Simulation test design-fused natural storage reliability evaluation method for load-bearing structure

Abstract

The invention provides a load-bearing structure natural storage reliability evaluation method fused with simulation test design. The method comprises the following steps: step 1, carrying out material-level degradation modeling; 2, designing a structure-level simulation test and modeling a response surface; and step 3, evaluating the structure-level bearing capacity degradation reliability. The method is suitable for natural storage evaluation of the load-bearing structure product; the problem that material-level performance degradation information cannot be fused in a traditional system comprehensive method is solved, physical structure characteristics are considered through simulation analysis and response surface modeling, then the material-level natural storage degradation information is input to the structure level, a large number of structure-level natural storage tests do not need to be carried out, the needed cost is low, and the method is suitable for popularization and application. Wide application prospects and development spaces are realized.

Description

Technical Field

[0001] The present invention relates to a method for evaluating the natural storage reliability of a load-bearing structure integrated with simulation test design, which is a method for evaluating the storage reliability of a load-bearing structure based on simulation test design. Based on the degradation evaluation theory, it conducts degradation modeling on the mechanical properties of the load-bearing structure and uses it as input to carry out structural mechanics simulation response analysis, establish a response surface model of the structural bearing performance, and finally evaluate the reliability of the load-bearing structure during storage. It is applicable to fields such as degradation evaluation of structural-level natural storage products. Background Art

[0002] As a type of complex long-term storage equipment, the mechanical properties of the internal load-bearing structures (such as cabin structures) of missile and rocket products are crucial for the overall performance and safety of the products. During the storage period of the products, due to the influence of environmental factors, the performance of these load-bearing structures may degrade, thus affecting the reliability and safety of missile and rocket products. Therefore, evaluating and modeling the mechanical properties of load-bearing structures during storage is an important means to ensure product quality and performance.

[0003] In the field of storage degradation evaluation, converting the model of material property degradation over time into a model describing the change of the overall bearing capacity of the structure over time is a challenging task. This is mainly because there are complex and difficult-to-intuitively-understand physical connections between materials and structures, making it difficult for simple reliability block diagram methods to accurately capture such inter-level interactions. Simulation tests are a commonly used modeling method to characterize the influence of materials on structural responses. Due to the large computational time cost of simulation models, using the response surface modeling method can significantly improve the analysis efficiency.

[0004] Based on this, the present invention proposes a method for evaluating the natural storage reliability of a load-bearing structure with simulation test design, considering material-level and structural-level simulation data, and giving material-level degradation modeling, structural-level degradation models, and storage reliability evaluation results. Summary of the Invention

[0005] The object of the present invention is: aiming at the problem that traditional system integration methods cannot be used for evaluating the storage degradation of load-bearing structures, to provide a method for evaluating the natural storage reliability of a load-bearing structure, which is a structural-level natural storage degradation evaluation method including material-level degradation modeling, structural-level simulation test design and response surface modeling, and structural-level bearing capacity degradation evaluation. Based on the degradation evaluation theory, it conducts degradation modeling on the mechanical properties of the load-bearing structure materials and uses it as input to carry out the response analysis of structural mechanics simulation, establish a response surface model of the structural bearing performance, and finally evaluate the storage reliability of the load-bearing structure's bearing capacity.

[0006] To achieve the above object, the present invention needs to establish the following basic settings:

[0007] Setting 1: The storage degradation law of the structural material follows one of the linear degradation, exponential degradation, and power function degradation models. The expressions of each model are as follows:

[0008] Linear degradation model:

[0009] y(t) = α + β·t + ε (1)

[0010] Exponential degradation model:

[0011] y(t) = μ·exp(λ·t) + ε (2)

[0012] Power function degradation model:

[0013] y(t) = η·t θ + ε (3)

[0014] Among them, α and β represent the linear degradation model parameters, μ and λ represent the exponential degradation model parameters, η and θ represent the power function degradation model parameters, and ε represents the error with a mean of 0 and a variance of σ 2 . t represents the degradation time.

