Mixed time-varying reliability analysis method for solid rocket engine shell structure

Abstract

The invention discloses a mixed time-varying reliability analysis method for a solid rocket engine shell structure. Uncertain parameters and distribution are determined according to complex characteristics such as high-temperature and high-pressure time-varying load borne by a solid rocket engine shell structure, geometric sudden change in a star hole charging combustion stage, a throat ablation non-stationary interval process and a time-varying correction coefficient random process, and the random and interval processes are processed in a unified mode through equivalent time-varying uncertainty conversion. Input dimension explosion is avoided, specifically, a random process vector and an interval process vector are converted into an equivalent random vector, so that a time-varying limit state function is equivalently converted into a static function, the input dimension of the RBF combination model is effectively prevented from being increased, the advantages of multiple basis functions are fused through the radial basis function RBF combination model, the calculation cost is reduced, and the calculation efficiency is improved. The modeling precision of the strong nonlinear limit state function of the solid rocket engine shell is improved, the nonlinear mixed time-varying reliability analysis problem is efficiently solved, and the calculation precision is high.

Description

Technical Field

[0001] The present invention belongs to the technical field of reliability analysis of solid rocket motor casings, and relates to a hybrid time-varying reliability analysis method and system for a solid rocket motor casing structure. Background Art

[0002] When solid rocket motor casings operate in high-temperature and high-pressure environments, their failure probability varies dynamically over time, necessitating the use of hybrid time-variant reliability analysis (HTRA) to assess the cumulative failure probability. Traditional reliability analysis methods rely on linear approximation models, which are inaccurate for analyzing nonlinear limit-state functions. Second-order approximation methods require the calculation of the Hessian matrix, which is computationally expensive. Furthermore, existing methods must decompose time-varying uncertainties such as random and interval processes into multidimensional variables, resulting in a surge in the dimensionality of the surrogate model and low modeling efficiency. Therefore, a hybrid time-variant reliability analysis method that balances computational efficiency and accuracy is urgently needed.

[0003] As a critical load-bearing component subjected to high-temperature, high-pressure combustion gases, the structural reliability of solid rocket motor cases directly determines the safety performance of the vehicle. Traditional reliability analysis methods have significant limitations when addressing the time-varying, mixed uncertainties of case structures. First, parameters such as combustion chamber pressure and throat ablation exhibit strong time-varying characteristics during case operation. Existing methods employ stochastic process decomposition strategies, which significantly increase model dimensionality and exponentially increase computational complexity. Second, the case failure mechanism involves a highly nonlinear coupling between the burning rate equation and the interior ballistic differential equation. Reliability models based on linear approximations can produce significant deviations when solving the limit state function. Third, existing single-surrogate model techniques are insufficient for synergistically characterizing mixed uncertainties, making it difficult to accurately capture the interaction between the throat diameter interval process and the random process of material properties. More importantly, traditional methods lack targeted optimization of sample selection strategies for time-varying failure boundaries, consuming significant computational resources for inefficient sampling and failing to meet the real-time requirements for long-term reliability assessment of case structures in engineering. Therefore, developing a hybrid, time-varying reliability analysis method that balances computational accuracy and efficiency has become a key technology for improving the structural safety assessment of solid rocket motors. Summary of the Invention

[0004] The purpose of the present invention is to solve the problems of the existing technology in analyzing the reliability of the engine casing, such as the random process decomposition strategy, the complex calculation process, the inability to adapt to the characteristics of the casing during operation, the deviation of the analysis results, the insufficient collaborative characterization capability of uncertainty, and the lack of directional optimization of the time-varying failure boundary in the sample selection strategy of the traditional method, which cannot meet the real-time requirements of the long-term reliability evaluation of the casing structure in engineering. A hybrid time-varying reliability analysis method and system for the solid rocket engine casing structure are provided.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A hybrid time-varying reliability analysis method for a solid rocket motor casing structure comprises the following steps:

[0007] Obtain the uncertainty parameters and distribution of the hybrid time-varying reliability analysis problem of the engine casing structure, and input the uncertainty parameters and distribution into the RBF combination model of the limit state function response Obtain reliability analysis results;

[0008] The RBF combination model The acquisition includes:

[0009] Divide the uncertainty parameters and distribution into random vector X, random process vector S(t), interval vector Y and interval process vector I(t), determine the time parameter t for reliability analysis, and obtain the limit state function g(X, Y, S(t), I(t), t);

[0010] The random process vector S(t) and the interval process vector I(t) are equivalently transformed into random vectors S′ and I′, and the time parameter t is transformed into a uniform variable t′ to obtain the transformed limit state function g e (V), where V = [X, Y, S', I', t'], and the RBF combination model is constructed based on the distribution of V = [X, Y, S', I', t']

[0011] A further improvement of the present invention is:

[0012] The equivalent conversion of the random process vector S(t) and the interval process vector I(t) into random vectors S′ and I′ includes:

[0013] The time parameter t∈[t s , t e ] Equal distance scattered for n s Time t i (i=1,2,...,n s ), at each discrete moment t i (i=1,2,...,ns ), random process S(t) and interval process I(t) are random variables and interval variables respectively;

[0014] The distribution probability density functions of the random process S(t) and the interval process I(t) at each discrete moment are weighted averaged to obtain the probability density functions of the transformed random variables S′ and I′.

