Reliability modeling and evaluation method for three-phase converter system

Abstract

The invention discloses a reliability modeling and evaluation method for a three-phase converter system. The method comprises the following steps: step 1, analyzing key components of the three-phase converter system; step 2, Bayesian network (BN) modeling is carried out; step 3, BN parameter learning based on maximum likelihood estimation (MLE); step 4, carrying out component multi-performance characteristic related degradation modeling based on a Copula function; step 5, determining initial distribution of root nodes; step 6, performing causal reasoning of the BN; and 7, calculating the reliability of the system. On the basis of considering the degradation correlation of different types of components, the system reliability modeling and evaluation method is researched by using the degradation data, so that the engineering application of the reliability analysis technology of the three-phase converter system considering the correlation is promoted.

Description

Technical Field

[0001] The invention relates to a reliability modeling and evaluation method for a three-phase converter system. Background Art

[0002] The present invention focuses on the field of reliability analysis of electronic products, and specifically discusses a reliability modeling and evaluation method for a three-phase inverter system. In the context of the continuous changes in today's society, culture and technology, the concept of reliability has gradually become a universal attribute with both qualitative and quantitative connotations, and the reliability construction and processing of engineering systems and major equipment have therefore received increasing attention and attention. With the rapid development of data science, intelligent hardware and software tools, data-driven methods have been widely used in the field of reliability. However, traditional reliability assessment methods mainly rely on historical failure data, which faces many challenges in practice. For example, as product reliability improves, the failure time becomes longer, and it becomes more difficult to obtain this data. At the same time, tests in specific environments may be destructive or not applicable to expensive equipment. More importantly, failure data often come from specific environments and operating conditions, which cannot guarantee that the failure behavior of the system remains unchanged during the actual life cycle.

[0003] Therefore, we need a better assessment method that can use easily accessible and highly available data. Therefore, the degradation-based reliability assessment method came into being. This method maps the degradation data of system performance characteristics to health indicators to predict upcoming failure events. This method has become one of the most commonly used methods in the reliability field, and its application scope has gradually expanded from single components to multi-component systems.

[0004] However, in a multi-component system, the degradation processes of components may be interdependent, which greatly increases the complexity of system reliability modeling and calculation. At present, system reliability analysis considering component degradation correlation is still a challenging problem, especially the correlation research involving multi-state components is even more scarce.

[0005] Therefore, the present invention focuses on the system composed of continuously degraded components and multi-state components, deeply considers the correlation of component degradation, and conducts an innovative study on the system reliability modeling and evaluation method related to multi-type degraded components. This study is expected to provide a more accurate and effective method for reliability analysis of three-phase inverter systems. Summary of the invention

[0006] The purpose of the present invention is to overcome the deficiencies of the prior art and to provide a reliability modeling and evaluation method for a three-phase converter system that can take into account the correlation of component degradation, thereby being able to more accurately evaluate component life and make the system safer.

[0007] The objective of the present invention is achieved through the following technical solution: A three-phase converter system reliability modeling and evaluation method comprises the following steps:

[0008] S1. Analyze the components in the three-phase converter system and select the performance characteristics of representative key components in the system and the output characteristics of the system level as the basic variables for constructing BN;

[0009] S2. Construct BN model and DAG model based on basic variables;

[0010] S3, then learn the CPT parameters of BN based on MLE;

[0011] S4, perform component-level related degradation modeling, and use a multi-dimensional inverse transform sampling algorithm with Copula to obtain edge degradation simulation data under a large number of samples;

[0012] S5. Statistically obtain the probability of each state based on the discretization process, that is, obtain the initial distribution of the root node;

[0013] S6, using the joint tree algorithm for causal reasoning of BN;

[0014] S7. Based on the trained BN reasoning, the joint state probability distribution of multiple performance indicator nodes of the three-phase converter system is obtained, thereby calculating the system reliability.