[0015] Setting 2: The simulation model of the structure is known. That is, when the m-dimensional performance parameter y is input, the response value of the structural bearing capacity can be obtained. The input-output relationship is defined as:

[0016] z = G(y) (4)

[0017] z represents the structural response quantity, and G(y) represents the function of the input variable.

[0018] The quadratic response surface model can be used to replace the above input-output relationship, that is

[0019]

[0020] Among them, z represents the structural response quantity; y i (i = 1, 2, …, n) represents the basic input variables; α i (i = 0, 1, 2, …, n) and α ij (i, j = 1, 2, …, n) are all the coefficients to be determined in the model. f(y i , t) represents the function related to the input and time, and f(t) represents the function related to time.

[0021] Generally, f(x i , t) = α i ′x i t. The mean and standard deviation of the above response surface model are as follows:

[0022]

[0023] Among them, the parameter μ z (t) represents the mean of the response surface model, represents the mean of the input quantity, represents a function of the mean and time, and σ z (t) represents the standard deviation of the response surface model, and D z (t) represents the variance of the response surface model.

[0024] Among them,

[0025]

[0026] Among them, D(y i ) represents the variance of the input quantity, D(y i y j ) represents the variance of the input quantity y i y j , Cov(y i , y i y j ) represents the covariance between y i and y i y j , Cov(y i y j , y i y k ) represents the covariance between y i y j and y i y k .

[0027] Setting 3: Assume that there are m performance indicators for the load-bearing structure material for natural storage tests, and the time measurement points are all t1, t2,... t n , and the j-th sample degradation data measured at the corresponding time measurement point t i is y i,j , where j = 1, 2,..., n. The storage period to be evaluated is [0, T], and the structural load-bearing threshold is w.

[0028] Based on the above basic settings, a method for evaluating the natural storage reliability of a load-bearing structure level integrating simulation test design according to the present invention comprises the following steps:

[0029] Step 1: Material-level degradation modeling

[0030] First, for the performance degradation test data of the material, respectively based on the linear degradation model, the exponential degradation model, and the power function degradation model, use the maximum likelihood estimation method to carry out parameter estimation of the degradation model, and the likelihood functions are respectively:

[0031]

[0032] Among them, y(t) adopts one of the linear degradation model, exponential degradation model, and power function degradation model, and θ(S) adopts one of the Arrhenius model and inverse power law model.

[0033] The corresponding model parameter estimation values are:

[0034]

[0035] lnL represents the likelihood function.

[0036] Among them, represents the parameters of the selected degradation model and acceleration model. The AIC criterion (i.e., Akaike information criterion, a standard for measuring the goodness of fit of a statistical model) can be used to select the optimal model, that is:

[0037] AIC = 2k - 2lnL (11)

[0038] Among them, k is the number of model parameters. The model and parameter estimation values with the smallest AIC value should be selected.

[0039] Step 2: Structural-level simulation experiment design and response surface modeling

[0040] Use the central composite design (CCDs) to generate a candidate set U of standard normal random samples with size N and dimension m CCD ; Uniformly and randomly generate one-dimensional samples of the same size within the storage period [0, T], denoted as t0. By combining the material-level parameter evaluation results, the input design parameters of the simulation experiment are given For the performance y i , i = 1, 2..., m, its design value can be calculated according to the selected model as:

[0041] Linear degradation model:

[0042]

[0043] Exponential degradation model:

[0044]

[0045] Power function degradation model:

[0046]

[0047] Among them, and represent the parameters of the linear degradation model, and represent the parameters of the exponential degradation model, and represent the parameters of the power function degradation model, Denotes the standard deviation.

[0048] Substitute the initial sampling point Y0 into the simulation model G(y), and denote the obtained response value as Z0. Based on the data set D0 = (Y0, Z0), fit the response surface model as shown in Equation (5).

