A method and system for analyzing the reliability of capacitance performance of an operational amplifier

Abstract

The present invention provides a method and system for analyzing the reliability of capacitor performance of an operational amplifier, relating to the technical field of reliability analysis of electronic components. The method comprises performing an accelerated degradation test on the ceramic capacitor of the operational amplifier to obtain degradation information of the electrical and non-electrical parameters of the capacitor. N parameters with obvious degradation trends are selected from a large number of parameters as key degradation parameters, and a reliability assessment process of the capacitor is carried out based on this. The degradation information of the electrical and non-electrical parameters of the capacitor is analyzed to obtain the reliability value of the capacitor under the single performance of the N key parameters. Based on the reliability functions of different single performance degradation amounts, an appropriate copula function is selected as a connection function and the reliability function value under multiple performance is calculated based on this. The present invention solves the problem that it is difficult to accurately analyze the capacitor performance of an operational amplifier.

Description

Technical Field

[0001] This specification relates to the technical field of electronic component reliability analysis, and specifically to a method and system for analyzing the reliability of capacitance performance of an operational amplifier. Background Art

[0002] Operational amplifiers (OPA) perform functions such as signal processing, system control, and analog computing, and are widely used in various circuits. They play a crucial role in electronic engineering. Ensuring the reliability of OPA is crucial for ensuring the proper performance and stable operation of electronic equipment. Statistics on the root causes of OPA failures show that ceramic capacitor failure accounts for over 30% of OPA system failures. Generally speaking, the lifespan of ceramic capacitors decreases by half for every 10°C increase in temperature. Therefore, over time, internal cracks and oxide vacancy migration are likely to develop, making ceramic capacitors the weakest component in the OPA system. Ceramic capacitor damage can easily lead to failure of other related components, disrupting the normal operation of the entire OPA system and reducing system reliability. Therefore, to maintain stable and reliable operation of the OPA system and improve system reliability, it is necessary to accurately understand the degradation patterns of ceramic capacitors and study their degradation states.

[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 at the microscopic level inside the capacitor, which will lead to changes in the electrical parameters (such as equivalent series resistance and capacitance) 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 judged. Before it fails to cause damage, it can be replaced in time to avoid cascading failures and improve the reliability of the op amp system.

[0004] In order to improve efficiency or gain time and cost advantages, degradation data of capacitor-related parameters can be obtained through accelerated degradation tests. Currently, 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 degradation of capacitors has large differences in performance degradation trajectories between individual products, making it difficult to determine the performance degradation model; and the performance degradation data of the product cannot be measured repeatedly, making it impossible to model the complete degradation process of the product. Therefore, we choose the 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, we also adopt a multi-performance degradation technology with Copula function as the connection function. 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 present invention adopts a technical solution: a method for analyzing the reliability of capacitance performance of an operational amplifier, comprising:

[0007] Step 1: Perform accelerated degradation tests on the ceramic capacitors of the operational amplifier to obtain degradation information of the capacitor's electrical and non-electrical parameters. N parameters with obvious degradation trends are selected as key degradation parameters, which serve as the basis for the capacitor reliability assessment process.

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

[0009] Step 3: Based on the fitted distributions corresponding to the N key degradation parameters obtained in step 2, select the top two distributions with the best fit. For the original data of the N key degradation parameters in step 1, obtain new sample data through repeated sampling with replacement. Based on the expanded sample data, use the bootstrap method 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. Data fitting is performed on it, and various error indicators are comprehensively evaluated to select the most appropriate mathematical model for the time variation of the unknown parameters.

[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. The intelligent algorithm particle swarm optimization is used to iterate out the unknown parameters to obtain the mixed degradation quantity distribution degradation model of each key parameter.

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

[0013] Step 7: Based on 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 performance conditions.

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

[0015] Step 31: Select the top two best fitting distributions from the N key degradation parameters obtained in step 2.

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

[0017] Step 33: sort the original data of the N key degradation parameters from small to large to obtain order statistics;

[0018] Step 34: Based on the obtained order statistics, the simplest estimation method is used to obtain the cumulative probability value of each location, and a first empirical cumulative distribution function is constructed based on the cumulative probability value;

[0019] Step 35: Simulate and generate a random sample that obeys the first empirical cumulative distribution function, where 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: Statistically analyze the obtained set of Bootstrap estimated values ​​of the unknown parameters, and estimate the statistical value of the unknown parameter of the fitting distribution of each key parameter to obtain the unknown parameter estimated values ​​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 reliability value is expressed as follows:

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

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

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

[0030] Step 71: Fitting respective degradation curve models to the reliability values ​​of different degradation amounts, and estimating pseudo life values ​​under different performance degradation amounts in combination with failure thresholds;

