Arrhenius model-based variable environmental input life evaluation method and system
By combining the Arrhenius model with a specified distribution function, the uncertainty of the relationship between performance and aging time in traditional models under unsteady conditions is solved, and effective probabilistic prediction and continuous performance variation of devices under varying temperatures are realized.
Patent Information
- Application Number
- CN202211314650.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-10-26
- Publication Date
- 2026-03-03
- Estimated Expiration
- 2042-10-26
AI Technical Summary
Traditional Arrhenius models fail to effectively describe performance uncertainty and time volatility when simulating the relationship between performance and aging time under unsteady conditions, leading to inaccurate predictions.
By combining a specified distribution function with the Arrhenius model, the effective probability of the device under unsteady environmental conditions is predicted through parameter calculation under time series unsteady environmental conditions. The probabilistic relationship between performance and aging time is obtained by fitting the maximum distribution function and other methods.
It enables continuous prediction of device performance changes under unsteady conditions, provides effective probabilistic prediction of devices at varying temperatures, and expands the scope of data applications.
Smart Images
Figure CN115577550B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of electronic digital data processing technology, and in particular to a method and system for assessing the lifetime of variable environmental inputs based on the Arrhenius model. Background Technology
[0002] Traditional Arrhenius models can calculate the relationship between performance and aging time under a certain steady environment by using experimental data from different environments. However, in reality, the environment changes over time, and simulations using simple steady-state environments are often unsuitable for practical problems.
[0003] Meanwhile, the relationship between performance and aging time calculated by the traditional Arrhenius model under a certain constant environment is deterministic. However, in reality, the relationship between performance and aging time is uncertain (there is a probabilistic relationship between the two). Using a deterministic curve to describe it often ignores the fluctuation of performance over time. Summary of the Invention
[0004] To address the aforementioned issues, this invention proposes a method and system for estimating lifetime under varying environmental inputs based on the Arrhenius model. This method combines a specified distribution function under unsteady time-series environmental inputs with the Arrhenius model to predict the effective probability of devices. This approach can solve the aforementioned problems and can also be used for prediction methods of other similar distributions and models.
[0005] The technical solution adopted in this invention is as follows:
[0006] A method for assessing lifetime under varying environmental inputs based on the Arrhenius model includes the following steps:
[0007] S1. Load training data, obtain performance and aging time under varying environmental conditions, use least squares method multiple times to solve the parameters of Arrhenius model under a single temperature, and generalize to solve the parameters of Arrhenius model under other temperatures in the training data.
[0008] S2. Based on the parameters of the Arrhenius model at different temperatures in the training data obtained in step S1, and using the time series under unsteady environmental conditions as input, the parameters of the Arrhenius model under unsteady environmental conditions are obtained through interpolation, and then the performance value under unsteady environmental conditions is obtained.
[0009] S3. Based on the performance values obtained in step S2, and in conjunction with the performance values in the training data, determine the parameters of the preset distribution function at different temperatures;
[0010] S4. By fitting the relationship between environmental conditions and preset distribution function parameters under time series input, a given threshold is used to solve and plot the probability distribution under unsteady environmental conditions when the time series is the input, thereby predicting the effective probability of the device under test under unsteady environmental conditions.
[0011] Furthermore, the preset distribution function includes a maximum distribution function, a normal distribution function, and a t-distribution function.
[0012] Furthermore, the preset distribution function is set as the maximum value distribution function. In this case, step S3 includes: determining the mean and standard deviation of the performance samples based on the performance values obtained in step S2 and the performance values in the training data, and then using the mean and standard deviation to obtain the parameters of the maximum value distribution function at different temperatures.
[0013] Furthermore, the failure probability of the device under test is:
[0014]
[0015] In the formula, t is time, and μ and σ are the distribution parameters of the maximum distribution function.
[0016] Furthermore, the variance of the performance samples in the training data is used as the expected value μ + γσ of the maximum value distribution function, where γ = 0.577; the performance values based on the time series input are used as the variance of the maximum value distribution function. Thus, the distribution parameters μ and σ can be obtained.
[0017] Furthermore, by inputting the distribution parameters μ and σ and the time series, the relationship between the distribution parameters μ and σ and the time series is obtained by fitting using the least squares method.
[0018] Furthermore, substituting the fitted distribution parameters μ and σ into the maximum distribution function, the effective probability corresponding to the time point is calculated as 1-p1, where:
[0019]
[0020] In the formula, threshold is the threshold value, and f(t) is the probability density function of the maximum distribution F(t).
[0021] A variable environmental input lifetime assessment system based on the Arrhenius model includes:
[0022] The model parameter calculation module is used to load training data, obtain performance and aging time under varying environmental conditions, and solve the parameters of the Arrhenius model at a single temperature multiple times using the least squares method, and then generalize it to solve the parameters of the Arrhenius model at other temperatures in the training data.
