A method for modeling and evaluating reliability of voltage withstand performance of planar transformer

Abstract

The application relates to the technical field of electronic component reliability, and discloses a flat transformer voltage withstand performance sure reliability modeling and evaluation method, which comprises the following steps: firstly, a constitutive model fusing a physical mechanism is constructed, a time degradation model and a temperature influence model are established based on the geometric size, material properties and environmental stress of an insulating layer, and a process capability parameter is introduced to represent manufacturing fluctuation; secondly, a reliability evaluation model is established, a failure threshold and a margin equation are defined, and physical parameters are identified as random variables to quantify uncertainty; then, Monte Carlo algorithm is used to sample random variables, virtual samples are generated, and voltage withstand margin is calculated on an evaluation time sequence; finally, the number of samples meeting a safety criterion is counted, instantaneous reliability is calculated, and a full-life-cycle reliability curve is generated. The application effectively decouples and quantifies the influence of manufacturing processes, temperature stress and time degradation on voltage withstand performance, and realizes sure reliability evaluation with high confidence.

Description

Technical Field

[0001] This invention relates to the field of electronic component reliability technology, specifically to a method for reliable modeling and evaluation of the withstand voltage performance of a planar transformer. Background Technology

[0002] Planar transformers, with their flat structural design, high power density, and excellent high-frequency characteristics, have become core magnetic components in switching power supplies, electric vehicle on-board chargers, and aerospace power systems. As planar transformers trend towards miniaturization and high integration, the thickness of their insulation layers is continuously decreasing, while the operating electric field strength and environmental thermal stress are increasing. This makes the withstand voltage performance of the insulation structure a key factor restricting the safe operation and service life of the product. Therefore, establishing an accurate withstand voltage performance reliability assessment model is of great significance for the optimized design and operation and maintenance management of the product.

[0003] Existing methods for evaluating the insulation withstand voltage of planar transformers primarily rely on physical models based on deterministic parameters or accelerated life testing based on finite samples. However, these traditional methods have limitations in practical engineering applications. Firstly, traditional physical models typically calculate based on nominal values ​​of material properties and geometric dimensions (i.e., ideal design values), neglecting the objective process variations and material dispersion inherent in actual manufacturing. For example, non-uniformity in the insulation coating process can lead to random distributions of insulation thickness or dielectric constant within a certain range. This uncertainty in parameters results in some products having actual withstand voltage capabilities lower than the design average. Using only deterministic models for evaluation often leads to overly optimistic results, failing to identify early failure risks located at the tail end of the statistical distribution, and thus failing to meet the zero-defect control requirements of high-reliability applications.

[0004] On the other hand, the degradation of the withstand voltage performance of insulation materials is a complex dynamic process involving the coupling of multiple physical fields, including electrical, thermal, and mechanical fields. Existing assessment methods often struggle to effectively decouple the independent effects of environmental temperature stress and time-related degradation mechanisms on insulation performance. While some empirical models consider temperature acceleration effects, they lack quantitative characterization of manufacturing process quality and cannot distinguish between failures caused by insufficient thermal design and those caused by manufacturing defects. Furthermore, traditional lifetime prediction methods typically output a single average lifetime value, lacking dynamic reliability probability curves that evolve over time. This makes it difficult to intuitively present the reliability degradation trajectory of a product throughout its entire lifecycle and fails to provide accurate data support for targeted process improvements or preventative maintenance strategies. Therefore, there is an urgent need for a method for confident reliability modeling and assessment of planar transformer withstand voltage performance that can integrate physical mechanisms, quantify process fluctuations, and achieve full-parameter spatial uncertainty analysis. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a reliable modeling and evaluation method for the withstand voltage performance of planar transformers. This method solves the problems of existing methods for evaluating the withstand voltage performance of planar transformers, which rely on a large number of physical tests, resulting in long evaluation cycles and high costs. Furthermore, traditional models are unable to effectively guide product optimization design because they cannot quantify the impact of uncertainties.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] This invention provides a method for reliable modeling and evaluation of the withstand voltage performance of planar transformers. The method mainly includes four logically closely related steps: constructing a constitutive model that integrates physical mechanisms, establishing a reliability evaluation model and quantifying parameter uncertainty, dynamic evaluation based on Monte Carlo simulation, and reliability calculation and curve generation.

[0008] In constructing the constitutive model integrating physical mechanisms, based on the geometry, material properties, and environmental stress of the planar transformer insulation layer, a time degradation model and a temperature influence model are established respectively. Process capability parameters are also introduced to construct a fusion constitutive equation for calculating the instantaneous withstand voltage of the planar transformer. Specifically, regarding the temperature influence, the Arrhenius relation is used to describe the functional dependence between the ideal dielectric constant of the insulation layer and the operating temperature. The ideal dielectric constant is characterized as a function jointly determined by the pre-exponential factor, the base of the natural logarithm, the activation energy, the Boltzmann constant, and the absolute temperature of the operating environment. The activation energy is used to characterize the sensitivity of the insulation material's withstand voltage performance to temperature changes. Regarding the time degradation mechanism, an exponential decay function is used to describe the evolution of insulation performance over service time. This exponential decay function includes a degradation rate parameter and a degradation order parameter.

