A clock battery reliability prediction method based on multi-stress collaborative accelerated degradation and probability distribution fitting

Abstract

The application discloses a clock battery reliability prediction method based on multi-stress collaborative accelerated degradation and probability distribution fitting, and belongs to the field of electronic component reliability evaluation techniques. In order to solve the problem that the clock battery prediction model is significantly deviated from the actual working condition, the application comprises the following steps: defining a performance field function based on position and time in an internal state space, and constructing a macroscopic entropy function; constructing a time-space evolution equation of the performance field function, and constructing an evolution equation of the macroscopic entropy function; obtaining a parameter set of the time-space evolution equation of the performance field function and a parameter set of the evolution equation of the macroscopic entropy function; establishing a double-layer optimization framework, simultaneously calibrating the parameter set of the time-space evolution equation of the performance field function and the parameter set of the evolution equation of the macroscopic entropy function, and predicting the failure time of the first clock battery sample; constructing a parameterized model for representing a probability density function, setting the time integral of the probability density function of each clock battery sample as the reliability of the clock battery sample, and completing the clock battery reliability prediction.

Description

Technical Field

[0001] This invention belongs to the field of electronic component reliability assessment, specifically relating to a clock battery reliability prediction method based on multi-stress synergistic accelerated degradation and probability distribution fitting. Background Technology

[0002] In today's world of increasingly prevalent electronic devices and systems, real-time clock circuits have become an indispensable basic functional module in critical equipment such as smart meters, IoT terminals, communication devices, and data storage systems. As the energy source for maintaining uninterrupted timing and preserving critical configuration information, the performance and reliability of the real-time clock battery directly affect the long-term stable operation and data security of the entire device. These batteries are typically required to possess extremely high reliability and extremely long service life, often designed to last for ten or even several decades.

[0003] However, conducting direct lifespan verification and reliability assessment of such long-life battery products faces enormous technical challenges and cost pressures. How to establish a reliability prediction method that accurately reflects the synergistic mechanism of multiple stresses, fully utilizes full-process degradation data, and provides clear physical meaning and statistical confidence has become a key technical bottleneck restricting the development of high-reliability, long-life clock battery technology, and a problem that those skilled in the art have long strived to solve but have yet to fully resolve.

[0004] Existing technologies have at least the following technical problems: Existing technologies generally use a single stress factor for acceleration, which cannot truly reflect the complex degradation mechanism of clock batteries under the combined effects of multiple stresses such as temperature and current in actual use, resulting in significant deviations between prediction models and actual operating conditions; Existing methods are mostly limited to simple statistical analysis of the failure time of individual batteries, failing to capture the overall evolution law and related characteristics of battery group performance degradation at the system level, and ignoring the important information contained in the performance dispersion between samples; Traditional reliability prediction models usually rely on simple extrapolation of specific lifetime distribution parameters. This approach cannot accurately describe the complex nonlinear evolution of the distribution shape as stress conditions change, resulting in significant uncertainty in long-term extrapolation prediction results. Summary of the Invention

[0005] This invention addresses the problem that existing technologies generally use a single stress factor for acceleration, which fails to accurately reflect the complex degradation mechanism of clock batteries under the combined effects of multiple stresses such as temperature and current in actual use, leading to significant deviations between the prediction model and actual operating conditions. The invention proposes a clock battery reliability prediction method based on multi-stress synergistic accelerated degradation and probability distribution fitting.

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

[0007] A clock battery reliability prediction method based on multi-stress synergistic accelerated degradation and probability distribution fitting includes the following steps:

[0008] S1. Construct an internal state space, mapping each clock battery sample to a point in the internal state space; define a performance field function based on location and time in the internal state space, and set the actual measured clock battery voltage as the integral average of the performance field function in the local region; construct a macroscopic entropy function based on the voltage measurements of all clock battery samples to quantify the consistency or dispersion of the clock battery group performance.

