed, in which the floating factor f is used to illustrate the stability of the trend of degradation and its acceptable range;

and 4, compressing the time window step by step, and removing two leftmost features in the left time window if the calculated degradation growth rate is less than (1+ f), wherein after one compression, the time window is changed into: ws₁＝ws ₀1, recalculating the degradation growth rate in the corresponding compression time window by using the method in step 2, repeating step 4 until the degradation growth rate is not less than (1+ f), and after k steps of 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,k2Is a feature matrix after k-step compression, ws_i,kFor a corresponding time window size, M_i,k1 and M_i,k2Is W_i,k1 and W_i,k2The average value of (a) of (b),r_i,kthe corresponding degradation growth rate;

step 5, if r_i,k>(1+ f), then a degradation anomaly detection is performed: defining h as an alert value if the feature matrix W_i,k2Exceeds h, a smaller time window ws_sFor detecting degradation anomalies if in a time window ws_sThe middle and right side features are all compared with W_i,k2The remaining features in (1) are large, in which case the degradation is considered abnormal, otherwise, the 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_sThe features in (1) are used to train the ANN; if no degeneration anomaly has occurred, then W_i,k1 and W_i,k2The input sample and the output sample are used for training the ANN, and the number of neurons in an input layer is the same as that of neurons in an output layer;

step 7, performing prediction

When the degradation abnormality occurs and is detected, a linear model is used for predicting, when the predicted value exceeds a preset failure threshold value, the prediction is stopped, if the extracted degradation feature is multidimensional, a main element is used for predicting and comparing with the preset failure threshold value;

when the degeneration abnormity does not occur, the ANN is used for prediction, and multi-step prediction is executed; at each prediction there is ws_i,kIndividual degradation characteristics are predicted. Rolling prediction is performed as follows:

in the course of the training of the ANN,

and

is treated as input and output of training samples, and then, degenerates the characteristics

For predicting degradation characteristics

In each prediction there are ws_i,kA degradation characteristic is predicted;

step 8, failure risk assessment is carried out

The risk of failure of a component can be expressed in terms of degradation characteristics, which are expressed as follows:

WD_i＝[D_i,1；D_i,2；…；D_i,STP；WPD_i,P]

the above equation includes two parts, one is a degradation feature extracted from the condition monitoring data, and the other is a predicted degradation feature, in which WD_iIs the overall degradation characteristic of component i; d_i,1；D_i,2；…；D_i,STPIs a known moiety; WPD_i,PIncluding the degradation features predicted from the ANN or linear model, all the degradation features are normalized according to the following equation:

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

in the formula ,WDN_iFor the normalized degradation feature matrix of component i, cumsum represents the cumulative sum, FR_iFor accumulating failure risk vectors, monotonically increasing between intervals (0,1), FR_i＝[F_i,1；F_i,2；......；F_i,T]，F_i,TIs the risk of failure of component i at time T, which is the predicted time to failure;

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

the total cost of the system during the task period is expressed as follows:

C_Total＝C_EF+C_EP+C_DA

in the formula ,C_TotalFor the total cost, C_EFCost expected for replacement of failure, C_EPTo prevent replacement of the expected cost, C_DATotal disassembly and assembly costs;

for the problem of determining how many components are to be replaced simultaneously in each replacement, a current cost rate function is defined first, assuming that there are N total locations in the system for installing such key components, and assuming that N components are replaced together, and m components are replaced together, and the remaining components are replaced separately, the corresponding current cost rate calculation formula is:

t≥STP,n≤N.

t≥STP,m≤N.

t≥STP,l＝1,2,...,N-n-m.

in the formula ,C_RscnCost rate for replacement of n components together, C_RscmCost rate for m components to be replaced together, C_RsclCost rate for individual replacement of components, C_fFor a cost of replacement by one failure, C_pTo prevent replacement costs at one time, F_x,t、F_y,t and F_l,tRisk of failure of component x, component y and component l at time t, c_DAFor one disassembly and assembly cost, since the components may be replaced at the same time,the disassembly and assembly costs can be shared by each component for the total cost ratio C_RThe calculation formula is as follows:

in the formula ,

and

to minimize the cost rate of replacement components in a group,

minimum cost rate for individually replaced components;