[0015] 2. The specific implementation method of S3 is: let BN and DAG be denoted by B and G respectively, and the number of nodes be n. Then, B is composed of G and the parameter set θ={θ1,θ2,...,θ n}, that is, B=(G,θ). G contains nodes (also called variables) X={X1,X2,...,X n} and a set of directed edges E, namely G = (X, E), X i The CPT (i=1,2,...,n) of i The joint probability distribution P(X) of all variables can be expressed as:

[0016]

[0017] Where Pa(X i )(i=1,2,...,n) represents X i Therefore, P(X i ) can be expressed as:

[0018]

[0019] The BN parameter P(X i = k|Pa(Xi )=j) is expressed as θ ijk ,k∈{1,2,...,r i} represents X i The state of j∈{1,2,...,q i} represents Pa(X i ) combined state, therefore, θ i It is a q i × i This paper aims to use a set of sample data D = {D1, D2, ..., D N}(a total of N samples) learn the parameter set θ of BN, D l (l=1,2,...,N) defines the value of each variable in X, that is, in represents the variable X in the lth sample j The value or state of . MLE is a purely data-driven parameter learning method. The log-likelihood function of θ is as follows:

[0020]

[0021] In the formula, c represents a constant; χ(X i = k, Pa (X i )=j:D l ) means D l The characteristic function of is defined as follows:

[0022]

[0023] Therefore, the log-likelihood function can be simplified to:

[0024]

[0025] Where N ijk Indicates that D satisfies X i = k and Pa(X i ) = the number of j records, by maximizing the above formula, we get θ ijk The estimated value of is as follows:

[0026]

[0027] Where N ij It means that when Pa(X i ) = j when X i ∈{1,2,...,r i} records. Therefore, the following holds true:

[0028]

[0029] 3. The specific implementation method of step 4 is: let the number of root nodes of BN be m, that is, the component level has m continuously degraded and related performance characteristics. The degradation process of the performance characteristics of m components is recorded as:

[0030]

[0031] In BN, the observations of all variables represented by the root nodes occur simultaneously. The total number of observations is z and the same observation time series is t = (t1, t2, ..., t z ). The degradation process Y of the performance characteristics of the i-th (i=1,2,...,m)) component i (t), the degradation data collected is y i =(y i,1 ,y i,2 ,...,y i,z ), where y i,j (j=1,2,...,z) is at time t j Y i The observed value of (t), that is, y i,j The theoretical value is Y i (t j ). Let Δy i =(Δy i,1 ,Δy i,2 ,...,Δy i,z ), satisfying Δy i,1 =y i,1 and Δy i,j =y i,j -y i,j-1 (j=2,3,...,z). The degradation correlation of the performance characteristics of these m components can be characterized by connecting the marginal distribution of degradation increments using the vine copula method. Therefore, the quantitative description of the degradation law of multiple performance characteristics of components can be achieved by only using the multivariate joint degradation modeling method and the model parameter estimation method. At this time, the joint distribution of the degradation increments of multiple performance characteristics of components is:

[0032] F(Δy 1,j ,Δy 2,j ,...,Δy m,j )=C(F1(Δy 1,j ),F2(Δy 2,j ),...,F m (Δy m,j );θ)

[0033] In the formula, F i (·)(i=1,2,...,m) represents the marginal distribution of degenerate increments; C(·;θ) represents the m-dimensional Copula function with parameter set θ.

[0034] The above formula is the key to predicting the degradation of multiple performance characteristics of components. As mentioned above, due to the existence of correlation, it is very difficult to directly obtain the analytical form of the degradation distribution of multiple performance characteristics of components at any time. Therefore, this paper generates relevant random numbers based on an inverse transform sampling algorithm with Copula to simulate the degradation path of multiple performance characteristics of components, and then complete the approximate estimation of the initial distribution. Taking m=3 as an example, it is assumed that the Copula function in the formula can be decomposed into a pair-Copula function C based on the vine Copula method. 12 , C 23 and C 13|2 ,The key steps of degradation path simulation are as follows:

[0035] S301: Generate a random number w from uniform distribution U(0,1) k (k=1,2,3).

[0036] S302: Let u1=w1.

