Variable rigorous coefficient method for verifying storage reliability of composite material structure

Abstract

The invention provides a variable rigorous coefficient method for verifying storage reliability of a composite material structure. The variable rigorous coefficient method comprises the following steps: step 1, estimating parameters of a performance degradation model of the composite material structure; step 2, equivalent load mapping and variable rigorous coefficient construction under the condition of variable storage period; and step 3, a reliability index verification method considering the variable obturation coefficient. Aiming at the problem that the storage reliability of the composite material structure is difficult to accurately verify, verification test data under different moments and different load conditions are analyzed, the utilization efficiency of various test data is remarkably improved, and the dependence of a traditional obturation method on the test time sequence and the strict consistency of the load conditions is avoided. The method is suitable for verifying the long-term storage reliability index of the composite material structure complying with various degradation laws, is wide in application range, and has theoretical innovation and engineering practicability. The method is simple in calculation, low in operation difficulty and convenient for engineering application.

Description

Technical Field

[0001] This invention relates to a variable tightening coefficient method for verifying the storage reliability of composite material structures. This method, based on statistical reliability verification, aims to improve the accuracy and applicability of verifying the storage reliability of composite material structures under multiple storage periods and load conditions. It first collects verification test data at different times, constructs a degradation model to describe the performance degradation over time, and estimates its parameters. Second, it constructs a load mapping relationship between different storage periods and the target storage period using an equivalent load mapping method, obtaining the corresponding variable tightening coefficients. Finally, it calculates the reliability index under tightened conditions, enabling the determination of whether the structure meets the index during the target storage period. The method proposed in this invention is applicable to the storage reliability assessment and verification of composite material structures in aerospace, weaponry, and other fields. Background Technology

[0002] Composite material structures are widely used in critical components of aircraft, missile systems, and other applications. During long-term storage, the mechanical and thermal protection properties of these composite structures gradually degrade. If their reliability during storage cannot be verified, it can easily lead to equipment failure during use, thereby affecting the stability and safety of the system. Therefore, rigorous testing is typically required to verify reliability and determine whether the structures meet the targets for the intended storage period.

[0003] Traditional methods typically assume that all verification tests are conducted under uniformly tightened loading conditions and storage times, using a constant-tightening model to evaluate composite material structures. However, in practical engineering applications, verification tests are often difficult to conduct strictly according to the target storage period, and some verification test data may come from earlier tests, failing to cover the complete target storage cycle. In such cases, discrepancies exist between verification tests with different storage times and tightened loading conditions, making it difficult to conduct reliability assessments under a unified standard. Therefore, traditional methods are prone to significant result deviations and poor engineering adaptability when facing these problems.

[0004] The reliability verification method that considers variable tightening and variable storage period can more realistically reflect the actual implementation of verification tests in engineering applications. It breaks through the strict consistency requirements of traditional verification methods on storage period and tightened load conditions, and can effectively expand the applicability and engineering adaptability of the verification model.

[0005] Based on this, the present invention proposes a variable tightening coefficient method for verifying the storage reliability of composite material structures. Facing verification tests under different storage periods and different tightening load conditions, it combines the parameter estimation of structural performance degradation model and the calculation method of equivalent load to improve the accuracy and engineering adaptability of the reliability index evaluation model of composite material structures under long-term storage conditions. It is applicable to the unified verification of the storage reliability of composite material structures in multiple scenarios. Summary of the Invention

[0006] (1) Purpose of the present invention: In view of a series of problems that make it difficult to accurately verify the storage reliability of composite material structures due to various situations in engineering practice, the present invention provides a variable tightening coefficient method for verifying the storage reliability of composite material structures, so as to complete the judgment on whether the composite material structure can pass the reliability verification during the target storage period.

[0007] (2) Technical solution:

[0008] The following basic settings are required for this invention:

[0009] Setting 1: Set the data storage time required for model building to t. i For i = 1, 2, ..., m, the corresponding load performance degradation is x. ij i = 1, 2, ..., m, j = 1, 2, ..., n i m represents the number of storage time points, n i This indicates the number of data points at different times.

[0010] Setting 2: Set the verification test data storage time to T. i For each i = 1, 2, ..., m′, verification tests are conducted during the storage period, and the corresponding load performance degradation is X. ij ,i=1,2,…,m′,j=1,2,…,n i ′, m′ represents the number of storage time points in the verification experiment, n i ′ represents the number of trials conducted at the i-th time point.