[0023] The performance value calculation module is used to calculate the parameters of the Arrhenius model at different temperatures in the training data obtained by the model parameter calculation module. It takes the time series under unsteady environmental conditions as input, and obtains the parameters of the Arrhenius model under unsteady environmental conditions through interpolation methods, thereby obtaining the performance value under unsteady environmental conditions.
[0024] The distribution parameter calculation module is used to determine the parameters of the preset distribution function at different temperatures based on the performance value obtained by the performance value calculation module and the performance value in the training data.
[0025] The effective probability prediction module is used to obtain the relationship between environmental conditions and preset distribution function parameters under time series input by fitting, solve and draw the probability distribution map of the device under test under unsteady environmental conditions when the time series is the input, and thus predict the effective probability of the device under test under unsteady environmental conditions.
[0026] The beneficial effects of this invention are as follows:
[0027] 1. This invention utilizes the traditional Arrhenius model to calculate the correlation parameters between performance and aging time under different environments. For time series in unsteady environments, the calculated correlation parameters under different environments are used for interpolation. Simultaneously, in order to transform it into a probabilistic model, a Type I maximum distribution is used as an example (other distributions, such as normal distribution, t-distribution, etc., can be used), illustrating that a specified distribution function can predict the effective probability of a device based on a time series and a given threshold. When a time series under an unsteady environment is input, the relationship between performance and aging time under the unsteady environment is linked to the parameters of the specified distribution function, thereby obtaining the effective probability of the device under the time series in the unsteady environment.
[0028] 2. This invention is based on the Arrhenius model with time-series input under unsteady conditions, which can realize the continuous change of device performance at varying temperature and time points.
[0029] 3. This invention predicts the effective probability of a device by measuring the changes in the parameters of the Arrhenius model and the parameters of a specified distribution function under time series input, which enables the expansion of data applications and provides ideas for subsequent applications. Attached Figure Description
[0030] Figure 1 This is a flowchart of the variable environment input lifetime assessment method based on the Arrhenius model of the present invention.
[0031] Figure 2 This is a diagram illustrating the abrupt change in the performance curve.
[0032] Figure 3 This is a diagram illustrating the sharp change in the processing performance curve.
[0033] Figure 4 This is the result chart with instance data.
[0034] Figure 5 This is a schematic diagram of the probability density distribution at a certain time point in an unsteady environment. Detailed Implementation
[0035] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments are now described. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention; that is, the described embodiments are only a part of the embodiments of the invention, not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.
[0036] Example 1
[0037] This embodiment provides a method for assessing lifetime under varying environmental inputs based on the Arrhenius model, including the following steps:
[0038] S1. Load training data, obtain performance and aging time under varying environmental conditions, use least squares method multiple times to solve the parameters of Arrhenius model under a single temperature, and generalize to solve the parameters of Arrhenius model under other temperatures in the training data.
[0039] S2. Based on the parameters of the Arrhenius model at different temperatures in the training data obtained in step S1, and using the time series under unsteady environmental conditions as input, the parameters of the Arrhenius model under unsteady environmental conditions are obtained through interpolation, and then the performance value under unsteady environmental conditions is obtained.
[0040] S3. Based on the performance values obtained in step S2, and in conjunction with the performance values in the training data, determine the parameters of the preset distribution function at different temperatures;
[0041] S4. By fitting the relationship between environmental conditions and preset distribution function parameters under time series input, a given threshold is used to solve and plot the probability distribution under unsteady environmental conditions when the time series is the input, thereby predicting the effective probability of the device under test under unsteady environmental conditions.
[0042] Specifically, such as Figure 1 As shown, the variable environment input lifetime assessment method in this embodiment specifically includes the following steps:
[0043] Step 1: Input training and test data.
[0044] Read environmental factors such as temperature and their corresponding performance and aging time from the training data, such as time (segment) and its corresponding temperature, performance and aging time corresponding to each temperature or time (segment), and read the time series and environmental conditions from the test data.
[0045] Assume that in the training data, an aging time τ is obtained at the i-th aging test temperature. ij With performance change index P ij :
[0046]
[0047] Where i is the experimental temperature sequence number, representing the i-th aging test temperature; j is the experimental time sequence number, representing the j-th moment in the experimental record; m i The experimental time.
[0048] Step 2: Calculate the Arrhenius model parameters at a certain steady temperature.
[0049] The Arrhenius model is shown below:
[0050]
[0051] Where P is the performance index, A is the experimental constant, w is the aging parameter, τ is the aging time, and K is the aging reaction rate constant K = Be. -E / RT , where B, E and R are constants, and T is the temperature in Kelvin.
