Honeycomb structure uncertain factor reliability analysis method and system

Abstract

The invention discloses a honeycomb structure uncertain factor reliability analysis method and system, belongs to the technical field of honeycomb structure reliability analysis, and solves the problem of how to reduce the calculation cost of honeycomb structure uncertain factor reliability analysis. Safety bubbles are generated in a safety domain of a random space, failure bubbles are generated in a failure domain of the random space, a large number of sample points are generated according to random variable distribution information, the sample points are filtered through the generated bubbles, and the failure probability and the variation coefficient of the lattice structure are calculated. According to the method, the calculation precision is ensured by utilizing the derived radius iterative formula, and meanwhile, the evaluation calculation of filtering a large number of samples by virtue of the generated bubbles can be realized, so that the calculation cost of reliability analysis is greatly reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of honeycomb structure reliability analysis, and in particular relates to a honeycomb structure uncertainty factor reliability analysis method and system. Background Art

[0002] Honeycomb structures are widely used in aerospace, biomedicine, military equipment and other fields due to their excellent mechanical properties such as light weight, high specific energy absorption, impact resistance, and multifunctional properties such as heat insulation and wave absorption.

[0003] Different from traditional material structures, honeycomb structures have high porosity and infinitely changing microstructures, which also means an increase in uncertainties in the manufacturing process. In addition, the service environment of honeycomb structures is often harsh, and the uncertainties they face during their service are more diverse. These uncertainties will threaten the stability of the honeycomb structure system and pose a significant threat to the safety and reliability of related structural equipment. Therefore, uncertainty reliability analysis of honeycomb structures is extremely important.

[0004] Among the many methods of reliability analysis, numerical simulation methods represented by Monte Carlo simulation have been recognized by many scholars and engineers due to their simple procedures and wide applicability. However, such methods require a large number of samples, especially when dealing with complex failure domains or problems with extremely small failure probabilities. The calculation cost is expensive and requires a large amount of computing resources. This also hinders its promotion and application in dealing with honeycomb structure reliability analysis problems. Summary of the invention

[0005] The technical problem to be solved by the present invention is how to reduce the computational cost of reliability analysis of uncertain factors of honeycomb structures.

[0006] The present invention solves the above technical problems through the following technical solutions:

[0007] The present invention provides a reliability analysis method for uncertain factors of a honeycomb structure, comprising the following steps:

[0008] Step 1: construct a safety bubble for filtering safety samples in the safety domain of the random space. The calculation formula of the safety bubble is as follows:

[0009]

[0010] Among them, x si represents the endpoint of the radius of the i-th safety bubble, represents the midpoint of the ith safety bubble, g(·) represents the performance function, r is the radius, and d represents the design variable;

[0011] Step 2: construct failure bubbles for filtering failed samples in the failure domain of the random space. The calculation formula of the failure bubbles is as follows:

[0012]

[0013] Among them, x fi represents the endpoint of the radius of the i-th failure bubble, represents the midpoint of the i-th failed bubble;

[0014] The iterative formula of the radius r is as follows:

[0015]

[0016] x k+1 =x k +γ k (x k+1 -x k )

[0017]

[0018] Among them, γ k is the control factor, whose range is [0,1], x k-1 、x k 、x k+1 Respectively represent the endpoints of the bubble radius of the k-1th, kth, and k+1th iterations, x o represents the center point of the k-th iteration bubble, ||·|| represents the norm, represents the gradient function, θ k ,θ k+1 are the angles of the kth and k+1th iteration steps, R k is the radius of the kth iteration step, γ is the control factor;

[0019] Step 3: Generate sample points that obey the distribution type based on the mean and variance of the input parameters;

[0020] Step 4: Use the generated bubbles to screen the sample points: the samples falling into the safe bubble are identified as safe samples, and the samples falling into the invalid bubble are identified as invalid samples;

[0021] Step 5: Calculate the failure probability and coefficient of variation of the honeycomb structure.

[0022] Furthermore, the calculation formula of the failure probability described in step 5 is as follows:

[0023]

[0024] Among them, P f is the failure probability, represents the number of samples falling into the i-th safety bubble, k 1 represents the number of safety bubbles, N represents the total number of samples drawn, is an indicator function, which takes the value of 1 for safe samples outside the bubble and 0 otherwise.

