Capacitance performance reliability analysis method and system of operational amplifier

Abstract

The invention provides a capacitive performance reliability analysis method and system for an operational amplifier, and relates to the technical field of reliability analysis of electronic components, and the method comprises the steps: carrying out an accelerated degradation test on a ceramic capacitor of the operational amplifier, and obtaining degradation information of electrical parameters and non-electrical parameters of the capacitor; selecting N parameters with an obvious degradation trend from the numerous parameters as key degradation parameters, and carrying out a reliability evaluation process of the capacitor on the basis of the key degradation parameters; analyzing the degradation information of the electrical parameters and the non-electrical parameters of the capacitor to obtain the reliability value of the capacitor under the single performance of the N key parameters; and according to different single-performance degradation amount reliability functions, selecting an appropriate Copula function as a connection function, and calculating a reliability function value under multiple performances according to the connection function. The problem that the capacitance performance of the operational amplifier is difficult to accurately analyze is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of reliability analysis of electronic components, and in particular to a method and system for analyzing the reliability of capacitance performance of an operational amplifier. Background Art

[0002] Operational amplifiers have functions such as signal processing, system control, and analog calculation. They are widely used in various circuits and play an important role in electronic engineering. Ensuring the reliability of operational amplifiers is crucial to ensuring the normal performance and stable operation of electronic equipment. According to statistics on the root causes of operational amplifier failures, operational amplifier system failures caused by ceramic capacitor failure account for more than 30%. Generally speaking, the life of ceramic capacitors will be reduced by half for every 10°C increase in temperature. Therefore, over time, internal cracks and oxide vacancy migration are likely to occur, making ceramic capacitors the weakest device in the operational amplifier system. Damage to ceramic capacitors can easily lead to failures of other related components, interrupting the normal operation of the entire operational amplifier system and reducing system reliability. Therefore, in order to maintain the stable and reliable operation of the operational amplifier system and improve the reliability of the system, it is necessary to accurately grasp the degradation law of ceramic capacitors and study their degradation state.

[0003] Ceramic capacitors are mainly composed of dielectric ceramics, metal electrodes and metal terminals. The failure of ceramic capacitors is mainly caused by internal cracks caused by mechanical vibration and thermal expansion. Under the action of key stresses (such as voltage, current and ambient temperature), the electrical parameters of ceramic capacitors will eventually drift. As the stress applied in the capacitor evolves on a time scale, a series of physical and chemical changes will occur inside the capacitor at the microscopic level, leading to changes in the electrical parameters (such as equivalent series resistance and capacitance, etc.) and non-electrical parameters (such as weight) of the capacitor. By selecting key degradation parameters from many parameters and monitoring these key parameters, the degradation state of the capacitor can be determined, and it can be replaced in time before a destructive failure occurs to avoid cascading failures, thereby improving the reliability of the op amp system.

[0004] In order to improve efficiency or gain time and cost advantages, the degradation data of capacitor-related parameters can be obtained through accelerated degradation tests. At present, the reliability modeling methods based on accelerated degradation data can be divided into three categories: methods based on degradation trajectories, methods based on degradation quantity distribution, and methods based on random processes. However, the performance degradation trajectories of capacitors vary greatly among individual products, making it difficult to determine the performance degradation model; and the performance degradation data of the product cannot be measured repeatedly, so the complete degradation process of the product cannot be modeled. Therefore, we choose a more advantageous modeling method based on degradation quantity distribution, and comprehensively utilize the statistical advantages of multiple degradation quantity distributions to more accurately characterize its degradation trajectory situation. In order to more comprehensively utilize the degradation information of multiple parameters and accurately evaluate the reliability of the capacitor, a multi-performance degradation technology with Copula function as the connection function is adopted. Summary of the invention

[0005] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method and system for analyzing the reliability of capacitance performance of an operational amplifier, which solves the problem that it is difficult to accurately analyze the capacitance performance of an operational amplifier.

[0006] In order to achieve the above objectives, the technical solution adopted by the present invention is: a capacitance performance reliability analysis method of an operational amplifier, comprising:

[0007] Step 1: Perform an accelerated degradation test on the ceramic capacitor of the operational amplifier to obtain the degradation information of the electrical parameters and non-electrical parameters of the capacitor, and select N parameters with obvious degradation trends as key degradation parameters, based on which to carry out the reliability evaluation process of the capacitor;

[0008] Step 2: For each of the N key degradation parameters obtained in step 1, calculate the difference between their empirical cumulative probability and theoretical cumulative probability. In the probability distribution commonly used in engineering, the obtained Anderson-Darling statistic value is used to measure the degree to which the performance data of the above key degradation parameters obey a specific distribution. For a specific data set and distribution, the better the distribution fits the data, the smaller the statistic value.