[0015] The RBF combination model is constructed based on the distribution of V=[X, Y, S', I', t'] include:

[0016] S1: Based on the parameter distribution of V = [X, Y, S', I', t'], extract the total sample pool S tp ; From the total sample pool S tp Extract n init Initial samples constitute the initial sample training set;

[0017] S2: Constructing an RBF combination model based on the initial sample training set Through RBF combination model For the total sample pool S tp Make predictions and obtain the sign of the predicted value for each sample;

[0018] S3: Introducing active learning ELF function, in the total sample pool S tp Select the sample point V that makes the ELF function minimum * Add to the initial sample training set and perform the RBF combination model Update and calculate the total sample pool S obtained after the update tp The sign of the predicted value of each sample is calculated by the model in S2 and the model in S3 for the total sample pool S tp agreement rate of symbol prediction judgments;

[0019] S4: Set the newly added sample point V * The number of new , the model update algebra is K, compare n new and K:

[0020] If K < n new , return to S3, RBF combination model Update and calculate the total sample pool S of the model in S2 and the model in S3 tp The consistency rate of symbol prediction judgment, until K = n new ;

[0021] If K≥n new , judge the RBF combination model Is it converged? If not, return to S3, update the combined model, and calculate the effect of the model in S2 and the model in S3 on the total sample pool S. tp Consistency rate of symbol prediction judgment, up to RBF combination model Satisfy the convergence conditions.

[0022] The obtaining of reliability analysis results includes:

[0023] The uncertainty parameters of the original obtained hybrid time-varying reliability analysis problem of the engine casing structure are sampled to generate N MCS random vectors and random process vector samples, and N IA Samples of interval vectors and interval process vectors;

[0024] The N MCS random vectors and random process vector samples and N IA The samples of interval vectors and interval process vectors are input into the RBF combination model Estimate the jth (j=1,2,…,N MCS The upper bound of the limit state function corresponding to ) samples and the lower bound

[0025] Based on the upper bound and the lower bound Obtain the upper and lower bounds of the cumulative failure probability and complete the reliability analysis.

[0026] The generated N MCS random vectors and random process vector samples, and N IA The samples of interval vectors and interval process vectors are expressed as follows:

[0027] Let the jth S(t) and I(t) samples be T s，j With T I，j :

[0028]

[0029]

[0030] Among them, T s，j is m×n d , m is the number of components of the random process vector S(t); T I，j is q×n d , q is the number of components of the interval process vector I(t).

[0031] The upper bound of the limit state function and the lower bound Calculated by the following formula:

[0032]

[0033]

[0034] Among them, T I，j (t i ) represents a random vector; Y L With Y U Respectively represent the upper and lower bounds of the interval vector Y; and They represent the interval process at time t i The upper and lower bounds of the value range of T S,j (t i ) represents the jth random process sample at time t i discrete values ​​of .

[0035] Based on the upper bound and the lower bound The upper and lower bounds of the cumulative failure probability are calculated using the following formula:

[0036]

[0037]

[0038] in, and Both are failure indicator functions.

[0039] A hybrid time-varying reliability analysis system for a solid rocket motor casing structure, comprising:

[0040] Reliability analysis module, used to obtain the uncertainty parameters and distribution of the mixed time-varying reliability analysis problem of the engine casing structure, and input the uncertainty parameters and distribution into the RBF combination model of the limit state function response Obtain reliability analysis results;

[0041] The combined model acquisition module is used to divide the uncertainty parameters and distribution into random vector X, random process vector S(t), interval vector Y and interval process vector I(t), determine the time parameter t for reliability analysis, and obtain the limit state function g(X, Y, S(t), I(t), t); convert the random process vector S(t) and the interval process vector I(t) into random vectors S′ and I′, convert the time parameter t into a uniform variable t′, and obtain the transformed limit state function g e (V), where V = [X, Y, S′, I′, t′], and the RBF combination model is constructed based on the distribution of V = [X, Y, S′, I′, t′]

[0042] A terminal device comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of any one of the methods of the present invention when executing the computer program.