[0009] S2. Construct the spatiotemporal evolution equation of the performance field function, construct the evolution equation of the macroscopic entropy function, and obtain the parameter set of the spatiotemporal evolution equation of the performance field function and the parameter set of the evolution equation of the macroscopic entropy function;

[0010] S3. Establish a two-layer optimization framework, and simultaneously calibrate the parameter set of the spatiotemporal evolution equation of the performance field function and the parameter set of the evolution equation of the macroscopic entropy function to achieve the best match between the simulation results and experimental observations, and predict the failure time of the first clock battery sample.

[0011] S4. Construct a parameterized model to represent the probability density function, set the time integral of the probability density function of each clock battery sample as the reliability of the clock battery sample, and complete the clock battery reliability prediction based on multi-stress synergistic accelerated degradation and probability distribution fitting.

[0012] Furthermore, the specific implementation method of step S1 includes the following steps:

[0013] S1.1. Construct the internal state space, with coordinates as follows: ;

[0014] S1.2. Set the first The initial state coordinates of each battery sample at the initial moment of the test are as follows: The initial state coordinates are assigned randomly;

[0015] S1.3. Define the performance field function based on location and time. ,in For ambient temperature, For load current, For time;

[0016] S1.4. Assume the actual measured battery voltage It is the performance field function in the cell's initial state coordinates. The integral average over a local circular region centered at R with radius R;

[0017] S1.5. Construct the macroscopic entropy function, with the following expression:

[0018]

[0019] in, Represents macroscopic entropy; and These are the maximum and minimum values ​​of the battery sample voltage at time t, respectively; It is the normalization coefficient, and its value is... This is to ensure that the entropy value is within the range of [0,1]. This represents the total number of battery samples.

[0020] Furthermore, the specific implementation method of step S2 includes the following steps:

[0021] S2.1. The spatiotemporal evolution equation of the performance field function is constructed as a stochastic dynamic equation driven by stress, expressed as:

[0022]

[0023] in, It is a performance field Partial derivative with respect to time t; It is a diffusion term. It is the Laplace operator. It is the diffusion coefficient; set to... ,in It is the baseline diffusion coefficient to be fitted. It is the equivalent activation energy of the diffusion process. It is the Boltzmann constant; It is a nonlinear drift term. It is the restoring strength coefficient, set to ,in It is the baseline coefficient of recovery. It is the current attenuation coefficient; It is the stable reference state of the performance field; It is a random force term. It is Gaussian white noise. It is the noise intensity factor, set to , It is the reference noise amplitude;

[0024] Set the parameter set of the spatiotemporal evolution equation of the performance field function. for ;

[0025] S2.2. Construct the evolution equation of the macroscopic entropy function, where the entropy value is regarded as the reaction coordinate of the activation process, and the expression is:

[0026]

[0027] in, It is a macroscopic entropy function The first derivative with respect to time t; It's the frequency of attempts. , It is the baseline attempt frequency coefficient. It is the stress synergy index, which describes the synergistic amplification effect of temperature and current on the frequency of the test. It is the generalized activation Gibbs free energy. ,in It is the activation enthalpy. It is a microscopic entropy change, obtained through nonlinear least squares fitting. It is the current energy coupling coefficient;

[0028] Set the parameter set of the evolution equation for the macroscopic entropy function. for .

[0029] Furthermore, the specific implementation method of step S3 includes the following steps:

[0030] S3.1. Establish a two-layer optimization framework, and set the inner layer optimization as... The outer layer is optimized to The random approximation EM algorithm or Bayesian computation method is used to obtain the following results. ;

[0031] S3.2. Predict the failure time of the first clock battery sample, satisfying the following integral equation:

[0032]

[0033] in, It is the moment when the performance parameters of the first battery sample reach or exceed the preset failure threshold; It is the integral variable, time; It is the critical constant of the system.

