A method for reliability evaluation of structural integrity of a solid rocket engine grain

Abstract

This invention provides a reliability assessment method for the structural integrity of propellant grains in solid rocket motors. The method includes: constructing an initial training set through clustering and selective sampling; training a first kriging model; and iteratively updating the model to meet convergence conditions. Subsequently, a second kriging model is further trained based on the updated sample pool, which is ultimately used to calculate the failure probability of the propellant grain at its maximum strain. This invention achieves coordinated handling of stochastic and cognitive uncertainties in the propellant grain structural response by introducing a clustering screening and learning function-guided sample selection mechanism, as well as a two-stage progressive model update strategy. This method significantly reduces computational resource consumption while ensuring prediction accuracy, improving the efficiency and applicability of reliability assessment. It is particularly suitable for the integrity analysis of complex propellant grain structures with multi-source uncertainties, providing more accurate and efficient technical support for the reliability design and life assessment of solid rocket motors.

Description

Technical Field

[0001] This invention generally relates to the field of solid rocket motor technology, and specifically to a reliability assessment method for the structural integrity of a solid rocket motor propellant grain. Background Technology

[0002] Solid rocket motors are chemical propulsion devices that use solid propellants. They have many advantages, such as simple structure, ease of use, and the ability to maintain a state of combat readiness for extended periods, and are widely used in the military and aerospace fields. As the energy carrier and load-bearing component of a solid rocket motor, the structural integrity and reliability of the composite solid propellant grain directly affect the motor's performance and lifespan.

[0003] However, due to the combined effects of factors such as the dispersion of material properties, geometric deviations introduced during manufacturing and assembly, and complex and variable service environment conditions, the propellant grains exhibit significant uncertainties in their mechanical response during stress.

[0004] In existing methods for assessing the reliability of propellant charge structures, uncertainties are typically either treated entirely as random uncertainties (randomness) and measured using probability theory, without fully considering the impact of cognitive uncertainties such as the dispersion of material properties; or they are completely classified as cognitive uncertainties and described using interval methods from non-probabilistic theory.

[0005] Neither of these two approaches adequately distinguished and comprehensively addressed the different characteristics of the two types of uncertainty, resulting in insufficient accuracy in the reliability assessment of the propellant column structure. Summary of the Invention

[0006] In view of the above-mentioned defects or deficiencies in the prior art, it is desirable to provide a reliability assessment method for the structural integrity of solid rocket motor propellant grains.

[0007] This invention provides a reliability assessment method for the structural integrity of a solid rocket motor propellant grain, comprising: S1: Obtain the initial Kriging model; the Kriging model is used to calculate the failure probability of the propellant grain at maximum strain in a solid rocket motor. S2: Initialize or update the first sample pool; the first sample pool contains multiple combinations of geometric parameters of the drug column; S3: Cluster all sample points in the first sample pool to obtain multiple clusters; extract multiple sample points according to the clusters; obtain the first training set based on the multiple sample points; the number of sample points in the first training set is less than the number of sample points in the first sample pool, and is used for training the first Kriging model in this first loop; S4: Train the first Kriging model to be trained using the first training set to obtain the first Kriging model; the first Kriging model to be trained is initially the initial Kriging model, and the subsequent models are the first Kriging models obtained in the previous first loop. S5: If the first kriging model obtained in the first cycle satisfies the first convergence criterion, then proceed to steps S6 to S7; otherwise, repeat the first cycle, including steps S2 to S5. S6: Update the first kriging model based on the current first sample pool to obtain the second kriging model; S7: Calculate the failure probability of the solid rocket motor propellant grain with maximum strain using the second Kriging model.

[0008] According to the technical solution provided by the present invention, obtaining an initial kriging model includes: S1-1: Obtain the distribution function of various geometric parameters of the propellant grain; the geometric parameters of the propellant grain include: star hole depth, corner radius, and propellant grain inner diameter; S1-2: Generate the initial sample pool based on the distribution function of each geometric parameter; S1-3: Construct an initial kriging model using a portion of the sample points in the initial sample pool.