[0009] To quantify the impact of manufacturing process variations on product performance, this invention introduces a dimensionless process capability parameter, whose value ranges from greater than 0 to less than or equal to 1. This parameter quantifies the degree to which manufacturing process variations correct for the ideal dielectric constant of the insulation layer, expressing the actual dielectric constant as the product of the process capability parameter and the ideal dielectric constant. When the process capability parameter is close to 1, it indicates that the manufacturing process level allows the product performance to approach the theoretical design value. The final fusion constitutive equation is obtained by multiplying the geometric dimensions (such as insulation layer thickness), the dielectric constant corrected by the process capability parameter (i.e., the product of the process capability parameter and the temperature dependence term), and a time degradation function containing the degradation rate and degradation order. This equation is used to calculate the instantaneous withstand voltage of the planar transformer during service time and operating temperature.

[0010] In establishing the reliability assessment model and quantifying parameter uncertainties, a failure threshold for the planar transformer is defined, and a margin equation is established between the withstand voltage and the failure threshold. Based on the rated operating voltage of the planar transformer, a determined failure threshold is set, and the margin is defined as the difference between the instantaneous withstand voltage and the failure threshold. A failure criterion is established: when the calculated margin is greater than 0, the planar transformer is considered to be in a safe and reliable state; when the calculated margin is less than or equal to 0, the planar transformer is considered to have failed. Simultaneously, to address the uncertainty of physical parameters, the physical parameters in the fusion constitutive equation are identified as random variables, and a probability distribution model of the random variables is constructed. Insulation layer thickness, process capability parameters, activation energy, degradation rate, and degradation order are selected as the set of uncertainties to be quantified. Based on historical reliability data or expert experience, the probability distribution type of each parameter is identified, and the distribution parameters are estimated. For example, insulation layer thickness can be characterized as following a normal distribution, and activation energy can be characterized as a uniform distribution over an interval.

[0011] In the dynamic evaluation step based on Monte Carlo simulation, the number of simulation samplings and the evaluation time series are set, and the Monte Carlo algorithm is used to randomly sample random variables. In each simulation cycle, based on the probability density function established for each uncertainty parameter, a set of random parameter samples is independently extracted. This sample includes at least randomly generated insulation layer thickness, process capability parameters, activation energy, degradation rate, and degradation order, which are combined to form a virtual planar transformer sample. Subsequently, virtual samples are generated, and margin values ​​are calculated at each node of the time series. That is, each discrete time point in the set evaluation time series is traversed, and the current time point value, the set operating temperature, and the random parameter sample generated in this sampling are substituted into the margin equation to calculate the margin value of the virtual planar transformer sample at that discrete time point. This process is repeated until all preset number of simulation cycles are completed, generating a margin data matrix.

[0012] In the reliability calculation and curve generation steps, the number of samples satisfying the safety criteria at each time point is counted to calculate the instantaneous reliability of the planar transformer. Specifically, for each discrete time point in the evaluation time series, the margin values ​​of all virtual samples in the margin data matrix at that moment are traversed, and the total number of samples with margin values ​​greater than 0 is counted. This total number of samples is divided by the total number of simulation samplings to obtain the instantaneous reliability assessment value at that time point. Finally, the instantaneous reliability assessment values ​​at each time point are concatenated and numerically smoothed to generate a reliability curve showing the change in the withstand voltage performance of the planar transformer over time.

[0013] This invention provides a method for reliable modeling and evaluation of the withstand voltage performance of planar transformers. It offers the following advantages:

[0014] 1. This invention overcomes the shortcomings of traditional deterministic evaluation methods that ignore manufacturing tolerances and material discreteness by introducing dimensionless process capability parameters into the physical constitutive equation and characterizing physical parameters such as insulation layer thickness and activation energy as random variables following a probability distribution. This setup enables the model to simulate the deviation of dielectric properties caused by process fluctuations in actual production, thereby accurately quantifying the limiting effect of manufacturing quality on withstand voltage reliability and effectively identifying the risk of early failure caused by process defects.

[0015] 2. The fusion constitutive model established in this invention integrates the Arrhenius relation describing temperature dependence with the exponential decay function describing aging characteristics, achieving effective decoupling of environmental thermal stress and time degradation mechanisms. This method can accurately capture the nonlinear accelerated degradation effect of high-temperature conditions on insulation performance, quantitatively converting thermal stress into a reliability probability loss value, thus providing a quantitative basis consistent with physical laws for the thermal design optimization and derating specification formulation of planar transformers under different temperature scenarios.

[0016] 3. This invention utilizes the Monte Carlo algorithm to perform full-space random sampling of multi-source uncertainty parameters and calculates dynamic margins based on time series data, thus realizing the transformation from static lifetime estimation to dynamic probability assessment. By generating a confidence reliability curve covering the entire lifecycle, this method can capture the very few failure events located at the tail of the statistical distribution, solving the problem that the mean estimation method cannot quantify low-probability failure risks, and providing highly confident statistical support for product lifecycle maintenance decisions. Attached Figure Description

[0017] Figure 1 This is a flowchart of the reliable modeling and evaluation method for the withstand voltage performance of a planar transformer according to the present invention;

[0018] Figure 2 This is the reliability curve for Case 1 of the present invention;

[0019] Figure 3 This is the reliability curve for Case 2 of the present invention;

[0020] Figure 4 This is the reliability curve for Case 3 of the present invention. Detailed Implementation

[0021] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] See attached document Figure 1This invention provides a method for modeling and evaluating the reliable withstand voltage performance of a planar transformer, which includes the step of constructing a constitutive model that integrates physical mechanisms.

[0023] In this step, a planar transformer is selected as the evaluation object, and its insulation withstand voltage performance is used as the specific evaluation index. The purpose of constructing the constitutive model is to determine the withstand voltage strength of the planar transformer. The mathematical mapping relationship between the key physical parameters provides a mathematical basis for subsequent multi-source uncertainty quantification.