[0009] Step 3: According to the fitted distributions corresponding to the N key degradation parameters obtained in step 2, the first two distributions with the best fit are selected respectively. For the original data of the N key degradation parameters in step 1, new sample data are obtained by repeated sampling with replacement. Based on the expanded sample data, the Bootstrap method is used to perform statistical analysis and estimate the statistical value of the unknown parameter of the fitted distribution of each key degradation parameter;

[0010] Step 4: Based on the unknown parameter estimates of the optimal fitting distribution selected for the N key degradation parameters obtained in step 3 at each monitoring moment, this set of time series data reflects the degradation of the distribution, and data fitting is performed on it, and various error indicators are comprehensively evaluated to select the most appropriate mathematical model for the change of unknown parameters over time;

[0011] Step 5: Based on the two fitted distribution mathematical models under the N key degradation parameters obtained in step 4, a mixed degradation quantity distribution model is constructed, and the intelligent algorithm particle swarm algorithm is used to optimize and iterate the unknown parameters to obtain the mixed degradation quantity distribution degradation model of each key parameter;

[0012] Step 6: Set the failure threshold of key parameters based on engineering experience. According to the essential definition of reliability in the probabilistic sense, substitute the unknown parameter degradation model obtained in step 5 into it to solve it, and obtain the reliability value of the capacitor under the single performance of N key degradation parameters;

[0013] Step 7: According to the reliability values ​​of different single performance degradation quantities obtained in step 6, select a suitable Copula function as the connection function and use it to calculate the reliability function value under multiple performances.

[0014] Furthermore, the step 3 comprises the following steps:

[0015] Step 31, according to the fitting distributions corresponding to the N key degradation parameters obtained in step 2, respectively select the first two distributions with the best fitting;

[0016] Step 32: for the original data of the N key degradation parameters in step 1, new sample data is obtained by a repeated sampling method with replacement to obtain expanded sample data, wherein the expanded sample data is used as the input of the original data;

[0017] Step 33, sorting the original data of the N key degradation parameters in ascending order to obtain order statistics;

[0018] Step 34: According to the obtained order statistics, the cumulative probability value of each location is obtained by using the simplest estimation method, and a first empirical cumulative distribution function is constructed according to the cumulative probability value;

[0019] Step 35, generating by simulation a random sample that obeys a first empirical cumulative distribution function, wherein the random sample is a bootstrap sample;

[0020] Step 36: construct a second empirical cumulative distribution function using the bootstrap sample, and analyze the Bootstrap estimate of the unknown parameter based on the second empirical cumulative distribution function;

[0021] Step 37, determine whether the number of iterations has been reached, if so, obtain a set of Bootstrap estimates of the unknown parameters and proceed to step 38, otherwise, return to step 35;

[0022] Step 38: Perform statistical analysis on a set of Bootstrap estimated values ​​of the unknown parameters obtained, and estimate the statistical value of the unknown parameters of the fitting distribution of each key parameter, to obtain the unknown parameter estimates of the optimal fitting distribution selected for the N key parameters at each monitoring moment.

[0023] Furthermore, the expression of the mixed degradation amount distribution degradation model is as follows:

[0024]

[0025] Where F(x) represents the empirical distribution function of the degradation amount, a and b represent unknown parameters, η and β represent the scaling factor and shape parameter of the Weibull distribution respectively, x represents the degradation amount, erf() represents the error function, μ represents the mean, σ represents the standard deviation, and t' represents the independent variable for solving the integral.

[0026] Furthermore, the expression of the reliability value is as follows:

[0027] R1(t)=P{X>D1}

[0028] Among them, R1(t) represents the reliability value, D1 represents the failure threshold of the key parameter, P represents the solution of probability, and X represents the degradation amount.

[0029] Furthermore, the step 7 comprises the following steps:

[0030] Step 71, fitting respective degradation curve models for different degradation reliability values, and estimating pseudo life values ​​under different performance degradation amounts in combination with failure thresholds;

[0031] Step 72: using the pseudo life value as sample data, estimating the unknown parameters of each Copula function using the maximum likelihood function method, and obtaining the estimated values ​​of the unknown parameters of each Copula function;

[0032] Step 73, according to the estimation of the unknown parameters of each Copula function, combined with the original data of the degradation parameter, calculate the AIC and BIC values ​​respectively to obtain the most suitable Copula function;

[0033] Step 74: Use the most suitable Copula function obtained as the connection function between different performance degradation quantities, and calculate the reliability function value under multiple performances to complete the performance reliability analysis of the operational amplifier capacitor.

