A method for determining stresses and samples in adhesive degradation tests under multiple stresses

Abstract

The application discloses a stress and sample determination method in adhesive degradation test under multiple stresses, belongs to the field of adhesive reliability analysis, and is especially for adhesive accelerated degradation test scheme design. When optimal stress level and optimal sample number are solved in the optimization design of the adhesive accelerated degradation test, a dispersion process model considering random initial values is used to analyze the test optimization problem, estimation accuracy of subsequent reliability analysis is improved, and a new idea is provided for other high-reliability products with random effects.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of reliability analysis of adhesive bonding strength, and particularly to the design of adhesive accelerated degradation test scheme. BACKGROUND

[0002] The conventional adhesive accelerated life test has the disadvantages of long test time and large sample size. The current mainstream test research is mainly for single stress condition. However, the degradation process of the product under actual working conditions is often related to multiple factors. In the accelerated life test, only failure data can be used for life estimation, and for high-reliability products, the time of occurrence of failure is difficult to estimate. Therefore, the adhesive is subjected to accelerated degradation test under higher than normal stress conditions to obtain degradation data in a short time without sample failure or failure. In the optimization design of the accelerated degradation test scheme, due to the inability to determine the performance initial value of different products, the initial degradation value is often assumed to be 0 or transformed to 0 in the previous research. However, in the actual process flow, the inconsistency and uncertainty of the product will produce differences in the performance degradation initial value. Such differences may have a great influence on the life prediction of these products. Therefore, the initial degradation levels of different adhesive samples are different, which indicates that the initial state must have random effects. SUMMARY

[0003] The present application is based on the randomness of the test sample and the precision requirements of the test scheme to build an objective function for test optimization. The present application uses a dispersion process model considering random initial value to analyze the test optimization problem.

[0004] The technical scheme of the present application is a stress and sample determination method for adhesive degradation test under multiple stresses. The method comprises the following steps:

[0005] Step 1: Assume that the adhesive has l stress factors {S1, S2, …, Sl}, each stress factor contains L stress levels {S1, S2, …, SL}, i = 1, 2, …, l, when S1 < S2 < … < SL, S1 is the normal stress level and SL is the limit stress level; the total number of test samples is n, the samples are divided into L groups, the sample allocation ratio under the kth stress is p k, and the sample quantity is n k = n·p k; for the kth stress level, the test time t k is determined according to the following formula: l i1 i2 iL i0 iM i0 i1 iL iM k k k t k = t 0 · (S k - S 1) / (S L - S 1)​​​​​​​​​​​​k = t · r k , r k represents the time allocation ratio, interval time Δt, and the number of detections is M k = t k / Δt = t · r k / Δt, k = 1, 2, …, L

[0006] Step 2: Establishing an adhesive dispersion process model, the specific steps are as follows:

[0007] Step 2.1: Assuming that the initial degradation value of the adhesive obeys a normal distribution, the model expression is as follows:

[0008] Y(t) = μt + σB(t) + X0

[0009] In the formula, Y(t) is the adhesive performance degradation process, μ is the drift coefficient, σ is the diffusion coefficient, σ > 0, which describes the difference caused by individuals, environment, operation, etc., and is usually a constant that does not change with time and stress; B(t) represents a standard Brownian motion with a mean of 0 and a variance of t, X0 is the initial degradation value, which obeys a normal distribution X0 ~ N(θ, ε 2 ), θ represents the expectation, and ε 2 represents the standard deviation and is independent of stress; at any time t, there is:

[0010] Y(t) ~ N(θ + μt, ε 2 + σ 2 t)

[0011] Step 2.2: Normalizing the acceleration model function under multiple stresses is:

[0012]

[0013] wherein, represents the combination form of stress and stress;

[0014] Step 2.3: The test is carried out under the total test time t, and the test time t k = t · r k under each stress level, and the number of detections under each stress level is M k = t k / Δt = t · r k / Δt, the detection interval is Δt, and the performance degradation amount of the ith sample under the kth stress level at the jth measurement is y kij , the detection time is t kij and y kij ~ N(θ + μt kij , ε 2 + σ 2 t kij), thus obtaining the jth group of measurement data as (y k11 ,…,y ki1 ), k12 ,…,y ki2 ), k1j ,…,y kij );

[0015] The increment is Δy kij =y kij -y ki(j-1) ;

[0016] The time interval is Δt kij =t kij -t ki(j-1) , k = 1, 2, …, L, i = 1, 2, …, n k , j = 1, 2, …, M k ;

[0017] The probability density function is:

[0018]

[0019] wherein f(y) and f(Δy) represent the probability density functions of the measurement data and the increment data respectively;

[0020] Let the test time interval f = Δt kij = Δt, and the log-likelihood function is:

