A small sample nano-tio2 modified polyimide film life evaluation method based on a gray neural network model

Abstract

The application provides a small sample nano-TiO2 modified polyimide (PI) film life evaluation method based on a grey neural network model; step 1, nano-TiO2 modified PI film is prepared, an accelerated electrical aging test is carried out, and failure data are obtained; step 2, a grey neural network is constructed and trained, and expanded data similar to original data characteristics and change rules are obtained; and step 3, parameter estimation is carried out by adopting a least square method, and life evaluation results of different failure data sample amounts, distribution models, experience cumulative failure functions and electrical life models are analyzed and compared, so that the life of the nano-TiO2 modified PI film can be more accurately predicted.

Description

Technical Field

[0001] This invention relates to the field of aging lifetime assessment technology for insulating materials, and in particular to a method for assessing the electrical lifetime of small-sample nano-TiO2 modified polyimide films using a gray neural network model. Background Technology

[0002] Polyimide (PI) film is one of the important insulating materials in the electrical field, and its excellent performance has led to its widespread application in industries such as electrical insulation, flexible displays, aerospace, and 5G communications. The reliability of nanoparticle-modified PI films has improved with advancements in fabrication processes and dielectric property modulation technologies, but this has also resulted in longer life testing times, increased testing costs, and fewer failure data points. This limits the application of traditional insulation life assessment methods based on large sample sizes to address insulation life assessment problems with small sample data.

[0003] Therefore, it is necessary to study methods that can accurately assess the lifetime of nanoparticle-modified PI films with small sample sizes. Summary of the Invention

[0004] This invention proposes a small-sample method for evaluating the electrical lifetime of nano-TiO2 modified polyimide films based on a grey neural network model. The method includes the following steps:

[0005] Step 1: Prepare nano-TiO2 modified polyimide (PI) films with a thickness of 25±1μm by in-situ polymerization. Select modified PI films from the same batch prepared by the same process with slight performance differences as test samples. Conduct constant voltage accelerated electro-aging failure tests at different voltage levels to obtain accelerated failure data of nano-TiO2 modified PI films. The accelerated failure data includes the failure time of individual samples, mathematical average failure time and statistical failure time at a specified voltage level.

[0006] Step 2: Establish a grey neural network model. Generate a new sequence by forward accumulating the accelerated failure data described in Step 1. Use the new sequence as the training set and test set of the grey neural network model.

[0007] Step 3: Using different empirical cumulative failure functions as input to the trained grey neural network model, expanded data with similar characteristics and variation patterns to the original data is obtained. Parameter estimation is performed using the least squares method, and the sample size of the failure data before and after expansion is analyzed and compared. Different failure data probability distribution models are used: Weibull distribution model and log-normal distribution model; different empirical cumulative failure functions are used: mathematical expectation formula, median formula, Blom formula, and Hessian formula; different electrical lifetime models are used: exponential function electrical lifetime model and inverse power function electrical lifetime model, and their lifetime assessment results are analyzed.

[0008] Further, the preparation method of nano-TiO2 modified PI film is as follows: First, nano-TiO2 particles and dimethylacetamide (DMAC) solution are added to a round-bottom flask and stirred for 1.5 h to obtain a uniformly distributed suspension. Then, 4,4′-diaminodiphenyl ether (ODA), which has been dried in a vacuum drying oven for 3 h in advance, is added to the flask, and the solution is ultrasonically vibrated for 30 min until the ODA is completely dissolved.

[0009] Further, the dried pyranoic anhydride (PMDA) was divided into five portions and slowly poured into the suspension sequentially, with a mass ratio of ODA to PMDA of 1:1.05. After the PMDA was completely dissolved, the mixture was stirred for 4 hours and then cast onto a custom-made glass plate coated with a neutral release agent. The glass plate was then placed in a vacuum drying oven and dried for 2 hours. Finally, it was subjected to gradient curing at 100, 140, 180, 220, and 260 °C for 1 hour each, respectively, to peel off a 25 ± 1 μm thick nano-TiO2 modified PI film from the glass plate.

[0010] Furthermore, at several voltage values ​​U1, U2, ..., U i Under the conditions of using a cylindrical electrode, electrode gap d1, test temperature T1, and voltage frequency f1, the electrical lifetime of the sample, i.e., the failure time of each nano-TiO2 modified PI film sample, is obtained.