[0037] S303: Order in It is C 2|1 The inverse function of (w2|u1), C 2|1 The expression of (w2|u1) is:

[0038]

[0039] S304: Order in It is C 3|12 The inverse function C of (w3|u1,u2) 3|12 The expression of (w3|u1,u2) is:

[0040]

[0041] In the formula, C 3|2 (w3|u2) and C 1|2 The expression of (u1|u2) is:

[0042]

[0043] S305: Calculation in Yes F i The inverse function of (·).

[0044] 4. The specific implementation method of S6 is: using the joint tree algorithm to perform causal reasoning of BN. The main process of the joint tree algorithm is as follows: Figure 2 Shown

[0045] 5. The specific implementation method of S7 is: the expression of system reliability R(t) is:

[0046] R(t)=P(S1(t)>0,S2(t)>0,...,S d (t)>0)

[0047] Where d represents the number of system-level nodes; S i (t)(i=1,2,...,d) represents the state of the i-th node at time t.

[0048] The beneficial effects of the present invention are: it is possible to consider the correlation of component degradation and carry out reliability modeling and evaluation of multiple types of three-phase converter systems, thereby being able to more accurately evaluate the component life and make the system safer. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 A schematic diagram of a process for reliability modeling and evaluation of a three-phase converter system of the present invention;

[0050] Figure 2 The main process of implementing the union tree algorithm;

[0051] Figure 3 The 5-node BN of the three-phase converter is simplified for this implementation;

[0052] Figure 4 Accelerated degradation test data for component performance characteristics

[0053] Figure 5 Scatter plot of pseudo-observations of degradation increments at different temperatures for this implementation;

[0054] Figure 6 This is the initial distribution of resistance A at normal storage temperature for this implementation;

[0055] Figure 7 For this implementation, the initial distribution of capacitance value B at normal storage temperature;

[0056] Figure 8 The state probability distribution of node X is implemented in this way;

[0057] Fig. 9 To implement the reliability of three-phase converter system; DETAILED DESCRIPTION

[0058] The principles and features of the present invention are described below in conjunction with the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0059] Example

[0060] A three-phase converter system reliability modeling and evaluation method of the present invention is as follows: Figure 1 As shown, the following steps are included:

[0061] S1: Analyze the components in the three-phase converter system and select the performance characteristics of representative key components in the system and the output characteristics of the system level as the basic variables for constructing BN;

[0062] The components in the three-phase converter system are analyzed, and the performance characteristics of the representative key components in the system are selected as the resistance value A of the resistor and the capacitance value B of a certain type of metallized film capacitor. The system-level output characteristics include the amplitude X, frequency Y and phase angle Z of the steady-state output voltage of the three-phase converter as the basic variables for constructing BN.

[0063] S2: Building a BN model and a DAG model based on basic variables, the step S2 includes:

[0064] S201: Based on the performance characteristics of the key components obtained in S1, the resistance value A of the resistor, the capacitance value B of a certain type of metallized film capacitor, and the system-level output characteristics, including the amplitude X, frequency Y and phase angle Z of the steady-state output voltage of the three-phase inverter, can be established as basic variables. Figure 3 The 5-node BN model shown;

[0065] S202: Since the degradation behavior of the three-phase converter resistors and capacitors under normal storage stress is not significant, the degradation data of resistance A and capacitance B are collected using an accelerated degradation test. The test selects temperature as the accelerated stress, and sets 30 resistor and capacitor samples at three constant stress levels of 80°C, 100°C, and 120°C. At the same time, the measurement time interval Δt = 1 day, the test duration is 56 days, and the accelerated degradation test data of the component performance characteristics collected are as follows: Figure 4 It can be found that temperature has a significant catalytic effect on the degradation of the performance characteristics of the two components. These data will be used to model the joint correlation degradation of resistance A and capacitance B.

[0066] S203: For the system-level performance indicators, the present invention obtains its state data based on the assumed BN parameter simulation. Specifically, combined with the state classification standard shown in Table 1, based on the following formula:

[0067]

[0068] The discrete state data of the BN root node can be obtained. Among them, the resistance value A and the capacitance value B are assumed to be divided into 4 states and 3 states respectively. Further, based on the assumed CPT of amplitude X, frequency Y and phase angle Z and the discrete state data of the BN root node, the state data of amplitude X, frequency Y and phase angle Z are generated and uniformly organized into a node state data set as shown in Table 1. In order to simplify the analysis, amplitude X, frequency Y and phase angle Z are divided into 3 states.