[0031] Step 72: Using the pseudo lifespan as sample data, the maximum likelihood function method is used to estimate the unknown parameters of each copula function to obtain estimated values ​​of the unknown parameters of each copula function;

[0032] Step 73: Based on the estimates of the unknown parameters of each copula function and the original data of the degradation parameters, calculate the AIC and BIC values ​​respectively to obtain the most suitable copula function;

[0033] Step 74 : Using the most appropriate Copula function obtained as the connection function between different performance degradation amounts, and calculating the reliability function values ​​under multiple performance conditions, thereby completing 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 under the degradation amount of capacity value, T2 represents the pseudo-life value of the random variable obtained under the time insulation resistance value, t represents time, R1(t) represents the reliability obtained under the degradation amount of capacity value, R2(t) represents the reliability obtained under the degradation amount of insulation resistance value, 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 for operational amplifier capacitors described in the present invention analyzes the distribution characteristics of key degradation parameters of multiple samples at each moment, comprehensively evaluates the degree of fit between common degradation distribution types and actual capacitance data based on AD statistics, and selects two suitable fitting distributions for key parameters. Based on 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. A degradation model of the mixed degradation quantity distribution is constructed based on the particle swarm algorithm, and finally a single performance reliability model is solved. This method overcomes the problems that the performance degradation trajectories of individual products vary greatly, making it difficult to determine the performance degradation model; and the performance degradation data of the product cannot be repeatedly measured, making it impossible to model the complete degradation process of the product.

[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; using the pseudo-life value as the sample data, 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 result obtained only when each degradation amount does not reach the failure threshold is the reliability of multiple performance. However, since 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, establishing a capacitor multi-performance parameter reliability evaluation model based on Copula theory that includes the correlation information between the performance parameters can significantly improve its reliability prediction accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0042] Figure 2 Schematic diagram of the capacity change curve over time of the batch of samples under the 1500V model in the example of the present invention.

[0043] Figure 3 Schematic diagram of the insulation resistance value of this batch of samples under the 1500V model in the example of the present invention changing over time.

[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 FIG. 1 is a schematic diagram of a curve showing 1500V withstand voltage reliability with capacity as the degradation amount in an example of the present invention.

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

[0048] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts 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 its implementation method is as follows:

[0051] Step 1: Perform accelerated degradation tests on the ceramic capacitors of the operational amplifier to obtain degradation information of the capacitor's electrical and non-electrical parameters. N parameters with obvious degradation trends are selected as key degradation parameters, which serve as the basis for the capacitor reliability assessment process.

[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) and non-electrical parameters (such as weight). N parameters with obvious degradation trends are selected from a large number of 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 degradation acceleration 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 probabilities and theoretical cumulative probabilities. Using the Anderson-Darling statistic, a probability distribution commonly used in engineering, the degree to which the performance data of these key degradation parameters conform to a specific distribution is measured based on the obtained Anderson-Darling statistic. For a specific data set and distribution, the better the distribution fits the data, the smaller the statistic value.

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

[0056] In this example, based on the raw degradation data (N key degradation parameters) obtained in step 1, two sets of comparative tests were conducted, each with 11 samples, yielding degradation data values ​​at 18 measurement moments. AD tests were performed on the data at these 18 measurement moments, and the results are shown in Table 1, which shows the best-fit distribution (capacity value) table.

[0057] Table 1

[0058]

[0059]

[0060] Step 3: Based on the fitted distributions corresponding to the N key degradation parameters obtained in step 2, select the top two best fitting distributions for each. For the original data of the N key degradation parameters in step 1, obtain new sample data through repeated sampling with replacement. Based on the expanded sample data, use the Bootstrap method 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: Select the top two best fitting distributions from the N key degradation parameters obtained in step 2.

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

[0063] Step 33: sort the original data of the N key degradation parameters from small to large to obtain order statistics;

[0064] Step 34: Based on the obtained order statistics, the simplest estimation method is used to obtain the cumulative probability value of each location, and a first empirical cumulative distribution function is constructed based on the cumulative probability value;

[0065] Step 35: Simulate and generate a random sample that obeys the first empirical cumulative distribution function, where 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: Statistically analyze the obtained set of Bootstrap estimated values ​​of the unknown parameters, and estimate the statistical value of the unknown parameter of the fitting distribution of each key parameter to obtain the unknown parameter estimated values ​​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 time are mostly subject to Weibull distribution and lognormal distribution, so it can be considered that the mixed fitting distribution type of the capacity value is Weibull distribution and lognormal distribution. Under the condition of the 1500V withstand voltage 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, and use the maximum likelihood function method to estimate the statistical values ​​of the unknown parameters η and β at this moment. Then, the mean is calculated 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. 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: η = (-0.001343) × t + 566.5; β = 0.03892 × t + 152.9.