[0025] Furthermore, the calculation formula of the coefficient of variation described in step 5 is as follows:

[0026]

[0027] in,

[0028]

[0029] Among them, COV[P f ] is the coefficient of variation, E(P f ) is the mean of the failure probability, Var(P f ) is the variance of the failure probability.

[0030] The present invention also provides a reliability analysis system for uncertain factors of honeycomb structures, comprising: a bubble construction module, a sample generation and filtering module, and a calculation module;

[0031] The bubble construction module is used to construct safety bubbles and failure bubbles in random space;

[0032] The calculation formula of the safety bubble is as follows:

[0033]

[0034] Among them, x si represents the endpoint of the radius of the i-th safety bubble, represents the midpoint of the ith safety bubble, g(·) represents the performance function, r is the radius, and d represents the design variable;

[0035] The calculation formula of the failure bubble is as follows:

[0036]

[0037] Among them, x fi represents the endpoint of the radius of the i-th failure bubble, represents the midpoint of the i-th failed bubble;

[0038] The iterative formula of the radius r is as follows:

[0039]

[0040] x k+1 =x k +γ k (xk+1 -x k )

[0041]

[0042] Among them, γ k is the control factor, whose range is [0,1], x k-1 、x k 、x k+1 Respectively represent the endpoints of the bubble radius of the k-1th, kth, and k+1th iterations, x o represents the center point of the k-th iteration bubble, ||·|| represents the norm, represents the gradient function, θ k ,θ k+1 are the angles of the kth and k+1th iteration steps, R k is the radius of the kth iteration step, γ is the control factor;

[0043] The sample generation and filtering module generates sample points that obey the distribution type based on the mean and variance of the input parameters, and uses the generated bubbles to screen the sample points, that is, the samples that fall into the safe bubble are identified as safe samples, and the samples that fall into the invalid bubble are identified as invalid samples;

[0044] The calculation module is used to calculate the failure probability and coefficient of variation of the honeycomb structure.

[0045] Furthermore, the calculation formula of the failure probability is as follows:

[0046]

[0047] Among them, P f is the failure probability, represents the number of samples falling into the i-th safety bubble, k 1 represents the number of safety bubbles, N represents the total number of samples drawn, is an indicator function, which takes the value of 1 for safe samples outside the bubble and 0 otherwise.

[0048] Furthermore, the calculation formula of the coefficient of variation is as follows:

[0049]

[0050] in,

[0051]

[0052] Among them, COV【P f ] is the coefficient of variation, E(P f ) is the mean of the failure probability, Var(P f ) is the variance of the failure probability.

[0053] The present invention also provides a storage medium on which a computer program is stored. When the computer program is run by a processor, the steps of the above-mentioned method for analyzing the reliability of uncertain factors of a cellular structure are executed.

[0054] The present invention also provides an electronic device, comprising a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the above-mentioned cellular structure uncertainty factor reliability analysis method, and the processor is configured to execute the program stored in the memory.

[0055] The advantages of the present invention are:

[0056] The present invention generates safety bubbles in a safety domain of a random space, generates failure bubbles in a failure domain of a random space, generates a large number of sample points according to random variable distribution information, uses the generated bubbles to filter the sample points, and calculates the failure probability and coefficient of variation of the lattice structure; the present invention uses the derived radius iteration formula to ensure the calculation accuracy, and can also rely on the generated bubbles to filter the evaluation calculation of a large number of samples, thereby greatly reducing the calculation cost of reliability analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a flow chart of the reliability analysis method of the uncertain factors of the honeycomb structure of the present invention;

[0058] Figure 2 It is a schematic structural diagram of a non-uniform rectangular honeycomb sandwich panel of the present invention;

[0059] Figure 3 It is a partial schematic diagram of the finite element analysis results of the non-uniform rectangular honeycomb sandwich panel of the present invention. DETAILED DESCRIPTION

[0060] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described in combination with the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0061] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and specific embodiments:

[0062] Embodiment 1

[0063] like Figure 1 As shown, a reliability analysis method for uncertain factors of a honeycomb structure in this embodiment includes the following steps:

[0064] Step 1: Construct a safety bubble in the safety domain of the random space to filter safety samples.

[0065] Step 2: construct failure bubbles in the failure domain of the random space to filter the failed samples.