[0034] Furthermore, the specific implementation method of step S4 includes the following steps:

[0035] S4.1. Construct a parameterized model to represent the probability density function, expressed as:

[0036]

[0037] in, It is a probability density function; It is a normalized partition function; It is a pre-selected set of k-th order orthogonal basis functions, whose function is to construct a feature space describing the shape of the distribution; It is the k-th order coupling coefficient, each The value of determines its corresponding basis functions. The weight it occupies in the final shape of the probability density function; It is the truncation order of the expansion;

[0038] ;

[0039] S4.2. Set the time integral of the probability density function of each clock battery sample as its reliability. The reliability provides a probability estimate that the product can still work normally at a specified time t under normal use conditions, thus completing the entire process from multi-stress accelerated degradation data to long-term reliability prediction.

[0040] The beneficial effects of this invention are:

[0041] The present invention describes a clock battery reliability prediction method based on multi-stress synergistic accelerated degradation and probability distribution fitting. By constructing the stochastic dynamic equation of the performance field and establishing its intrinsic connection with the macroscopic observable entropy function, we can understand and describe the degradation process of the battery population at a deeper level, namely, the correlation between microscopic state fluctuations and macroscopic performance dispersion. This field theory-based modeling approach can more fundamentally reveal the complex physicochemical mechanism of the synergistic effect of multiple stresses such as temperature and load current.

[0042] The clock battery reliability prediction method based on multi-stress synergistic accelerated degradation and probability distribution fitting described in this invention cleverly utilizes the real-time voltage data of all samples to dynamically quantify the consistency and dispersion of battery group performance using the defined macroscopic entropy function. By viewing the growth of entropy as an activation process that needs to overcome the generalized Gibbs free energy barrier, we can indirectly and sensitively predict the occurrence time of the first failure sample and even the evolution of the entire lifetime distribution by monitoring the early evolution trend of the dispersion of group performance.

[0043] The present invention discloses a clock battery reliability prediction method based on multi-stress synergistic accelerated degradation and probability distribution fitting. The method employs a two-layer optimization framework that integrates the simultaneous calibration of microscopic parameters of the performance field and macroscopic entropy evolution parameters, ensuring logical consistency and mathematical rigor from microscopic mechanisms to macroscopic statistical behavior. By combining computationally expensive field simulation with operable entropy path fitting, the method ensures the physical depth of the model while also considering the feasibility of parameter identification, thus achieving efficient and robust extraction of key lifetime statistical features from short-term degradation data of the population.

[0044] The present invention discloses a clock battery reliability prediction method based on multi-stress synergistic accelerated degradation and probability distribution fitting. It represents the lifetime distribution as an exponential family model in which the coupling coefficient depends on the stress, and establishes a nonlinear dynamic system in which the coupling coefficient changes with the stress. This allows the final form of the distribution under normal use conditions to be "evolved" from high stress by solving a dynamic system. It can capture the complex nonlinear changes in the distribution shape that may occur under different stresses, thereby predicting a lifetime distribution shape that is more in line with the actual physical laws and cannot appear in traditional extrapolation models. This greatly improves the accuracy and confidence level of long-term reliability prediction. Attached Figure Description

[0045] Figure 1 This is a flowchart of a clock battery reliability prediction method based on multi-stress synergistic accelerated degradation and probability distribution fitting, as described in this invention. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention; that is, the described specific embodiments are merely a part of the embodiments of the invention, and not all of them. The components of the specific embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations, and the invention may also have other embodiments.

[0047] Therefore, the following detailed description of specific embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected specific embodiments of the invention. All other specific embodiments obtained by those skilled in the art based on these specific embodiments without inventive effort are within the scope of protection of this invention.