[0073] In this embodiment, based on the estimated values ​​in step 3, taking into account the fitting error and fitting effect, 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 moment. Then the mean 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 results are 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. The intelligent algorithm particle swarm optimization is used to iterate out 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 optimization 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] Where a and b are unknown parameters. The particle swarm optimization algorithm is used to iteratively optimize the solution with mean square error as the loss function, and finally obtains their estimated values: 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, and σ represents the standard deviation. t' represents the independent variable for which the integral is to be solved.

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

[0083] In this embodiment, based on the fitting distribution model and the failure threshold D1 of the capacitance value in engineering experience, the reliability calculation formula is R1(t)=P{X>D1}. Substituting the unknown parameters into the fitting model, the capacitance 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 used 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. Assuming the number of hyperparameter resampling times M = 10000, the estimated value of the distribution parameter is calculated and the fitting formula is obtained accordingly. Based on work experience, the failure threshold D2 of the degradation amount insulation resistance is set, and finally substituted into the fitting model of the unknown parameters, the reliability evaluation value under 1500V withstand voltage can be obtained with the insulation resistance as the degradation amount.

[0085] Step 7: Based on 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 performance conditions. The implementation method is as follows:

[0086] Step 71: Fitting respective degradation curve models to the reliability values ​​of different degradation amounts, and estimating pseudo life values ​​under different performance degradation amounts in combination with failure thresholds;

[0087] Step 72: Using the pseudo lifespan as sample data, the maximum likelihood function method is used to estimate the unknown parameters of each copula function to obtain estimated values ​​of the unknown parameters of each copula function;

[0088] Step 73: Based on the estimates of the unknown parameters of each copula function and the original data of the degradation parameters, calculate the AIC and BIC values ​​respectively to obtain the most suitable copula function;

[0089] Step 74 : Using the most appropriate Copula function obtained as the connection function between different performance degradation amounts, and calculating the reliability function values ​​under multiple performance conditions, thereby completing 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 degradation data of key parameters, explore the inherent degradation laws, and carry out reliability evaluation of multiple performance degradation quantities, the details are as follows:

[0092] When batch samples use capacity and insulation resistance values ​​as degradation measures, fitting their respective degradation curve models and combining them with the failure thresholds (D1 for capacity and D2 for insulation resistance) allows estimation of pseudo-lifetime values ​​for a single performance degradation measure. Using pseudo-lifetime values ​​T1 and T2 as sample data, the maximum likelihood function method is used to estimate the unknown parameters of each copula function. The results are shown in Table 2. Table 2 shows the parameter estimates for 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 ​​were calculated respectively based on the sample data. The results are shown in Table 3. Table 3 is the AIC / BIC value table of the Copula function.

[0096] Table 3

[0097]

[0098] Based on the results (AIC / BIC values) calculated above, the Clayton Copula was selected as the optimal copula to evaluate the correlation between the two degradation quantities, capacitance and insulation resistance, where α = 0.1629. For multiple performance degradation quantities, the reliability of multiple performance is only obtained when each degradation quantity does not reach the failure threshold. Therefore, the reliability is calculated using capacitance and insulation resistance as the two correlated performance degradation quantities:

[0099]

[0100] Among them, R 1,2 (t) represents the reliability function value under multiple performance conditions, 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 includes a processor, and the processor is used to execute the capacitance performance reliability analysis method for an operational amplifier described in Example 1.

[0103] In this embodiment, the processor performs the following:

[0104] The first processing module conducts accelerated degradation tests on the ceramic capacitors of the operational amplifier to obtain degradation information of the capacitor's electrical parameters (such as equivalent series resistance and capacitance) and non-electrical parameters (such as weight). N parameters with obvious degradation trends are selected from the numerous parameters as key degradation parameters, and the reliability assessment 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 each of the N key degradation parameters obtained in the first processing module. Using the Anderson-Darling statistic (hereinafter referred to as the AD statistic), the second processing module measures the degree to which the performance data of these key degradation parameters conform to a specific distribution, using commonly used probability distributions in engineering, such as the normal distribution, Weibull distribution, lognormal distribution, and exponential distribution. For a specific data set and distribution, the better the distribution fits the data, the smaller the value of this statistic.

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

[0107] The fourth processing module selects the estimated values ​​of the unknown parameters of the optimal fitting distribution at each monitoring moment based on the N key parameters obtained in the third processing module. 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.

[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, 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. Based on the essential definition of reliability in a probabilistic sense, the unknown parameter degradation model obtained in the fifth processing module is substituted into it 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 based on the reliability functions of different single performance degradation amounts obtained by the sixth processing module and calculates the reliability function value under multiple performance conditions based on it.