[0043] A computer-readable storage medium stores a computer program, wherein the computer program implements the steps of any method described in the present invention when executed by a processor.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] The present invention discloses a hybrid time-varying reliability analysis method for a solid rocket engine casing structure. The uncertainty parameters and distribution are determined based on complex characteristics of the solid rocket engine casing structure, such as high-temperature and high-pressure time-varying loads, geometric mutations in the star-hole charge combustion stage, non-stationary interval processes of throat ablation, and random processes with time-varying correction coefficients. The method utilizes equivalent time-varying uncertainty transformation to uniformly process random and interval processes, thereby avoiding input dimension explosion. Specifically, the random process and interval process vectors are transformed into equivalent random vectors, thereby equivalently transforming the time-varying limit state function into a static function, effectively avoiding increasing the input dimension of an RBF combination model. The radial basis function (RBF) combination model integrates the advantages of multiple basis functions, better adapts to the characteristics of the casing during operation, and reduces computational costs. Compared with a single Kriging or RBF model, the RBF combination model has a stronger approximation capability for complex functions, significantly improves the modeling accuracy of the strong nonlinear limit state function of the solid rocket engine casing, efficiently solves the nonlinear hybrid time-varying reliability analysis problem, and has high computational accuracy.

[0046] Furthermore, the present invention combines active learning technology with directional sampling in the acquisition of radial basis function (RBF) combination models to improve computational efficiency by 2-3 orders of magnitude compared with traditional Monte Carlo simulation. At the same time, there is no need for second-order approximation to calculate the Hessian matrix or search for the maximum possible point of the boundary. The reliability of low-probability failure boundary estimation is enhanced through the convergence criterion, and nonlinear mixed time-varying reliability analysis problems can be efficiently solved with high computational accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0048] Figure 1 Flowchart of hybrid time-varying reliability analysis method for solid rocket engine casing;

[0049] Figure 2 Schematic diagram of the equivalent transformation process of time-varying uncertainty (a is the equivalent transformation of a random process; b is the equivalent transformation of an interval process);

[0050] Figure 3 Construct a flowchart for the RBF combination model;

[0051] Figure 4 This is a schematic diagram of a solid rocket engine;

[0052] Figure 5 This is a schematic diagram of the star hole charge structure;

[0053] Figure 6 is the cumulative failure probability curve of the solid rocket motor case; (where a is the lower bound of the cumulative failure probability; b is the upper bound of the cumulative failure probability);

[0054] Figure 7 is the boundary extreme value distribution of the limit state function of the solid rocket motor case; (where a is the lower bound of the limit state function; b is the upper bound of the limit state function). DETAILED DESCRIPTION

[0055] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0056] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort are intended to fall within the scope of protection of the present invention.

[0057] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not require further definition or explanation in subsequent drawings.

[0058] In the description of the embodiments of the present invention, it should be noted that if the terms "upper," "lower," "horizontal," "inner," etc. appear, the orientation or positional relationship indicated is based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the inventive product is typically placed when in use. These terms are merely for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or component referred to must have a specific orientation, be constructed, or operate in a specific orientation. Therefore, they should not be construed as limitations on the present invention. In addition, the terms "first," "second," etc. are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0059] In addition, if the term "horizontal" appears, it does not mean that the component must be absolutely horizontal, but can be slightly tilted. For example, "horizontal" only means that its direction is more horizontal than "vertical", and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0060] In the description of the embodiments of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "disposed," "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0061] The present invention is described in further detail below with reference to the accompanying drawings:

[0062] See also Figure 1 The embodiment of the present invention discloses a hybrid time-varying reliability analysis method for a solid rocket engine casing structure, which realizes high-precision and high-efficiency cumulative failure probability estimation through equivalent uncertainty transformation, RBF combined agent model construction and active learning technology.

[0063] The following steps are involved:

[0064] Step 1: Determine the hybrid time-varying reliability analysis problem of the solid rocket motor case structure;

[0065] Specifically include:

[0066] Step 1.1: Analyze the structure of the solid rocket motor and the load it bears, and determine the failure mode and conditions of the motor case structure;

[0067] Step 1.2: Conduct uncertainty tracing to obtain relevant parameters and their distributions for the hybrid time-varying reliability analysis problem of the engine casing structure;

[0068] Step 1.3: Divide the uncertainty parameters obtained in step 1.2 into random vector X, random process vector S(t) = [S1(t), S2(t), ... S m (t)] (m is the number of components of the random process vector), the interval vector Y and the interval process vector I(t) = [I1(t), I2(t), ...I q (t)] (q is the number of components of the random process vector), construct the limit state function g(X,Y,S(t),I(t),t), and determine the time interval t∈[t s ,t e ].

[0069] Step 2: Based on time discretization and ETUT, the random process S(t) and interval process vector I(t) obtained in step 1.3 are equivalently converted into random vectors S′ and I′. At the same time, the time parameter t is processed into a uniform variable t′. At this time, the time-varying limit state function g(X, Y, S(t), I(t), t) is converted into a static limit state function g e (V), where V = [X, Y, S′, I′, t′], see Figure 2 .

[0070] Specifically include:

[0071] Step 2.1: Set the time interval [t s ,t e ] Equal distance scattered for n s Time t i (i=1,2,...,n s ), at each discrete moment t i (i=1,2,...,n s ), random process and interval process are random variables and interval variables respectively;

[0072] Step 2.2: Perform weighted averaging on the distribution probability density functions of the random process S(t) and the interval process I(t) at each discrete moment to obtain the probability density functions of the transformed random variables S′ and I′.