[0048] To further understand the invention's content, features, and effects, the following specific embodiments are provided, along with accompanying drawings. Figure 1 Detailed explanation is as follows:

[0049] Example 1:

[0050] A clock battery reliability prediction method based on multi-stress synergistic accelerated degradation and probability distribution fitting includes the following steps:

[0051] S1. Construct an internal state space, mapping each clock battery sample to a point in the internal state space; define a performance field function based on location and time in the internal state space, and set the actual measured clock battery voltage as the integral average of the performance field function in the local region; construct a macroscopic entropy function based on the voltage measurements of all clock battery samples to quantify the consistency or dispersion of the clock battery group performance.

[0052] Furthermore, the specific implementation method of step S1 includes the following steps:

[0053] S1.1. Construct the internal state space, with coordinates as follows: The two-dimensional internal state space represents the set of all microscopic physicochemical states inside the battery that cannot be directly observed.

[0054] S1.2. Set the first The initial state coordinates of each battery sample at the initial moment of the test are as follows: The initial state coordinates are assigned randomly;

[0055] S1.3. Define the performance field function based on location and time. ,in For ambient temperature, For load current, For time; describes the stress condition Below, located The macroscopic performance corresponding to the local microscopic state of a point;

[0056] S1.4. Assume the actual measured battery voltage It is the performance field function in the cell's initial state coordinates. The integral average within a local circular region centered on R and with radius R acts as a low-pass filter.

[0057] S1.5. Construct the macroscopic entropy function, with the following expression:

[0058]

[0059] in, Represents macroscopic entropy; and These are the maximum and minimum values ​​of the battery sample voltage at time t, respectively; It is the normalization coefficient, and its value is... This is to ensure that the entropy value is within the range of [0,1]. This represents the total number of battery samples. After establishing the relationship between the performance field and the observed data, to quantify the overall degradation behavior of the battery group under stress, a global parameter that can sensitively reflect the performance dispersion among battery samples needs to be constructed. Based on the voltage measurements of all batteries at time t, a macroscopic entropy function is constructed. The definition of the macroscopic entropy function borrows from the form of information entropy but is adaptively modified. When the voltages of all battery samples are highly concentrated, the macroscopic entropy value is close to zero, indicating that the system is ordered; the greater the difference between battery voltages, the higher the macroscopic entropy value, indicating that the system is disordered.

[0060] Furthermore, by introducing an internal state space to characterize the complex state inside the battery that cannot be directly observed, and mapping each battery sample to a point in the space, a performance field function that depends on location and time is defined. The actual measured battery voltage is the integral average of the performance field in the local region. Based on the voltage measurement values ​​of all battery samples, a macroscopic entropy function is constructed to quantify the consistency or dispersion of the battery group performance.

[0061] Clock battery samples were placed in a precisely controlled integrated environmental stress chamber, which could independently and precisely adjust the key stress factors—ambient temperature (T) and load current (I). Based on experimental design theory, an accelerated test matrix containing multiple combinations of different temperature and current levels was constructed. Under each set stress combination, a group of parallel clock battery samples were subjected to a continuous or periodic constant current load to simulate their operation in a real circuit. Throughout the test cycle, a data acquisition system synchronously recorded the key performance parameters of all samples, primarily their terminal voltage values, at fixed time intervals.

[0062] S2. Construct the spatiotemporal evolution equation of the performance field function, construct the evolution equation of the macroscopic entropy function, and obtain the parameter set of the spatiotemporal evolution equation of the performance field function and the parameter set of the evolution equation of the macroscopic entropy function;

[0063] The spatiotemporal evolution of the performance field is governed by a stress-driven stochastic dynamic equation. The evolution of macroscopic entropy is modeled as an activation process that needs to overcome an energy barrier. The parameters in the two evolution equations constitute two sets of parameters to be solved, which together characterize the complete dynamic behavior of the battery system from microscopic to macroscopic under multiple stresses.