[0052] (1) First, give w(0) <w<1);
[0053] (2) Calculate A i and K i Let Y = ln(P), X = τ ω Given a = ln(A) and b = -K, solve the equation Y = a + bx to obtain the least squares solution, A = e a K = -b. The parameter A at the i aging test temperatures can then be obtained. i and K i , take A=(A1+A2+…+A m ) / m, where m is the total number of experimental temperatures;
[0054] (3) Calculate E / R and B: Let Y = ln(K), X = 1 / T, a1 = ln(B), b1 = -E / R, solve the equation Y = a1 + b1x to obtain the least squares solution, B = e a1 E / R = -b1;
[0055] (4) Obtain K i The estimated value Ki = Be -E / RT ;
[0056] (5) Obtain A, K, w to get the final solution.
[0057] Assume the error is:
[0058]
[0059] Using the successive approximation method, first calculate the corresponding error values when w takes 0.5 and 0.51. If J 0.5 < J 0.51 , then 0.5 < w < 1. Successively narrow the search space until the accuracy requirement is met, and the solution A, K, w that makes the J value the smallest is the final solution.
[0060] Step 3: Calculate the performance of the Arrhenius model for the unsteady environmental time series.
[0061] Use the Arrhenius model to calculate the parameters A, B, w, E / R corresponding to each environment in the training data; under the input of the unsteady environmental time series, the parameters of the Arrhenius model obtained from the training data can be used to calculate the parameters of the Arrhenius model at any temperature using interpolation. Since the environmental conditions are different in each time period, substitute the obtained parameters A, B, w, E / R and the corresponding temperature and time into the Arrhenius model to calculate the corresponding performance values. Save the calculated performance values for subsequent calculation of the mean.
[0062] Due to the change of environmental conditions in the time series, the temperature in each time period will also change. If the performance curves are directly drawn using the parameters obtained under each environmental condition, it will lead to discontinuous performance curves. Figure 2 The two curves in [[ ]] represent the performance curves at different temperatures (102° and 105°). Assume that the temperature condition is 102° within the time range of 5 - τ and 105° within the time range of τ - 15. If the curves are directly combined, there will be a performance abrupt change situation that does not conform to the physical state as shown in [[ ]]. Figure 2 as shown in [[ ]].
[0063] Considering that the performance is continuous when the environment changes, and the change after the interval point should follow the performance change under the new temperature, as shown in [[ ]], consider moving the performance curve at 102° temperature to make the change of performance continuous. Figure 3 as shown in [[ ]].
[0064] As [[ ]] Figure 4 is the curve of performance changing with the time series, save the obtained performance for subsequent calculation of the standard deviation and mean of the performance data samples.
[0065] Step 4: Solve by specifying distribution parameters.
[0066] Due to its excellent simulation performance, the maximum distribution is often used for reliability prediction of precision devices. This embodiment uses the maximum distribution as an example to illustrate the parameter solving of a specified distribution function:
[0067] The distribution of the maxima is shown below:
[0068]
[0069] Where F(t) is the failure probability, t is time, and μ and σ are the maximum distribution parameters.
[0070] Based on the characteristics of the maximum distribution, its expected value is μ + γσ, and its variance is... Where γ = 0.577. The performance sample variance from the training data is used as the expectation, and the performance values based on the time-series input are used as the variance to solve for the maximum distribution parameters μ and σ. (μ and σ differ for temperature or time segment.)
[0071] Input μ(σ) and time series, and obtain the relationship between μ(σ) and time (environment) by fitting using the least squares method.
[0072] Step 5: Probability calculation under time series conditions.
[0073] Substitute the μ and σ obtained from the previous fitting step into the maximum distribution to calculate the probability corresponding to the time point. Given a threshold, the failure probability is defined as:
[0074]
[0075] Where f(t) is the probability density function of the maximum distribution F(t), then the effective probability is 1-p1.
[0076] like Figure 5 As shown, the probability density distribution curves of the performance curve at times t1 and t2 are displayed, and the horizontal dashed line in the figure is taken as the threshold. The integral from the threshold is as follows: Figure 5 The probability value under unsteady conditions can be obtained from the shaded area in the middle diagonal line.
[0077] Example 2
[0078] This embodiment is based on embodiment 1:
[0079] This embodiment provides a variable environmental input lifetime assessment system based on the Arrhenius model, including:
[0080] The model parameter calculation module is used to load training data, obtain performance and aging time under varying environmental conditions, and solve the parameters of the Arrhenius model at a single temperature multiple times using the least squares method, and then generalize it to solve the parameters of the Arrhenius model at other temperatures in the training data.