[0066] Step 3: Generate a large number of sample points that obey their distribution type based on the distribution information of the input parameters (ie, mean, variance).

[0067] Step 4: Use the generated bubbles to screen the sample points. The samples that fall into the safe bubble are identified as safe samples, and the samples that fall into the invalid bubble are identified as invalid samples.

[0068] Step 5: Calculate the failure probability and coefficient of variation of the honeycomb structure.

[0069] The following is an example of the reliability analysis of non-uniform rectangular honeycomb sandwich panels.

[0070] like Figure 2 As shown, the non-uniform rectangular honeycomb sandwich panel consists of two thin face sheets and a thicker honeycomb core with periodic rectangular cells, whose honeycomb walls are curved. The top and bottom face sheets provide bending and shear stiffness, while the middle honeycomb core stabilizes the face sheets and bears lateral shear loads. In Cartesian coordinates (x, y, z), the dimensions of the sandwich panel are a×b×h, where z=0 corresponds to the mid-plane of the sandwich panel. The thickness of the face sheet is h f , the height of the honeycomb core is h c , so the total height h = h c +2×h f The spacing between the honeycomb walls in the x and y directions is l a and l b The honeycomb wall is in the local coordinate system Details such as Figure 3 This model considers the thickness of the structural panel x 1 , core layer height x 2 , x and y distances from the cell wall 3 ,x 4 , control point coordinates (x 5 ,x 6 ,x 7 ),(x 8 ,x 9 ,x 10 ), elastic modulus x 11 and Poisson's ratio x 12 The maximum allowable deflection of the structure is 0.137 m, so the performance function can be defined as follows:

[0071] g=0.137-Δ

[0072] Where Δ represents the maximum displacement of the structure.

[0073] Table 1 Material properties

[0074]

[0075] Firstly, a safety bubble for filtering safety samples is constructed in the safety domain of random space.

[0076] The safety bubble is located in the safety domain, and the radius r is the shortest distance from the center to the performance function. Therefore, the corresponding optimization formula of the safety bubble can be expressed as:

[0077]

[0078] Among them, x si represents the endpoint of the radius of the i-th safety bubble, represents the midpoint of the ith safety bubble (the mean point of the input variable is taken as the center of the first safety bubble), g(·) represents the performance function, r is the radius, and d represents the design variable.

[0079] Secondly, failure bubbles are constructed in the failure domain of the random space to filter the failed samples.

[0080] The failure bubble is located in the failure domain, and the radius r is the shortest distance from the center to the performance function. Therefore, the corresponding optimization formula of the failure bubble can be expressed as:

[0081]

[0082] Among them, x fi represents the endpoint of the radius of the i-th failure bubble, represents the midpoint of the ith failure bubble, and g(·) represents the performance function.

[0083] The calculation formulas for the radius r of the safety bubble and the failure bubble are as follows:

[0084]

[0085] x k+1 =x k +γ k (x k+1 -x k )

[0086]

[0087] Angle θ k It can be obtained by the following formula:

[0088]

[0089] Among them, γk is the control factor, whose range is [0,1], x k-1 、x k 、x k+1 Respectively represent the endpoints of the bubble radius of the k-1th, kth, and k+1th iterations, x o represents the center point of the k-th iteration bubble, ||·|| represents the norm, represents the gradient function, θ k ,θ k+1 are the angles of the kth and k+1th iteration steps, R k is the radius of the kth iteration step and γ is the control factor.

[0090] Then, based on the distribution information of the input parameters (ie, mean, variance), a large number of sample points that obey their distribution type are generated.

[0091] Afterwards, the generated bubbles are used to screen the sample points. The samples that fall into the safe bubbles are identified as safe samples, and the samples that fall into the invalid bubbles are identified as invalid samples.

[0092] Finally, the failure probability and coefficient of variation of the honeycomb structure are calculated.

[0093] The formula for calculating the failure probability is as follows:

[0094]

[0095] in, represents the number of samples falling into the i-th safety bubble, k 1 represents the number of safety bubbles, N represents the total number of samples drawn, is an indicator function, which takes the value of 1 for safe samples outside the bubble and 0 otherwise.

[0096] The formula for calculating the coefficient of variation is as follows:

[0097]

[0098] Among them, the mean failure probability E(P f ) is calculated as follows:

[0099]

[0100] The variance of failure probability Var(P f ) is calculated as follows:

[0101]

[0102] The reliability analysis results of different methods are shown in Table 2.