[0011] Furthermore, the grey neural network model is established as follows: Define U i The original failure data sequence of nano-TiO2 modified PI film under voltage is x (0) (k) (k = 1, 2, ..., N), for x (0) (k) Perform forward accumulation to obtain a new sequence. Establish x (1) Differential equation of (k) Its corresponding discrete-time series response function is After processing, the training and test sets of the grey neural network are obtained. A neural network for the failure time of nano-TiO2 modified PI thin films was established and trained, and the learning rate, maximum number of training iterations, and minimum mean square error of training were set.

[0012] Furthermore, by using different empirical cumulative failure functions, the cumulative failure probability values ​​corresponding to different voltages in the probability distribution model are obtained.

[0013] The empirical cumulative failure probability function is as follows:

[0014] Mathematical expectation formula:

[0015]

[0016] Mean value formula:

[0017]

[0018] Blom formula:

[0019]

[0020] Hessian formula:

[0021]

[0022] Furthermore, the distribution of electrical lifetime data of nano-TiO2 modified PI thin films was simulated using different probability distribution models.

[0023] The probability distribution function of the Weibull distribution model is:

[0024]

[0025] Density function:

[0026]

[0027] Furthermore, taking two logarithmic operations yields:

[0028] Y = ln[-ln F] i [(t)]=βln t i -βlnα

[0029] Wherein: F i (t) represents the cumulative failure probability; t represents the sample breakdown time; α represents the scale parameter; and β represents the shape parameter.

[0030] Log-normal distribution model probability distribution function:

[0031]

[0032] Density function:

[0033]

[0034] Where Φ(x) is the standard normal distribution function.

[0035] Furthermore, the electrical lifetime of nano-TiO2 modified PI films was characterized by the Weibull scale parameter α and the expected value μ of the log-normal distribution, respectively.

[0036] Furthermore, the characteristic electrical lifetime data of nano-TiO2 modified PI films under different probability models were fitted using a lifetime assessment model. The exponential function electrical lifetime model (EM) and the inverse power function electrical lifetime model (IPM) are as follows:

[0037] L=c·exp(-kU)

[0038] L=aU -n

[0039] Where L is the failure time of the sample under the test voltage, in seconds; U is the test voltage applied to the sample, in kV; n, a, k, and c are constants related to the test environment, sample material properties, electro-aging mechanism, and sample geometry, which are obtained through experiments.

[0040] Furthermore, the least squares method was used to obtain lifetime assessment results for different failure data sample sizes, distribution models, empirical cumulative failure functions, and electrical lifetime models. Attached Figure Description

[0041] Figure 1 The present invention provides a flowchart for the preparation of nano-TiO2 modified PI thin films;

[0042] Figure 2 A schematic flowchart illustrating a method for evaluating the electrical lifetime of small-sample nano-TiO2 modified polyimide films based on a gray neural network model, provided by this invention.

[0043] Figure 3 Table of electrical lifetime test data for nano-TiO2 modified polyimide films provided by this invention;

[0044] Figure 4 This is a comparison table of lifetime assessment before and after the expansion of failure data for nano-TiO2 modified PI films provided by this invention. Detailed Implementation

[0045] This invention proposes a small-sample method for evaluating the electrical lifetime of nano-TiO2 modified polyimide films based on a grey neural network model. The method includes the following steps:

[0046] Step 1: Prepare nano-TiO2 modified polyimide (PI) films with a thickness of 25±1μm by in-situ polymerization. Select modified PI films from the same batch prepared by the same process with slight performance differences as test samples. Conduct constant voltage accelerated electro-aging failure tests at different voltage levels to obtain accelerated failure data of nano-TiO2 modified PI films. The accelerated failure data includes the failure time of individual samples, mathematical average failure time and statistical failure time at a specified voltage level.

[0047] Step 2: Establish a grey neural network model. Generate a new sequence by forward accumulating the accelerated failure data described in Step 1. Use the new sequence as the training set and test set of the grey neural network model.

[0048] Step 3: Using different empirical cumulative failure functions as input to the trained grey neural network model, expanded data with similar characteristics and variation patterns to the original data is obtained. Parameter estimation is performed using the least squares method, and the sample size of the failure data before and after expansion is analyzed and compared. Different failure data probability distribution models are used: Weibull distribution model and log-normal distribution model; different empirical cumulative failure functions are used: mathematical expectation formula, median formula, Blom formula, and Hessian formula; different electrical lifetime models are used: exponential function electrical lifetime model and inverse power function electrical lifetime model, and their lifetime assessment results are analyzed.

