Wiener-IG fusion life prediction method for motor GW insulating material

Abstract

The invention relates to the technical field of life prediction of motor insulating materials, and discloses a Wiener-IG fusion life prediction method for a motor GW insulating material, which is used for performing a high-temperature accelerated degradation test on the motor GW insulating material (especially a polyimide film). According to the method, four key insulation indexes of insulation resistance, insulation capacitance, dielectric loss tangent and maximum partial discharge under accelerated stress are obtained, then a Wiener-Inverse Gaussian (IG) fusion model is constructed to predict the maximum partial discharge of the GW insulation material, and then the service life of the GW insulation material (polyimide film) at different temperatures is predicted. The fusion model can better fit degradation data under different failure mechanisms, and further accurately predict the service life of the GW insulating material.

Description

Technical Field

[0001] The invention relates to the technical field of life prediction of motor ground wall insulation materials, in particular to a Wiener-IG fusion life prediction method for motor GW insulation materials. Background Art

[0002] Electric motors are widely used in power systems, and their safe and reliable operation is very important. Ground wall (GW) insulation is more likely to fail due to manufacturing processes, vibration, thermal expansion, and other reasons. About one-third of motor failures are insulation failures. Establishing a degradation model based on accelerated degradation test (ADT) data and then predicting insulation life is an important method to prevent insulation failure.

[0003] However, when the stress level exceeds the tolerance value, the failure mechanism of the product may change. The traditional random process cannot accurately simulate the evolution of degradation data under different failure mechanisms, and there are few studies on reliability assessment under different failure mechanisms. ADT is limited by the consistency of the failure mechanism of the research object, and the data obtained cannot be used for reliability assessment under different failure mechanisms. Therefore, those skilled in the art need a method that can fit degradation data under different failure mechanisms. Summary of the invention

[0004] The purpose of the present invention is to solve the above problems and to design a Wiener-IG fusion life prediction method for motor GW insulation materials.

[0005] To achieve the above-mentioned purpose, the technical solution of the present invention is a Wiener-IG fusion life prediction method for motor GW insulation materials, comprising:

[0006] A degradation model of GW (ground wall) insulation materials (especially polyimide film) is established based on Wiener process and IG process;

[0007] The failure mechanism of GW insulation materials (especially polyimide films) is introduced and its consistency is analyzed. Based on the degradation model of GW insulation materials, a method that can accurately fit ΔQ is constructed. m Wiener-IG fusion model.

[0008] The establishment process of the degradation model of the GW insulation material is as follows:

[0009] Construct a degradation model for a one-dimensional linear Wiener process:

[0010] X(t)=μt+σB(t) (1)

[0011] Where t is the degradation time; X(t) is the cumulative degradation level at time t; μ is the drift parameter; σ is the diffusion parameter; B(t) is the standard Brownian motion; the maximum likelihood function of the degradation degree of the segment is:

[0012]

[0013] Among them, x ij represents the segmented degradation level of the i-th sample at the j-th cycle;

[0014] i=1,2,…n;j=1,2,…m;Δt is the period interval;

[0015] The maximum likelihood estimates of μ and σ are:

[0016]

[0017] X im is the segmented degradation level of the i-th sample at the m-th cycle;

[0018] Then the probability density function of the IG distribution is:

[0019]

[0020] Where y is the degradation index, u is the positioning parameter, and v is the scale parameter;

[0021] Let Y(t) be the cumulative degradation level at time t, y ij is the segmented degradation level of the i-th sample in the j-th cycle, i = 1, 2, ..., n, j = 1, 2, ..., m; let the location parameter be μ1 and the scale parameter be λ, then the maximum likelihood estimate of μ1 and λ is:

[0022]

[0023] From (3) and (5), we can obtain the degradation model of GW insulating material, where μ in the Wiener process is equal to μ1 in the IG process.

[0024] The analysis process of the failure mechanism is as follows:

[0025] Assume that the motor U b and U N The relationship is:

[0026]

[0027] Among them, U b is the residual breakdown voltage of the motor, U N is the rated voltage of the motor, R1, C0, tanδ, Q mAll of them are degradation indicators of GW insulation materials, R1 is insulation resistance, C0 is insulation capacitance, tanδ is dielectric loss tangent, Q m The partial discharge of the GW insulation material is then used to generate the partial discharge Q m Data to verify the consistency of failure mechanisms;

[0028] The degradation models of R1, C0, and tanδ are established by curve fitting, as shown in equations (7), (8), and (9), respectively, where T c is the temperature in Celsius;

[0029]

[0030]

[0031]

[0032] The segment degradation level ΔQ is analyzed by equations (7), (8) and (9): m distribution, and determine that as the temperature increases, Q m The degradation model is transformed from Wiener process to IG process.