[0049] Step 3: Structural-level bearing capacity degradation reliability assessment

[0050] Given the storage period t, according to the sample set U LHS and t = [t; t;...; t], as well as the parameter evaluation results, the candidate sampling set Y can also be obtained according to Equations (12) - (14). Substitute Y into the established response surface model, and obtain the response prediction value based on Equations (6) - (8) and the standard deviation σ z (t), then the reliability at the storage period t can be evaluated as:

[0051]

[0052] where Φ(·) is the cumulative distribution function of the standard normal distribution.

[0053] The "central composite design" mentioned in Step 2 is a composite design composed of a factorial design or a fractional factorial design including a center point, and enhanced with a set of axial points for curvature estimation. Each factor has five levels: ±α, 0, ±1. For the circumscribed central composite design, α can be taken as where k is the number of factors. Given the storage time t, the output response characteristic of the material property that can be extrapolated is x(t), which follows a normal distribution and can be characterized by μ x (t) ± σ x (t) for its highest and lowest levels. Specifically, it can be achieved through the following steps:

[0054] a) Determine the factors and levels according to the experimental purpose;

[0055] b) Construct the central composite design and determine the experimental points, including the center point, axial points, and cube points;

[0056] c) Conduct the experiment and fit the response surface model.

[0057] The advantages and beneficial effects of the present invention are as follows:

[0058] ① The present invention is applicable to the natural storage assessment of load-bearing structure products;

[0059] ②The present invention solves the problem that the traditional system integration method cannot integrate the material-level performance degradation information. By means of simulation analysis and response surface modeling, the physical structure characteristics are considered, and then the material-level natural storage degradation information is input into the structural level. Moreover, it is not necessary to conduct a large number of structural-level natural storage tests, and the required cost is relatively low, having broad application prospects and development space. Description of the Drawings

[0060] Figure 1 Flow chart of the method of the present invention. Detailed Description of the Invention

[0061] The present invention will be further described in detail below with reference to examples.

[0062] A natural storage degradation test was carried out on a load-bearing structure, and a total of 3 performance indicators, namely A, B, and C, were measured. The test data are shown in Tables 1 to 3.

[0063] Table 1 Natural degradation test data of performance indicator A of a load-bearing structure

[0064] Test time (days) Degradation amount (Gpa) 0 204 8 180 13 171 20 165 25 159

[0065] Table 2 Natural degradation test data of performance indicator B of a load-bearing structure

[0066] Test time (days) Degradation amount (MPa) 0 6 4 52.4 8 50.4 13 33.4 20 23.7 25 21.2

[0067] Table 3 Natural degradation test data of performance indicator C of a load-bearing structure

[0068]

[0069]

[0070] Assume that the simulation model of the load-bearing structure is known, and its simulation response characteristics can be obtained based on the test parameters. Now, according to the method for evaluating the natural storage reliability of the load-bearing structure based on the response surface model proposed in this specification, the degradation modeling analysis and parameter evaluation of the load-bearing structure are carried out, and the storage reliability under a given storage period is predicted.

[0071] See Figure 1 , a method for evaluating the natural storage reliability of a load-bearing structure integrating simulation test design according to the present invention is realized through the following steps:

[0072] Step 1: Material-level natural degradation modeling

[0073] First, the degradation model parameters of performance indicators A, B, and C are estimated by maximum likelihood, and the optimal model is determined according to AIC, that is:

[0074] ①Performance indicator A

[0075] The optimal degradation model is an exponential model, and the parameter estimation results are λ = -0.009903, μ = 198.7, and ε = 0.9710.

[0076] The degradation model is:

[0077] y A = 198.7exp(-0.009903t) + 0.9710ε

[0078] ② Performance index B

[0079] The optimal degradation model is an exponential model, and the parameter estimation results are λ = -0.007228, μ = 33.88, and ε = 0.1353.