[0024] Specifically, establish a description of compressive strength The fundamental physical equation for a planar transformer is as follows: The insulation withstand voltage of a planar transformer depends on the dielectric properties of the insulating material and the physical geometry of the insulating layers.

[0025] ;

[0026] in, This indicates the withstand voltage of a planar transformer, measured in volts (V). The dielectric constant of the insulating layer is expressed in volts per mil (V / mil). This indicates the physical thickness of the insulation layer, measured in mils (mils).

[0027] This fundamental physical equation characterizes the linear relationship between withstand voltage, dielectric constant, and insulation layer thickness. In subsequent steps, time degradation variables, temperature covariates, and process capability parameters will be introduced based on this equation to form a complete confidence reliability assessment model.

[0028] In constructing a constitutive model that integrates physical mechanisms, this method further includes establishing a time-degradation model. During the actual full lifespan of a planar transformer, the material properties of the insulation layer are not constant; rather, they degrade under the influence of environmental factors such as electrical and thermal stresses over time. This material aging phenomenon directly leads to a decay in the dielectric constant of the insulation layer over time. Therefore, the dielectric constant is characterized as a function of time, rather than a fixed constant.

[0029] To accurately quantify this material aging characteristic that evolves over time, this invention introduces a time variable into the fundamental physical equations. An exponential decay function is used to describe the degradation of the dielectric constant. This time-degradation model is expressed by the following formula:

[0030] ;

[0031] in, Indicates the service time as The instantaneous dielectric constant of the insulating layer at a given moment; This represents the ideal dielectric constant of the insulating material in its initial state, i.e., its dielectric constant over time. The theoretical value of dielectric properties before aging occurs; This indicates the cumulative service time of the planar transformer.

[0032] In the formula and These are all time-degradation parameters describing the aging characteristics of insulating materials. Specifically, This parameter represents the degradation rate and is used to quantify the rate at which dielectric properties decay over time. The value of this parameter is related to the material's inherent resistance to aging. The degradation order parameter is used to characterize the nonlinear features of the aging process. By introducing this time-degradation model, the static physical equations of compressive strength are transformed into a dynamic model that reflects the material's evolution over time, thereby supporting the calculation of compressive strength retention at different service time points in subsequent steps.

[0033] In constructing a constitutive model that integrates physical mechanisms, this method further includes establishing a temperature-effect model to introduce a temperature covariate to characterize the physical effect of thermal stress on insulation performance. When a planar transformer operates under different temperature environments, the internal microstructure and physicochemical activity state of its insulating material are directly affected by thermal excitation, leading to changes in the intrinsic dielectric properties of the material. To accurately quantify this effect caused by ambient temperature... To address the resulting performance differences and determine the baseline parameters in the aforementioned time degradation model, this invention employs the Arrhenius relation to describe the ideal dielectric constant. The functional dependency between temperature and operating temperature is shown in the following formula:

[0034] ;

[0035] In this formula, This is a temperature-dependent term, corresponding to the aforementioned time-degradation model. The initial dielectric constant at time 0 is no longer considered a single fixed constant, but a variable that changes with temperature. The absolute temperature of the working environment of the planar transformer is expressed in Kelvin (K). This parameter serves as the main environmental covariate in the model. Let represent the Boltzmann constant, a physical constant, with a value of 8.617 × 10⁻⁶. -5 Electron volts per Kelvin (eV / K).

[0036] In the formula The activation energy is expressed in electron volts (eV). Activation energy is the energy barrier that an insulating material must overcome to undergo physical or chemical changes. This parameter reflects the sensitivity of the insulating material's withstand voltage performance to temperature changes. The exponential factor (or frequency factor) is a constant parameter related to the specific material properties and structural characteristics of the product. By introducing this temperature-affected model, the macroscopic operating temperature parameter is mapped to the microscopic material dielectric property parameter, thus realizing the physical characterization of the withstand voltage benchmark value of the planar transformer under different temperature conditions.

[0037] In constructing a constitutive model that integrates physical mechanisms, this method further includes introducing process capability parameters and establishing integrated constitutive equations. In the actual manufacturing process of planar transformers, due to limitations in manufacturing equipment precision, batch variations in raw materials, and fluctuations in process control levels, the actual insulation performance of the product often fails to fully meet the ideal values ​​calculated theoretically during the design phase. To objectively characterize this performance degradation caused by differences in manufacturing process levels at the mathematical model level, this invention introduces dimensionless process capability parameters. .

[0038] Process capability parameters Defined as a coefficient whose value ranges from 0 to 1 (0 < 1). ≤1), used to quantify the degree to which manufacturing process variations correct for the ideal dielectric constant of the insulation layer. This parameter characterizes the dielectric properties of the actually formed insulation layer relative to the ideal dielectric constant under manufacturing process conditions. The retention rate. When The closer the value is to 1, the higher the level of manufacturing process, and the closer the product performance is to the theoretical design value; conversely, when... A small value indicates significant fluctuations or defects in the manufacturing process, leading to a decrease in dielectric properties. Incorporating this parameter into the model results in a lower actual dielectric constant. It is expressed as the product of the process capability parameter and the ideal dielectric constant, i.e.:

[0039] ;