[0064] Furthermore, the specific implementation method of step S2 includes the following steps:

[0065] S2.1. The spatiotemporal evolution equation of the performance field function is constructed as a stochastic dynamic equation driven by stress, expressed as:

[0066]

[0067] in, It is a performance field The partial derivative with respect to time t represents the instantaneous rate of change of the performance field with time at a fixed point x in the internal state space. It is a diffusion term. It is the Laplace operator, which measures the "smoothing" or "flattening" tendency of a field in its internal state space. It is the diffusion coefficient; set to... ,in It is the baseline diffusion coefficient to be fitted. It is the equivalent activation energy of the diffusion process. It is the Boltzmann constant; It is a nonlinear drift term, representing the field's tendency to move towards a stable reference state. The trend of return It is the restoring strength coefficient, set to ,in It is the baseline coefficient of recovery. It is the current attenuation coefficient, which means that a large current will weaken the battery's ability to maintain a stable state; It is the stable reference state of the performance field, representing the state that the performance field is expected to maintain under ideal conditions; It is a random force term. It is Gaussian white noise. It is the noise intensity factor, set to , It is the reference noise amplitude, indicating that temperature and current amplify the random fluctuations of microscopic processes;

[0068] Set the parameter set of the spatiotemporal evolution equation of the performance field function. for ;

[0069] The stochastic dynamics equations of the performance field, through their diffusion, nonlinear drift, and stochastic force terms, collectively determine the set of voltage trajectories for all clock battery samples, and thus the simulated entropy path. However, directly predicting entropy evolution through expensive field simulations is impractical. Therefore, it is necessary to find an equation that can directly describe the time evolution of macroscopic entropy itself.

[0070] Through dimensional analysis and observation of simulation and experimental data, it was found that the evolution rate of macroscopic entropy is not constant, but closely related to the current disordered state of the system itself and external stress. The growth process of macroscopic entropy is analogous to an activation process that needs to overcome an energy barrier, and the entropy value is regarded as the response coordinate of the activation process; the lower the entropy value, the slower the evolution.

[0071] S2.2. Construct the evolution equation of the macroscopic entropy function, where the entropy value is regarded as the reaction coordinate of the activation process, and the expression is:

[0072]

[0073] in, It is a macroscopic entropy function The first derivative with respect to time t represents the instantaneous rate of change of the performance dispersion of the battery group; It is the frequency of attempts, characterizing the inherent speed of system evolution. , It is the baseline trial frequency coefficient, representing the natural frequency at which the microstate of the system changes under a normalized unit stress metric. It is the stress synergy index, which describes the synergistic amplification effect of temperature and current on the frequency of the test. It is the generalized activation Gibbs free energy, derived from the activation energy of chemical reactions and the thermodynamic Gibbs free energy. It represents the energy barrier that a system needs to overcome to evolve from a low-entropy ordered state to a high-entropy disordered state. ,in It is the activation enthalpy, which represents the energy required to maintain the stability of the battery's internal structure. It is a microscopic entropy change, obtained through nonlinear least squares fitting. It is the current energy coupling coefficient;

[0074] Set the parameter set of the evolution equation for the macroscopic entropy function. for .

[0075] S3. Establish a two-layer optimization framework, and simultaneously calibrate the parameter set of the spatiotemporal evolution equation of the performance field function and the parameter set of the evolution equation of the macroscopic entropy function to achieve the best match between the simulation results and experimental observations, and predict the failure time of the first clock battery sample.

[0076] Furthermore, the specific implementation method of step S3 includes the following steps:

[0077] S3.1. Establish a two-layer optimization framework, and set the inner layer optimization as... The outer layer is optimized to The random approximation EM algorithm or Bayesian computation method is used to obtain the following results. ;

[0078] Furthermore, in the established two-level optimization problem, the inner optimization is fixed. By simulating the performance field equations using Monte Carlo simulation, a large number of virtual battery sample trajectories are generated. The simulated entropy path is calculated, and its difference from the real entropy path calculated using real voltage data is minimized. Outer layer optimization involves adjusting... This ensures that the entropy path obtained by integrating the stochastic dynamics equations also matches the true entropy path. The ultimate goal is to find a set of... This ensures that both the entropy paths calculated by the inner and outer optimization layers best fit the true entropy path in the least squares sense. This calculation process employs either the stochastic approximation EM algorithm or a Bayesian computation method.