[0021]

[0022] Step 3: Establish the optimization objective of the adhesive accelerated degradation model in combination with the log-likelihood function of Step 2;

[0023] Step 3.1: Let the total cost of the test be C, the unit price of the sample be C u , the unit time implementation cost be C o , and the optimization criterion be to maximize the determinant of the Fisher information matrix, and the optimization problem is:

[0024] Max det[I(ξ)]

[0025] s.t.C u ·n+C0·t≤C

[0026] wherein det[I(ξ)] represents the determinant of the matrix I(ξ), and I(ξ) represents the Fisher information matrix;

[0027] Step 3.2: Decompose |I(ξ)| into f(n,t,Δt) × g(p k ,r k ,S ik), where f(n, t, At) is a function only related to sample number, test time, interval time, g(p k ,r k ,S ik ) is a function related to sample allocation ratio, test number, decision variable to be optimized, and the optimization objective is expressed as:

[0028] Max det[I(ξ)]=f(n,t,Δt)×g(p k ,r k ,S ik )

[0029] s.t.C u ·n+C0·t≤C

[0030] S i0 <S i1 <S i2 <…<…S iL <S max

[0031]

[0032]

[0033] Step 3.3: According to the sub-expression of the log-likelihood function in step 2.3, the Fisher information matrix I(ξ) is derived, and the elements in the Fisher information matrix are the negative expectations of the second-order partial derivatives of the log-likelihood function with respect to the unknown model parameters, where the set of unknown model parameters is ξ=(…, θ, ε 2 ,σ 2 ), and each element in the Fisher information matrix is expressed as E(·) represents expectation;

[0034] Step 4: For the adhesive accelerated degradation model optimization problem established in step 3, a genetic algorithm is used to solve the objective function to obtain the optimal stress level S k and sample ratio p k ;

[0035] Step 4.1: Randomly generate a number of binary chromosomes, and encode the chromosomes according to the number of experimental design variables to be optimized;

[0036] Step 4.2: Set the population size, variable dimension, variable constraints, termination condition, crossover rate, and mutation rate, and initialize the population;

[0037] Step 4.3: Take the optimization objective function as the fitness function, evaluate the fitness of each individual in the population, and select and eliminate the inferior individuals;

[0038] Step 4.4: Chromosome crossover, genetic, mutation, etc. are performed on the remaining individuals in step 3 to generate a new generation of population.

[0039] Step 4.5: Steps 4.2 and 4.3 are repeated until the fitness function reaches the maximum, or the population reaches the maximum genetic generation;

[0040] Step 4.6: The chromosome of the individual with the maximum fitness function is decoded to obtain the optimal solution of the optimization variable, that is, the optimal design scheme of the test.

[0041] The present application has the beneficial effects that: through test analysis, the random degradation initial value problem caused by the actual process flow of the adhesive sample is considered when the adhesive accelerated degradation test scheme optimization design is carried out, the best stress level and test sample distribution ratio under a group of multi-stress combination are found, a more accurate test scheme is obtained, the estimation accuracy of subsequent reliability analysis is improved, and a new idea is provided for other high-reliability products with random effects. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 Flow chart for adhesive accelerated degradation test optimization design considering random initial degradation value. DETAILED DESCRIPTION

[0043] Step 1: The stresses applied to the adhesive are temperature and voltage. 2 stress factors are represented as {S1, S2}, each stress factor contains 2-5 stress levels, here 5 stress levels are analyzed {S 11 ,S 12 ,…,S 15 ,S 21 ,S 22 ,…,S 25}, the normal temperature stress level is 40℃, the limit temperature stress level is 110℃, the normal voltage stress level is 5V, and the limit voltage stress level is 15V; the total number of test samples is 100, the samples are divided into 5 groups, the sample distribution ratio under the kth stress is p k , the sample number is n k =n·p k ; for the kth stress level, the test time t k =t·r k , the interval time Δt, the detection number is M k =t k / Δt=t·r k / Δt, k=1,2,…,5.

[0044] Step 2: A dispersion process model considering random initial value is established, the specific steps are as follows:

[0045] Step 2.1: Assuming that the initial degradation value obeys a normal distribution, the model expression is as follows:

[0046] Y(t) = μt + σB(t) + X0

[0047] where Y(t) is the performance degradation process; μ is the drift coefficient, which is a function related to stress, i.e., an acceleration model; σ is the diffusion coefficient (σ > 0), which describes the difference caused by individuals, environment, operation, etc., and is usually a constant that does not change with time and stress; B(t) represents a standard Brownian motion with a mean of 0 and a variance of t; X0 is the initial degradation value, which obeys a normal distribution X0 ~ N(θ, ε 2 ), and is independent of stress. At any time t, there is the following formula:

[0048] Y(t) ~ N(θ + μt, ε 2 + σ 2 t)

[0049] Step 2.2: The adhesive is affected by two stresses of temperature and voltage, and the stress interaction is not considered, and two stress acceleration models are obtained by combining physical acceleration models such as Arrhenius model and Eyring model, as follows:

[0050] μ(S) = exp(A + B / T + C·lnV)

[0051] where T is the temperature stress; V is the electric stress; A, B, and C are unknown parameters of the model.