[0040] Based on this, the present invention performs a fusion operation of multiple source models. The aforementioned time degradation model, temperature influence model, and dielectric constant model corrected for process capability parameters are uniformly substituted into the fundamental physical equations, thereby constructing a constitutive equation for the withstand voltage performance of a planar transformer that incorporates process capability, time degradation, and temperature covariates. This fused constitutive equation is shown below:

[0041] ;

[0042] This equation establishes a multi-dimensional physical model that incorporates geometric dimensions, material properties, environmental stress, time evolution, and manufacturing processes. Indicates service time and operating temperature Instantaneous withstand voltage of a planar transformer under certain conditions; The thickness of the insulating layer characterizes geometric dimensional factors; These are process capability parameters, characterizing manufacturing process factors; and These are the pre-exponential factor and activation energy, respectively, which characterize the temperature response properties of the material. and These represent the degradation rate and degradation order, respectively, characterizing the aging properties of the material. This equation forms the core mathematical foundation for subsequent reliability margin calculations and uncertainty quantification.

[0043] This method, after constructing constitutive equations that integrate physical mechanisms, further includes establishing a reliability assessment model. This step aims to establish a failure criterion for the withstand voltage capability of planar transformers based on stress-strength interference theory and to construct a mathematical model for measuring reliability. Specifically, it first defines the failure threshold for planar transformers. This is a definite numerical value characterizing the minimum withstand voltage requirement that a product must meet. This value is based on the rated operating voltage of the planar transformer. And relevant electrical safety standards are set (e.g., set to 2000 volts). During the reliability assessment process, the failure threshold... As a baseline for measuring product failure, a constant stress value is considered. Based on this, a margin equation describing the product's safety state is constructed. Margin Defined as a planar transformer at any service time and operating temperature Actual pressure resistance With failure threshold The difference between them. Substituting the fusion constitutive equation established in the previous steps into it, we obtain the margin equation as shown below:

[0044] ;

[0045] This margin equation establishes a dynamic evaluation function for real-time calculation of the product's withstand voltage capability relative to safety requirements. Based on this margin equation, the failure criterion for planar transformers is established:

[0046] When the calculated margin When the value is greater than 0, it indicates that the current withstand voltage of the planar transformer is higher than the failure threshold, and the product is judged to be in a safe and reliable state.

[0047] When the calculated margin When the value is ≤0, it indicates that the current withstand voltage of the planar transformer is lower than or equal to the failure threshold, the insulation layer has been broken down or cannot meet the withstand voltage requirements, and the product is judged to have failed.

[0048] Based on the above failure criteria, a reliability measurement model is established. Considering the uncertainties in the process parameters, material parameters, and geometric dimensions in the constitutive equation, the compressive strength... It behaves as a random variable, therefore the margin It is also a random variable. This invention addresses the withstand voltage reliability of planar transformers. Defined as at a specific moment and temperature Below, margin A probability measure greater than 0. This reliability function is expressed as:

[0049] ;

[0050] This formula transforms the deterministic physical margin into a reliability index in a probabilistic sense, providing a mathematical basis for calculating the survival probability of a product at different stages of its life cycle through statistical simulation methods.

[0051] This method, based on the established reliability assessment model, further includes the quantification of uncertainties in the multi-source parameters of the fused constitutive equation. In the practical engineering applications of planar transformers, the physical parameters involved in the aforementioned fused constitutive equation are not constant, precise values, but are affected by factors such as batch differences in raw materials, manufacturing tolerances, process stability, and the heterogeneity of material microstructure, exhibiting statistically regular random variables. To ensure the confidence level of the assessment results, this invention abandons the traditional approach of using only the nominal values ​​(i.e., the mean) of the parameters for point estimation, and instead constructs a probability distribution model for each nondeterministic parameter in the equation.

[0052] Specifically, the set of parameters that need to be quantified for uncertainty includes: the insulation layer thickness characterizing the geometric dimensions. Process capability parameters characterizing manufacturing level Degradation rate characterizing the aging properties of materials and degeneration order And the pre-exponential factor characterizing the temperature response properties of materials. and activation energy These parameters together constitute the multi-source uncertainty input vector that affects the pressure resistance.

[0053] This invention obtains statistical characteristic data of the above parameters through multiple channels. Data sources include, but are not limited to: historical reliability test data of past models of planar transformers, experience data from experts in related fields, detailed technical specifications provided by raw material suppliers, and manufacturing process control (SPC) monitoring data on the production line. Based on the obtained data samples, statistical inference methods are used to identify the probability distribution type of each parameter and estimate its distribution parameters.

[0054] Different probability density functions are assigned to different parameter characteristics. For example, for the thickness of the insulating layer... Since its value is affected by the coating process precision and usually fluctuates around the design target value, this embodiment characterizes it as following a normal distribution. ,in The average thickness The standard deviation is given by the activation energy. In the absence of massive amounts of measured data but with known physical value ranges, it is characterized as being within the interval uniform distribution on .

[0055] For process capability parameters Degradation rate Other parameters, similarly, are modeled using corresponding normal distributions or other statistical distributions based on their actual data distribution characteristics. This process transforms the uncertainties in the physical model into mathematical probability distribution inputs, providing precise input conditions for subsequent random sampling across the entire space using Monte Carlo simulations.

[0056] After quantifying the uncertainty of multi-source parameters, this method further includes Monte Carlo simulation and reliability assessment steps, which first involves the design of the simulation algorithm and the construction of its execution architecture. Given that the aforementioned constructed fusion constitutive equation has highly nonlinear characteristics and involves multiple random variables following different probability distributions, traditional analytical mathematical methods are insufficient to directly obtain closed-form solutions for reliability. Therefore, this embodiment employs the Monte Carlo numerical simulation method, using a computer to generate a large number of random experimental samples to approximate the actual physical failure process.

