Reliability modeling and evaluation method for multi-batch aluminum silver oxide battery rupture membrane

Abstract

The invention discloses a reliability modeling and evaluation method of a multi-batch aluminum silver oxide battery rupture membrane, which aims at the actual demand of reliability evaluation of the aluminum silver oxide battery rupture membrane, comprehensively considers the bimodal distribution characteristic of the opening pressure of the rupture membrane in the batch and the difference between different batches, and improves the reliability of the rupture membrane. According to the method, technical means of Gaussian mixture distribution, a random effect model, an Expectation-Maximization (EM) algorithm and the like are applied, and the reliability modeling and evaluation problem of intra-batch and inter-batch differences of multiple batches of rupture membranes at the same time is solved. The method belongs to the technical field of reliability modeling and evaluation.

Description

Technical Field

[0001] The present invention belongs to the technical field of reliability modeling and evaluation, and in particular relates to a reliability modeling and evaluation method for ruptured membranes of multiple batches of aluminum silver oxide batteries. Background Art

[0002] Aluminum silver oxide batteries (ASO) are the primary power source for electric torpedoes. They consist of two components: the battery itself and an auxiliary system. The battery itself converts chemical energy into electrical energy, while the auxiliary system provides suitable electrolyte conditions for the battery itself. During operation, when the ASO battery receives an activation signal, the activation valve opens, allowing seawater to enter the battery, dissolving the electrolyte to form an electrolyte. When the pressure within the battery compartment rises to a certain level, the rupture membrane opens, allowing electrolyte to enter the battery itself, and the battery begins to output electrical energy. The opening pressure of the rupture membrane plays a significant role in the activation process. On the one hand, if the rupture membrane opens when the compartment pressure is low, the amount of water entering the battery compartment is limited, and the battery cannot provide stable electrolyte conditions, thus affecting its electrical performance and even leading to mission failure. On the other hand, if the rupture membrane still fails to open even when the compartment pressure reaches maximum, the electrolyte cannot enter the battery itself, and the battery cannot output electrical energy. Therefore, rationally modeling the opening pressure of the rupture membrane and accurately evaluating its reliability are crucial for analyzing the mission success of ASO batteries.

[0003] The rupture membrane of an aluminum silver oxide battery is formed by vacuum diffusion welding a diaphragm and a cutter. Due to the differences in the conditions of the two cutter surfaces, welding different cutter surfaces to the diaphragm will result in different opening pressures for the rupture membrane. Analysis of the opening pressures of an entire batch of rupture membranes reveals a bimodal distribution. Furthermore, during the production of multiple batches of rupture membranes, the opening pressures of different batches vary due to factors such as equipment status, environmental conditions, and process operations. Therefore, it is necessary to develop a targeted performance distribution model to accurately characterize the opening pressure distribution characteristics of multiple batches of rupture membranes. Summary of the Invention

[0004] In response to the problems existing in the prior art, the present invention provides a reliability modeling and evaluation method for ruptured membranes of multiple batches of aluminum silver oxide batteries. First, for the ruptured membranes of the same batch, a mixed Gaussian distribution is used to describe the bimodal distribution characteristics of the opening pressure. Then, a random effect is used to characterize the differences in performance parameters of products from different batches. Finally, the EM algorithm is used to estimate the model parameters, and the reliability of the product is evaluated in combination with failure criteria.

[0005] The present invention is achieved by providing a reliability modeling and evaluation method for ruptured membranes of multiple batches of aluminum silver oxide batteries, comprising the following steps:

[0006] Step 1: Establish a mixed Gaussian distribution model including random effects

[0007] Assume that there are L batches of rupture membranes, and the opening pressure of the jth rupture membrane in the i-th batch is X ij , i=1,2,…,L, j=1,2,…,n i , where n i is the number of ruptured membranes in the i-th batch;

[0008] Opening pressure X ij Obeying mixed Gaussian distribution Among them, μ i1 and μ i2 is the mean, σ1 and σ2 are the standard deviations, and q1 is the value of X ij From a normal distribution The probability of q2 is X ij From a normal distribution The probability of q1+q2=1;

[0009] Mean vector μ i =(μ i1 ,μ i2 )′ obeys the bivariate normal distribution BVN(θ,∑), where θ is μ i The mean of i The covariance matrix of

[0010] The parameters to be estimated in the above model are q1,q2,σ1,σ2,θ,Σ;

[0011] Step 2: Establish a parameter estimation method based on the EM algorithm

[0012] (1) μ1, μ2, …, μ L As a hidden variable, set the hidden variable ω ijk , i=1,2,…,L, j=1,2,…,n i ,k=1,2,define ω ijk is the indicator function, and its specific value is

[0013]

[0014] Among them, ω ij1 +ω ij2 =1;

[0015] make D=(X′1,X′2,…,X′ L )′, μ=(μ′1,μ′2,…,μ′ L )′,ω={ω ijk ,i=1,2,…,L, j=1,2,…,n i , k = 1, 2};

[0016] (2) The specific steps of the EM algorithm are as follows:

[0017] a) Let s = 1, and set the initial value based on experience

[0018] b) Using the Metropolis-Hastings (MH) sampling method, G groups are selected to obey p(μ,ω|Ψ (s) ,D) samples, denoted as μ (s,r) and ω (s,r) ,r=1,2,…,G, where

[0019]

[0020] c) Calculation in

[0021]

[0022] d) If ||Ψ (s+1) -Ψ (s) ||<δ, the EM algorithm stops, where ‖·‖ represents the sum of the two norms of the internal elements and δ is the preset maximum allowable error; otherwise, let s = s + 1 and repeat b), c), and d);

[0023] Step 3: Calculate reliability

[0024] Assume that the rupture membrane opening pressure X meets the requirements in the range of Ω=[T L ,T U ], let μ=(μ (1) ,μ (2) )′, then the reliability of the rupture membrane is expressed as

[0025]

[0026] in

[0027]

[0028] Advantages and technical effects of this invention: This invention addresses the practical issue of reliability assessment for rupture membranes in aluminum-silver-oxide batteries. By considering the bimodal distribution of rupture membrane opening pressure and analyzing the differences between different batches of rupture membranes, this invention establishes a reliability modeling and assessment method applicable to multiple batches of rupture membranes in aluminum-silver-oxide batteries, which has important engineering application value. The analysis process is scientific, rational, and realistic, resulting in reliable reliability assessment results. The reliability assessment method proposed in this invention is clear and easy to use. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1It is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0030] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only used to illustrate the present invention.

[0031] like Figure 1 As shown, the reliability modeling and evaluation method of multiple batches of aluminum silver oxide battery rupture membranes of the present invention includes the following steps:

[0032] Step 1: Establish a mixed Gaussian distribution model including random effects

[0033] Assume that there are L batches of rupture membranes, and the opening pressure of the jth rupture membrane in the i-th batch is X ij , i=1,2,…,L, j=1,2,…,n i , where n i is the number of ruptured membranes in the i-th batch;

[0034] Opening pressure X ij Obeying mixed Gaussian distribution Among them, μ i1 and μ i2 is the mean, σ1 and σ2 are the standard deviations, and q1 is the value of X ij From a normal distribution The probability of q2 is X ij From a normal distribution The probability of q1+q2=1;

[0035] Mean vector μ i =(μ i1 ,μ i2 )′ obeys the bivariate normal distribution BVN(θ,∑), where θ is μ i The mean of i The covariance matrix of

[0036] The parameters to be estimated in the above model are q1,q2,σ1,σ2,θ,∑;

[0037] Step 2: Establish a parameter estimation method based on the EM algorithm

[0038] (1) μ1, μ2, …, μ L As a hidden variable, set the hidden variable ω ijk , i=1,2,…,L, j=1,2,…,n i ,k=1,2,define ω ijk is the indicator function, and its specific value is

[0039]

[0040] Among them, ω ij1 +ω ij2 =1;

[0041] make D=(X′1,X′2,…,X′ L )′, μ=(μ′1,μ′2,…,μ′ L )′,ω={ω ijk ,i=1,2,…,L, j=1,2,…,n i , k=1,2];

[0042] (2) The specific steps of the EM algorithm are as follows:

[0043] a) Let S = 1, and set the initial value based on experience

[0044] b) Using the Metropolis-Hastings (MH) sampling method, G groups are selected to obey P(μ,ω|Ψ (s) ,D) samples, denoted as μ (s,r) and ω (s,r) ,r=1,2,…,G, where

[0045]

[0046] c) Calculation in

[0047]

[0048] d) If ||Ψ (s+1) -Ψ (s) ||<δ, the EM algorithm stops, where ‖·‖ represents the sum of the two norms of the internal elements and δ is the preset maximum allowable error; otherwise, let s = s + 1 and repeat b), c), and d);

[0049] Step 3: Calculate reliability

[0050] Assume that the rupture membrane opening pressure X meets the requirements in the range of Ω=[T L ,T U ], let μ=(μ (1) ,μ (2) )′, then the reliability of the rupture membrane is expressed as

[0051]

[0052] in

[0053]

[0054]

[0055] The present invention comprehensively analyzes the dispersion of the rupture membrane opening pressure within a batch and between batches, and uses technical means such as mixed Gaussian distribution, random effect model, and EM algorithm to propose a reliability modeling and evaluation method suitable for the rupture membrane of multiple batches of aluminum silver oxide batteries, providing a technical supplement for the reliability modeling and evaluation of multiple batches of products.

[0056] Taking the rupture membrane test data of a certain aluminum silver oxide battery during its development as an example, the present invention is further explained in detail. The specific implementation steps are as follows:

[0057] Step 1: Build a mixed Gaussian distribution model with random effects

[0058] During the development process, six batches of rupture membranes were tested, with a sample size of 16 in each batch. The opening pressure data were

[0059] X1=(359,323,260,235,363,233,347,249,336,349,251,331,243,236,332,344)′ 4,256,236,238,361,239,245,255,357)′ X4=(273,282,283,267,331,272,344,347,328,271,258,297,347,331,292,288)′X5=(337,253,238,330,251,339,232,34 8,327,237,246,343,249,327,250,247)′

[0060] The opening pressure X of the jth rupture membrane in the i-th batch ij Obeying mixed Gaussian distribution i=1,2,…,6,j=1,2,…,16,opening pressure X ij The probability density function of

[0061]

[0062] Among them, μ i1 and μi2 is the mean, σ1 and σ2 are the standard deviations, and q1 is the value of X ij From a normal distribution The probability of q2 is X ij From a normal distribution The probability is q1+q2=1.