[0011] Setting 3: The degradation model of the load performance variable is defined as X(t). The performance degradation law can be a linear degradation model, an exponential degradation model, or a power function degradation model, and its formula can be expressed as follows:

[0012] (1) Linear degeneracy model:

[0013] X1(t)=a1+b1t+εσ1 (1)

[0014] In the formula, X1(t) represents the performance in the linear degradation model; ε~N(0,1) represents the random perturbation variable of the standard normal distribution; a1 and b1 are the parameters of the linear degradation model; and σ1 is the standard deviation of the perturbation term in the linear degradation process.

[0015] (2) Exponential degradation model:

[0016]

[0017] In the formula, X2(t) represents the performance in the exponential degradation model; ε~N(0,1) represents the random perturbation variable of the standard normal distribution; a2 and b2 are the parameters of the linear degradation model; and σ2 is the standard deviation of the perturbation term in the exponential degradation process.

[0018] (3) Power function degenerate model:

[0019]

[0020] In the formula, X3(t) represents the performance in the power function degradation model; ε~N(0,1) represents the random perturbation variable of the standard normal distribution; a3 and b3 are the parameters of the power function degradation model; and σ3 is the standard deviation of the perturbation term in the power function degradation process.

[0021] Set the target storage verification time for structure 4 to T. s The reliability index corresponding to the target storage period is set as R. s The performance degradation under normal operating load is X0.

[0022] The method proposed in this invention mainly focuses on the degradation data collected from verification tests of composite material structures under different storage periods, and estimates the parameters of the performance degradation model. Equivalent load calculations are performed on the test data under different storage periods to construct an equivalent tightening coefficient for the target storage period. The data is then substituted into the reliability calculation model to ultimately determine whether the composite material structure can pass reliability verification within the target storage period.

[0023] Based on the above settings, the variable tightening coefficient method for verifying the storage reliability of composite material structures in this invention is implemented through the following steps:

[0024] Step 1: Parameter estimation for the performance degradation model of composite material structures

[0025] When modeling and estimating the performance degradation of composite material structures over storage time, it is considered that the degradation process of different performance indicators may be affected by multiple mechanisms and have different trends. This invention estimates the parameters of three typical degradation models: linear degradation model, exponential degradation model, and power function degradation model, as shown in Figure 3. The degradation models are uniformly represented as follows:

[0026]

[0027] In the formula, X(t) i f(t) is a degradation model; i ,θ) corresponds to the deterministic part of the model; θ=(a,b) are the model parameters; ε~N(0,1) are the random perturbation variables of the standard normal distribution; σ is the standard deviation of the perturbation term of the degradation process.

[0028] The likelihood function L(θ,σ) is constructed for it as follows:

[0029]

[0030] By maximizing the above likelihood function, we obtain the estimated values ​​of the model parameters θ=(a,b) and σ, which are used in the subsequent reliability calculation of the performance distribution of composite material structures.

[0031] Step 2: Equivalent load mapping and construction of variable tightening coefficients under variable storage period conditions

[0032] After estimating the parameters of the degradation model, the next step is to perform an equivalent transformation on the variable tightening load at different storage periods in the verification experiment. The equivalent transformation is mainly based on the quantile probability equivalence concept, that is, at T... i The failure probability obtained at the target storage period T is related to the failure probability obtained at the target storage period T. s The failure probabilities obtained at each location are equal, and the different storage times T obtained from the verification experiment will be used to verify this. i The load performance degradation X ij Equivalent mapping to target storage period T s The equivalent load performance degradation X corresponding to the time ij ':

[0033]

[0034] From this, we can deduce that:

[0035]

[0036] In the formula, μ(T) i ), σ(T) i ) respectively represent T i Mean and standard deviation of the degradation model at the location; μ(T) s ), σ(T) s ) respectively represent T s The mean and standard deviation of the degradation model at the given location.

[0037] The degradation of normal working load performance X0 and the equivalent load performance degradation X in the verification experiment based on the composite material structure ij ', Define the tightening coefficient k for the i-th trial. i for:

[0038]

[0039] In the formula, X0 represents the performance degradation under normal operating load; X ij 'For T s The corresponding equivalent load performance degradation.

[0040] Step 3: Consider the reliability index verification method with variable tightening coefficients.