[0033] The construction process of the Wiener-IG fusion model is as follows:

[0034] First, by measuring ΔQ m The weight is obtained by the similarity between the probability density curve of the Wiener distribution and the probability density curve of the IG distribution. Let ΔQ m The probability density curve of and the probability density curves of Wiener distribution and IG distribution are f1(x) and f2(x) respectively, and two sets of data are obtained by linear interpolation:

[0035] y x,1 =f1(x),y x,2 =f2(x) (10)

[0036] Among them, the average value of the second set of data is:

[0037]

[0038] Coefficient of determination R 2 is the similarity between the two curves, and its expression is shown in formula (12).

[0039]

[0040] Normalized similarity R 2 are the weights of the Wiener process and the IG process, denoted as c1 and c2 respectively; c1, c2 and temperature T c The relationship is:

[0041]

[0042] In which, c1 and c2 in formula (13) are set to 0 respectively, and we get:

[0043]

[0044] In the formula, "c1 = 1, c2 = 0" or "c1 = 0, c2 = 1" respectively indicates that the degradation model is the Wiener model or the IG model. Based on the above model fusion method, the probability density function of the segmented degradation level of the Wiener-IG fusion model is derived as follows:

[0045]

[0046] Compared with the prior art, the present invention has the following advantages:

[0047] 1. The present invention uses the proposed Wiener-IG fusion model to accurately fit the degradation data of GW insulation materials under different failure mechanisms at 290°C-320°C, and uses an accurate GW material insulation degradation model to provide a solid foundation for the prediction of motor insulation condition and motor life;

[0048] 2. The present invention applies ADT based on GW insulation materials, proving that the damage mechanism of the material at different temperatures of 290°C-320°C is inconsistent, and transforms the degradation model of maximum partial discharge from Wiener process to IG process;

[0049] 3. The Wiener-IG fusion model proposed in the present invention can accurately simulate the transformation of the maximum partial discharge degradation model from the Wiener process to the IG process, and can fit the degradation data under different failure mechanisms, thereby achieving high modeling accuracy, strong fitting ability, and high prediction accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a flow chart of a Wiener-IG fusion life prediction method for motor GW insulation materials according to the present invention;

[0051] Figure 2 is a distribution diagram of segmented degradation levels under different temperature stresses according to the present invention;

[0052] Figure 3 is a comparison diagram of the models at different temperatures described in the present invention;

[0053] Figure 4 is the area ratio map obtained from Monte Carlo sampling according to the present invention;

[0054] Figure 5is a T test result table of the consistency of the failure mechanism described in the present invention;

[0055] Figure 6 is a weight coefficient table of the model described in the present invention;

[0056] Figure 7 is the similarity evaluation and KS test result table of the present invention;

[0057] Figure 8 It is the AIC result table of the three models described in the present invention at different temperatures;

[0058] Fig. 9 Result table of the area ratios described in the present invention. DETAILED DESCRIPTION

[0059] The present invention will be described in detail below in conjunction with the accompanying drawings. Figure 1-9 As shown;

[0060] This application selects temperature as the accelerated stress. Residual breakdown voltage U b It is the maximum voltage that the insulation material can withstand without breakdown, and is the most intuitive indicator for evaluating the degradation of the insulation material of the motor. Therefore, this application also establishes a model to represent the insulation condition of GW. b The test is destructive, so the test sample is tested at different temperatures. b Changes cannot be obtained directly through testing. In this application, U b The insulation resistance R1, insulation capacitance C0, dielectric loss tangent tanδ, and maximum partial discharge Q m The exported model is obtained indirectly.

[0061] The ADT of GW insulation material (polyimide (PI) film) was designed according to the international standard IEC60505-2011. The PI film sample size was 10 cm × 10 cm × 0.25 mm, and the temperature was set at 290 °C, 300 °C, 310 °C, and 320 °C.

[0062] The degradation rate of thermal insulation materials during production and use is affected by a variety of random factors, so it is more appropriate to describe the degradation process of thermal insulation materials using random processes. The Wiener process and the IG process are two classic random processes widely used to simulate the degradation process.