[0069] Table 1 Node status dataset

[0070] state 0 1 2 3 Resistance [800,+∞) [700,800) [400,700) [0,400) Capacitance value B / μF [120,+∞) [80,120) [0,80) -

[0071] Table 2 Combination of node status data

[0072]

[0073] During the analysis, the amplitude X, frequency Y, and phase angle Z are all assumed to be divided into three states. It should be noted that since the stress level does not affect the mapping relationship of each node in the BN, Table 2 contains the state data combination of each node under all stress levels.

[0074] S3: Then, the CPT parameters of BN are learned based on MLE. The step S3 includes:

[0075] S301: By using 80% of the state data set as the training set of BN and the remaining 20% ​​of the data as the test set, the parameter learning of BN and the accuracy test of the results are performed respectively. Taking the node of amplitude X as an example, Table 3 shows the estimated value and true value of its CPT parameter (the estimated value and the true value are respectively before and after " / "). Through calculation, the absolute value of the relative error of all parameters does not exceed 1.31%, and the parameter estimation effect is very good. On the other hand, based on the CPT estimation results of amplitude X, frequency Y and phase angle Z, that is, the mapping relationship model between the multi-performance characteristics of components and the multi-performance indicators of the system, the root node state data in the test set is used as input, and the predicted results of the leaf node state are compared with the true results, and the accuracy rate is 95.89%, indicating that the error of BN parameter learning is within an acceptable range and can be used for subsequent system reliability estimation.

[0076] Table 3 Estimated and true values ​​of CPT parameters

[0077] A B Pr{X=0|A,B} Pr{X=1|A,B} Pr{X=2|A,B} 0 0 1 / 1 0 / 0 0 / 0 1 0 1 / 1 0 / 0 0 / 0 2 0 1 / 1 0 / 0 0 / 0 3 0 1 / 1 0 / 0 0 / 0 0 1 1 / 1 0 / 0 0 / 0 1 1 0.30052 / 0.3 0.59817 / 0.6 0.10131 / 0.1 2 1 0.19877 / 0.2 0.65004 / 0.65 0.15119 / 0.15 3 1 0.10037 / 0.1 0.70048 / 0.7 0.19916 / 0.2 0 2 1 / 1 0 / 0 0 / 0 1 2 0.20219 / 0.2 0.64871 / 0.65 0.14910 / 0.15 2 2 0.09985 / 0.1 0.69941 / 0.7 0.20074 / 0.2 3 2 0 / 0 0 / 0 1 / 1

[0078] S302: For the related degradation modeling of multiple performance characteristics of components, due to the high level of temperature stress applied, this paper introduces the Arrhenius model to reflect the influence of temperature on the degradation parameters, and its expression is:

[0079]

[0080] In the formula, H represents the degradation parameter, such as the drift parameter of the Wiener process, the shape parameter of the Gamma process, and the mean parameter of the IG process; a and b represent the model parameters; and T represents the absolute temperature. For both component performance characteristics, the alternative edge acceleration degradation models include: (1) Under the Wiener process, (2) Under the Gamma process, Δy ij ~Ga(H(T)w ij ,β i ); (3) Under the IG process, The parameter estimation results based on MLE are shown in Table 4. Comparing the AIC values ​​under each model, the results show that the degradation of resistance A and capacitance B are more suitable for description by Wiener process. Using the parameter estimation values ​​of the Wiener process, the pseudo-observation value of the marginal degradation process increment can be calculated, and the calculation results of 5 samples at each temperature level can be plotted as shown in the figure. Figure 5 Scatter plot shown.