[0034] Furthermore, the expression of the reliability function value under multiple performances is as follows:

[0035]

[0036] Among them, R 1,2 (t) represents the reliability function value under multiple performances, P represents the solution of probability, T1 represents the pseudo-life value of the random variable obtained when the degradation amount is the capacity value, T2 represents the pseudo-life value of the random variable obtained when the insulation resistance value is the time value, t represents time, R1(t) represents the reliability obtained when the capacity value is degraded, R2(t) represents the reliability obtained when the insulation resistance value is degraded, F 1,2 (t) represents the joint distribution function of random variables T1 and T2, C clayton () represents the Copula function, and α represents the unknown parameter of the Copula function.

[0037] The present invention also provides a capacitance performance reliability analysis system for an operational amplifier, comprising a processor, wherein the processor is used for the capacitance performance reliability analysis method for the operational amplifier.

[0038] The beneficial effects of the present invention are:

[0039] (1) The performance reliability analysis method of the operational amplifier capacitor described in the present invention analyzes the distribution characteristics of key degradation parameters of multiple samples at each moment, comprehensively judges the fitting degree of common degradation distribution types and actual capacitance data according to AD statistics, and selects two suitable fitting distributions of key parameters from them. On the basis of the original test sample data, the original data is resampled by computer to estimate the statistical characteristics of the unknown parameter statistics of the suitable fitting distribution and obtain the final estimated value, and the degradation model of the mixed degradation quantity distribution is constructed based on the particle swarm algorithm, and finally the single performance reliability model is solved. This method overcomes the problems that the performance degradation trajectories between individual products are quite different, making it difficult to determine the performance degradation model; and the performance degradation data of the product cannot be repeatedly measured, and the complete degradation process of the product cannot be modeled.

[0040] (2) After determining the degradation amount of the batch samples, fit the respective degradation curve models, and then estimate the pseudo-life value under a single performance degradation amount in combination with the failure threshold; take the pseudo-life value as the sample data, and use the maximum likelihood function method to estimate the unknown parameters of the five common Copula functions; after obtaining the estimated values ​​of the unknown parameters of the five Copula functions, calculate the AIC / BIC values ​​in combination with the sample data and select the appropriate Copula function as the connection function between different performance degradation amounts. For multiple performance degradation amounts, the results obtained only when each degradation amount does not reach the failure threshold are the reliability of multiple performances. However, in view of the fact that the performance status of capacitors often requires multiple performance monitoring parameters to jointly characterize, and the interactions between the performance monitoring parameters have a certain correlation, a capacitor multi-performance parameter reliability evaluation model based on the Copula theory that contains the correlation information between the performance parameters can significantly improve its reliability prediction accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 The figure is an exemplary flow chart of a capacitance performance reliability analysis method of an operational amplifier in an example of the present invention.

[0042] Figure 2 It is a schematic diagram of the capacity value change curve of this batch of samples under the 1500V model in the example of the present invention over time.

[0043] Figure 3 It is a schematic diagram of the insulation resistance value of this batch of samples under the 1500V model in the example of the present invention.

[0044] Figure 4 Schematic diagram of the estimated values ​​of η and β at various moments in the example of the present invention.

[0045] Figure 5 Schematic diagram of the estimated values ​​of μ and σ at various moments in the example of the present invention.

[0046] Figure 6 It is a curve diagram of 1500V withstand voltage reliability with capacity as degradation amount in an example of the present invention.

[0047] Figure 7 Schematic diagram of reliability curve of two related performance degradation quantities in an example of the present invention. DETAILED DESCRIPTION

[0048] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0049] Example 1

[0050] like Figure 1 As shown, the present invention provides a method for analyzing the reliability of capacitance performance of an operational amplifier, and the implementation method thereof is as follows:

[0051] Step 1: Perform an accelerated degradation test on the ceramic capacitor of the operational amplifier to obtain the degradation information of the electrical parameters and non-electrical parameters of the capacitor, and select N parameters with obvious degradation trends as key degradation parameters, based on which to carry out the reliability evaluation process of the capacitor;

[0052] In this embodiment, an accelerated degradation test is performed on the ceramic capacitor of the operational amplifier to obtain degradation information of the electrical parameters (such as equivalent series resistance and capacitance, etc.) and non-electrical parameters (such as weight, etc.) of the capacitor, and N parameters with obvious degradation trends are selected from many parameters as key degradation parameters, and the reliability evaluation process of the capacitor is carried out based on this.