[0073] Step 3: Construct RBF combination model of limit state function

[0074] See also Figure 3 , specifically including:

[0075] Step 3.1: Based on the distribution of V obtained in step 2, extract n init initial samples, and n init >>n total The total sample pool S of samples tp ;

[0076] Step 3.2: n init Initial samples constitute the initial training sample set, and the RBF combination model is constructed based on the corresponding initial training sample set. For the total sample pool S tp Make predictions and record the sign of the predicted value for each sample;

[0077] Step 3.3: Based on the active learning ELF function, in the total sample pool S tp Select a new sample point V that minimizes the ELF function * Add the training set, update the combined model, calculate the sign of the sample prediction value of the total sample pool, and calculate the consistency rate of the sign judgment of the total sample pool by the previous and next generation models;

[0078] Step 3.4: For the increased number of samples n new Compare with the model update algebra K set:

[0079] If K < n new , return to step 3.3, update the combined model, and calculate the consistency rate of the two generations of models on the symbol judgment of the total sample pool until K = n new .

[0080] If K≥n new , then substitute the convergence criterion of the combined model to determine whether it has converged. If not, return to step 3.3, update the combined model, and calculate the consistency rate of the symbol judgment of the two generations of models for the total sample pool until the combined model meets the convergence criteria.

[0081] Furthermore, in this step, the construction process of the RBF combination model includes:

[0082] Using the training samples, m RBF models are constructed using different basis functions such as Gaussian function (G), multi-quadric function (MQ), and inverse multi-quadric function (IMQ), and a combined model is formed through weighted averaging.

[0083] Adjust the weight coefficient λ of the combined model according to the prediction error dynamics of the single RBF model (whether a detailed formula is needed) j (j=1,2,3…,m). The specific process is as follows:

[0084]

[0085] Where, is the predicted value of the j-th RBF model at V; j is the weight of the j-th model prediction value. Weight coefficient λ jBased on the prediction error e of each model LOOCV To determine:

[0086]

[0087] Where, e LOOCV,j is the prediction error of the j-th RBF model; e LOOCV,avg is the average prediction error of m RBF models; α and β are set to 0.05 and 1 respectively.

[0088] Furthermore, in this step, the active learning ELF function and convergence criteria are specifically as follows:

[0089] Taking into account the prediction error, sample space distribution uniformity and distance from the origin, the active learning function ELF(x) is defined as:

[0090]

[0091] Where um(x) is a function that measures the importance of a sample and is defined as the absolute value of the ratio of the predicted value of the RBF combination model at x to its prediction error. d(x) represents the value of the minimum Euclidean distance between x and the existing samples normalized to the range of um(x);

[0092] The convergence index is defined as the mean of the agreement rates of the symbolic predictions of the consecutive K generations of models. The specific expression is Where r s,i The consistency rate of the prediction of the sample symbols in the sample pool between the model trained after adding i samples and the model trained after adding i-1 samples. When it is close to 1, the combined model is considered to have converged.

[0093] Step 4: RBF combination model obtained in step 3 The Monte Carlo simulation method is used to calculate the time-varying hybrid reliability of the solid rocket motor case structure, and the upper and lower bounds of the cumulative failure probability of the case structure are obtained.

[0094] Specifically include:

[0095] Step 4.1: Set the time interval [t s , t e ] Equal distance scattered for n d Through steps 2 and 3, the time-varying uncertainty has been integrated into the model construction, and the constructed RBF combination model can directly map the original parameters to the cumulative failure probability. Therefore, based on the actual distribution of the original uncertainty-related parameters before the equivalent time-varying uncertainty conversion, N MCS Random vectors and random process vector samples, and at the same time, generate N IAThe samples of interval vector and interval process vector. Specifically, let the jth S(t) and I(t) samples be T s,j With T I,j , which is expressed as follows:

[0096]

[0097]

[0098] Among them, T s，j is m×n d , m is the number of components of the random process vector S(t); T I,j is q×n d , q is the number of components of the interval process vector I(t).

[0099] Step 4.2: RBF combination model based on limit state function response And the sample obtained in step 4.1, estimate the jth (j=1,2,…,N MCS The upper bound of the limit state function corresponding to ) samples and the lower bound Specifically, the estimation formulas for the upper and lower bounds of the limit state function are:

[0100]

[0101]

[0102] Among them, T I,j (t i ) represents a random vector

[0103] Step 4.3: Based on the upper and lower bounds of the time-varying limit state response, estimate the upper and lower bounds of the cumulative failure probability. Specifically, the estimation formula for the cumulative failure probability is:

[0104]

[0105]

[0106] in, and is the failure indicator function, which is defined as follows:

[0107]

[0108]

[0109] This embodiment processes time-varying uncertainties based on equivalent time-varying uncertainty conversion, converting random process and interval process vectors into equivalent random vectors, thereby converting the time-varying limit state function into a static function, effectively avoiding increasing the input dimension of the RBF combination model. In order to reduce computational costs, a combined proxy model construction method based on active learning and radial basis function (RBF) is proposed to efficiently construct an approximate model of the static limit state function. Compared with a single Kriging or RBF model, the RBF combination model has a stronger approximation ability for complex functions. Based on the constructed RBF combination model of the limit state function response, combined with the original uncertainty distribution sampling and Monte Carlo simulation method, it can efficiently solve the nonlinear mixed time-varying reliability analysis problem with high computational accuracy.