[0009] According to the technical solution provided by the present invention, the method for initially setting or updating the first sample pool is as follows: multiple sample points are extracted from the initial sample pool without repetition using a simple rejection sampling method to form a new first sample pool.

[0010] According to the technical solution provided by the present invention, a first training set is obtained based on multiple sample points, including: For each sample point extracted from the cluster, an interval variable is matched to maximize the model prediction failure probability of the maximum strain of the solid rocket motor propellant grain; the interval variable includes equilibrium modulus, Poisson's ratio, and expansion coefficient. Multiple sample points extracted from the cluster and their corresponding interval variables are input into the first learning function to calculate multiple first learning values; the first learning function is used to assist in selecting sample points that are effective in improving the prediction accuracy of the first Kriging model to be trained. The sample points corresponding to the minimum set number of the first learning values ​​are combined to form the first training set.

[0011] According to the technical solution provided by the present invention, an interval variable is matched for each sample point extracted from the cluster to maximize the model prediction failure probability of the maximum strain of the solid rocket motor propellant grain, including: The first expression for the failure probability of the maximum strain of the solid rocket motor propellant grain for each sample point extracted from the cluster is calculated using the first Kriging model; the first expression contains unknown interval variables; The interval variable that corresponds to each sample point and maximizes the probability of model prediction failure is calculated based on the first expression.

[0012] According to the technical solution provided by the present invention, the first learning function is:

[0013] in, For the first learning function ， e is the natural index. The model predicts the failure probability for the normalized maximum strain of the propellant grain in a solid rocket motor. The standard deviation of the Kriging model's predictions. The minimum normalized distance between new samples added to the Kriging model and the existing training sample set.

[0014] According to the technical solution provided by the present invention, the first convergence criterion is: The average prediction bias of the first Kriging model is less than the first set value, and the number of sample points in the existing training sample set is greater than the second set value.

[0015] According to the technical solution provided by the present invention, updating the first kriging model based on the current first sample pool to obtain the second kriging model includes: S6-1: Initialize or update the first sample pool, and generate new sample points based on the updated first sample pool; S6-2: Use the newly added sample points to train the second kriging model to obtain the second kriging model; the second kriging model to be trained is initially the first kriging model, and then the second kriging model obtained in the previous second loop. S6-3: If the second Kriging model obtained in this second cycle satisfies the second convergence criterion, then proceed to step S7; otherwise, repeat the second cycle, including steps S6-1 to S6-3.

[0016] According to the technical solution provided by the present invention, generating new sample points based on the updated first sample pool includes: Match interval variables for each sample point in the current first sample pool to maximize the model prediction failure probability of the maximum strain of the solid rocket motor propellant grain; Multiple sample points and their corresponding interval variables are input into the second learning function to calculate multiple second learning values; the second learning function is used to assist in selecting effective sample points to improve the prediction accuracy of the second Kriging model to be trained. The sample point corresponding to the smallest second learning value is taken as the new sample point.

[0017] According to the technical solution provided by the present invention, the second learning function is:

[0018] in, m This represents the predicted mean of the Kriging model. Let be the standard deviation of the Kriging model's predictions, and e be the natural index. error This is the deviation index; The minimum normalized distance between newly added sample points in the Kriging model and the existing training sample set.