[0053] In this embodiment, in the accelerated degradation test of ceramic capacitors using a self-made experimental platform, the physical quantities selected to characterize the degradation properties are capacitance value and insulation resistance value. The change trend of capacitance value and insulation resistance value of this batch of products over time is as follows Figure 2 and Figure 3 shown.

[0054] Step 2: For each of the N key degradation parameters obtained in step 1, calculate the difference between their empirical cumulative probability and theoretical cumulative probability. In the probability distribution commonly used in engineering, the obtained Anderson-Darling statistic value is used to measure the degree to which the performance data of the above key degradation parameters obey a specific distribution. For a specific data set and distribution, the better the distribution fits the data, the smaller the statistic value.

[0055] In this embodiment, for each of the N key degradation parameters obtained in step 1, the difference between the empirical cumulative probability and the theoretical cumulative probability is calculated, and in the probability distribution commonly used in engineering (such as normal distribution, Weibull distribution, lognormal distribution and exponential distribution, etc.), the obtained Anderson-Darling statistic (hereinafter referred to as AD statistic) value is used to measure the degree to which the above key degradation parameter performance data obeys a specific distribution. For a specific data set and distribution, the better the distribution fits the data, the smaller the statistic value.

[0056] In this embodiment, according to the original degradation data (N key degradation parameters) obtained in step 1, a total of 2 groups of comparative tests were performed, each group of tests had 11 samples, and the degradation data values ​​at 18 moments were obtained. AD test was performed on the data at 18 measurement moments, and the results obtained are shown in Table 1, which is the best fitting distribution (capacity value) table.

[0057] Table 1

[0058]

[0059]

[0060] Step 3: According to the fitted distributions corresponding to the N key degradation parameters obtained in step 2, the first two distributions with the best fit are selected respectively. For the original data of the N key degradation parameters in step 1, new sample data are obtained by repeated sampling with replacement. Based on the expanded sample data, the Bootstrap method is used to perform statistical analysis and estimate the statistical value of the unknown parameter of the fitted distribution of each key degradation parameter. The implementation method is as follows:

[0061] Step 31, according to the fitting distributions corresponding to the N key degradation parameters obtained in step 2, respectively select the first two distributions with the best fitting;

[0062] Step 32: for the original data of the N key degradation parameters in step 1, new sample data is obtained by a repeated sampling method with replacement to obtain expanded sample data, wherein the expanded sample data is used as the input of the original data;

[0063] Step 33, sorting the original data of the N key degradation parameters in ascending order to obtain order statistics;

[0064] Step 34: According to the obtained order statistics, the cumulative probability value of each location is obtained by using the simplest estimation method, and a first empirical cumulative distribution function is constructed according to the cumulative probability value;

[0065] Step 35, generating by simulation a random sample that obeys a first empirical cumulative distribution function, wherein the random sample is a bootstrap sample;

[0066] Step 36: construct a second empirical cumulative distribution function using the bootstrap sample, and analyze the Bootstrap estimate of the unknown parameter based on the second empirical cumulative distribution function;

[0067] Step 37, determine whether the number of iterations has been reached, if so, obtain a set of Bootstrap estimates of the unknown parameters and proceed to step 38, otherwise, return to step 35;

[0068] Step 38: Perform statistical analysis on a set of Bootstrap estimated values ​​of the unknown parameters obtained, and estimate the statistical value of the unknown parameters of the fitting distribution of each key parameter, to obtain the unknown parameter estimates of the optimal fitting distribution selected for the N key parameters at each monitoring moment.

[0069] In this embodiment, according to the test results of step 2, the capacity values ​​of the batch samples at each moment mostly obey the Weibull distribution and the lognormal distribution, so it can be considered that the mixed fitting distribution type of the capacity value is the Weibull distribution and the lognormal distribution. Under the condition of the withstand voltage 1500V model, assuming that the capacity value X obeys the two-parameter Weibull distribution, its distribution function is:

[0070]

[0071] Among them, the unknown parameters η and β are scaling factors and shape parameters respectively. Assume that the number of hyperparameter resampling is M = 10000, use the maximum likelihood function method to estimate the statistical values ​​of the unknown parameters η and β at this time, and then calculate the average to obtain the final estimated value. The result is as follows: Figure 4 As shown, Figure 4 In the equation, the unknown parameters yinta and beita are the scaling factor and shape parameter of the Weibull distribution, respectively.