[0081] Table 4 Parameter estimation results based on MLE

[0082]

[0083] S4: performing component-level related degradation modeling, using a multi-dimensional inverse transformation sampling algorithm with Copula to obtain edge degradation simulation data under a large number of samples, the step S4 includes:

[0084] S401: Figure 4 The distribution trends of the data points at the three temperature levels all show that there is a significant upper tail correlation. Here, it is assumed that temperature does not affect the correlation structure between component performance characteristics, so it can be based on the following formula:

[0085]

[0086] The estimated parameter of the Gumbel Copula function is 1.82, that is:

[0087]

[0088] In the formula, F1(Δy 1j ) and F2(Δy 2j ) represent the cumulative distribution functions of the j-th degradation increment of resistance A and capacitance B, respectively.

[0089] S402: According to Figure 2, then we need to determine the initial distribution of the root node. According to the accelerated degradation theory, temperature does not affect the law of performance degradation but only affects the degradation model parameters. Therefore, the edge degradation model under normal storage temperature can be obtained by extrapolating the edge accelerated degradation model. The normal storage temperature here is 25°C, that is, the absolute temperature is 298.15K, which is substituted into the following formula:

[0090]

[0091] The edge degradation model at normal storage temperature can be obtained as:

[0092]

[0093] S5: Statistically obtain the probability of each state based on the discretization process, that is, obtain the initial distribution of the root node;

[0094] based on and The law of the initial distribution of the root nodes changing with time at normal storage temperature is obtained as follows Figure 6 and Figure 7 As shown in the figure, for the performance characteristics at the component level, it is always in a perfect state at the beginning. From time zero onwards, the probability of being in a perfect state gradually decreases to zero. The probability of being in each intermediate state (i.e., state 2 and state 1 of resistance value A and state 1 of capacitance value B) increases from zero to a peak value and then decreases to zero. The probability of being in state 0 gradually increases from 0 to 1.

[0095] S6: Use the joint tree algorithm for causal reasoning in BN;

[0096] Taking the initial distribution of the root node at each moment as input, through the causal reasoning of BN, we can obtain the law of the state probability distribution of the three system-level nodes, amplitude X, frequency Y and phase angle Z, changing over time. Taking node X as an example, Figure 8 The state probability distribution under the real CPT and the estimated CPT at each moment is given. From Table 3, the real CPT and the estimated CPT are very close, so the probability of each state of node X based on the reasoning of the two is almost equal at all moments.

[0097] S7: Based on the trained BN reasoning, the joint state probability distribution of multiple performance indicator nodes of the system is obtained to calculate the system reliability;

[0098] According to R(t)=P(S1(t)>0,S2(t)>0,...,S d (t)>0) calculate the system reliability, the result is as follows Fig. 9As shown in the figure, the system reliability under the real CPT is very close to that under the estimated CPT, and the system reliability without considering the correlation of component performance characteristic degradation is lower than the two, which is reasonable. In summary, the proposed method can effectively evaluate the system reliability of the three-phase converter.

Claims

1. A three-phase converter system reliability modeling and evaluation method, comprising the following steps: S1. Analyze the components in the three-phase converter system and select the performance characteristics of representative key components in the system and the output characteristics of the system level as the basic variables for constructing BN; S2. Construct BN model and DAG model based on basic variables; S3, then learn the CPT parameters of BN based on MLE; S4, perform component-level related degradation modeling, and use a multi-dimensional inverse transform sampling algorithm with Copula to obtain edge degradation simulation data under a large number of samples; S5. Statistically obtain the probability of each state based on the discretization process, that is, obtain the initial distribution of the root node; S6, using the joint tree algorithm for causal reasoning of BN; S7. Based on the trained BN reasoning, the joint state probability distribution of the system's multiple performance indicator nodes is obtained, thereby calculating the reliability of the three-phase converter system.