[0110] See also Figures 4 to 7 , the present invention also discloses a specific embodiment:

[0111] Step 1: Determine the hybrid time-varying reliability analysis problem of the solid rocket motor case structure;

[0112] Specifically include:

[0113] Step 1.1: Analyze the structural form and load form of the solid rocket motor, and determine the failure mode and conditions of the motor case structure.

[0114] The solid rocket engine of this embodiment is divided into a metal shell, a heat-insulating layer and a propellant column. The charge structure adopts a star-hole charge. The specific structure is as follows: Figure 4 and Figure 5 As shown. The outer diameter of the propellant grain is D s , the length of the grain is L, the initial grain thickness is H0, and the initial diameter of the nozzle throat is D t0 The specific geometric parameters and corresponding symbols of the star hole charge are given in Table 1.

[0115] Table 1 Geometric parameters of star hole charge

[0116]

[0117] In this embodiment, the transition arc radius r is 2 mm, and the number of star angles n is s is 6, the star side angle θ p The angle is 60°, the star angle coefficient ε is 0.8974, and the star angle arc radius r1 is 1 mm. During the operation of a solid rocket rocket, its metal shell is subjected to high temperature and high pressure. Considering the influence of temperature, the allowable internal pressure of the shell is assumed to vary with time as follows:

[0118] P a (t) = (1 - 0.002t)Pa0 (9)

[0119] In the formula, P a0 is the initial value of P a (t). When the internal pressure P(t) of the engine is greater than P a (t), the shell structure of the engine fails.

[0120] Step 1.2: Conduct uncertainty tracing to obtain the relevant parameters and their distributions of the mixed time-varying reliability analysis problem of the engine shell structure.

[0121] Considering combustion instability, a correction coefficient k(t) is added to the internal pressure of the engine and modeled as a stochastic process. At this time, when k(t)·P(t)>P a (t), it is considered that the shell structure of the engine fails. Denote the throat area and combustion area of the engine as A t (t) and A b (t) respectively. On the premise of knowing the grain thickness H(t), grain mass M(t) and free volume V(t) of the combustion chamber, the combustion chamber pressure P(t) can be obtained by solving the following differential equations.

[0122]

[0123] In the formula, ρ p is the grain density; a and n are the burning rate coefficient and pressure exponent respectively; where γ = 1.252 is the specific heat ratio; C * is the characteristic velocity. The relationship between the burning grain thickness H b and A b (t) can be calculated based on the parallel translation hypothesis, and it can be mainly divided into the following three stages:

[0124] (1) When 0 ≤ H b < r1:

[0125]

[0126] (2) When r1 ≤ H b < H * , H * = lsin(εβ) / cos(θ / 2):

[0127]

[0128] (3) When H * ≤ H) b < H0 After the star side disappears:

[0129]

[0130] The initial ventilation area of ​​the star-hole charge can be calculated using formula (4-31).

[0131]

[0132] Solving the zero-dimensional interior ballistic differential equations also requires initial conditions for the differential components. In this embodiment, the initial conditions are given as follows:

[0133]

[0134] Based on the above initial conditions, the Runge-Kutta method can be used to solve Equation (10). Considering the ablation of the throat, the throat diameter D t (t) is modeled as a non-stationary interval process, and its characteristic function is given as follows.

[0135]

[0136] Based on the above analysis, the relevant parameters and their distribution forms of the hybrid time-varying reliability analysis problem are statistically analyzed as shown in Table 2.

[0137] Table 2 Distribution of relevant parameters for the hybrid time-varying reliability analysis problem of solid rocket motor case structure

[0138]

[0139] Step 1.3: Divide the uncertainty parameters related to the reliability analysis of the engine casing structure obtained in step 1.2 into random vectors X = [C * ,ρ,D s ,H0,L,a], random process vector S(t)=k(t), interval vector Y=P a0 , interval process vector I(t)=D t (t). According to the definition of failure mode and failure condition of solid motor shell structure in step 1.2, the limit state function g(t)=k(t)·P(t)-P a (t), after substituting the relevant parameters, the limit state function is simplified to g(X,Y,S(t),I(t),t). Finally, the time interval of interest in the reliability analysis of the solid rocket motor case structure is determined to be [t s , t e ]=[0,7] seconds.