[0049] Preparation method of nano-TiO2 modified PI film: First, add nano-TiO2 particles and dimethylacetamide (DMAC) solution to a round bottom flask, stir with a stirrer for 1.5 h to obtain a uniformly distributed suspension.

[0050] Add 4,4′-diaminodiphenyl ether (ODA), which has been dried in a vacuum drying oven for 3 hours, to the flask, and sonicate the solution for 30 minutes until the ODA is completely dissolved.

[0051] Five portions of dried pyranoic anhydride (PMDA) were slowly poured into the suspension in sequence, with a mass fraction ratio of ODA to PMDA of 1:1.05.

[0052] After the PMDA is completely dissolved, the mixture is stirred with a stirrer for 4 hours and then cast onto a custom glass plate coated with a neutral release agent.

[0053] Place the glass plate in a vacuum drying oven and dry for 2 hours.

[0054] Finally, the nano-TiO2 modified PI film with a thickness of 25±1μm was peeled off from the glass plate by gradient curing at 100, 140, 180, 220 and 260℃ for 1h respectively in an oven.

[0055] Given several voltage values ​​U1, U2, ..., U i Under the conditions of using a cylindrical electrode, electrode gap d1, test temperature T1, and voltage frequency f1, the electrical lifetime of the sample, i.e., the failure time of each nano-TiO2 modified PI film sample, is obtained.

[0056] The grey neural network model is established as follows: Define U i The original failure data sequence of nano-TiO2 modified PI film under voltage is x (0) (k) (k = 1, 2, ..., N), for x (0) (k) Perform forward accumulation to obtain a new sequence.

[0057] Establish x (1) Differential equation of (k) Its corresponding discrete-time series response function is

[0058] After processing, the training and test sets of the grey neural network are obtained.

[0059] A neural network was established and trained to study the failure time of nano-TiO2 modified PI films, with a learning rate of 0.05.

[0060] Set the maximum number of learning attempts to 2000.

[0061] The minimum mean square error for training is set to 0.001;

[0062] The neural network is trained to generate predicted and ideal values ​​for the capacity sequence, and the error between the ideal and the expected values ​​is obtained.

[0063] Randomly select the next learning sample vector and provide it to the network, then return to the previous step until all training samples have been trained.

[0064] A new set of input and output samples is randomly selected from the learning samples until the global error of the network is less than a pre-set minimum value, that is, the network converges and the learning ends;

[0065] By using different empirical cumulative failure functions, the cumulative failure probability values ​​corresponding to different voltages in the probability distribution model are obtained;

[0066] The empirical cumulative failure probability function is as follows:

[0067] Mathematical expectation formula:

[0068]

[0069] Mean value formula:

[0070]

[0071] Blom formula:

[0072]

[0073] Hessian formula:

[0074]

[0075] The distribution of electrical lifetime data of nano-TiO2 modified PI thin films was simulated using different probability distribution models.

[0076] The probability distribution function of the Weibull distribution model is:

[0077]

[0078] Density function:

[0079]

[0080] Furthermore, taking two logarithmic operations yields:

[0081] Y = ln[-ln F] i [(t)]=βln t i -βlnα

[0082] Wherein: F i (t) represents the cumulative failure probability; t represents the sample breakdown time; α represents the scale parameter; and β represents the shape parameter.

[0083] Log-normal distribution model probability distribution function:

[0084]

[0085] Density function:

[0086]

[0087] Where Φ(x) is the standard normal distribution function.

[0088] The electrical lifetime of nano-TiO2 modified PI films was characterized by the Weibull scale parameter α and the expected value μ of the log-normal distribution, respectively.

[0089] The characteristic electrical lifetime data of nano-TiO2 modified PI films under different probability models were fitted using a lifetime assessment model. The exponential function electrical lifetime model (EM) and the inverse power function electrical lifetime model (IPM) are as follows:

[0090] L=c·exp(-kU)

[0091] L=aU -n

[0092] Where L is the failure time of the sample under the test voltage, in seconds; U is the test voltage applied to the sample, in kV; n, a, k, and c are constants related to the test environment, sample material properties, electro-aging mechanism, and sample geometry, which are obtained through experiments.

[0093] The least squares method was used to obtain lifetime assessment results for different data sample sizes, distribution models, empirical cumulative failure functions, and electrical lifetime models.