[0063] The degradation model of the one-dimensional linear Wiener process is:

[0064] X(t)=μt+σB(t)(1)

[0065] Where t is the degradation time; X(t) is the cumulative degradation level at time t; μ is the drift parameter; σ is the diffusion parameter; and B(t) is the standard Brownian motion.ij Denotes the segment degradation level (i=1,2,…n) and (j=1,2,…,m) of the i-th sample at the j-th cycle, then the maximum likelihood function of the segment degradation degree is:

[0066]

[0067] The maximum likelihood estimates of μ and σ are:

[0068]

[0069] The probability density function of the IG distribution is:

[0070]

[0071] Where y is the degradation index, u is the positioning parameter, and v is the scale parameter.

[0072] Let Y(t) be the cumulative degradation level at time t, y ij is the segmented degradation level of the i-th sample in the j-th cycle, (i=1,2,…,n,j=1,2,…,m). Let the location parameter be μ1 and the scale parameter be λ, and their maximum likelihood estimates are:

[0073]

[0074] From (3) and (5), we can see that μ in the Wiener process is equal to μ1 in the IG process.

[0075] The purpose of ADT on GW insulation material is to obtain sufficient degradation data in a short time, and then use the ADT data and acceleration model to infer the life of the material under different stress levels. In order to ensure the validity and accuracy of the extrapolated results, it is necessary to analyze the consistency of the failure mechanism. b From the empirical equation we get:

[0076]

[0077] Among them, UN is the rated voltage of the motor, R1, C0, tanδ, Q m The above four degradation indicators. Partial discharge can characterize the degradation degree of internal defects of insulation materials and is an important indicator for evaluating insulation conditions. m The data is used to verify the consistency of the failure mechanism. The partial discharge test results are as follows Figure 5 shown.

[0078] The results show that the failure mechanism of GW insulation material is consistent at 290℃, 300℃ and 310℃, while at 320℃, its failure mechanism is different from the first three stress levels. m Modeling does not guarantee the accuracy of forecasts.

[0079] The degradation models of R1, C0, and tanδ are established by curve fitting, as shown in equations (7), (8), and (9), respectively, where T c The temperature is in degrees Celsius.

[0080]

[0081]

[0082]

[0083] Modeling the degradation of GW insulation materials under different failure mechanisms and analyzing the segmented degradation level ΔQ m It is found that with the increase of temperature, Q m The degradation model of is transformed from Wiener process to IG process, such as Figure 2 shown.

[0084] In order to establish a more accurate Q m degradation model, thereby achieving more accurate data fitting and life prediction, and constructing a m Wiener-IG fusion model:

[0085] First, two weights need to be introduced to simulate Q m The transition process of the degradation model. By measuring ΔQ m The probability density curve of Figure 2 The weight is obtained by the similarity of the probability density curves of the Wiener distribution and the IG distribution. Let the two test curves be f1(x) and f2(x), and use linear interpolation to get two sets of data:

[0086] y x,1 =f1(x),y x,2 =f2(x)(10)

[0087] The average value of the second set of data is:

[0088]

[0089] Coefficient of determination R 2 As shown in (12), this is the similarity of the two curves:

[0090]

[0091] Will Figure 2 Substituting the two curves of the measured value and the Wiener process into (10), (11), and (12), we can get the similarity of the two curves. Similarly, we can get the similarity of the measured value and the curve of the IG process. The normalized similarity R 2 are the weights of the Wiener process and the IG process, denoted as c1 and c2 respectively, such as Figure 6 shown.

[0092] according to Figure 6 Data, c1, c2 and temperature T c The relationship can be obtained as:

[0093]

[0094] Wherein, c1 and c2 in formula (13) are set to 0, and two boundary temperatures of 230°C and 380°C are obtained. The weights below 230°C and above 380°C are

[0095]

[0096] Wherein "c1 = 1, c2 = 0" or "c1 = 0, c2 = 1" indicates that the degradation model is the Wiener model or the IG model, respectively. When the temperature is between 230°C and 380°C, the degradation model is the Wiener-IG fusion model.

[0097] Based on the above model fusion method, the probability density function of the piecewise degradation level of the Wiener-IG fusion model is derived as follows:

[0098]

[0099] Using the proposed Wiener-IG fusion model, the degradation data of GW insulation materials under different failure mechanisms at 290℃-320℃ can be accurately fitted. An accurate GW material insulation degradation model is of great significance for evaluating the insulation condition of motors and predicting motor life. Based on the ADT of GW insulation materials, it is proved that the damage mechanism of the material at different temperatures of 290℃-320℃ is inconsistent, and the degradation model of maximum local discharge is transformed from the Wiener process to the IG process. The Wiener-IG fusion model proposed in this application can accurately simulate this transformation process and fit the degradation data under different failure mechanisms. The Wiener-IG fusion model proposed in this application has high modeling accuracy, strong fitting ability, and high prediction accuracy for the maximum local discharge degradation process of GW insulation materials.