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

wherein ,

and

for an optimal replacement time for a set of replacement components,

as a single replacement groupOptimum time of piece, corresponding optimum replacement time T_S,tComprises the following steps:

the theoretical optimal replacement time is

Is the smallest value among them,

the time is replaced for the first time under the scene; as the detection time advances, the predicted values of remaining life and failure risk change accordingly, so the replacement strategy should also be dynamically adjusted:

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

Preferably, in step 6, if a degradation anomaly is detected in step 5, in a time window ws_sThe 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_iAre parameters of the linear model; epsilon_i,tIs the measurement error of component i at time t; d_i,tIs the degradation element selected for prediction.

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

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

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'For normalized degradation characteristics of component i at any time t_i,t'Is the predicted degradation characteristic after denormalization, H is a predetermined failure threshold, RUL_iIs the remaining life of component i

The invention has the following advantages:

1. the model provided by the invention is provided from the perspective of engineering practice by combining the theoretical meanings of different methods, and the provided model is beneficial to guiding the engineering practice and can bring certain economic value to a factory or ensure the safe operation of equipment.

2. The degradation prediction and residual life prediction method adopted by the invention can achieve a better prediction result by only utilizing partial data rather than 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 the following specific examples. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present invention. Further, it should be understood that various changes or modifications of the present invention may be made by those skilled in the art after reading the teaching of the present invention, and such equivalents may fall within the scope of the present invention as defined in the appended claims.

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

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

Step 1, monitoring the state of the part and extracting degradation characteristics capable of reflecting the degradation condition of the part. In this section, the degenerate feature vector of component i at time t is denoted as D_i,t. In the specification, D_i,tMay be one-dimensional or multi-dimensional. Its dimensionality is affected by the feature extraction method. For example, if a peak is extracted as a degenerate feature, it is one-dimensional. If wavelet packet analysis is used, db4 is the wavelet basis 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. Firstly, an initial time window ws is given₀And a start prediction time point STP. Herein ws₀And STP is not associated with component i. Since all components are assumed to be under the same condition monitoring policy. The degradation characteristic of component i within a time window is denoted W_i,1 and W_i,2，W_i,1 and W_i,2Is scaled by ws₀And feature extraction method decision. Wherein STP and ws₀、W_i,1 and W_i,2The relationship of (a) is shown in FIG. 1.

In the formulae (2) and (3), M_i,1 and M_i,2Are respectively W_i,1 and W_i,2Is measured. And W_i,1 and W_i,2Similarly, M_i,1 and M_i,2And may also be multi-dimensional. If M is_i,1 and M_i,2Is multi-dimensional. One of the dimensions is selected as the primary element for the calculation.

And

is the corresponding mean value in the main element, used for calculating the initial degradation growth rate r_i,0. As shown in equation (3), the degradation growth rate is the ratio of the mean values in 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. Due to the influence of workload or other factors, the degradation features extracted from condition monitoring tend to increase in a fluctuating manner, and it is difficult to obtain a monotonically increasing trend to reflect the degradation condition of the component. Therefore, the ratio of the mean values is used to account for the degradation trend over the time window.

And step 3, comparing the initial degradation growth rate with the floating factor. The floating factor f is the stability and its acceptable range to account for the tendency of degradation. In general, f is set in the interval [0,0.1 ]]In the meantime. If r is_i,0>(1+ f), which shows that the degradation speed is relatively high in a relatively short time, step 5 is executed to perform degradation abnormality detection. Otherwise, step 4 is executed.

And 4, compressing the time window step by step. The direction of compression is shown in figure 1. If the calculated degradation growth rate is less than (1+ f), then the two leftmost features in the left time window are removed. At this time, after one compression, the time window becomes: ws₁＝ws₀-1, the degradation growth rate within the corresponding compression time window is recalculated. This step is repeated until the degradation growth rate is not less than (1+ f). After k-step compression, the characteristic, mean and degradation growth rate in the time window are shown as formulas (4) to (6).

In formulae (4) to (6), W_i,k1 and W_i,k2Is a feature matrix after k-step compression, ws_i,kIs the corresponding time window size. M_i,k1 and M_i,k2Is W_i,k1 and W_i,k2Mean value of r_i,kThe corresponding degradation growth rate.