[0140] Step 2: Based on time discretization and equivalent time-varying uncertainty transformation (ETUT), the random process S(t) and interval process vector I(t) obtained in step 1.3 are equivalently transformed into random vectors S′ and I′. At the same time, the time parameter t is processed into a uniform variable t′. Thus, the time-varying limit state function g(X, Y, S(t), I(t), t) can be transformed into a static limit state function ge (X,Y,S′,I′,t′).

[0141] Specifically include:

[0142] Step 2.1: Set the time interval [t s ,t e ] Equal distance scattered for n s = 100 moments t i (i=1,2,...,n s ). At each discrete moment t i (i=1,2,...,n s ), random process and interval process are random variables and interval variables respectively;

[0143] Step 2.2: For each discrete moment random process S(t) and interval process I(t), the distribution probability density function f pdf (S(t i ))、f pdf (I(t i )) Perform weighted averaging to obtain the probability density function f of the transformed random vectors S′ and I′ pdf (S′) and f pdf (I′). At this time, the time-varying limit state function g(X, Y, S(t), I(t), t) is transformed into a static limit state function g e (V), where V=[X, Y, S′, I′, t′].

[0144] Step 3: Construct an RBF combination model that approximates the limit state function

[0145] Specifically include:

[0146] Step 3.1: Based on the distribution of V obtained in step 2, extract n init = 20 initial samples and n total >>Total sample pool S of 20 samples tp , and set the model update algebra K of this embodiment to 5.

[0147] Step 3.2: Based on the initial training sample set, select three basis functions: G (Gaussian), MQ (Multi-quadric) and IMQ (Inverse Multi-quadric) to build the initial RBF combination model Make predictions for the total sample pool and record the sign of the predicted value for each sample;

[0148] Step 3.3: Based on the active learning ELF function, in the total sample pool S tp Select the new sample (V* , g e (V * )) Add the training sample set, update the RBF combination model, calculate the sign of the sample prediction value of the total sample pool, and calculate the consistency rate of the sign judgment of the total sample pool by the previous and next generation models;

[0149] Step 3.4: For the increased number of samples n new Compare with the model update algebra K: If K<n new , return to step 3.3, update the combined model, and calculate the consistency rate of the two generations of models on the symbol judgment of the total sample pool until K = n new ; If K ≥ n new , then substitute the convergence criterion of the RBF combination model to determine whether it converges. If not, return to step 3.3, update the combination model, and calculate the consistency rate of the two generations of models on the total sample pool sign judgment until the combination model meets the convergence condition, and obtain the RBF combination model of the approximate limit state function Specifically, for this embodiment, the RBF combination model convergence condition is set to It is a convergence indicator, defined as the mean of the consistency rate of symbol predictions of consecutive K generations of models. The specific expression is as follows:

[0150]

[0151] Where r s,i It is the consistency rate of the prediction of the sample symbols in the sample pool between the model trained after adding i new samples and the model trained after adding i-1 samples.

[0152] Step 4: RBF combination model obtained in step 3 The Monte Carlo simulation method is used to calculate the time-varying hybrid reliability of the solid rocket motor case structure, and the upper and lower bounds of the cumulative failure probability of the case structure are obtained.

[0153] Step 4.1: Set the time interval [t s , t e ] Equal distance scattered for n d = 100 moments. Based on the distribution of relevant parameters [X, Y, S((t, I(t), t] before equivalent time-varying uncertainty conversion, N is obtained. MCS =1×10 6 Random vector X and random process vector S(t) samples. At the same time, generate N IA = 30 samples of interval vector Y and interval process vector I(t). Specifically, let the jth S(t) and I(t) samples be T s，j With T I，j , which is expressed as follows:

[0154]

[0155]

[0156] Step 4.2: RBF combination model based on limit state function And the samples obtained in step 4.1, the jth (j=1,2,…,N) is estimated by equations 5 and 6. MCS The upper bound of the limit state function corresponding to ) samples and the lower bound Then, using Equations 7 and 8, we can estimate the upper bound of the cumulative failure probability of the rocket engine casing structure: and the Nether

[0157] For this embodiment, after ten solutions in the above process, an RBF combination model of the limit state function that meets the accuracy requirements is obtained by adding an average of 59.7 new sample points, and the average cumulative failure probability result is In addition, the traditional high-precision but computationally time-consuming MCS method was used to solve this embodiment ten times to obtain the upper and lower bounds of the average cumulative failure probability. The specific results of the hybrid time-varying reliability analysis of this embodiment using the two methods are shown in Table 3:

[0158] Table 3 Results of hybrid time-varying reliability analysis of solid rocket motor case structure

[0159]

[0160] In this embodiment, the upper and lower bounds of the cumulative failure probability estimated by the MCS method are 3.706×10 -2 and 3.438×10 -3 , it can be considered that the result converges to the true solution. The upper and lower bounds of the cumulative failure probability estimated by the method provided by the present invention are 3.706×10 -2 and 3.438×10 -3 , the error relative to the MCS method is and In terms of computational efficiency, the ERBFBM method proposed in this chapter only needs to call the original limit state function N FE = 59.7 times to construct an approximate model of the time-varying limit state function for cumulative failure probability estimation, which is much smaller than the N required by the MCS method. FE =3×10 10 Second-rate.