[0100] Example 1

[0101] Using the same test scheme as 290℃-320℃, more experimental verification was performed at 210℃, 220℃, 380℃ and 390℃. Combined with the degradation data at 290℃-320℃, the results were divided into low temperature (210℃, 220℃) data, medium temperature (290℃~320℃) data and high temperature (380℃, 390℃) data.

[0102] When the temperature is below 230℃, 230℃-380℃ and above 380℃, Q m The degradation process of follows the Wiener process, Wiener-IG fusion model and IG process respectively. In order to verify this conclusion and the accuracy of the Wiener-IG fusion model, this example selects the optimal model at different temperatures by comparing the curve similarity and uses the KS test method to evaluate ΔQ m distribution.

[0103] The similarity between the probability density curves of the segmented degradation degree of different models and the measured values ​​is analyzed and compared, such as Figure 3 As shown, the measured values ​​are subjected to KS test. Usually, the significance level of KS test is set to 0.05. The similarity evaluation results and KS test results are shown in Figure 7 As shown, where h=0 means the measured value conforms to the model, and 1 means the measured value does not conform to the model.

[0104] Depend on Figure 3 and Figure 7 It can be seen that Q m The degradation process of Q can be modeled by the Wiener process at 210℃ and 220℃, the IG process at 380℃ and 390℃, and the Wiener-IG fusion process at 290℃-320℃. Therefore, the Wiener-IG fusion model can accurately fit Q m The degree of segmental degeneration.

[0105] AIC can be used to determine the optimal model with low complexity and good fitting performance, which is calculated as:

[0106] AIC=2K-2InL(16)

[0107] Where K is the number of unknown parameters of the model, and L is the likelihood function of the model.

[0108] The likelihood function of the Wiener process is shown in (2). The likelihood function of the IG process and the proposed Wiener-IG fusion model are shown in (17) and (18), respectively.

[0109]

[0110]

[0111] Substitute ΔQ m into Eqs. (2), (17), and (18) respectively to obtain the AIC results of the three models, as Figure 8 shown.

[0112] From Figure 8 it can be seen that the AIC of the Wiener-IG fusion model is lower than that of the Wiener process and the IG process, indicating that the fusion model has better fitting performance.

[0113] The cumulative error of the model prediction results can be evaluated by the integral area between the two reliability curves at different stress levels. The area is calculated as Eq. (19), where R1(t) and R2(t) represent the two reliability curves respectively.

[0114]

[0115] However, the reliability evaluation of this application is based on Monte Carlo simulation, and the analytical solutions of R1(t) and R2(t) cannot be obtained. To solve this problem, the area ratio based on Monte Carlo simulation is used to evaluate the accuracy of the model prediction, thus coordinating the complex integral into probability statistics. The area ratio w is:

[0116]

[0117] The steps to calculate the area ratio are as follows:

[0118] (i) Let R1(t) < R2(t), and determine the boundary abscissa t* according to the two reliability curves. Then, the sampling region is enclosed by (0,0), (0,1), (t*,1), and (t*,0);

[0119] (ii) Randomly select a point (t, R) within the sampling region;

[0120] (iii) Check whether the sampling point (t, R) is between R1(t) and the coordinate axes or between R1(t) and R2(t);

[0121] (iv) Repeat steps (ii) and (iii) N times, and record the number of sampling points falling between R1(t) and R2(t) as N1, and the number of sampling points falling between R1(t) and the coordinate axes as N2. The area between R1(t) and R2(t) and the area between R1(t) and the coordinate axes can be derived through the above steps, as shown in Eqs. (21) and (22):

[0122]

[0123]

[0124] Then the area ratio w is

[0125]

[0126] Based on the reliability curve of 290℃-320℃ obtained from the medium and low temperature ADT data, assuming N=5000, N1, N2 and w can be obtained through Monte Carlo simulation. The results are shown in Figure 4 and Fig. 9 shown.

[0127] Figure 4 In the figure, R1(t) and R2(t) are the reliability curves derived from medium-temperature data and low-temperature data, respectively; M1 and M2 are the number of sampling points between R1(t) and R2(t) and between R1(t) and the coordinate axis, respectively.

[0128] Usually, the area ratio threshold can be set to 0.2. If w≤0.2, the model prediction results are accurate and effective. It can be seen that the area ratios are all less than the threshold, indicating that the GW insulation material life prediction is accurate and effective.