[0103] Table 2 Calculation results

[0104]

[0105] Monte Carlo simulation used 40,000 samples to calculate the failure probability of the structure and used the calculated results as reference values, and its calculation time was 53,380 seconds. The subset simulation method has a certain degree of reduction in the number of function calls compared to the Monte Carlo simulation, but its calculation cost is still high, and the total calculation time is 8,010 seconds. The weight fitting method called the true function 7,000 times, but its calculation error was 88.78%, and its calculation time was 9,306 seconds. The importance sampling method called the true function 1,620 times and the calculation error was 4.67%, and the total calculation time was also 2,162 seconds. The method of the present invention called the true function 1,125 times, the calculation error was 1.87%, and the calculation time was 1,501 seconds. This shows that the method of the present invention can significantly reduce the computational cost of the reliability analysis process of honeycomb structures.

[0106] Embodiment 2

[0107] A reliability analysis system for uncertain factors of honeycomb structures, comprising: a bubble construction module, a sample generation and filtering module, and a calculation module;

[0108] The bubble construction module is used to construct safety bubbles and failure bubbles in random space;

[0109] The calculation formula of the safety bubble is as follows:

[0110]

[0111] Among them, x si represents the endpoint of the radius of the i-th safety bubble, represents the midpoint of the ith safety bubble, g(·) represents the performance function, r is the radius, and d represents the design variable;

[0112] The calculation formula of the failure bubble is as follows:

[0113]

[0114] Among them, x fi represents the endpoint of the radius of the i-th failure bubble, represents the midpoint of the i-th failed bubble;

[0115] The iterative formula of the radius r is as follows:

[0116]

[0117] x k+1 =x k +γ k (x k+1 -xk )

[0118]

[0119] Among them, γ k is the control factor, whose range is [0,1], x k-1 、x k 、x k+1 Respectively represent the endpoints of the bubble radius of the k-1th, kth, and k+1th iterations, x o represents the center point of the k-th iteration bubble, ||·|| represents the norm, represents the gradient function, θ k ,θ k+1 are the angles of the kth and k+1th iteration steps, R k is the radius of the kth iteration step, γ is the control factor;

[0120] The sample generation and filtering module is used to generate a large number of samples for evaluating failure probability and filter these samples;

[0121] The details are as follows: based on the mean and variance of the input parameters, sample points that obey their distribution type are generated; the generated bubbles are used to screen the sample points: samples that fall into the safety bubble are identified as safe samples, and samples that fall into the failure bubble are identified as failure samples.

[0122] The calculation module is used to calculate the structural failure probability and the coefficient of variation based on the sample filtering and the evaluation results of the samples outside the bubble;

[0123] The calculation formula of the failure probability is as follows:

[0124]

[0125] Among them, P f is the failure probability, represents the number of samples falling into the i-th safety bubble, k 1 represents the number of safety bubbles, N represents the total number of samples drawn, is the indicator function, which has a value of 1 for safe samples outside the bubble and 0 otherwise;

[0126] The calculation formula of the coefficient of variation is as follows:

[0127]

[0128] in,

[0129]

[0130] Among them, COV【P f ] is the coefficient of variation, E(Pf ) is the mean of the failure probability, Var(P f ) is the variance of the failure probability.

[0131] Embodiment 3

[0132] A storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the method for analyzing the reliability of uncertain factors of a cellular structure described in the first embodiment are executed.

[0133] Embodiment 4

[0134] An electronic device includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the cellular structure uncertainty factor reliability analysis method described in Example 1, and the processor is configured to execute the program stored in the memory.