[0019] The beneficial effects of this invention are as follows: To address the problem of insufficient accuracy in existing solid rocket motor propellant grain reliability assessment methods due to their failure to adequately distinguish and comprehensively handle random and cognitive uncertainties, this invention employs a two-stage adaptive modeling and optimization reliability prediction scheme. This method first constructs an initial training set through clustering and selective sampling to train a first kriging model, which is then iteratively updated to meet convergence conditions. Subsequently, a second kriging model is further trained based on the updated sample pool, ultimately used to calculate the failure probability of the propellant grain at its maximum strain. This invention achieves the coordinated handling of randomness and cognitive uncertainty in the propellant grain structural response by introducing a clustering screening and learning function-guided sample selection mechanism, as well as a two-stage progressive model update strategy. This method significantly reduces computational resource consumption while maintaining prediction accuracy, improving the efficiency and applicability of reliability assessment. It is particularly suitable for the integrity analysis of complex propellant grain structures with multi-source uncertainties, providing more accurate and efficient technical support for the reliability design and life assessment of solid rocket motors. Attached Figure Description

[0020] Other features, objects, and advantages of the invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a flowchart illustrating a reliability assessment method for the structural integrity of a solid rocket motor propellant grain. Detailed Implementation

[0021] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0022] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0023] refer to Figure 1 This invention provides a reliability assessment method for the structural integrity of a solid rocket motor propellant grain, comprising: S1: Obtain the initial Kriging model; the Kriging model is used to calculate the failure probability of the propellant grain at maximum strain in a solid rocket motor. The Kriging model is a surrogate model based on spatial statistics that establishes an approximate functional relationship between input variables and output response using known sample points, and provides a probability distribution estimate of the predicted values. In this invention, the Kriging model is used to construct a mapping relationship between the structural response (maximum strain) of a propellant charge and random geometric parameters and interval material parameters. Through its inherent uncertainty quantification capabilities, it distinguishes and integrates accidental uncertainty and cognitive uncertainty, thereby achieving efficient and high-precision prediction of failure probability. This model is suitable for small-sample, high-dimensional nonlinear problems, providing a mathematical tool for propellant charge reliability analysis that balances accuracy and computational efficiency.

[0024] Specifically, S1 includes: S1-1: Obtain the distribution function of various geometric parameters of the propellant grain; the geometric parameters of the propellant grain include: star hole depth, corner radius, and propellant grain inner diameter; S1-2: Generate the initial sample pool based on the distribution function of each geometric parameter; S1-3: Construct an initial kriging model using a portion of the sample points in the initial sample pool.

[0025] The distribution function is the probability density function, typically a normal distribution, and has different means and standard deviations depending on the type of parameter. Generating an initial sample pool according to the parameter distribution can easily generate a large number of sample points.

[0026] A sample point is a combination of specific values ​​of various geometric parameters of a drug column, and different sample points are combinations of different values ​​of various geometric parameters.

[0027] Using an initial sample pool, which is based on existing technology, an initial surrogate model is trained using the Kriging interpolation method. This establishes an approximate mapping relationship from input parameters to output response and has the ability to quantify prediction uncertainty, providing a reliable iterative starting point and performance evaluation benchmark for subsequent two-stage adaptive optimization.

[0028] S2: Initialize or update the first sample pool (the first sample pool contains only random variables); the first sample pool contains multiple combinations of geometric parameters of the drug column; The first iteration of the first loop is used to initialize the first sample pool; subsequent iterations of the first loop are used to update the first sample pool.

[0029] Furthermore, the method for initially setting up or updating the first sample pool is as follows: multiple sample points are drawn without repetition from the initial sample pool using simple rejection sampling to form a new first sample pool.

[0030] The expression for simple rejection sampling is: Formula 1; in, Indicates the accepting domain, p A uniform distribution ranging from 0 to 1. Represents random variables The failure probability predicted by the Kriging model (in this example, the initial Kriging model is input) is expressed as follows: Formula 2; in, For interval variable sample points, The lower bound of the interval variable The upper bound of the interval variable, The cumulative distribution function value. To predict the mean for the model, This represents the standard deviation of the model's predictions.

[0031] The above method, through variance reduction sampling strategy, significantly reduces the size of the candidate sample pool, thereby greatly reducing the computational cost of subsequent finite element simulations or model calls. By filtering samples based on the model's predicted failure probability, the retained sample points are more concentrated near the failure boundary, improving the efficiency of evaluating low-probability failure events.