[0111] The capacitor performance reliability analysis system provided by the present invention can implement the technical solution shown in the capacitor performance reliability analysis method of the above method embodiment. 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 a software functional unit. It should be noted that the division of the units in the present invention is schematic and is only a logical division. In actual implementation, there may be other division methods.

[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 that perform corresponding functions. Those skilled in the art should easily realize that, in combination with the various 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 accelerated degradation tests on the ceramic capacitors of the operational amplifier to obtain degradation information of the capacitor's electrical and non-electrical parameters. N parameters with obvious degradation trends are selected as key degradation parameters, which serve as the basis for the capacitor reliability assessment process. Step 2: For each of the N key degradation parameters obtained in Step 1, calculate the difference between their empirical cumulative probabilities and theoretical cumulative probabilities. Using the Anderson-Darling statistic, a probability distribution commonly used in engineering, the degree to which the performance data of these key degradation parameters conform to a specific distribution is measured based on the obtained Anderson-Darling statistic. For a specific data set and distribution, the better the distribution fits the data, the smaller the statistic value. Step 3: Based on the fitted distributions corresponding to the N key degradation parameters obtained in step 2, select the top two distributions with the best fit. For the original data of the N key degradation parameters in step 1, obtain new sample data through repeated sampling with replacement. Based on the expanded sample data, use the bootstrap method 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. Data fitting is performed on it, and various error indicators are comprehensively evaluated to select the most appropriate mathematical model for the time variation of the unknown parameters. 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. The intelligent algorithm particle swarm optimization is used to iterate out the unknown parameters to obtain the mixed degradation quantity distribution degradation model of each key parameter. Step 6: Based on engineering experience, set the failure thresholds of key parameters. Based on the essential definition of reliability in a probabilistic sense, substitute the unknown parameter degradation model obtained in Step 5 into the model and solve it to obtain the reliability value of the capacitor under the single performance of N key degradation parameters. Step 7: Based on 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 performance conditions.

2. The capacitance performance reliability analysis method of an operational amplifier according to claim 1, wherein: The step 3 comprises the following steps: Step 31: Select the top two best fitting distributions from the N key degradation parameters obtained in step 2. Step 32: For the original data of the N key degradation parameters in step 1, obtain new sample data by repeated sampling with replacement to obtain expanded sample data, wherein the expanded sample data is used as the input of the original data; Step 33: sort the original data of the N key degradation parameters from small to large to obtain order statistics; Step 34: Based on the obtained order statistics, the simplest estimation method is used to obtain the cumulative probability value of each location, and a first empirical cumulative distribution function is constructed based on the cumulative probability value; Step 35: Simulate and generate a random sample that obeys the first empirical cumulative distribution function, where 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: Statistically analyze the obtained set of Bootstrap estimated values ​​of the unknown parameters, and estimate the statistical value of the unknown parameter of the fitting distribution of each key parameter to obtain the unknown parameter estimated values ​​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, wherein: 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, wherein: The expression of the reliability value is as follows: R1(t)=P{X>D1} Where R1(t) represents the reliability value, D1 represents the failure threshold of the key parameter, P represents the solution of the probability, and X represents the degradation amount.

5. The capacitance performance reliability analysis method of an operational amplifier according to claim 1, wherein: The step 7 comprises the following steps: Step 71: Fitting respective degradation curve models to the reliability values ​​of different degradation amounts, and estimating pseudo life values ​​under different performance degradation amounts in combination with failure thresholds; Step 72: Using the pseudo lifespan as sample data, the maximum likelihood function method is used to estimate the unknown parameters of each copula function to obtain estimated values ​​of the unknown parameters of each copula function; Step 73: Based on the estimates of the unknown parameters of each copula function and the original data of the degradation parameters, calculate the AIC and BIC values ​​respectively to obtain the most suitable copula function; Step 74 : Using the most appropriate Copula function obtained as the connection function between different performance degradation amounts, and calculating the reliability function values ​​under multiple performance conditions, thereby completing the performance reliability analysis of the operational amplifier capacitor.

6. The method for analyzing the reliability of capacitance performance of an operational amplifier according to claim 5, wherein: The expression of the reliability function value under multiple performance conditions 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 under the degradation amount of capacity value, T2 represents the pseudo-life value of the random variable obtained under the time insulation resistance value, t represents time, R1(t) represents the reliability obtained under the degradation amount of capacity value, R2(t) represents the reliability obtained under the degradation amount of insulation resistance value, 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: The method comprises a processor configured to execute the capacitance performance reliability analysis method of an operational amplifier according to any one of claims 1 to 6.

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