[0057] Specifically, the design of the simulation algorithm includes the following initialization settings and random sampling process:

[0058] First, define the parameter space for the simulation. Define the total number of samples for the Monte Carlo simulation. To ensure statistical convergence of the simulation results and to approximate the true probability according to the law of large numbers, the total number of samples is [number missing]. Set to a sufficiently large integer (e.g., set to...) (No less than 10,000 times). Simultaneously, a time domain for dynamic evaluation is defined, and a discrete evaluation time series covering the entire lifecycle of the planar transformer is established. The sequence consists of a series of specific time points, for example... ,in For the end of the evaluation cycle (e.g., 50,000 hours), the time interval can be set to be equal or non-equal intervals depending on the required evaluation accuracy.

[0059] Secondly, a random sampling process based on probability distribution is performed. In the... Second-rate( The value range is from 1 to In the simulation loop, the algorithm generates a set of independent random parameter samples based on the probability density functions established for each nondeterministic parameter in the preceding steps. This random parameter sample vector is denoted as... .

[0060] in, These are random values ​​drawn based on the distribution of process capability parameters. These are random values ​​extracted based on the thickness distribution of the insulation layer. These are random values ​​drawn based on the distribution of degradation characteristics. These are random values ​​drawn according to the Arrhenius parameter distribution. This set of random parameters constitutes a concrete, physically-attributed virtual planar transformer sample.

[0061] Finally, margin calculation based on the time series is performed. This is done for each discrete time point in the time series. Set the current time value and the Random parameter set generated by the second sampling Along with the set operating temperature (Consider this as a constant operating condition input), and substitute it into the previously established margin equation. Calculate the first... A virtual sample in Margin value at time The calculation formula is as follows:

[0062] ;

[0063] Through the above steps This simulation cycle will generate a dimension of The margin data matrix. Each element of this matrix... Each represents the withstand voltage safety status of a virtual planar transformer at the time of service, providing a complete numerical basis for subsequent failure statistics and reliability curve generation.

[0064] After using the Monte Carlo algorithm to complete the margin calculation of massive virtual samples, this method further includes steps such as statistical processing of simulation data, calculation of reliability assessment values, and generation of dynamic assessment curves.

[0065] Specifically, this step first performs time-slice-based failure statistics. This is done for each discrete time point in the pre-defined evaluation time series. The calculation obtained by traversing the aforementioned steps The set of margin values ​​for each virtual sample at that moment Based on the established failure criteria, the margin status of each sample is determined one by one. Statistics are then compiled at that time point. Below, satisfy the margin The total number of samples meeting the condition > 0 is denoted as . This statistical process transforms continuous physical simulation data into discrete, binary state (safety or failure) statistics.

[0066] Subsequently, instantaneous reliability calculations are performed. Based on the law of large numbers and the probability definition of the frequentist school, when the number of simulation samplings... When the sample size is sufficiently large, the frequency of safety events in the sample converges to the probability of that event occurring. Therefore, this invention calculates the planar transformer at a given time point. Reliability assessment value The calculation formula is as follows:

[0067] ;

[0068] The formula calculates the value. Characterized at that service time After considering factors such as process fluctuations, temperature effects, and material aging, the probability that the withstand voltage of the planar transformer is still higher than the failure threshold is considered.

[0069] Finally, reliability curve generation is performed. This is done by analyzing all time points in the time series. Repeat the above statistical and calculation process to obtain a series of discrete time reliability data pairs. Numerical fitting algorithms (such as least squares or spline interpolation) are used to smooth and fit these discrete data points, constructing a continuous time-varying reliability curve for the withstand voltage performance of the planar transformer. Changing function curve This curve visually illustrates the reliability degradation trajectory of a product from its initial stage to the end of its lifespan, providing quantitative data support for assessing the failure risk of a product at different stages of its life cycle.

[0070] See attached document Figure 2 -Appendix Figure 4In practical implementation, the evaluation method provided by this invention verifies the model's sensitivity and predictive ability to temperature stress and process fluctuation factors by constructing a specific simulation evaluation environment and setting differentiated working condition cases.

[0071] In this specific implementation, the insulation structure of a planar transformer is selected as the simulation evaluation object. To comprehensively evaluate the withstand voltage reliability of this planar transformer under different application scenarios and manufacturing quality levels, this embodiment sets up three sets of comparative simulation experimental cases (Case 1, Case 2, and Case 3). These three cases share the same basic model architecture and simulation control parameters in the Monte Carlo simulation algorithm, but differ in operating temperature. and process capability parameters There are clear gradient differences in the settings, thus forming a group of control variables.

[0072] First, set the simulation control parameters and basic material properties that are common to all cases. For the simulation control parameters, set the total number of samplings for the Monte Carlo simulation. The number of trials is set to 10,000 to ensure that the output reliability probability values ​​have statistically sufficient confidence interval convergence. The time span for dynamic evaluation is set to 0 to 50,000 hours, with a time step of 1,000 hours. Discretization sampling is performed. A withstand voltage failure threshold is set for the planar transformer. The standard is 2000V, which serves as a unified benchmark for determining whether a product has failed.

[0073] For the material and geometric fundamental properties, based on the design specifications and material property test data of this type of planar transformer, the following probability distribution is set as input:

[0074] Insulation layer thickness Assume it follows a normal distribution. , where the mean Set to 3.0 mil, standard deviation It is set to 0.05 mil to simulate the thickness tolerance under precision coating process.