[0161] Further, Figure 6 and Figure 7The time-varying curves of the upper and lower bounds of the cumulative failure probability and the extreme value distribution of the upper and lower bounds of the limit state function with respect to time obtained by the two methods are given respectively. Figure 6 It can be seen that the method provided by the present invention can well predict the upper and lower bounds of the cumulative failure probability within the time interval of interest.

[0162] Therefore, the proposed hybrid time-varying reliability analysis method for the solid rocket engine case structure was verified through a specific implementation case of the reliability analysis of the solid rocket case structure. The proposed reliability analysis method can effectively obtain the cumulative failure probability index.

[0163] This embodiment also discloses a hybrid time-varying reliability analysis system for a solid rocket motor casing structure, comprising:

[0164] Reliability analysis module, used to obtain the uncertainty parameters and distribution of the mixed time-varying reliability analysis problem of the engine casing structure, and input the uncertainty parameters and distribution into the RBF combination model of the limit state function response Obtain reliability analysis results;

[0165] The combined model acquisition module is used to divide the uncertainty parameters and distribution into random vector X, random process vector S(t), interval vector Y and interval process vector I(t), determine the time parameter t for reliability analysis, and obtain the limit state function g(X, Y, S(t), 1(t), t); convert the random process vector S(t) and the interval process vector I(t) into random vectors S′ and I′, convert the time parameter t into a uniform variable t′, and obtain the transformed limit state function g e (V), where V = [X, Y, S', I', t'], and the RBF combination model is constructed based on the distribution of V = [X, Y, S', I', t']

[0166] This method addresses the complex characteristics of solid rocket motor case structures, such as high-temperature and high-pressure time-varying loads, geometric mutations during the starhole charge combustion phase, non-stationary interval processes of throat ablation, and random processes with time-varying correction coefficients. By integrating the advantages of multiple basis functions through a radial basis function (RBF) combination model, the modeling accuracy of the strongly nonlinear limit state function of the solid rocket motor case is significantly improved. The equivalent time-varying uncertainty transformation (ETUT) is used to uniformly process random and interval processes to avoid input dimension explosion. Active learning technology is combined with targeted sampling to improve computational efficiency by 2-3 orders of magnitude compared to traditional Monte Carlo simulations. At the same time, there is no need for second-order approximation to calculate the Hessian matrix or search for the maximum possible point on the boundary, and the reliability of low-probability failure boundary estimation is enhanced through convergence criteria. The present invention systematically addresses the shortcomings of existing methods in terms of accuracy, efficiency, dimensionality curse, and mixed uncertainty splitting, providing a new, efficient and accurate method for reliability analysis of complex aerospace structures.

[0167] A schematic diagram of a terminal device provided in one embodiment of the present invention. The terminal device in this embodiment includes: a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of each of the aforementioned method embodiments are implemented. Alternatively, when the processor executes the computer program, the functions of each module / unit in each of the aforementioned device embodiments are implemented.

[0168] The computer program may be divided into one or more modules / units, which are stored in the memory and executed by the processor to accomplish the present invention.

[0169] The terminal device may be a computing device such as a desktop computer, a notebook computer, a PDA, a cloud server, etc. The terminal device may include, but is not limited to, a processor and a memory.

[0170] The processor can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0171] The memory may be used to store the computer programs and / or modules, and the processor implements various functions of the terminal device by running or executing the computer programs and / or modules stored in the memory and calling the data stored in the memory.

[0172] If the module / unit integrated in the terminal device is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present invention implements all or part of the process in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, it can implement the steps of each of the above-mentioned method embodiments. The computer program includes computer program code, which can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electric carrier signal, telecommunication signal and software distribution medium. It should be noted that the content contained in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electric carrier signals and telecommunication signals.

[0173] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A hybrid time-varying reliability analysis method for a solid rocket motor casing structure, characterized in that: The following steps are involved: Obtain the uncertainty parameters and distribution of the hybrid time-varying reliability analysis problem of the engine casing structure, and input the uncertainty parameters and distribution into the RBF combination model of the limit state function response Obtain reliability analysis results; The RBF combination model The acquisition includes: Divide the uncertainty parameters and distribution into random vector X, random process vector S(t), interval vector Y and interval process vector I(t), determine the time parameter t for reliability analysis, and obtain the limit state function g(X, Y, S(t), I(t), t); The random process vector S(t) and the interval process vector I(t) are equivalently transformed into random vectors S′ and I′, and the time parameter t is transformed into a uniform variable t′ to obtain the transformed limit state function g e (V), where V = [X, Y, S', I', t'], and the RBF combination model is constructed based on the distribution of V = [X, Y, S', I', t'] 2. The hybrid time-varying reliability analysis method for a solid rocket motor casing structure according to claim 1, characterized in that: The equivalent conversion of the random process vector S(t) and the interval process vector I(t) into random vectors S′ and I′ includes: The time parameter t∈[t s , t e ] Equal distance scattered for n s Time t i (i=1,2,...,n s ), at each discrete moment t i (i=1,2,...,n s ), random process S(t) and interval process I(t) are random variables and interval variables respectively; The distribution probability density functions of the random process S(t) and the interval process I(t) at each discrete moment are weighted averaged to obtain the probability density functions of the transformed random variables S′ and I′.