[0079] After all parameters have been successfully calibrated, the random evolution of the performance field leads to the dispersion of the clock battery voltage trajectory. When the simulated voltage of any sample first falls below the failure threshold, it marks that the system has evolved to a critical state in the macroscopic entropy path. The time of failure of the first sample is defined as the moment when the simulated voltage of any battery first falls below the preset threshold.

[0080] S3.2. Predict the failure time of the first clock battery sample, satisfying the following integral equation:

[0081]

[0082] in, It is the moment when the performance parameters of the first battery sample reach or exceed the preset failure threshold; It is the integral variable, time; This is the system's critical constant. It represents the critical threshold that the accumulated "normalized evolutionary momentum" of the entire system needs to reach from the start of the experiment to the occurrence of the first failure sample. It is obtained by inverting experimental data under the highest stress conditions. Furthermore, an empirical relationship between the first failure time and the more commonly used median lifetime is established, thereby bypassing the traditional individual lifetime fitting and directly extracting key lifetime statistics from the population entropy evolution.

[0083] S4. Construct a parameterized model to represent the probability density function, set the time integral of the probability density function of each clock battery sample as the reliability of the clock battery sample, and complete the clock battery reliability prediction based on multi-stress synergistic accelerated degradation and probability distribution fitting.

[0084] Furthermore, the specific implementation method of step S4 includes the following steps:

[0085] S4.1. Construct a parameterized model to represent the probability density function, expressed as:

[0086]

[0087] in, It is a probability density function; It is a normalized partition function; It is a pre-selected set of k-th order orthogonal basis functions, whose function is to construct a feature space describing the shape of the distribution; It is the k-th order coupling coefficient, each The value of determines its corresponding basis functions. The weight it occupies in the final shape of the probability density function; It is the truncation order of the expansion;

[0088] ;

[0089] S4.2. Set the time integral of the probability density function of each clock battery sample as its reliability. The reliability provides a probability estimate that the product can still work normally at a specified time t under normal use conditions, thus completing the entire process from multi-stress accelerated degradation data to long-term reliability prediction.

[0090] It should be noted that relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0091] Although this application has been described above with reference to specific embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of this application. In particular, as long as there is no structural conflict, the features in the specific embodiments disclosed in this application can be combined with each other in any way. The lack of an exhaustive description of these combinations in this specification is merely for the sake of brevity and resource conservation. Therefore, this application is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A clock battery reliability prediction method based on multi-stress synergistic accelerated degradation and probability distribution fitting, characterized in that, Includes the following steps: S1. Construct an internal state space, mapping each clock battery sample to a point in the internal state space; define a performance field function based on location and time in the internal state space, and set the actual measured clock battery voltage as the integral average of the performance field function in the local region; Based on the voltage measurements of all clock battery samples, a macroscopic entropy function is constructed to quantify the uniformity or dispersion of the clock battery group performance. S2. Construct the spatiotemporal evolution equation of the performance field function, construct the evolution equation of the macroscopic entropy function, and obtain the parameter set of the spatiotemporal evolution equation of the performance field function and the parameter set of the evolution equation of the macroscopic entropy function; S3. Establish a two-layer optimization framework, and simultaneously calibrate the parameter set of the spatiotemporal evolution equation of the performance field function and the parameter set of the evolution equation of the macroscopic entropy function to achieve the best match between the simulation results and experimental observations, and predict the failure time of the first clock battery sample. S4. Construct a parameterized model to represent the probability density function, set the time integral of the probability density function of each clock battery sample as the reliability of the clock battery sample, and complete the clock battery reliability prediction based on multi-stress synergistic accelerated degradation and probability distribution fitting.