[0080] The degradation model is:

[0081] y B = 33.88exp(-0.007228t) + 0.1353ε

[0082] ③ Performance index C

[0083] The optimal degradation model is an exponential model, and the parameter estimation results are λ = -0.03009, μ = 3.078×10 4 , ε = 0.8590.

[0084] The degradation model is:

[0085] y C = 3.078×10 4 exp(-0.03009t) + 0.8590ε

[0086] Step 2: Structural-level simulation test design and response surface modeling

[0087] Use the central composite design (CCDs) to generate a candidate set U of standard normal random samples with a size of N = 1000 and a dimension of m = 3 CCD ; Uniformly and randomly generate a 1-dimensional sample t with a size of N = 1000 within the storage period [0, 25] years. CCD .

[0088] Step 3: Structural-level load-carrying capacity degradation reliability assessment

[0089] Given the storage period t = [0, 25] years, regenerate the sample set U with a sample size of N = 1000 CCD and t = [t; t;...; t], and similarly, the candidate sampling set Y can be obtained according to equations (12) to (14). Substitute Y into the established response surface model, and based on equations (6) to (8), obtain the response prediction value and the standard deviation σ zIf it is (t), the storage period with a reliability of 0.9 is:

[0090] t = 21.0069 (years)

[0091] In summary, the present invention relates to a method for evaluating the natural storage reliability of a load-bearing structure by integrating simulation test design, which is a method for evaluating the natural storage reliability of a load-bearing structure based on simulation test design. Based on the degradation evaluation theory, it conducts degradation modeling on the mechanical properties of the load-bearing structure and uses it as input to carry out structural mechanics simulation response analysis, establish a response surface model of the structural load-bearing performance, and is used to evaluate the reliability of the load-bearing structure during storage, solving the problem that the traditional system integration method cannot integrate material-level performance degradation information; the specific steps of this method are: 1. Material-level natural degradation modeling; 2. Structural-level simulation test design and response surface modeling; 3. Structural-level load-bearing capacity degradation reliability evaluation; this method is applicable to the evaluation of the natural storage reliability of load-bearing structures, without the need to conduct a large number of structural-level natural storage tests, and the required cost is relatively low.

Claims

1. A natural storage reliability assessment method for load-bearing structures integrating simulation test design requires the following settings: Setting 1: The storage degradation law of the structural material obeys one of the linear degradation, exponential degradation and power function degradation models; Setting 2: The simulation model of the structure is known, that is, when the m-dimensional performance parameter y is input, the response value of the structural bearing capacity can be obtained. Setting 3: Assume that the load-bearing structural material has a total of m performance indicators and a natural storage test is carried out, and the time measurement points are t1, t2, ...t n , corresponding to the time measurement point t i The measured degradation data of the jth sample is y i,j , j = 1, 2, ..., n; the storage period to be evaluated is [0, T], and the structural load threshold is w; Based on the above configuration, it is characterized in that: The steps include: Step 1: Material-level degradation modeling For the performance degradation test data of the material, the maximum likelihood estimation method is used to estimate the parameters of the degradation model based on the linear degradation model, exponential degradation model and power function degradation model. Step 2: Structural-level simulation experiment design and response surface modeling Generate a standard normal random sample candidate set U of size N and dimension m using central composite design CCDs CCD ; Uniformly and randomly generate one-dimensional samples of the same size within the storage period [0, T], denoted as t0; By combining the material-level parameter evaluation results, the input design parameters of the simulation test are given Step 3: Reliability assessment of structural load-bearing capacity degradation Given a storage period t, based on the sample set U LHS and t = [t; t; ...; t], and the parameter evaluation results, obtain the candidate sampling set Y, substitute Y into the established response surface model, and obtain the response estimate and standard deviation σ z (t), evaluate the reliability at storage period t.