Claims

1. A method for evaluating the electrical endurance of a small sample of a TiO2 modified polyimide (PI) film based on a grey neural network model, characterized in that, The method comprises the following steps: Step 1: First, a nano-TiO2 modified PI film with a thickness of 25±1 μm The same batch of modified PI films prepared by the same process and with little performance difference were selected as test samples, and constant voltage accelerated electrical aging failure tests were carried out under different voltage levels to obtain accelerated failure data of the nano-TiO2 modified PI film, wherein the accelerated failure data includes the failure time of individual samples under a specified voltage level. Step 2: Establish a grey neural network model, generate a new sequence by accumulating the accelerated failure data in step 1 in a forward sequence, and take the new sequence as a training set and a test set of the grey neural network model; The step 2 specifically comprises: definition The original failure data sequence of nano-TiO2 modified PI films under voltage is as follows ,right Perform forward accumulation to obtain a new sequence. ;Establish differential equations Its corresponding discrete-time series response function is After processing, the training and test sets of the grey neural network are obtained. ; Establish and train a neural network for nano-TiO2 modified PI thin films, and set the learning rate, maximum number of learning iterations, and minimum mean square error of training. Step 3: Take different empirical cumulative failure functions as inputs of the trained grey neural network model to obtain expanded data similar to the original data characteristics and variation rules; perform parameter estimation by using a least square method, analyze and compare failure data sample sizes before and after expansion; different failure data probability distribution models: Weibull distribution model and lognormal distribution model; different empirical cumulative failure functions: mathematical expectation formula, median formula, Blom formula and Hesien formula; and different electrical life models: life evaluation results of an exponential function electrical life model and an inverse power function electrical life model.

2. The small sample nanometer TiO2 modified polyimide film electrical endurance evaluation method based on the gray neural network model according to claim 1, characterized in that, Step 1 specifically includes: First, adding nano-TiO2 particles and dimethylacetamide (DMAC) solution to a round-bottom flask and stirring for 1.5 hours to obtain a uniformly distributed suspension; adding 4,4′-diaminodiphenyl ether (ODA) that has been dried in a vacuum drying oven for 3 hours in advance to the flask, and using ultrasonic vibration for 30 minutes until the ODA is completely dissolved; then, dividing the dried pyranoic anhydride (PMDA) into 5 portions and slowly pouring them into the suspension in sequence, with a mass fraction ratio of ODA to PMDA of 1:1.05; after the PMDA is completely dissolved, stirring the mixture for 4 hours and casting it onto a custom glass plate coated with a neutral release agent; placing the glass plate in a vacuum drying oven and drying for 2 hours; finally, performing gradient curing in an oven at 100, 140, 180, 220, and 260°C for 1 hour respectively, and peeling off a 25±1mm thick layer from the glass plate. μm Nano-TiO2 modified PI film; then at several voltage values Below, using a cylindrical plate electrode, the electrode gap... Test temperature voltage frequency The electrical lifetime of the sample is obtained, that is, the failure time of each nano-TiO2 modified PI film sample.

3. The small sample nanometer TiO2 modified polyimide film electrical life evaluation method of the grey neural network model according to claim 1, wherein the step 2 specifically comprises: By using different empirical cumulative failure functions, the cumulative failure probability values corresponding to different voltages of the probability distribution model are obtained; The empirical cumulative failure probability function is: Mathematical expectation formula: Median formula: Blom formula: Hesien formula: The distribution of the nanometer TiO2 modified PI film electrical life data is simulated by using different probability distribution models; The Weibull distribution model probability distribution function is: Density function: The logarithm operation is performed twice to obtain: wherein: F i (t) is the cumulative failure probability; t is the sample breakdown time; α is the scale parameter; β is the shape parameter; The lognormal distribution model probability distribution function is: Density function: wherein Φ(x) is the standard normal distribution function; The scale parameter of Weibull distribution α and the expectation of lognormal distribution μ characterize the electrical lifetime of the PI film modified by nano-TiO2. The characteristic electrical life data of the nanometer TiO2 modified PI film under different probability models are fitted by using a life evaluation model; the exponential function electrical life model (EM) and the inverse power function electrical life model (IPM) are respectively: wherein, L is the failure time of the sample at the test voltage, s U is the test voltage applied to the sample, kv n , a , k , c are constants related to the test environment, the material properties of the sample, the mechanism of electrical aging and the geometry of the sample, and are determined by the test;​​ The life evaluation results of different failure data sample sizes, distribution models, empirical cumulative failure functions and electrical life models are obtained by using a least square method.

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