2. The clock battery reliability prediction method based on multi-stress synergistic accelerated degradation and probability distribution fitting according to claim 1, characterized in that, The specific implementation method of step S1 includes the following steps: S1.

1. Construct the internal state space, with coordinates as follows: ; S1.

2. Set the first The initial state coordinates of each battery sample at the initial moment of the test are as follows: The initial state coordinates are assigned randomly; S1.

3. Define the performance field function based on location and time. ,in For ambient temperature, For load current, For time; S1.

4. Assume the actual measured battery voltage It is the performance field function in the cell's initial state coordinates. The integral average over a local circular region centered at R with radius R; S1.

5. Construct the macroscopic entropy function, with the following expression: ； in, Represents macroscopic entropy; and These are the maximum and minimum values ​​of the battery sample voltage at time t, respectively; It is the normalization coefficient, and its value is... This is to ensure that the entropy value is within the range of [0,1]. This represents the total number of battery samples.

3. The clock battery reliability prediction method based on multi-stress synergistic accelerated degradation and probability distribution fitting according to claim 2, characterized in that, The specific implementation method of step S2 includes the following steps: S2.

1. The spatiotemporal evolution equation of the performance field function is constructed as a stochastic dynamic equation driven by stress, expressed as: ； in, It is a performance field Partial derivative with respect to time t; It is a diffusion term. It is the Laplace operator. It is the diffusion coefficient; set to... ,in It is the baseline diffusion coefficient to be fitted. It is the equivalent activation energy of the diffusion process. It is the Boltzmann constant; It is a nonlinear drift term. It is the restoring strength coefficient, set to ,in It is the baseline coefficient of recovery. It is the current attenuation coefficient; It is the stable reference state of the performance field; It is a random force term. It is Gaussian white noise. It is the noise intensity factor, set to , It is the reference noise amplitude; Set the parameter set of the spatiotemporal evolution equation of the performance field function. for ; S2.

2. Construct the evolution equation of the macroscopic entropy function, where the entropy value is regarded as the reaction coordinate of the activation process, and the expression is: ； in, It is a macroscopic entropy function The first derivative with respect to time t; It's the frequency of attempts. , It is the baseline attempt frequency coefficient. It is the stress synergy index, which describes the synergistic amplification effect of temperature and current on the frequency of the test. It is the generalized activation Gibbs free energy. ,in It is the activation enthalpy. It is a microscopic entropy change, obtained through nonlinear least squares fitting. It is the current energy coupling coefficient; Set the parameter set of the evolution equation for the macroscopic entropy function. for .

4. The clock battery reliability prediction method based on multi-stress synergistic accelerated degradation and probability distribution fitting according to claim 3, characterized in that, The specific implementation method of step S3 includes the following steps: S3.

1. Establish a two-layer optimization framework, and set the inner layer optimization as... The outer layer is optimized to The random approximation EM algorithm or Bayesian computation method is used to obtain the following results. ; S3.

2. Predict the failure time of the first clock battery sample, satisfying the following integral equation: ； in, It is the moment when the performance parameters of the first battery sample reach or exceed the preset failure threshold; It is the integral variable, time; It is the critical constant of the system.

5. The clock battery reliability prediction method based on multi-stress synergistic accelerated degradation and probability distribution fitting according to claim 4, characterized in that, The specific implementation method of step S4 includes the following steps: S4.

1. Construct a parameterized model to represent the probability density function, expressed as: ； in, It is a probability density function; It is a normalized partition function; It is a pre-selected set of k-th order orthogonal basis functions, whose function is to construct a feature space describing the shape of the distribution; It is the k-th order coupling coefficient, each The value of determines its corresponding basis functions. The weight it occupies in the final shape of the probability density function; It is the truncation order of the expansion; ； S4.

2. Set the time integral of the probability density function of each clock battery sample as its reliability. The reliability provides a probability estimate that the product can still work normally at a specified time t under normal use conditions, thus completing the entire process from multi-stress accelerated degradation data to long-term reliability prediction.

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