[0041] After constructing the variable tightening coefficient, this invention verifies the reliability of the obtained variable tightening coefficient. First, the coefficient of variation under the target storage period is determined:

[0042] C s =μ(T) s ) / σ(T s (9)

[0043] In the formula, C s μ(T) is the coefficient of variation. s ) indicates the target storage period t s The mean of the degradation model at σ(T) s ) indicates the target storage period T s The standard deviation of the degradation model at that location.

[0044] The three degradation processes of composite materials under arbitrary storage time can be described by a normal distribution, yielding the composite material structure at the target storage period T. s Reliability index R at the location s for:

[0045]

[0046] In the formula, Φ(·) represents the cumulative distribution function of the standard normal distribution. From this, the critical survival coefficient η can be obtained. s Represented as:

[0047]

[0048] In the formula, Φ -1 (·) represents the inverse function of the cumulative distribution function of the standard normal distribution. This corresponds to the variable tightening coefficient k. i Reliability index R at the location s,i for:

[0049]

[0050] Let α be the confidence level required for structural reliability verification. The reliability events at each test point are independent of each other. The following formula is used to verify whether the reliability index meets the requirements:

[0051]

[0052] If the above formula is met, the reliability verification is considered successful; otherwise, it is considered unsuccessful. The above steps are used to verify the reliability indicators of composite material structures under varying stringent conditions and varying storage periods.

[0053] (3) Advantages and benefits: This invention is a variable tightening coefficient method for verifying the storage reliability of composite material structures, and its advantages are:

[0054] ① This invention addresses the problem of difficulty in accurately verifying the storage reliability of composite material structures by analyzing verification test data under different times and load conditions, which significantly improves the utilization efficiency of various test data and avoids the dependence of traditional stringent methods on the strict consistency of test timing and load conditions.

[0055] ②This invention is applicable to the verification of long-term storage reliability indicators of composite material structures that conform to multiple degradation laws. It has a wide range of applications and combines theoretical innovation with engineering practicality.

[0056] ③ This invention is simple to calculate, easy to operate, and convenient for engineering applications. Attached Figure Description

[0057] Figure 1 The flowchart of the method described in this invention. Detailed Implementation

[0058] The invention will be further described in detail below with reference to implementation examples.

[0059] Using data obtained from verification tests at different storage periods, the reliability index verification of composite material structures under varying tightening conditions and storage periods is studied according to the variable tightening coefficient method for storage reliability verification proposed in this invention. The variable tightening coefficient is calculated, and it is determined whether the reliability verification index is ultimately met.

[0060] See Figure 1 The variable tightening coefficient method for verifying the storage reliability of composite material structures in this invention is achieved through the following steps:

[0061] Step 1: Parameter estimation for the performance degradation model of composite material structures

[0062] In this implementation case, a composite material structure of an aero-engine is used as the experimental object, and the required storage verification period for the structure is set to 20 years. During long-term storage, the structure's load-bearing limit, compressive strength, and thermal protection performance will all change over time. This degradation performance data is used to establish a performance degradation model. A reliability index R corresponding to the target storage period is set. s The value is 0.9; the normal operating load performance degradation X0 is 150kN. First, a degradation model is established for the corresponding degradation data to describe the change of its load performance degradation with storage time. The data distribution is shown in Table 1 below.

[0063] Table 1. Distribution of Degradation Data

[0064] Storage time (years) 8 10 Increased load (kN) 200.0 210.0

[0065] The degradation data distribution showed a higher fit to the linear degradation model; therefore, the linear degradation model was chosen for subsequent reliability calculations of the composite material's load-bearing performance. To ensure the model's statistical reliability, the maximum likelihood estimation method was used to estimate the parameters of the established linear model, obtaining the optimal degradation model parameters. The parameter estimation results are shown in Table 2 below.

[0066] Table 2. Parameter estimation results for the linear degradation model.

[0067] parameter <![CDATA[a1]]> <![CDATA[b1]]> <![CDATA[σ1]]> Estimation results 301.10 -4.10 27.54

[0068] The optimal parameters of the model are then used in subsequent reliability calculations of the composite material load performance.

[0069] Step 2: Equivalent load mapping and construction of variable tightening coefficients under variable storage period conditions

[0070] After estimating the parameters of the degradation model for the degradation data, the equivalent load performance degradation amount is obtained by equivalent transformation of the variable tightening load for different storage periods obtained from the verification test using Equation (7), and the variable tightening coefficient is obtained using Equation (8), thereby achieving uniformity of data for different storage periods under the target storage period. Substituting the storage time of the verification test into the linear degradation model, the transformed equivalent tightening load and variable tightening coefficient are calculated as shown in Table 2 below.