Step 5, if r is_i,k>(1+ f), the degradation abnormality detection is performed. H is defined as an alert value. If at W_i,k2Exceeds h, a smaller time window ws_sFor degradation anomaly detection. If at ws_sThe middle and right side features are all compared with W_i,k2The remaining features in (a) are large, in which case the degradation is considered abnormal, otherwise the degradation is considered stable. In FIG. 1, W is illustrated_i,k1 and ws_sThe relationship (2) of (c).

Two possibilities need to be considered, one being that at step 4, no features remain after compression. If this occurs, there is no need to make a degradation prediction, since the defect is deemed to be slow and takes a long time to degrade to failure. Another case is that in step 4, when the termination condition is reached, there are few features left. These remaining features are introduced into step 5 and abnormal degradation detection is performed. If the abnormity occurs, the linear model in the step 6 is used for prediction, otherwise, the prediction is not carried out, and the ANN cannot be well predicted because the data volume is too small.

And 6, determining a training sample. Two cases need to be considered, one is that a degenerative anomaly is detected in step 5, then at ws_sFeatures in (1) are used for prediction, not in W_i,k1And all features of the sum. Due to the fact that at ws_sThe number of features in (1) is small, and a simplified linear model is adopted, wherein the simplified linear model is expressed by the formula (7):

d_i,t＝a_i×t+b_i+ε_i,t(7)

in the formula (7), a_i and b_iAre parameters of the linear model. Epsilon_i,tIs the measurement error of component i at time t. Herein, the error terms are assumed to be independent of each other. The parameter a can be estimated by Least Squares (LSM)_i and b_i. Method taking into account feature extraction, D_i,tPossibly multi-dimensional. If D is_i,tIs multi-dimensional, then the dominant degenerate element d_i,tIs selected for prediction.

Another scenario is that no degradation anomalies have occurred. Then W_i,k1 and W_i,k2Are treated as input samples and output samples for training the ANN. The number of input layer and output layer neurons is the same.

And 7, executing prediction. Two cases are considered. One is that a degenerative anomaly has occurred and is detected, and therefore is predicted using a linear model. When the predicted value exceeds a predetermined failure threshold, the prediction is stopped. If the extracted degradation features are multi-dimensional, then the main elements are used for prediction and comparison with a predetermined failure threshold. In another case, a degenerative abnormality does not occur. Then the ANN is used for prediction. A multi-step prediction ahead is performed. At each prediction there is ws_i,kIndividual degradation characteristics are predicted. The rolling prediction is performed according to equation (8). In the course of the training of the ANN,

and

as input and output for training samples. Then, the characteristic of degradation

For predicting degradation characteristics

In each prediction there are ws_i,kIndividual degradation characteristics are predicted.

It should be noted that, due to the requirement of ANN, the degradation characteristics need to be normalized to predict again. After each prediction, the prediction result is processed according to equation (9). Equation (9) is based on two assumptions. One assumption is that the degree of degradation of a component increases with time of service; another assumption is that the degree of degradation is smooth since no degradation anomaly has occurred. The predicted termination condition is expression (10).

in the formula ,ND_i,t'For normalized degradation characteristics of component i at any time t_i,t'Is the predicted degradation characteristic after denormalization, H is a predetermined failure threshold, RUL_iIs the remaining life of component i. And D_i,tSimilarly, PD_i,t'Is also a vector. PD (photo diode)_i,t'Is determined by a feature extraction method, and D_i,tThe same is true. Similarly, if PD is_i,t'Is multidimensional, and a main element is selected from the dimensions for calculation and comparison. Selected primary element should sum with D_i,tAnd (5) the consistency is achieved.

And 8, carrying out failure risk assessment. The risk of failure of a component may be represented by a degradation signature. The degeneration characteristic can be expressed by equation (11). The expression (11) includes two parts, one part is a degradation feature extracted from the condition monitoring data, and the other part is a predicted degradation feature.