[0072] Step 4: Based on the unknown parameter estimates of the optimal fitting distribution selected for the N key parameters obtained in step 3 at each monitoring moment, this set of time series data more deeply reflects the degradation of the distribution, and performs data fitting on it, comprehensively evaluates various error indicators, and selects the most appropriate mathematical model for the change of unknown parameters over time: η = (-0.001343) × t + 566.5; β = 0.03892 × t + 152.9.

[0073] In this embodiment, according to the estimated value of step 3, the fitting error and fitting effect are comprehensively considered, and a suitable fitting model is selected to fit the relationship between the estimated values ​​of the above unknown parameters η and β and the time variation. The final result is η = (-0.001343) × t + 566.5; β = 0.03892 × t + 152.9.

[0074] In this embodiment, assuming that the capacity value X obeys a log-normal distribution, its distribution function is:

[0075]

[0076] Among them, the unknown parameters μ and σ are the mean and standard deviation respectively. Assume that the number of hyperparameter resampling is M = 10000. The maximum likelihood function method is used to estimate the statistical values ​​of the unknown parameters μ and σ at this time for the bootstrap sample, and then the average is calculated to obtain the final estimated value. The result is as follows: Figure 5 As shown, Figure 5 The unknown parameters miu and sigma are the mean and standard deviation of the lognormal distribution, respectively. A suitable fitting model is selected to fit the relationship between the estimated values ​​of the above unknown parameters μ and σ changing with time. The final result is μ = (-1.032e-06) × t^1.246 + 5.398; σ = 0.001042 × t^0.3578 + 0.248.

[0077] Step 5: Based on the two fitted distribution mathematical models under the N key degradation parameters obtained in step 4, a mixed degradation quantity distribution model is constructed, and the intelligent algorithm particle swarm algorithm is used to optimize and iterate the unknown parameters to obtain the mixed degradation quantity distribution degradation model of each key parameter;

[0078] In this embodiment, a degradation model of mixed degradation amount distribution under the particle swarm algorithm is constructed, which can comprehensively utilize the statistical characteristics of various distribution types, combine their statistical advantages, and more accurately characterize the degradation trajectory characteristics.

[0079] In this embodiment, a degradation model of the combined degradation amount distribution is constructed:

[0080]

[0081] Among them, a and b are unknown parameters, and the mean square error is used as the loss function. The particle swarm algorithm is used for optimization and iteration, and finally the estimated values ​​are obtained, a = 0.1667, b = 0.8333. F(x) represents the empirical distribution function of the degradation amount, η and β represent the scaling factor and shape parameter of the Weibull distribution respectively, x represents the degradation amount, erf() represents the error function, μ represents the mean, σ represents the standard deviation, t' represents the independent variable for which the integral is to be solved.

[0082] Step 6: Set the failure threshold of key parameters based on engineering experience. According to the essential definition of reliability in the probabilistic sense, substitute the unknown parameter degradation model obtained in step 5 into it to solve it, and obtain the reliability value of the capacitor under the single performance of N key degradation parameters;

[0083] In this embodiment, according to the fitting distribution model, combined with the failure threshold D1 of the capacity value in engineering experience, the reliability calculation formula is R1(t)=P{X>D1}, substituting the fitting model of unknown parameters, the capacity value is taken as the degradation amount, and the 1500V withstand voltage reliability curve is as follows: Figure 6 shown.

[0084] In this embodiment, the above operation is repeated, and the insulation resistance value is taken as the degradation amount. According to the AD statistic test results, it can be seen that the insulation resistance values ​​of this batch of samples at each moment mostly obey the lognormal distribution and Weibull distribution. Next, the maximum likelihood function method is used to estimate the unknown parameters of the lognormal distribution and Weibull distribution at each moment. Assume that the number of hyperparameter resampling times M = 10000, calculate the estimated value of the distribution parameter and obtain the fitting formula accordingly. Combined with work experience, the failure threshold D2 of the degradation insulation resistance is set, and finally substituted into the fitting model of the unknown parameters, then the reliability evaluation value under 1500V withstand voltage can be obtained with the insulation resistance as the degradation amount.