[0071] Table 2 Equivalent tightening load and variable tightening coefficient under different storage periods

[0072] Storage time (years) 8 10 Increased test load (kN) 200.0 210.0 Equivalent tightened load (kN) 150.8 169.0 Variable tightening coefficient 1.0053 1.1267

[0073] Step 3: Consider the reliability index verification method with variable tightening coefficients.

[0074] After constructing the variable tightening coefficient, the next step is to verify the reliability index based on the obtained variable tightening coefficient. The coefficient of variation under the target storage period is determined by equation (9):

[0075] C s =μ(T) s ) / σ(T s )=7.9557 (14)

[0076] In the formula, μ(T) s ), σ(T) s ) represent the target storage period T s The mean and standard deviation of the performance under the given conditions.

[0077] Subsequently, a confidence level of 0.8 was set for the reliability verification of the composite material structure. Considering the characteristics of the linear degradation model, a normal distribution was used to describe the reliability, and the reliability events at each test point were independent of each other. Based on this, the reliability index was verified to meet the requirements using the following formula:

[0078]

[0079] In the formula, R s,i For the target storage period T s Under increasingly stringent conditions k i The reliability index is α, where α is the confidence level.

[0080] Based on the above calculations, if equation (13) is satisfied, the structure is considered to have passed reliability verification. In this case, the reliability index does not meet the confidence condition, therefore it cannot pass verification. Based on this judgment, it is believed that the verification test design is unreasonable and cannot meet the requirements of engineering applications. To further advance reliability verification, an additional set of verification test data (T...) should be added. i ,X ij That is, (14, 220), and recalculated based on the new data. The calculation results are shown in Table 3 below.

[0081] Table 3 shows the equivalent tightening load and variable tightening coefficient for different storage periods after adding new data.

[0082]

[0083]

[0084] Based on the above data, a reliability index verification considering the variable tightening factor was performed with a confidence level of 0.8. The reliability index R under the target storage period after adding new data was then calculated. s,i 'for:

[0085]

[0086] Based on this, it can be concluded that the verification test after the addition of data meets the reliability index requirements, and the scheme is considered reasonable.

[0087] In summary, this invention relates to the variable tightening coefficient method for verifying the storage reliability of composite material structures. This method addresses issues such as inconsistent storage periods and varying test load conditions encountered in engineering practice. First, it estimates various degradation model parameters of the composite material structure using maximum likelihood estimation. Second, it constructs equivalent loads and variable tightening coefficients considering different storage periods and different tightening load conditions. Finally, it calculates reliability based on statistical confidence methods to determine whether the reliability index requirements within the target storage period are met. The specific steps of this method are: 1. Estimation of performance degradation model parameters for the composite material structure; 2. Mapping of equivalent loads and construction of variable tightening coefficients under varying storage period conditions; 3. Reliability index verification method considering variable tightening coefficients. The method proposed in this invention is applicable to fields such as reliability assessment of composite materials and has broad application prospects in high-requirement fields such as aerospace and weaponry, and is highly operable.

Claims

1. A variable acceleration factor method for composite structure storage reliability verification, characterized in that: Comprising the following steps: Step one: composite structure performance degradation model parameter estimation When modeling and parameter estimation of performance degradation of composite structure with storage time, parameter estimation of degradation model is carried out, which is linear degradation model, exponential degradation model and power function degradation model respectively; Step two: equivalent load mapping and variable severity factor construction under variable storage period condition After the estimation of the degradation model parameters, the load performance degradation of the different storage periods of the validation test is equivalent transformed; the equivalent transformation is based on the idea of equivalent quantile probability, that is, the failure probability obtained at T i is equal to the failure probability obtained at the target storage period T s , and the load performance degradation X i at different storage times T ij obtained by the validation test is equivalent mapped to the corresponding equivalent load performance degradation X s at the target storage period T ij . Step three: reliability index verification method considering variable severity factor After the construction of variable severity factor, reliability index verification is carried out for the obtained variable severity factor.

2. The variable acceleration factor method for composite structure storage reliability verification according to claim 1, wherein: The data storage time required for setting the model is t i i = 1, 2, …, m, and the corresponding load performance degradation amount is x ij i = 1, 2, …, m, j = 1, 2, …, n i m represents the number of storage time points, and n i represents the number of data at different time points.