WD_iIs the overall degradation characteristic of component i. D_i,1；D_i,2；…；D_i,STPIs a known partAnd (4) dividing. WPD_i,PIncluding degradation features predicted from ANN or linear models. All degradation features are normalized according to equation (12) and then failure risk calculations are performed according to equation (13). Note that if the degradation characteristic is multidimensional, equations (12) and (13) are calculated using the main element.

in the formula ,WDN_iIs the normalized degradation feature matrix for component i. cumsum denotes the accumulated sum. FR_iTo accumulate the failure risk vector, it is monotonically increasing between intervals (0, 1). FR_i＝[F_i,1；F_i,2；......；F_i,T]，F_i,TIs the risk of failure of component i at time T, which is the predicted time to failure.

As can be seen from equation (13), the risk of failure is related to the degree of degradation as a function of time of service. This generally accepted assumption: if the degradation characteristic is close to the failure threshold, the component has a higher risk of failure; if the component is in service for a longer time, the component has a higher risk of failure. That is, the risk of failure of a component is positively correlated to its degree of degradation and time of service. This assumption is also consistent with the results obtained from equation (13).

Method part 2 of the invention: opportunistic replacement modeling for multi-component systems

The total cost of the system during the task period can be expressed in terms of equation (14):

C_Total＝C_EF+C_EP+C_DA(14)

in the formula ,C_TotalFor the total cost, C_EFCost expected for replacement of failure, C_EPTo prevent replacement of the expected cost, C_DAFor the total disassembly and assembly costs. As the condition monitoring data is updated, the prediction and risk of failure assessment results may also change.

For the problem of determining how many components to replace at the same time for each replacement, a current cost rate function is first defined. Assume that there are a total of N locations in the system where such critical components are installed. Among the possible alternative combinations are: (1) all components being replaced by S alone₁1 is ═ 1; (2) two components are replaced together, the remaining components are replaced together or separately, S₂＝C_N ²(3) replacing the three components together, and replacing the rest components together or replacing S separately₃＝C_N ³And so on. S₂＝C_N ²、S₃＝C_N ³Indicating the meaning of permutation and combination, N is subscript, 2, 3 are superscript. Assume a scenario: n components are replaced together, and m components are replaced together, and the rest components are replaced independently. The corresponding current cost rate calculation formulas are formula (15) to formula (17).

wherein ,C_RscnCost rate for replacement of n components together, C_RscmCost rate for m components to be replaced together, C_RsclCost rate for individual replacement of components, C_fFor a cost of replacement by one failure, C_pTo prevent replacement costs at one time, F_x,t、F_y,t and F_l,tAs the risk of failure of component x, component y and component l at time t, which can be calculated according to equation (13), c_DAWhich is a one-time disassembly and assembly cost. Since the components may be replaced at the same time, the disassembly and installation costs may be amortized for each component. The calculation formula for the total cost rate is as shown in equation (18).

in the formula ,

and

to minimize the cost rate of replacement components in a group,

is the minimum cost rate of individually replaced components.

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

wherein ,

and

for an optimal replacement time for a set of replacement components,

for the optimal time to replace the components individually,

therefore, the corresponding optimal replacement time is:

equation (23) is the theoretical optimal replacement time,

of which is the minimum value.

In theory, the method has the advantages that,

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

A conservative time window is defined to determine the likely time of substitution. The conservative time window is located to the right of STP. As shown in fig. 2. If the STP is not less than the minimum value within the conservative time window, a substitution is immediately made. While the theoretical optimal replacement time may be greater than the replacement time within the conservative time window, if the maximum replacement time is waited for, the component may fail before that.

After the replacement is performed, the current cost rate and the optimal replacement strategy need to be recalculated due to the addition of the new component. The prediction-replacement is repeatedly performed until the task period is satisfied. Here a simple complexity analysis is performed: since the prediction result changes continuously with the increase of the detection time, the failure risk also changes, and the optimal replacement strategy is always dynamically changed. Especially when the number of components in the system increases, the number of alternative combinations will be larger and the amount of calculation will be larger. Therefore, the model has a certain complexity.

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

(1) single component degradation prediction method verification

The simulation experiment produced 50 bearings with outer ring failure. Assuming that the failure time of these bearings follows a weibull distribution with a scale 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 the balls is 9, the diameter of the balls is 15.00nm, and the contact angle is 0. Assume a rotation speed of 1800 rpm. The sampling interval was 1 second and the sampling frequency was 12 kHz. And (3) extracting degradation characteristics by wavelet packet analysis, wherein the wavelet base is db4, and the number of decomposition layers is 3. Wavelet packet factor energy is used as a degradation characteristic, and a failure threshold value is set to 14000 Hz.