[0085] Step 7: According to the reliability values ​​of different single performance degradation quantities obtained in step 6, select a suitable Copula function as the connection function and use it to calculate the reliability function value under multiple performances. The implementation method is as follows:

[0086] Step 71, fitting respective degradation curve models for different degradation reliability values, and estimating pseudo life values ​​under different performance degradation amounts in combination with failure thresholds;

[0087] Step 72: using the pseudo life value as sample data, estimating the unknown parameters of each Copula function using the maximum likelihood function method, and obtaining the estimated values ​​of the unknown parameters of each Copula function;

[0088] Step 73, according to the estimation of the unknown parameters of each Copula function, combined with the original data of the degradation parameter, calculate the AIC and BIC values ​​respectively to obtain the most suitable Copula function;

[0089] Step 74: Use the most suitable Copula function obtained as the connection function between different performance degradation quantities, and calculate the reliability function value under multiple performances to complete the performance reliability analysis of the operational amplifier capacitor.

[0090] In this embodiment, AIC (Akaike Information Criterion): Akaike Information Criterion; BIC (Bayesian Information Criterion): Bayesian Information Criterion.

[0091] In this embodiment, in order to fully utilize the key parameter degradation data, explore its inherent degradation law, and carry out reliability evaluation of multiple performance degradation quantities, the details are as follows:

[0092] When the batch samples use the capacity value and insulation resistance value as the degradation amount, the respective degradation curve models are fitted, and then combined with the failure threshold (D1 for the capacity value and D2 for the insulation resistance value), the pseudo life value under the single performance degradation amount can be estimated. Using the pseudo life values ​​T1 and T2 as sample data, the maximum likelihood function method is used to estimate the unknown parameters of each Copula function, and the results are shown in Table 2. Table 2 is the parameter estimation table of the five distributions.

[0093] Table 2

[0094]

[0095] After obtaining the estimated values ​​of the unknown parameters of the five Copula functions, the AIC / BIC values ​​are calculated respectively in combination with the sample data, and the results are shown in Table 3. Table 3 is the AIC / BIC value table of the Copula function.

[0096] Table 3

[0097]

[0098] According to the results obtained from the above calculations (AIC / BIC values), Clayton Copula is selected as the optimal Copula to evaluate the correlation between the two degradation quantities of capacity and insulation resistance, where α = 0.1629. For multiple performance degradation quantities, the results obtained only when each degradation quantity does not reach the failure threshold are the reliability of multiple performances. Therefore, the reliability is calculated with capacity and insulation resistance as the two related performance degradation quantities:

[0099]

[0100] Among them, R 1,2 (t) represents the reliability function value under multiple performances, P represents the solution of probability, the pseudo-life value of the random variable obtained when the degradation amount is the capacity value is T1, the pseudo-life value of the random variable obtained when the degradation amount is the insulation resistance value is T2, t represents time, R1(t) represents the reliability obtained when the capacity value is degraded, R2(t) represents the reliability obtained when the insulation resistance value is degraded, F 1,2 (t) represents the joint distribution function of random variables T1 and T2; C clayton () represents the Copula function, and α represents the unknown parameter of the Copula function. clayton (F1(t), F2(t); α) is the Clayton Copula function with α = 0.1629. Substituting the specific data into the reliability curve of the two related performance degradation quantities can be obtained. The results are as follows: Figure 7 shown.

[0101] Example 2

[0102] The present invention also provides a capacitance performance reliability analysis system for an operational amplifier, the system comprising a processor, and the processor is used to execute the capacitance performance reliability analysis method for the operational amplifier described in Example 1.

[0103] In this embodiment, the processor executes as follows:

[0104] In the first processing module, the ceramic capacitor of the operational amplifier is subjected to an accelerated degradation test to obtain the degradation information of the electrical parameters (such as equivalent series resistance and capacitance, etc.) and non-electrical parameters (such as weight, etc.) of the capacitor. N parameters with obvious degradation trends are selected from among many parameters as key degradation parameters, and the reliability evaluation process of the capacitor is carried out based on this.

[0105] The second processing module calculates the difference between the empirical cumulative probability and the theoretical cumulative probability for the N key degradation parameters obtained by the first processing module, and measures the degree to which the key degradation parameter performance data obeys a specific distribution according to the obtained Anderson-Darling statistic (hereinafter referred to as AD statistic) value in the probability distribution commonly used in engineering (such as normal distribution, Weibull distribution, lognormal distribution and exponential distribution, etc.). For a specific data set and distribution, the better the distribution fits the data, the smaller the statistic value.

[0106] The third processing module selects the first two best fitting distributions according to the fitting distributions corresponding to the N key degradation parameters obtained in the second processing module, obtains new sample data through repeated sampling with replacement for the original data of the N key parameters in step 1, and uses the Bootstrap method to perform statistical analysis based on the expanded sample data and estimate the statistical values ​​of the unknown parameters of the fitting distribution of each key parameter.