[0075] Aging Activation Energy Considering the inhomogeneity of the material's microstructure, it is assumed to follow a uniform distribution. eV characterizes the range of temperature resistance fluctuations of a material.

[0076] Degradation rate parameter With degeneration order parameter : Set as a determined empirical constant based on fitting historical aging data, where Set to 1.2×10 -5 , The value is set to 0.5 to characterize the inherent aging trajectory of the insulating material over time.

[0077] Pre-exponential factors It is set as an inherent physical constant of the material, with a value of 1.5 × 10⁻⁶. 6 V / mil.

[0078] Based on this, in order to separate and quantify the independent effects of temperature and manufacturing process on reliability, three sets of differentiated experimental case conditions are defined:

[0079] Case 1 (Baseline Operating Conditions):

[0080] This case study aims to simulate product performance under a standard design environment.

[0081] Operating temperature: Set to standard rated operating temperature = 323K (i.e. 50℃).

[0082] Process capability: Set as a high-level manufacturing process; process capability parameters. Follows a normal distribution with a high mean This distribution means that the actual dielectric properties of the insulation layer can reach 98% of the ideal value on average, with very little fluctuation, representing an ideal manufacturing state with strict process control.

[0083] Case 2 (High Temperature Stress Group):

[0084] This case study aims to assess the impact of high-temperature environments on the accelerated degradation of pressure resistance reliability.

[0085] Operating temperature: Set to high-temperature load temperature =398K (i.e. 125℃), higher than the benchmark group.

[0086] Process capability: Maintain the same parameter settings as in Case 1, i.e. To eliminate the interference of process factors, we only examine the impact of temperature variables on the Arrhenius term and the final reliability.

[0087] Case 3 (Process Fluctuation Group):

[0088] This case study aims to assess the impact of manufacturing process instability on pressure resistance reliability.

[0089] Operating temperature: Maintain the same parameter settings as in Case 1, i.e. =323K.

[0090] Process capability: Set as a low-level or highly fluctuating manufacturing process; process capability parameters. They follow a normal distribution with a low mean and a large variance. This distribution means that the actual dielectric properties are only 85% of the ideal value on average, and there is a large degree of dispersion, which indicates a production state with obvious defects in the manufacturing process or poor quality control.

[0091] Through the above three case studies, the simulation environment has constructed a numerical experimental platform capable of orthogonally analyzing the impact of physical stress (temperature) and manufacturing quality (process capability) on the withstand voltage reliability of planar transformers throughout their entire life cycle.

[0092] See attached document Figure 3 After completing the aforementioned simulation environment setup and case parameter settings, the Monte Carlo simulation algorithm was used to perform dynamic evaluations on three preset working condition cases (Case 1, Case 2, and Case 3). This embodiment statistically analyzed 10,000 random samples at different time points. The margin state was used to generate corresponding reliability data.

[0093] The following details the simulation implementation results and key time-bound statistics for each case study throughout its entire lifecycle:

[0094] For Case 1 (Benchmark Condition Group), this group was set to a standard operating temperature (323K) and the manufacturing process was well controlled. The mean value is 0.98). Simulation results show that the planar transformer exhibits high withstand voltage reliability under this operating condition. At the initial time ( (hours), statistical reliability A value of 1.000 indicates that, under design baseline conditions, the withstand voltage of all samples is higher than the failure threshold of 2000V. When the service life reaches 2×10... 4 After 1 hour, the reliability decreased slightly to 0.9999; to 3×10 4 The reliability is 0.9992 for 4×10 hours; up to 4×10 4 The reliability is 0.9917 for 1 hour; 5×10⁻⁶ hours until the end of the evaluation period. 4 Hours, reliability It eventually converges to 0.9643.

[0095] This indicates that, under the baseline design, the product's failure probability within 50,000 hours is controlled to within 3.57%.

[0096] For Case 2 (high-temperature stress group), this group was set to a high-temperature load environment. Simulation results show that temperature stress accelerates the rate of reliability degradation, exhibiting obvious nonlinear degradation characteristics. At the initial time ( ), reliability The value is 1.000. However, with the accumulation of thermal stress, at 1×10⁻⁶... 4 After hours, reliability drops to 0.9998; to 2×10 4After hours, reliability drops to 0.9963; to 3×10 4 After 1 hour, the reliability showed a significant inflection point, dropping to 0.9767; to 4×10 4 Within hours, reliability rapidly declined to 0.9196; by the end of the evaluation period (5×10⁻⁶), it had reached a critical level. 4 Hours, reliability It is only 0.8377.

[0097] Data comparison shows that, compared to the baseline group, high-temperature operating conditions reduced the product's reliability by approximately 12.66 percentage points after 50,000 hours.

[0098] For Case 3 (process fluctuation group), this group is set to have certain process parameter fluctuations. Simulation results show that its reliability performance is between the baseline group and the high-temperature group. At the initial time ( ) and the initial stage of service ( =1×10 4 (hours), reliability All values ​​remained at 1.000, indicating that process fluctuations had not yet triggered early failure. When the service life reached 2×10... 4 For hours, the reliability is 0.9999; up to 3×10 4 The reliability was 0.9990 for the hourly rate, slightly lower than the baseline group's level for the same period (0.9992); up to 4×10 4 After 5 hours, the reliability dropped to 0.9861; by the end of the evaluation period (5×10⁻⁶ hours). 4 Hours, reliability The final value is 0.9479.