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 the weights in both neurons. The maximum iteration number is set to 1000 generations, the learning rate is 0.05, and the error target is 1e^-10. The initial time window size is 100 and the float factor is 0.02. The window size for anomaly detection is 10.

It is assumed that at the beginning of the mission cycle, all simulated bearings are new, independently identically distributed, but have different lifetimes. These bearings are mounted in a support position. These simulated signals can be considered as real-time sensor data.

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

(2) Opportunistic replacement modeling method verification for multi-component system

Assume that there are four bearers HA, HB, HC, and HD. These components are embedded in the support base, and the possible alternative combinations of these components 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 boxed representation is replaced at the same time.

Let C be_f＝20，C_p＝14，C_DA4. Disassembly and assembly time is ignored herein. The delivery lead time of the spare parts is ignored, and the spare parts can be delivered in time as long as the spare parts are required. The conservative time window set for the replacement was 20 hours and the task cycle length was 5000 hours.

According to the calculation, the system is stopped for 3 times for replacement in 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 replaced on HA, HB, and HD. The 3 rd shutdown is at 4529 hours with components on the HA and HC replaced. A total of 6 spare parts are used. The system guarantee time is expected to be 5203 hours. The total replacement cost is 118.87. The cumulative repair cost rate is 0.0262.

Claims

1. A maintenance optimization method for the state opportunity of a multi-component system is characterized by comprising the following steps:

an initial time window ws is first given₀And a start prediction time point STP, the degradation characteristic of component i within the time window is denoted as W, assuming all components are under the same state monitoring strategy_i,1 and W_i,2，W_i,1 and W_i,2Is scaled by an initial time window ws₀And feature handleThe method of fetching determines that:

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

and

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

step 4, compressing the time window step by step, and if the calculated degradation growth rate is less than (1+ f), compressing the time window in the left sideThe two leftmost features are removed, at which point, after one compression, the time window becomes: ws₁＝ws₀1, recalculating the degradation growth rate in the corresponding compression time window by using the method in step 2, repeating step 4 until the degradation growth rate is not less than (1+ f), and after k steps of 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,k2Is a feature matrix after k-step compression, ws_i,kFor a corresponding time window size, M_i,k1 and M_i,k2Is W_i,k1 and W_i,k2Mean value of r_i,kThe corresponding degradation growth rate;

step 6, determining a training sample:

step 7, performing prediction

in the course of the training of the ANN,

and

For predicting degradation characteristics

In each prediction there are ws_i,kA degradation characteristic is predicted;

step 8, failure risk assessment is carried out

WD_i＝[D_i,1；D_i,2；…；D_i,STP；WPD_i,P]

the total cost of the system during the task period is expressed as follows:

C_Total＝C_EF+C_EP+C_DA

in the formula ,C_RscnCost rate for replacement of n components together, C_RscmCost rate for m components to be replaced together, C_RsclCost rate for individual replacement of components, C_fFor a cost of replacement by one failure, C_pTo prevent replacement costs at one time, F_x,t、F_y,t and F_l,tRisk of failure of component x, component y and component l at time t, c_DASince the components may be replaced at the same time for a single disassembly and assembly cost, the disassembly and assembly costs may be shared by each component, for a total cost ratio C_RThe calculation formula is as follows:

in the formula ,

and

to minimize the cost rate of replacement components in a group,

minimum cost rate for individually replaced components;

wherein ,

and

for an optimal replacement time for a set of replacement components,

for optimum time of individual replacement of components, corresponding optimum replacement time T_S,tComprises the following steps:

the theoretical optimal replacement time is

Is the smallest value among them,

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

d_i,t＝a_i×t+b_i+ε_i,t

3. The method for maintaining and optimizing multi-component system state opportunity according to claim 1, wherein in step 7, after each prediction, the prediction result is processed according to the following formula:

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'For normalized degradation characteristics of component i at any time t_i,t'Is the predicted degradation characteristic after denormalization, H is a predetermined failure threshold, RUL_iIs the remaining life of component i.