[0052] Step 2.3: Assuming that the test is carried out within a total test time t, therefore, the test time t k = t·r k under each stress level, and the detection frequency under each stress level is M k = t k / Δt = t·r k / Δt, where the detection interval is Δt. Therefore, the performance degradation amount of the i-th sample under the k-th stress level at the j-th measurement is y kij , the detection time is t kij , and y kij ~ N(θ + μt kij , ε 2 + σ 2 t kij ), so j sets of measurement data (y k11 ,…,y ki1 ), (y k12 ,…,y ki2 ), …, (y k1j ,…,y kij ) are obtained, and the increment is Δy kij = y kij - y ki(j-1), time interval Δt kij = t kij - t ki(j-1) , k = 1, 2,..., L, i = 1, 2,..., n k , j = 1, 2,..., M k , the probability density function is formula:

[0053]

[0054] Let the test time interval f = Δt kij = Δt = 1, the new form of the log-likelihood function can be expressed as formula:

[0055]

[0056] Step 3: The adhesive accelerated degradation test plan design problem is combined with the model established in step 2 to establish the optimization objective, as follows:

[0057] Step 3.1: Assuming that the total cost of the test is C, the sample unit price is C u , the implementation cost per unit time is C o , and the test cost is (C u , C0, C) = (3, 0.2, 15 x 0) 3 , the optimization criterion is to maximize the determinant of the Fisher information matrix, and the optimization problem can be expressed as:

[0058] Max det[I(ξ)]

[0059] s.t.C u ·n + C0·t ≤ C

[0060] Step 3.2: |I(ξ)| is decomposed into f(n,t,Δt) x g(p k , r k , S ik ), where f(n,t,Δt) is only related to the sample number and test time, and g(p k , r k , S ik ) is related to the sample allocation ratio and the test number of the decision variables to be optimized. Then the optimization objective is expressed as:

[0061] Max det[I(ξ)] = f(n,t,Δt) x g(p k , r k , S ik )

[0062] s.t.C u ·n + C0·t ≤ C

[0063] 40 < T1 < T2 <... < T5 < 110

[0064] 5 < V1 < V2 <... < V5 < 15

[0065]

[0066]

[0067] Step 3.3: According to the log-likelihood function in Step 2.3, the Fisher information matrix I(ξ) can be derived, where the elements of the matrix are the negative expectations of the second-order partial derivatives of the log-likelihood function with respect to the unknown model parameters ξ = (A, B, C, θ, ε 2 , σ 2 ), which can be expressed as

[0068] Step 4: Partial degradation data is obtained through the adhesive accelerated degradation pre-test, and the maximum likelihood estimation is used to obtain the model parameters ξ(A, B, C, θ, ε 2 , σ 2 ) = (10, -8704, 0.5, 0.122, 0.0101, 0.00612). Subsequently, the genetic algorithm is used to solve the objective function to obtain the optimal stress level S k and the sample proportion p k .

[0069] Step 4.1: A number of binary chromosomes are randomly generated, and the chromosomes are encoded according to the number of optimization design variables η = (S 11 ,…, S 15 , S 21 ,…, S 25 , p1,…, p5, n1,…, n5).

[0070] Step 4.2: Set the population size to 60, the crossover probability to 0.8 by default, the mutation probability to 0.01 by default, and the iteration number to 2000 or the iteration threshold to 10 -3 iterations are terminated, and the population is initialized.

[0071] Step 4.3: Take the optimization objective function as the fitness function, evaluate the fitness of each individual in the population, and select the best individuals to eliminate the inferior ones.

[0072] Step 4.4: Perform chromosome crossover, genetic, mutation, and other operations on the remaining individuals in Step 3 to generate a new generation of population.

[0073] Step 4.5: Repeat Step 4.2 and Step 4.3 until the fitness function reaches the maximum or the population reaches the maximum number of generations.

[0074] Step 4.6: Decode the chromosome of the individual with the maximum fitness function to obtain the optimal solution of the variables to be optimized, i.e. the optimal design scheme of the experiment.