2. The specific implementation method of S3 is: let BN and DAG be denoted by B and G respectively, and the number of nodes be n. Then, B is composed of G and the parameter set θ={θ1,θ2,...,θ n}, that is, B=(G,θ). G contains nodes (also called variables) X={X1,X2,...,X n} and a set of directed edges E, namely G = (X, E), X i The CPT (i=1,2,...,n) of i The joint probability distribution P(X) of all variables can be expressed as: Where Pa(X i )(i=1,2,...,n) represents X i Therefore, P(X i ) can be expressed as: The BN parameter P(X i = k|Pa(X i )=j) is expressed as θ ijk ,k∈{1,2,...,r i} represents X i The state of j∈{1,2,...,q i} represents Pa(X i ) combined state, therefore, θ i It is a q i × iThis paper aims to use a set of sample data D = {D1, D2, ..., D N}(a total of N samples) learn the parameter set θ of BN, D l (l=1,2,…,N) defines the value of each variable in X, that is, in represents the variable X in the lth sample j The value or state of . MLE is a purely data-driven parameter learning method. The log-likelihood function of θ is as follows: In the formula, c represents a constant; χ(X i = k, Pa (X i )=j:D l ) means D l The characteristic function of is defined as follows: Therefore, the log-likelihood function can be simplified to: Where N ijk Indicates that D satisfies X i = k and Pa(X i ) = the number of j records, and by maximizing formula (4-5), we get θ ijk The estimated value of is as follows: Where N ij It means that when Pa(X i ) = j when X i ∈{1,2,...,r i} records. Therefore, the following holds true:

3. The specific implementation method of S4 is: let the number of root nodes of BN be m, that is, the component level has m continuously degraded and related performance characteristics. The degradation process of the performance characteristics of m components is recorded as: In BN, the observations of all variables represented by the root nodes occur simultaneously. The total number of observations is z and the same observation time series is t = (t1, t2, ..., t z ). The degradation process Y for the performance characteristics of the i-th (i=1,2,…,m) component i (t), the degradation data collected is y i =(y i,1 ,y i,2 ,...,y i,z ), where y i,j(j=1,2,...,z) is at time t j Y i The observed value of (t), that is, y i,j The theoretical value is Y i (t j ). Let Δy i =(Δy i,1 ,Δy i,2 ,...,Δy i,z ), satisfying Δy i,1 =y i,1 and Δy i,j =y i,j -y i,j-1 (j=2,3,...,z). The degradation correlation of the m component performance characteristics can be characterized by connecting the marginal distributions of the degradation increments using the vine copula method. At this time, the joint distribution of the degradation increments of the component multi-performance characteristics is: F(Δy 1,j ,Δy 2,j ,...,Δy m,j )=C(F1(Δy 1,j ),F2(Δy 2,j ),...,F m (Δy m,j );θ) In the formula, F i (·)(i=1,2,...,m) represents the marginal distribution of degenerate increments; C(·;θ) represents the m-dimensional Copula function with parameter set θ. The above formula is the key to predicting the degradation of multiple performance characteristics of components. As mentioned above, due to the existence of correlation, it is very difficult to directly obtain the analytical form of the degradation distribution of multiple performance characteristics of components at any time. Therefore, this paper generates relevant random numbers based on an inverse transform sampling algorithm with Copula to simulate the degradation path of multiple performance characteristics of components, and then complete the approximate estimation of the initial distribution. Taking m=3 as an example, it is assumed that the Copula function in the formula can be decomposed into a pair-Copula function C based on the vine Copula method. 12 , C 23 and C 13|2 ,The key steps of degradation path simulation are as follows: S301: Generate a random number w from uniform distribution U(0,1) k (k=1,2,3). S302: Let u1=w1. S303: Order in It is C 2|1 The inverse function of (w2|u1), C 2|1The expression of (w2|u1) is: S304: Order in It is C 3|12 The inverse function C of (w3|u1,u2) 3|12 The expression of (w3|u1,u2) is: In the formula, C 3|2 (w3|u2) and C 1|2 The expression of (u1|u2) is: S305: Calculation in Yes F i The inverse function of (·).

4. The specific implementation method of S6 is: using the joint tree algorithm to perform causal reasoning of BN. The main process of the joint tree algorithm is shown in Figure 2.

5. The specific implementation method of S7 is: the expression of system reliability R(t) is: R(t)=P(S1(t)>0,S2(t)>0,...,S d (t)>0) Where d represents the number of system-level nodes; S i (t)(i=1,2,...,d) represents the state of the i-th node at time t.

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