3. The variable acceleration factor method for composite structure storage reliability verification of claim 1, wherein: Set the verification test data storage time as T i , i = 1, 2,..., m', respectively, in the storage period, the corresponding load performance degradation amount is X ij , i = 1, 2,..., m', j = 1, 2,..., n i ', m' represents the number of storage time points of the verification test, n i ' represents the number of tests carried out at the i th time point.

4. The variable severity factor method for composite structure storage reliability verification according to claim 1, characterized in that: The degradation model of load performance variable is expressed as X(t), and the performance degradation law is linear degradation model, exponential degradation model and power function degradation model, which are expressed as follows: (1) Linear degradation model: X1(t)=a1+b1t+εσ1 (1) In the formula, X1(t) is the performance in the linear degradation model; ε~N(0,1) is a random disturbance variable of standard normal distribution; a1 and b1 are parameters of the linear degradation model; and σ1 is the standard deviation of the disturbance term of the linear degradation process; (2) Exponential degradation model: In the formula, X2(t) is the performance in the exponential degradation model; ε~N(0,1) is a random disturbance variable of standard normal distribution; a2 and b2 are parameters of the linear degradation model; and σ2 is the standard deviation of the disturbance term of the exponential degradation process; (3) Power function degradation model: In the formula, X3(t) is the performance in the power function degradation model; ε~N(0,1) is a random disturbance variable of standard normal distribution; a3 and b3 are parameters of the power function degradation model; and σ3 is the standard deviation of the disturbance term of the power function degradation process.

5. The variable acceleration factor method for composite structure storage reliability verification according to claim 1 or 4, characterized in that: In step one, the degradation model is uniformly expressed as: X(t i ) = f(t i , θ) + εσ (4) where X(t i ) is the degradation model; f(t i , θ) is the deterministic part of the model; θ = (a, b) is the model parameter; ε ~ N(0, 1) is the random disturbance variable with standard normal distribution; and σ is the standard deviation of the disturbance term of the degradation process.

6. The variable acceleration factor method for composite structure storage reliability verification of claim 5, wherein: The likelihood function L(θ,σ) is established as follows: By maximizing the above likelihood function, the estimated values of model parameters θ=(a,b) and σ are obtained, which are used in subsequent reliability calculation of composite structure performance distribution.

7. The variable acceleration factor method for composite structure storage reliability verification of claim 1, wherein: In step two, the specific expression is: It is derived that: where μ(T i ), σ(T i ) are the mean and standard deviation of the degradation model at T i , respectively, and μ(T s ), σ(T s ) are the mean and standard deviation of the degradation model at T s , respectively.

8. The variable severity factor method for composite structure storage reliability verification according to claim 7, characterized in that: X0 is the performance degradation amount of the composite structure based on the normal working load, and X is the performance degradation amount of the composite structure based on the equivalent load of the verification experiment ij k is the variable coefficient of the i-th test i is defined as: In the formula, X0 is the amount of performance degradation of normal working load; X ij ' is the corresponding equivalent load performance degradation amount when T s ' is the corresponding equivalent load performance degradation amount when T 9. The variable acceleration factor method for composite structure storage reliability verification of claim 1, wherein: In step three, the variable coefficient of the target storage period is: C s = μ(T s ) / σ(T s ) (9) where C s is the coefficient of variation; μ(T s ) is the mean of the degradation model at the target storage period t s ; and σ(T s ) is the standard deviation of the degradation model at the target storage period T s . The three degradation processes of composite materials under arbitrary storage time are described by a normal distribution, yielding the composite structure at the target storage period T. s Reliability index R at the location s for: where Φ(·) denotes the cumulative distribution function of the standard normal distribution; and the critical survival coefficient η is given by s is given by: In the formula, Φ -1 (·) denotes the inverse function of the cumulative distribution function of the standard normal distribution.

10. The variable acceleration factor method for composite structure storage reliability verification of claim 1, wherein: The reliability index R at the variable gain coefficient k i s,i is given by:​ The confidence level required for structure reliability verification is set as α, and the reliability events of each test point are independent of each other. Whether the reliability index meets the requirements is verified by the following formula: If the above formula can be met, it is considered to pass the reliability verification; otherwise, it is considered to fail.

Images