[0129] An accurate insulation degradation model for GW materials is of great significance for evaluating the insulation condition of motors and predicting the life of motors. Based on the ADT of GW insulation materials, it is proved that the damage mechanism of the material at different temperatures of 290℃-320℃ is inconsistent, and the degradation model of maximum local discharge is transformed from Wiener process to IG process. The Wiener-IG fusion model proposed in this application can accurately simulate this transformation process and fit the degradation data under different failure mechanisms. The degradation data at different temperature levels show that the Wiener-IG fusion model has high modeling accuracy, strong fitting ability and high prediction accuracy for the maximum local discharge degradation process of PI film 6050.

[0130] It should be noted that, in this application, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions. The sentence "includes an element defined by ... does not exclude the existence of other identical elements in the process, method, article or device including the element".

[0131] The above technical solutions only reflect the preferred technical solutions of the technical solutions of the present invention. Some changes that may be made to certain parts thereof by technicians in this technical field all reflect the principles of the present invention and fall within the protection scope of the present invention.

Claims

1. A Wiener-IG fusion life prediction method for motor GW insulation materials, characterized in that: include: A degradation model of GW insulation materials is established based on Wiener process and IG process; The failure mechanism of GW insulation materials is introduced and its consistency is analyzed. Based on the degradation model of GW insulation materials, a method that can accurately fit ΔQ is constructed. m Wiener-IG fusion model.

2. A Wiener-IG fusion life prediction method for motor GW insulation materials according to claim 1, characterized in that: The establishment process of the degradation model of the GW insulation material is as follows: Construct a degradation model for a one-dimensional linear Wiener process: X(t)=μt+σB(t) (1) Where t is the degradation time; X(t) is the cumulative degradation level at time t; μ is the drift parameter; σ is the diffusion parameter; B(t) is the standard Brownian motion; the maximum likelihood function of the degradation degree of the segment is: Among them, x ij represents the segmented degradation level of the i-th sample at the j-th cycle; i=1,2,…n;j=1,2,…m;Δt is the period interval; The maximum likelihood estimates of μ and σ are: X im is the segmented degradation level of the i-th sample at the m-th cycle; Then the probability density function of the IG distribution is: Where y is the degradation index, u is the positioning parameter, and v is the scale parameter; Let Y(t) be the cumulative degradation level at time t, y ij is the segmented degradation level of the i-th sample in the j-th cycle, i = 1, 2, ..., n, j = 1, 2, ..., m; let the location parameter be μ1 and the scale parameter be λ, then the maximum likelihood estimate of μ1 and λ is: From (3) and (5), we can obtain the degradation model of GW insulating material, where μ in the Wiener process is equal to μ1 in the IG process.

3. The Wiener-IG fusion life prediction method for motor GW insulation materials according to claim 1 is characterized in that: The analysis process of the failure mechanism is as follows: Assume that the motor U b and U N The relationship is: Among them, U b is the residual breakdown voltage of the motor, U N is the rated voltage of the motor, R1, C0, tanδ, Q m All of them are degradation indicators of GW insulation materials, R1 is insulation resistance, C0 is insulation capacitance, tanδ is dielectric loss tangent, and then partial discharge Q m Data to verify the consistency of failure mechanisms; The degradation models of R1, C0, and tanδ are established by curve fitting, as shown in equations (7), (8), and (9), respectively, where T c is the temperature in Celsius; The segmented degradation level ΔQ is analyzed by equations (7), (8) and (9): m distribution, and determine that as the temperature increases, Q m The degradation model is transformed from Wiener process to IG process.

4. The Wiener-IG fusion life prediction method for motor GW insulation materials according to claim 1, characterized in that: The construction process of the Wiener-IG fusion model is as follows: First, by measuring ΔQ m The weight is obtained by the similarity between the probability density curve of the Wiener distribution and the probability density curve of the IG distribution. Let ΔQ m The probability density curve of and the probability density curves of Wiener distribution and IG distribution are f1(x) and f2(x) respectively, and two sets of data are obtained by linear interpolation: y x,1 =f1(x),y x,2 =f2(x)(10) Among them, the average value of the second set of data is: Coefficient of determination R 2 is the similarity between the two curves, and its expression is shown in formula (12). Normalized similarity R 2 are the weights of the Wiener process and the IG process, denoted as c1 and c2 respectively; c1, c2 and temperature T c The relationship is: In which, c1 and c2 in formula (13) are set to 0 respectively, and we get: In the formula, "c1=1, c2=0" or "c1=0, c2=1" respectively indicates that the degradation model is the Wiener model or the IG model. Based on the above model fusion method, the probability density function of the segmented degradation level of the Wiener-IG fusion model is derived as follows:

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