2. The method for evaluating the natural storage reliability of a load-bearing structure incorporating simulation test design according to claim 1 is characterized by: In setting 1, the sexual degradation model is: y(t)=α+β·t+ε (1) The exponential degradation model is: y(t)=μ·exp(λ·t)+ε (2) The power function degradation model is: y(t)=η·t θ +e (3) Among them, α and β represent the linear degradation model parameters, μ and λ represent the exponential degradation model parameters, η and θ represent the power function degradation model parameters, and ε represents the mean value of 0 and the variance of σ 2 The error of ; t represents the degradation time.

3. The natural storage reliability assessment method of a load-bearing structure integrating simulation test design according to claim 1 is characterized by: In setting 2, the input-output relationship is defined as: z=G(y) (4) z represents the structural response, G(y) represents the function of the input variable; The quadratic response surface model is used to replace the above input-output relationship, that is, Where z represents the structural response; y i represents the basic input variable; α i and α ij are all undetermined coefficients of the model; f(y i ,t) represents a function related to input and time, and f(t) represents a function related to time.

4. The natural storage reliability assessment method of a load-bearing structure integrating simulation test design according to claim 3 is characterized by: Let f(x i ,t)=α i 'x i t, the mean and standard deviation of the response surface model are as follows: Among them, the parameter μ z (t) represents the mean of the response surface model, represents the mean of the input quantity, represents the function of mean and time, σ z (t) represents the standard deviation of the response surface model, D z (t) represents the variance of the response surface model.

5. The method for evaluating the natural storage reliability of a load-bearing structure incorporating simulation test design according to claim 4 is characterized by: in, Among them, D(y i ) represents the variance of the input, D(y i y j ) represents the input quantity y i y j The variance of Cov(y i ,y i y j ) represents y i With y i y j The covariance of Cov(y i y j ,y i y k ) represents y i y j With y i y k The covariance of .

6. The natural storage reliability assessment method of a load-bearing structure integrating simulation test design according to claim 1 is characterized by: In step 1, the likelihood functions are: Among them, y(t) adopts one of the linear degradation model, exponential degradation model and power function degradation model, and θ(S) adopts one of the Arrhenius model and inverse power law model; The corresponding model parameter estimates are: lnL represents the likelihood function; in, Characterize the parameters of the selected degradation model and acceleration model; select the optimal model using the AIC criterion, namely: AIC=2k-2lnL (11) Where k is the number of model parameters; the model and parameter estimates with the smallest AIC value should be selected.

7. A method for evaluating the natural storage reliability of a load-bearing structure incorporating simulation test design according to claim 1 or 2, characterized in that: In step 2, the sexual degeneration model is: The exponential degradation model is: The power function degradation model is: in, and represents the parameters of the linear degradation model, and denotes the parameters of the exponential degradation model, and represents the parameters of the power function degradation model, represents standard deviation; Substitute the initial sampling point Y0 into the simulation model G(y), and the obtained response value is recorded as Z0; based on the data set D0=(Y0,Z0), fit the response surface model.

8. The method for evaluating the natural storage reliability of a load-bearing structure incorporating simulation test design according to claim 1 is characterized by: In step 3, the reliability evaluation at storage period t is: where Φ(·) is the cumulative distribution function of the standard normal distribution.

9. The method for evaluating the natural storage reliability of a load-bearing structure incorporating simulation test design according to claim 1 is characterized by: The central composite design mentioned in step 2 is a composite design consisting of a factorial design or a fractional factorial design containing a central point and augmented with a set of axial points to estimate the curvature; Each factor has five levels: ±α, 0, ±1; for the circumscribed central composite design, α is Where k is the number of factors; given a storage time t, the output response characteristic of the extrapolated material properties is x(t), which obeys the normal distribution x(t)~N(μ x (t),σ x 2 (t)), Use μ x (t)±σ x (t) Characterize its maximum and minimum levels.

10. The natural storage reliability assessment method of a load-bearing structure integrating simulation test design according to claim 9 is characterized by: This is achieved through the following steps: a) Determine factors and levels according to the experimental purpose; b) Construct a central composite design and determine the experimental points, including the center point, axial point, and cube point; c) Conduct experiments and fit a response surface model.

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