[0075] Table 1. Results of genetic algorithm optimization under temperature and voltage stress

[0076]

Claims

1. A method for determining stress and sample in adhesive degradation test under multiple stress, the method comprising the following steps: Step 1: Select the stress applied to the adhesive as a multi-stress combination; assume there are l stress factors {S1, S2, ... S}. l Each stress factor contains L stress levels {S}. i1 ,S i2 ,…,S iL }, i = 1, 2, ..., l, when S i0 For normal stress levels, S iM When S is the ultimate stress level, i0 <S i1 <...<S iL <S iM The total number of test samples is n, and the samples are divided into L groups. The sample allocation ratio under the stress of the k-th group is p. k The sample size is n k =n·p k For the k-th stress level, the test time t k =t·r k The interval time Δt and the number of detections are M. k =t k / Δt=t·r k / Δt, k=1,2,…,L; Step 2: establishing a dispersion process model considering random initial value; Step 3: establishing an optimization objective for adhesive accelerated degradation test scheme design problem in combination with the model of step 2, as follows: Step 3.1: Assume the total cost of the experiment is C, the sample unit price is C u , the implementation cost per unit time is C o , and the optimization criterion is to maximize the determinant of the Fisher information matrix. The optimization problem is represented as: Max det[I(ξ)] s.t.C u • n + Co · t ≤ C Step 3.2: |I(ξ)| is decomposed into f(n,t,Δt) x g(p k ,r k ,S ik ), where f(n,t,Δt) is only related to sample number and test time, and g(p k ,r k ,S ik ) is related to the decision variables to be optimized, then the optimization objective is expressed as: Max det [I(ξ)] = f(n, t, Δt) x g(p k , r k , S ik ) s.t.C u • n + Co · t ≤ C S i0 <S i1 <S i2 <… <S iL <S max (i = 1, 2,..., / ) Step 3.3: Derive the Fisher information matrix I(ξ) from the log-likelihood function in Step 2.3, where the elements of the matrix are the negative expected values of the second-order partial derivatives of the log-likelihood function with respect to the unknown model parameters, ξ = (A, B, C,..., θ, ε 2 , σ 2 ), and each element is expressed as Step 4: Genetic algorithm is used to solve the objective function to obtain the optimal stress level S for the optimization design problem of the adhesive accelerated degradation test scheme k and sample proportion p k ; Step 4.1: randomly generating a number of binary chromosomes, and encoding the chromosomes according to the number of variables to be optimized in the experimental design; Step 4.2: setting the population size, variable dimension, variable constraint, termination condition, crossover rate, mutation rate, and initializing the population; Step 4.3: taking the optimization objective function as the fitness function, evaluating the fitness of each individual in the population, and selecting and eliminating the inferior individuals; Step 4.4: performing chromosome crossover, genetic, and mutation operations on the remaining individuals in step 3 to generate a new generation of population; Step 4.5: repeating step 4.2 and step 4.3 until the fitness function reaches the maximum or the population reaches the maximum number of generations; Step 4.6: decoding the chromosome of the individual with the maximum fitness function to obtain the optimal solution of the variables to be optimized, i.e., the optimal design scheme of the test.

2. The method of claim 1, wherein the stresses and sample are determined by, The specific method of step 2 is as follows: Step 2.1: assuming that the initial degradation value follows a normal distribution, the model expression is as follows: Y(t) = μt + σB(t) + X0 where Y(t) is the performance degradation process; μ is the drift coefficient, which is a function of stress, i.e., an acceleration model; σ is the diffusion coefficient, σ > 0, which describes the variability due to individual, environment, operation, and is constant and does not change with time and stress; B(t) represents a standard Brownian motion with mean 0 and variance t; X0is the initial degradation value, which is normally distributed X0~ N(θ, ε 2 ), and is independent of stress; and at any time t, there is the equation: Y(t) = X0+ μt + σB(t) Y(t) ~ N(θ + μt, ε 2 +σ 2 t) Step 2.2: adopting a normalized acceleration model function under multiple stress, i.e., a standardized generalized Eyring model and a Peck model, and the general form is as follows: Step 2.3: Assuming the experiment is conducted over a total test time t, therefore, the test time t at each stress level is... k =t·r k The number of tests at each stress level is M. k =t k / Δt=t·r k / Δt, where the detection interval is Δt; therefore, the performance degradation of the i-th sample in the j-th measurement at the k-th stress level is y. kij The detection time is t kij And y kij ~N(θ+μt) kij ,ε 2 +σ 2 t kij Therefore, j sets of measurement data (y) are obtained. k11 ,…,y ki1 ),(y k12 ,…,y ki2 ),…,(y k1j ,…,y kij The increment is Δy. kij =y kij -y ki(j-1) The time interval is Δt kij =t kij -t ki(j-1) , k=1,2,…,L, i=1,2,…,n k j = 1, 2, ..., M k The probability density function is given by: Let the test time interval f = Δt kij = Δt, the new form of the log-likelihood function is given by

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