3. The hybrid time-varying reliability analysis method for a solid rocket motor casing structure according to claim 1, characterized in that: The RBF combination model is constructed based on the distribution of V=[X, Y, S', I', t'] include: S1: Based on the parameter distribution of V = [X, Y, S', I', t'], extract the total sample pool S tp ; From the total sample pool S tp Extract n init Initial samples constitute the initial sample training set; S2: Constructing an RBF combination model based on the initial sample training set Through RBF combination model For the total sample pool S tp Make predictions and obtain the sign of the predicted value for each sample; S3: Introducing active learning ELF function, in the total sample pool S tp Select the sample point V that makes the ELF function minimum * Add to the initial sample training set and perform the RBF combination model Update and calculate the total sample pool S obtained after the update tp The sign of the predicted value of each sample is calculated by the model in S2 and the model in S3 for the total sample pool S tp agreement rate of symbol prediction judgments; S4: Set the newly added sample point V * The number of new , the model update algebra is K, compare n new and K: If K < n new , return to S3, RBF combination model Update and calculate the total sample pool S of the model in S2 and the model in S3 tp The consistency rate of symbol prediction judgment, until K = n new ; If K≥n new , judge the RBF combination model Is it converged? If not, return to S3, update the combined model, and calculate the effect of the model in S2 and the model in S3 on the total sample pool S. tp Consistency rate of symbol prediction judgment, up to RBF combination model Satisfy the convergence conditions.

4. The hybrid time-varying reliability analysis method for a solid rocket motor casing structure according to claim 1, characterized in that: The obtaining of reliability analysis results includes: The uncertainty parameters of the original obtained hybrid time-varying reliability analysis problem of the engine casing structure are sampled to generate N MCS random vectors and random process vector samples, and N IA Samples of interval vectors and interval process vectors; The N MCS random vectors and random process vector samples and N IA The samples of interval vectors and interval process vectors are input into the RBF combination model Estimate the jth (j=1,2,…,N MCS The upper bound of the limit state function corresponding to ) samples and the lower bound Based on the upper bound and the lower bound Obtain the upper and lower bounds of the cumulative failure probability and complete the reliability analysis.

5. The hybrid time-varying reliability analysis method for a solid rocket motor casing structure according to claim 4, characterized in that: The generated N MCS random vectors and random process vector samples, and N IA The samples of interval vectors and interval process vectors are expressed as follows: Let the jth S(t) and I(t) samples be T s，j With T I，j : Among them, T s，j is m×n d , m is the number of components of the random process vector S(t); T I，j is q×n d , q is the number of components of the interval process vector I(t).

6. The hybrid time-varying reliability analysis method for a solid rocket motor casing structure according to claim 4, characterized in that: The upper bound of the limit state function and the lower bound Calculated by the following formula: Among them, T I，j (t i ) represents a random vector; Y L With Y U Respectively represent the upper and lower bounds of the interval vector Y; and They represent the interval process at time t i The upper and lower bounds of the value range of T S,j (t i ) represents the jth random process sample at time t i discrete values ​​of .

7. The hybrid time-varying reliability analysis method for a solid rocket motor casing structure according to claim 6, characterized in that: Based on the upper bound and the lower bound The upper and lower bounds of the cumulative failure probability are calculated using the following formula: in, and Both are failure indicator functions.

8. A hybrid time-varying reliability analysis system for a solid rocket motor casing structure, characterized in that: include: Reliability analysis module, used to obtain the uncertainty parameters and distribution of the mixed time-varying reliability analysis problem of the engine casing structure, and input the uncertainty parameters and distribution into the RBF combination model of the limit state function response Obtain reliability analysis results; The combined model acquisition module is used to divide the uncertainty parameters and distribution into random vector X, random process vector S(t), interval vector Y and interval process vector I(t), determine the time parameter t for reliability analysis, and obtain the limit state function g(X, Y, S(t), I(t), t); convert the random process vector S(t) and the interval process vector I(t) into random vectors S′ and I′, convert the time parameter t into a uniform variable t′, and obtain the transformed limit state function g e (V), where V = [X, Y, S', I', t'], and the RBF combination model is constructed based on the distribution of V = [X, Y, S', I', t'] 9. A terminal device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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