[0099] The results indicate that although process fluctuations did not cause an initial loss in yield, their negative impact on long-term reliability gradually became apparent as the service life progressed, with the final reliability being approximately 1.64 percentage points lower than the baseline group.

[0100] See attached document Figure 2 , Figure 3 and Figure 4 By comparing the reliability evolution curves under three different operating conditions, this invention further reveals the differential influence of environmental stress and process factors on the failure mechanism of planar transformers.

[0101] First, through comparison Figure 2 (Benchmark Group) and Figure 3 (High-temperature group) revealed the nonlinear acceleration mechanism of temperature stress on the insulation aging process.

[0102] exist Figure 2 In the middle, the curve shape is relatively flat, exhibiting a typical high-reliability, slow degradation mode. And... Figure 3 In the middle, the curve is =3×104 After several hours, a steep downward trend emerged (dropping rapidly from 0.9767 to 0.8377). This is due to the Arrhenius term in the constitutive model. The impact of temperature on the dielectric properties of materials is amplified. High-temperature environments not only reduce the current withstand voltage margin but also cause the cumulative damage rate within the insulation layer to increase exponentially. Once the service life exceeds a certain critical point (approximately 30,000 hours in this case), the thermal aging effect becomes dominant, leading to a sharp increase in the risk of failure. This suggests that in high-temperature applications, the safe replacement cycle for planar transformers should be shorter than that in ambient-temperature applications.

[0103] Secondly, through comparison Figure 2 (Benchmark Group) and Figure 4 (Process fluctuation group) reveals the hidden erosion effect of manufacturing process dispersion on long-life reliability.

[0104] It is worth noting that, Figure 4 Case 3 shown in =0 and =1×10 4 The reliability was 1.000 for all hours, indicating that even with process variations, the product met the pressure resistance requirements during the manufacturing and initial operation phases, and there was no zero-kilometer failure. However, as time progressed to 3×10 4 Hours later, Figure 4 The curve began to gradually deviate Figure 2 The baseline trajectory (e.g., in 5×10) 4 (hours, 0.9479 < 0.9643). Mechanism analysis shows that the process parameters... The increased dispersion increases the variance of the compressive strength distribution. Although initially the left tail of the distribution has not yet reached the failure threshold, the degradation term increases over time. Shifting the overall intensity distribution to the left, the sample group with greater process fluctuations (weaker individuals located on the left side of the distribution) reaches the failure boundary earlier than the sample group with better process consistency. This proves that the consistency of process quality not only affects yield but also directly impacts the long-term service life of the product.

[0105] See attached document Figure 2 , Figure 3 and Figure 4 This section verifies the effectiveness of the constructed constitutive model of the fusion physical mechanism and its evaluation method based on the corrected simulation data.

[0106] First, it verified the accuracy of the model's description of the monotonic degradation law. Observation Figures 2 to 4 All curves, in Within the hourly interval, the reliability values ​​all exhibit a monotonically non-increasing characteristic (i.e., And no reverse transition occurred. For example Figure 3 The data shows a monotonically decreasing value from 1.0 to 0.8377. This perfectly matches the objective law of irreversible degradation of the physical properties of insulating materials, proving the consistency between the mathematical logic and physical essence of the exponential time degradation model introduced in this invention.

[0107] Second, the model's sensitivity in capturing stress sensitivity was verified. The model can clearly distinguish reliability differences under different operating conditions. At the same time point (e.g., =5×10 4 (hours), the reliability calculated by the model shows The ranking clearly aligns with physical intuition: standard operating conditions are optimal, followed by process fluctuations, and high-temperature harsh conditions are the worst. In particular, the model accurately quantifies the more than 12% reliability loss caused by high temperatures, validating the effectiveness of the temperature covariate coupling mechanism in quantifying environmental impacts.

[0108] Third, the model's ability to capture low-probability failure events was verified. Figure 2 and Figure 4 Within the first 10,000 hours, the model output a reliability score of 1 or close to 1, while in the later stages, it can accurately calculate high-precision probability values ​​such as 0.9992 and 0.9917. This indicates that the Monte Carlo simulation-based evaluation method has extremely high resolution, capable of identifying the very few failure samples located at the tail end of the distribution. This overcomes the limitation of traditional mean estimation methods, which cannot quantify failure risks at the level of one in a million, and achieves a confident assessment of the withstand voltage performance of planar transformers throughout their entire life cycle.

Claims

1. A method for confident reliability modeling and evaluation of the withstand voltage performance of a planar transformer, characterized in that, Includes the following steps: Step S1: Construct a constitutive model integrating physical mechanisms: Based on the geometric dimensions, material properties, and environmental stress of the planar transformer insulation layer, establish a time degradation model and a temperature influence model respectively, and introduce a process capability parameter. The process capability parameter is used to quantify the degree of correction of the ideal dielectric constant of the insulation layer by manufacturing process fluctuations. The actual dielectric constant is expressed as the product of the process capability parameter and the ideal dielectric constant. Based on the actual dielectric constant, construct a fusion constitutive equation for calculating the instantaneous withstand voltage of the planar transformer. Step S2: Establish a reliability assessment model and quantify parameter uncertainty: Define the failure threshold of the planar transformer, construct a margin equation based on the difference between the instantaneous withstand voltage calculated by the fusion constitutive equation and the failure threshold, and identify the physical parameters in the fusion constitutive equation as random variables, and construct a probability distribution model of the random variables. Step S3: Dynamic evaluation based on Monte Carlo simulation: Set the number of simulation samplings and the evaluation time series, use the Monte Carlo algorithm to randomly sample the random variables according to the probability distribution model to generate virtual samples, and substitute the virtual samples into the margin equation to calculate the margin value at each node of the time series. Step S4: Reliability Calculation and Curve Generation: Based on the margin value calculated in Step S3, count the number of samples that meet the safety criteria at each time point, calculate the instantaneous reliability of the planar transformer, and fit and generate the withstand voltage performance reliability curve for the entire life cycle.