[0107] The fourth processing module selects the estimated values ​​of unknown parameters of the optimal fitting distribution at each monitoring moment based on the N key parameters obtained by the third processing module. This group of time series data more deeply reflects the degradation of the distribution, and performs data fitting on it, comprehensively evaluates various error indicators, and selects the most appropriate mathematical model for the change of unknown parameters over time.

[0108] The fifth processing module constructs a mixed degradation quantity distribution model based on the two fitting distribution models under N key parameters obtained in the fourth processing module, and uses the intelligent algorithm particle swarm algorithm to optimize and iterate the unknown parameters therein, and finally obtains the mixed degradation quantity distribution degradation model of each key parameter.

[0109] The sixth processing module sets the failure threshold of key parameters based on engineering experience. According to the essential definition of reliability in a probabilistic sense, the unknown parameter degradation model obtained in the fifth processing module is substituted into the module for solution, and finally the reliability value of the capacitor under the single performance of N key parameters is obtained.

[0110] The seventh processing module selects a suitable Copula function as a connection function according to the reliability functions of different single performance degradation quantities obtained by the sixth processing module, and calculates the reliability function value under multiple performances based on it.

[0111] The capacitor performance reliability analysis system provided by the present invention can execute the technical solution shown in the capacitor performance reliability analysis method of the above method embodiment, and its implementation principle and beneficial effects are similar and will not be repeated here.

[0112] In this embodiment, the present application can divide the functional units according to the capacitor performance reliability analysis method. For example, each function can be divided into each functional unit, or two or more functions can be integrated into one processing unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of software functional units. It should be noted that the division of units in the present invention is schematic and is only a logical division. There may be other division methods in actual implementation.

[0113] In this embodiment, in order to realize the principles and beneficial effects of the capacitor performance reliability analysis method, the capacitor performance reliability analysis system includes hardware structures and / or software modules corresponding to the execution of each function. Those skilled in the art should easily realize that, in combination with the schematic units and algorithm steps described in the embodiments disclosed in the present invention, the present invention can be implemented in the form of hardware and / or a combination of hardware and computer software. Whether a function is executed in a hardware or computer software driven manner depends on the specific application and design constraints of the technical solution. Different methods can be used for each specific application to implement the described function, but such implementation should not be considered to be beyond the scope of this application.

Claims

1. A method for analyzing the reliability of capacitance performance of an operational amplifier, characterized in that: include: Step 1: Perform an accelerated degradation test on the ceramic capacitor of the operational amplifier to obtain the degradation information of the electrical parameters and non-electrical parameters of the capacitor, and select N parameters with obvious degradation trends as key degradation parameters, based on which to carry out the reliability evaluation process of the capacitor; Step 2: For each of the N key degradation parameters obtained in step 1, calculate the difference between their empirical cumulative probability and theoretical cumulative probability. In the probability distribution commonly used in engineering, the obtained Anderson-Darling statistic value is used to measure the degree to which the performance data of the above key degradation parameters obey a specific distribution. For a specific data set and distribution, the better the distribution fits the data, the smaller the statistic value. Step 3: According to the fitted distributions corresponding to the N key degradation parameters obtained in step 2, the first two distributions with the best fit are selected respectively. For the original data of the N key degradation parameters in step 1, new sample data are obtained by repeated sampling with replacement. Based on the expanded sample data, the Bootstrap method is used to perform statistical analysis and estimate the statistical value of the unknown parameter of the fitted distribution of each key degradation parameter; Step 4: Based on the unknown parameter estimates of the optimal fitting distribution selected for the N key degradation parameters obtained in step 3 at each monitoring moment, this set of time series data reflects the degradation of the distribution, and data fitting is performed on it, and various error indicators are comprehensively evaluated to select the most appropriate mathematical model for the change of unknown parameters over time; Step 5: Based on the two fitted distribution mathematical models under the N key degradation parameters obtained in step 4, a mixed degradation quantity distribution model is constructed, and the intelligent algorithm particle swarm algorithm is used to optimize and iterate the unknown parameters to obtain the mixed degradation quantity distribution degradation model of each key parameter; Step 6: Set the failure threshold of key parameters based on engineering experience. According to the essential definition of reliability in the probabilistic sense, substitute the unknown parameter degradation model obtained in step 5 into it to solve it, and obtain the reliability value of the capacitor under the single performance of N key degradation parameters; Step 7: According to the reliability values ​​of different single performance degradation quantities obtained in step 6, select a suitable Copula function as the connection function and use it to calculate the reliability function value under multiple performances.