[0063] Mean vector μ i =(μ i1 ,μ i2 )′ obeys the bivariate normal distribution BVN(θ,∑), where θ is μ i The mean of i The covariance matrix, μ i The joint probability density function of

[0064]

[0065] Step 2: Establish a parameter estimation method based on the EM algorithm

[0066] Set μ1, μ2, …, μ6 as latent variables and set the latent variable ω ijk , i=1,2,…,6, j=1,2,…,16, k=1,2,ω ijk The value is

[0067]

[0068] Among them, ω ij1 +ω ij2 =1.

[0069] For the convenience of description, let X i =(X i1 ,X i2 ,…,X i,16 )′, D=(X′1,X′2,…,X′6)′, μ=(μ′1,μ′2,…,μ′6)′, ω={ω ijk ,i=1,2,…,6,j=1,2,…,16,k=1,2}.

[0070] The specific steps of the EM algorithm are as follows:

[0071] a) Let s = 1 and set the initial value Ψ (1) ,in

[0072]

[0073] θ (1) =(210,320)′

[0074]

[0075] b) Using the MH sampling method, 500 groups of samples were selected and followed by p(μ,ω|Ψ (s) ,D) samples, denoted as μ (s,r) and ω (s,r) ,r=1,2,...,500, where

[0076]

[0077] c) Calculation in

[0078]

[0079]

[0080] d) If ||Ψ (s+1) -Ψ (s) If ||<0.01, the algorithm stops; otherwise, set s=s+1 and repeat b), c), and d).

[0081] Step 3: Evaluate reliability

[0082] According to the actual use requirements, the opening pressure of the rupture membrane meets the required range Ω=[200,400], let μ=(μ (1) ,μ (2) )′, then the reliability of the rupture membrane is expressed as

[0083]

[0084] In summary, this paper presents a reliability modeling and assessment method for ruptured membranes in multiple batches of aluminum silver oxide batteries. By addressing the bimodal distribution of the opening pressures of ruptured membranes within a batch and considering the differences between ruptured membranes from different batches, a mixed Gaussian distribution model with random effects is proposed. A parameter estimation method based on the EM algorithm is established, and product reliability is assessed in conjunction with failure criteria. The analytical process is scientific and rational, resulting in credible reliability assessment results. Furthermore, the reliability assessment method proposed in this paper features a clear calculation process and strong operability.

[0085] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A reliability modeling and evaluation method for ruptured membranes of multiple batches of aluminum silver oxide batteries, characterized in that: The following steps are involved: Step 1: Establish a mixed Gaussian distribution model including random effects Assume that there are L batches of rupture membranes, and the opening pressure of the jth rupture membrane in the i-th batch is X ij , i=1,2,…,L, j=1,2,…,n i , where n i is the number of ruptured membranes in the i-th batch; Opening pressure X ij Obeying mixed Gaussian distribution Among them, μ i1 and μ i2 is the mean, σ1 and σ2 are the standard deviations, and q1 is the value of X ij From a normal distribution The probability of q2 is X ij From a normal distribution The probability of q1+q2=1; Mean vector μ i =(μ i1 ,μ i2 )′ obeys the bivariate normal distribution BVN(θ,∑), where θ is μ i The mean of i The covariance matrix of The parameters to be estimated in the above model are q1,q2,σ1,σ2,θ,∑; Step 2: Establish a parameter estimation method based on the EM algorithm (1) μ1, μ2, …, μ L As a hidden variable, set the hidden variable ω ijk , i=1,2,…,L, j=1,2,…,n i ,k=1,2,define ω ijk is the indicator function, and its specific value is Among them, oh ij1 +oh ij2 =1; Let D = (X ′ 1, X ′ 2, …, X ′ L )′, μ = (μ ′ 1, μ ′ 2, …, μ ′ L )′, ω = {ω ijk , i = 1, 2, …, L, j = 1, 2, …, n i , k = 1, 2}; (2) The specific steps of the EM algorithm are as follows: a) Let s = 1, and set the initial value based on experience b) Using the Metropolis-Hastings (MH) sampling method, G groups are selected to obey p(μ,ω|Ψ (s) ,D) samples, denoted as μ (s,r) and ω (s,r) ,r=1,2,…,G, where c) Calculation in d) If ||Ψ (s+1) - Ψ (s) || < δ, the EM algorithm stops, where ‖·‖ represents the sum of the two-norms of the internal elements, and δ is the pre-set maximum allowable error; otherwise, let s = s + 1 and repeat b), c), d); Step 3: Calculate reliability Assume that the rupture membrane opening pressure X meets the requirements in the range of Ω=[T L ,T U ], let μ=(μ (1) ,μ (2) )′, then the reliability of the rupture membrane is expressed as in

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