2. The method for reliable modeling and evaluation of the withstand voltage performance of a planar transformer according to claim 1, characterized in that, In step S1, establishing the temperature influence model specifically includes: The Arrennis relation is used to describe the functional dependence of the ideal dielectric constant of the insulating layer on the operating temperature; The ideal dielectric constant is characterized as a function of temperature, which is determined by the pre-exponential factor, the base of the natural logarithm, the activation energy, the Boltzmann constant, and the absolute temperature of the working environment. The activation energy is used to characterize the sensitivity of the withstand voltage performance of the insulating material to temperature changes.

3. The method for reliable modeling and evaluation of the withstand voltage performance of a planar transformer according to claim 1, characterized in that, In step S1, the process capability parameter is defined as a dimensionless process capability parameter, and the value range of the process capability parameter is greater than 0 and less than or equal to 1. When the process capability parameter is close to 1, it indicates that the manufacturing process level makes the product performance close to the theoretical design value.

4. The method for reliable modeling and evaluation of the withstand voltage performance of a planar transformer according to claim 1, characterized in that, In step S1, establishing the time degradation model specifically includes: An exponential decay function is used to describe the evolution of insulation performance over service time; The exponential decay function includes a degradation rate parameter and a degradation order parameter, which are used to characterize the aging characteristics of insulating materials under electrothermal stress. The fusion constitutive equation is obtained by multiplying the geometric dimensions, the dielectric constant modified by process capability parameters, and a time degradation function that includes the degradation rate and degradation order.

5. The method for reliable modeling and evaluation of the withstand voltage performance of a planar transformer according to claim 4, characterized in that, The fusion constitutive equation is used to calculate the instantaneous withstand voltage of the planar transformer under service time and operating temperature. The calculation logic is as follows: Instantaneous withstand voltage is equal to the product of process capability parameters, temperature dependence, time degradation, and insulation layer thickness; The temperature dependence term is obtained by multiplying the pre-exponential factor by a power function with the natural logarithm as the base and the ratio of the product of the activation energy, the Boltzmann constant, and the absolute temperature as the exponent. The time degradation term is obtained by a power function with the natural logarithm as the base and the product of the negative degradation rate and the degradation order of the service time raised to the power of the time of service as the exponent.

6. The method for reliable modeling and evaluation of the withstand voltage performance of a planar transformer according to claim 1, characterized in that, In step S2, constructing the margin equation based on the difference between the instantaneous withstand pressure calculated from the fused constitutive equation and the failure threshold specifically includes: The failure threshold is determined based on the rated operating voltage of the planar transformer; The margin is defined as the difference between the instantaneous withstand voltage of the planar transformer and the failure threshold. Establish failure criteria: when the calculated margin is greater than 0, the planar transformer is determined to be in a safe and reliable state; when the calculated margin is less than or equal to 0, the planar transformer is determined to have failed.

7. The method for reliable modeling and evaluation of the withstand voltage performance of a planar transformer according to claim 1, characterized in that, In step S2, constructing the probability distribution model of the random variable specifically includes: Insulation layer thickness, process capability parameters, activation energy, degradation rate, and degradation order are selected as the set of uncertainty parameters that need to be quantified; Based on historical reliability data or expert experience, identify the type of probability distribution that each parameter follows and estimate the distribution parameters; The thickness of the insulating layer is characterized as following a normal distribution, and the activation energy is characterized as being uniformly distributed over the interval.

8. The method for reliable modeling and evaluation of the withstand voltage performance of a planar transformer according to claim 1, characterized in that, In step S3, the random sampling of the random variable using the Monte Carlo algorithm specifically includes: In each simulation cycle, a set of random parameter samples is independently drawn based on the probability density function established for each uncertainty parameter; The random parameter sample includes at least randomly generated insulation layer thickness, process capability parameters, activation energy, degradation rate, and degradation order; This set of random parameter samples is combined to form a virtual planar transformer sample.

9. The method for reliable modeling and evaluation of the withstand voltage performance of a planar transformer according to claim 8, characterized in that, In step S3, generating virtual samples and calculating margin values ​​at each node of the time series specifically includes: Iterate through each discrete time point in the set evaluation time series; Substitute the current time value, the set operating temperature, and the random parameter sample generated in this sampling into the margin equation; Calculate the margin value of the virtual planar transformer sample at the discrete time point, and repeat this process until all preset number of simulation cycles are completed to generate a margin data matrix.

10. The method for reliable modeling and evaluation of the withstand voltage performance of a planar transformer according to claim 9, characterized in that, In step S4, the reliability calculation and curve generation specifically include: For each discrete time point in the evaluation time series, iterate through the margin values ​​of all virtual samples in the margin data matrix at that discrete time point; The total number of samples with a statistical margin greater than 0; Divide the total number of samples by the total number of simulation samplings to obtain the instantaneous reliability assessment value at the discrete time point; The instantaneous reliability assessment values ​​at each discrete time point are connected and numerically smoothed to generate a reliability curve of the planar transformer's withstand voltage performance as a function of time.

Images