[0081] The performance value calculation module is used to calculate the parameters of the Arrhenius model at different temperatures in the training data obtained by the model parameter calculation module. It takes the time series under unsteady environmental conditions as input, and obtains the parameters of the Arrhenius model under unsteady environmental conditions through interpolation methods, and then obtains the performance value under unsteady environmental conditions.
[0082] The distribution parameter calculation module is used to determine the parameters of the preset distribution function at different temperatures based on the performance values obtained from the performance value calculation module and the performance values in the training data.
[0083] The effective probability prediction module is used to obtain the relationship between environmental conditions and preset distribution function parameters under time series input by fitting, solve and draw the probability distribution map of the device under test under unsteady environmental conditions when the time series is the input, and thus predict the effective probability of the device under test under unsteady environmental conditions.
[0084] It should be noted that, for the sake of simplicity, the foregoing method embodiments are described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application.
Claims
1. A method for assessing lifetime under varying environmental inputs based on the Arrhenius model, characterized in that, Includes the following steps: S1. Load training data, obtain performance and aging time under varying environmental conditions, use least squares method multiple times to solve the parameters of Arrhenius model under a single temperature, and generalize to solve the parameters of Arrhenius model under other temperatures in the training data. S2. Based on the parameters of the Arrhenius model at different temperatures in the training data obtained in step S1, and using the time series under unsteady environmental conditions as input, the parameters of the Arrhenius model under unsteady environmental conditions are obtained through interpolation, and then the performance value under unsteady environmental conditions is obtained. S3. Based on the performance values obtained in step S2, and in conjunction with the performance values in the training data, determine the parameters of the preset distribution function at different temperatures; S4. By fitting the relationship between environmental conditions and preset distribution function parameters under time series input, a given threshold is used to solve and plot the probability distribution under unsteady environmental conditions when the time series is the input, thereby predicting the effective probability of the device under test under unsteady environmental conditions.
2. The method for assessing lifetime under varying environmental inputs based on the Arrhenius model according to claim 1, characterized in that, The preset distribution function includes the maximum distribution function, the normal distribution function, and the t-distribution function.
3. The method for assessing lifetime under varying environmental inputs based on the Arrhenius model according to claim 2, characterized in that, The preset distribution function is set as the maximum value distribution function. In this case, step S3 includes: determining the mean and standard deviation of the performance samples based on the performance values obtained in step S2 and the performance values in the training data, and then using the mean and standard deviation to obtain the parameters of the maximum value distribution function at different temperatures.
4. The method for assessing lifetime under varying environmental inputs based on the Arrhenius model according to claim 3, characterized in that, The failure probability of the device under test is: In the formula, t is time, and μ and σ are the distribution parameters of the maximum distribution function.
5. The method for assessing lifetime under varying environmental inputs based on the Arrhenius model according to claim 4, characterized in that, The expected value μ + γσ of the maximum value distribution function is calculated using the variance of the performance samples from the training data, where γ = 0.577; the variance of the maximum value distribution function is calculated using the performance values based on the time series input. Thus, the distribution parameters μ and σ can be obtained.
6. The method for assessing lifetime under varying environmental inputs based on the Arrhenius model according to claim 5, characterized in that, Input the distribution parameters μ and σ and the time series, and obtain the relationship between the distribution parameters μ and σ and the time series by fitting the data using the least squares method.
7. The method for assessing lifetime under varying environmental inputs based on the Arrhenius model according to claim 6, characterized in that, Substituting the fitted distribution parameters μ and σ into the maximum distribution function, the effective probability corresponding to the time point is calculated as 1-p1, where: p1=∫0 threshold f(t)dt In the formula, threshold is the threshold value, and f(t) is the probability density function of the maximum distribution F(t).
8. A variable environmental input lifetime assessment system based on the Arrhenius model, characterized in that, include: The model parameter calculation module is used to load training data, obtain performance and aging time under varying environmental conditions, and solve the parameters of the Arrhenius model at a single temperature multiple times using the least squares method, and then generalize it to solve the parameters of the Arrhenius model at other temperatures in the training data. The performance value calculation module is used to calculate the parameters of the Arrhenius model at different temperatures in the training data obtained by the model parameter calculation module. It takes the time series under unsteady environmental conditions as input, and obtains the parameters of the Arrhenius model under unsteady environmental conditions through interpolation methods, thereby obtaining the performance value under unsteady environmental conditions. The distribution parameter calculation module is used to determine the parameters of the preset distribution function at different temperatures based on the performance value obtained by the performance value calculation module and the performance value in the training data. The effective probability prediction module is used to obtain the relationship between environmental conditions and preset distribution function parameters under time series input by fitting, solve and draw the probability distribution map of the device under test under unsteady environmental conditions when the time series is the input, and thus predict the effective probability of the device under test under unsteady environmental conditions.