2. The capacitance performance reliability analysis method of an operational amplifier according to claim 1, characterized in that: The step 3 comprises the following steps: Step 31, according to the fitting distributions corresponding to the N key degradation parameters obtained in step 2, respectively select the first two distributions with the best fitting; Step 32: for the original data of the N key degradation parameters in step 1, new sample data is obtained by a repeated sampling method with replacement to obtain expanded sample data, wherein the expanded sample data is used as the input of the original data; Step 33, sorting the original data of the N key degradation parameters in ascending order to obtain order statistics; Step 34: According to the obtained order statistics, the cumulative probability value of each location is obtained by using the simplest estimation method, and a first empirical cumulative distribution function is constructed according to the cumulative probability value; Step 35, generating by simulation a random sample that obeys a first empirical cumulative distribution function, wherein the random sample is a bootstrap sample; Step 36: construct a second empirical cumulative distribution function using the bootstrap sample, and analyze the Bootstrap estimate of the unknown parameter based on the second empirical cumulative distribution function; Step 37, determine whether the number of iterations has been reached, if so, obtain a set of Bootstrap estimates of the unknown parameters and proceed to step 38, otherwise, return to step 35; Step 38: Perform statistical analysis on a set of Bootstrap estimated values ​​of the unknown parameters obtained, and estimate the statistical value of the unknown parameters of the fitting distribution of each key parameter, to obtain the unknown parameter estimates of the optimal fitting distribution selected for the N key parameters at each monitoring moment.

3. The capacitance performance reliability analysis method of an operational amplifier according to claim 1, characterized in that: The expression of the mixed degradation distribution degradation model is as follows: Where F(x) represents the empirical distribution function of the degradation amount, a and b represent unknown parameters, η and β represent the scaling factor and shape parameter of the Weibull distribution respectively, x represents the degradation amount, erf() represents the error function, μ represents the mean, σ represents the standard deviation, and t' represents the independent variable for solving the integral.

4. The capacitance performance reliability analysis method of an operational amplifier according to claim 1, characterized in that: The expression of the reliability value is as follows: R1(t)=P{X>D1} Among them, R1(t) represents the reliability value, D1 represents the failure threshold of the key parameter, P represents the solution of probability, and X represents the degradation amount.

5. The capacitance performance reliability analysis method of an operational amplifier according to claim 1, characterized in that: The step 7 comprises the following steps: Step 71, fitting respective degradation curve models for different degradation reliability values, and estimating pseudo life values ​​under different performance degradation amounts in combination with failure thresholds; Step 72: using the pseudo life value as sample data, estimating the unknown parameters of each Copula function using the maximum likelihood function method, and obtaining the estimated values ​​of the unknown parameters of each Copula function; Step 73, according to the estimation of the unknown parameters of each Copula function, combined with the original data of the degradation parameter, calculate the AIC and BIC values ​​respectively to obtain the most suitable Copula function; Step 74: Use the most suitable Copula function obtained as the connection function between different performance degradation quantities, and calculate the reliability function value under multiple performances to complete the performance reliability analysis of the operational amplifier capacitor.

6. The capacitance performance reliability analysis method of an operational amplifier according to claim 5, characterized in that: The expression of the reliability function value under the multiple performances is as follows: R 1,2 (t)=P{min(T1,T2)>t} =P{T1>t}+P{T2>t}-1+P{T1≤t,T2≤t} =R1(t)+R2(t)-1+F 1,2 (t) =R1(t)+R2(t)-1+C clayton (F1(t),F2(t);α) Among them, R 1,2 (t) represents the reliability function value under multiple performances, P represents the solution of probability, T1 represents the pseudo-life value of the random variable obtained when the degradation amount is the capacity value, T2 represents the pseudo-life value of the random variable obtained when the insulation resistance value is the time, t represents time, R1(t) represents the reliability obtained when the capacity value is degraded, R2(t) represents the reliability obtained when the insulation resistance value is degraded, F 1,2 (t) represents the joint distribution function of random variables T1 and T2, C clayton () represents the Copula function, and α represents the unknown parameter of the Copula function.

7. A capacitance performance reliability analysis system for an operational amplifier, characterized in that: It comprises a processor, wherein the processor is used to execute the capacitance performance reliability analysis method of the operational amplifier according to any one of claims 1-6.

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