[0135] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A reliability analysis method for uncertain factors of honeycomb structure, characterized in that: The following steps are involved: Step 1: construct a safety bubble for filtering safety samples in the safety domain of the random space. The calculation formula of the safety bubble is as follows: find d={x si } s.t.g(x si )=0 Among them, x si represents the endpoint of the radius of the i-th safety bubble, represents the midpoint of the ith safety bubble, g(·) represents the performance function, r is the radius, and d represents the design variable; Step 2: construct failure bubbles for filtering failed samples in the failure domain of the random space. The calculation formula of the failure bubbles is as follows: find d={x fi } s.t.g(x fi )=0 Among them, x fi represents the endpoint of the radius of the i-th failure bubble, represents the midpoint of the i-th failed bubble; The iterative formula of the radius r is as follows: x k+1 =x k +γ k (x k+1 -x k ) Among them, γ k is the control factor, whose range is [0,1], x k-1 、x k 、x k+1 Respectively represent the endpoints of the bubble radius of the k-1th, kth, and k+1th iterations, x o represents the center point of the k-th iteration bubble, ||·|| represents the norm, represents the gradient function, θ k ,θ k+1 are the angles of the kth and k+1th iteration steps, R k is the radius of the kth iteration step, γ is the control factor; Step 3: Generate sample points that obey the distribution type based on the mean and variance of the input parameters; Step 4: Use the generated bubbles to screen the sample points: the samples falling into the safe bubble are identified as safe samples, and the samples falling into the invalid bubble are identified as invalid samples; Step 5: Calculate the failure probability and coefficient of variation of the honeycomb structure.

2. The reliability analysis method of uncertain factors of honeycomb structure according to claim 1, characterized in that: The failure probability described in step 5 is calculated as follows: Among them, P f is the failure probability, represents the number of samples falling into the i-th safety bubble, k1 represents the number of safety bubbles, and N represents the total number of samples drawn. is an indicator function, which takes the value of 1 for safe samples outside the bubble and 0 otherwise.

3. The reliability analysis method of uncertain factors of honeycomb structure according to claim 2, characterized in that: The coefficient of variation described in step 5 is calculated as follows: in, Among them, COV[P f ] is the coefficient of variation, E(P f ) is the mean of the failure probability, Var(P f ) is the variance of the failure probability.

4. A reliability analysis system for uncertain factors of honeycomb structure, characterized in that: include: Bubble construction module, sample generation and filtering module, calculation module; The bubble construction module is used to construct safety bubbles and failure bubbles in random space; The calculation formula of the safety bubble is as follows: find d={x si } s.t.g(x si )=0 Among them, x si represents the endpoint of the radius of the i-th safety bubble, represents the midpoint of the ith safety bubble, g(·) represents the performance function, r is the radius, and d represents the design variable; The calculation formula of the failed bubbles is as follows: find d={x fi } s.t.g(x fi )=0 Among them, x fi represents the endpoint of the radius of the i-th failure bubble, represents the midpoint of the i-th failed bubble; The iterative formula of the radius r is as follows: x k+1 =x k +γ k (x k+1 -x k ) Among them, γ k is the control factor, whose range is [0,1], x k-1 、x k 、x k+1 Respectively represent the endpoints of the bubble radius of the k-1th, kth, and k+1th iterations, x o represents the center point of the k-th iteration bubble, ||·|| represents the norm, represents the gradient function, θ k ,θ k+1 are the angles of the kth and k+1th iteration steps, R k is the radius of the kth iteration step, γ is the control factor; The sample generation and filtering module generates sample points that obey the distribution type based on the mean and variance of the input parameters, and uses the generated bubbles to screen the sample points, that is, the samples that fall into the safe bubble are identified as safe samples, and the samples that fall into the invalid bubble are identified as invalid samples; The calculation module is used to calculate the failure probability and coefficient of variation of the honeycomb structure.

5. The honeycomb structure uncertainty factor reliability analysis system according to claim 4, characterized in that: The calculation formula of the failure probability is as follows: Among them, P f is the failure probability, represents the number of samples falling into the i-th safety bubble, k1 represents the number of safety bubbles, and N represents the total number of samples drawn. is an indicator function, which takes the value of 1 for safe samples outside the bubble and 0 otherwise.

6. The honeycomb structure uncertainty factor reliability analysis system according to claim 5, characterized in that: The calculation formula of the coefficient of variation is as follows: in, Among them, COV[P f ] is the coefficient of variation, E(P f ) is the mean of the failure probability, Var(P f ) is the variance of the failure probability.

7. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for analyzing the reliability of uncertain factors of a cellular structure according to any one of claims 1 to 3 are executed.

8. An electronic device, comprising a memory and a processor, characterized in that: The memory is used to store a program that supports the processor to execute the cellular structure uncertainty factor reliability analysis method according to any one of claims 1 to 3, and the processor is configured to execute the program stored in the memory.

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