[0032] S3: Cluster all sample points in the first sample pool to obtain multiple clusters; extract multiple sample points according to the clusters; obtain the first training set based on the multiple sample points; the number of sample points in the first training set is less than the number of sample points in the first sample pool, and is used for training the first Kriging model in this first loop; Specifically, K-means clustering is applied to the first sample pool to obtain multiple clusters. Then, the distance from each sample point in each cluster to the cluster center is calculated, and the points with the smallest distance from the cluster center are extracted to obtain the first training set.

[0033] Distance from sample point to cluster center in cluster According to formula three, the following is calculated: Formula 3; in, The dimension of the random variable (i.e., the dimension of the sample points; the number of terms with different parameters in a sample point is the dimension of the sample point). Let j be the position of the sample point in the j-th dimension. Let j be the position of the cluster center in the j-th dimension. Let be the shortest interval length with a confidence level of 95% in the j-th dimension.

[0034] Step S3 achieves a reasonable partitioning of the sample space and selection of representative points through clustering screening. While significantly reducing the number of training samples, it maintains the diversity and structural characteristics of the sample distribution, effectively avoids sample redundancy and information overlap, provides a data foundation for the efficient and stable training of the Kriging model, and improves the learning efficiency and generalization ability of the model under limited computing resources.

[0035] Furthermore, the first training set is obtained based on multiple sample points, including: S3-1: Match interval variables to each sample point extracted from the cluster to maximize the model prediction failure probability of the maximum strain of the solid rocket motor propellant grain; the interval variables include equilibrium modulus, Poisson's ratio, and expansion coefficient. Interval variables follow an interval distribution, as shown in Table 1. Table 1. Solid rocket motor propellant grain parameters

[0036] S3-1-1: The first expression for calculating the failure probability of the maximum strain of the solid rocket motor propellant grain for each sample point extracted from the cluster using the first Kriging model; the first expression contains unknown interval variables; S3-1-2: Calculate the interval variable corresponding to each sample point based on the first expression, which maximizes the probability of model prediction failure.

[0037] In this embodiment, the first expression is Formula 2 after substituting the specific values ​​of each parameter represented by the sample points; where only the interval variable and the failure probability are unknown, the interval variable that makes the model predict the failure probability to the maximum value can be calculated.

[0038] In this embodiment, step S3-1-2 achieves targeted optimization of cognitive uncertainty (interval variables) by actively matching each random variable sample point with an interval variable that maximizes the model's predicted failure probability. Its technical effect lies in: actively capturing and quantifying the impact of cognitive parameters such as material properties under the most unfavorable combination, thereby more accurately locating the "most dangerous" region in the mixed uncertainty space, providing crucial risk-oriented information for subsequent learning function selection, and effectively supporting the robust calculation of the upper bound of the failure probability.

[0039] S3-2: Input multiple sample points extracted from the cluster and their corresponding interval variables into the first learning function to calculate multiple first learning values; the first learning function is used to assist in selecting sample points that are effective in improving the prediction accuracy of the first Kriging model to be trained. Furthermore, the first learning function is: Formula 4; in, Let e ​​be the first learning function, and e be the natural exponent. The model predicts the failure probability for the normalized maximum strain of the propellant grain in a solid rocket motor. The standard deviation of the Kriging model's predictions. The minimum normalized distance between newly added samples for the Kriging model and the existing training sample set (the existing training sample set initially refers to a portion of the sample points in the initial sample pool, and the sample points will be gradually added during the first cycle, and the added sample points are the set number of sample points in the first training set generated each time).

[0040] In the specific calculation process, the sample points are input into the Kriging model to obtain the model's predicted failure probability, minimum normalized distance, and the Kriging model's prediction standard deviation, which are then substituted into the first learning function for calculation. The calculation process for the second learning function is similar.

[0041] Specifically, the normalized model for the maximum strain of the propellant grain in a solid rocket motor predicts the failure probability. The calculation method is expressed by Formula 5: Formula 5; in, For sample points The normalized model predicts the failure probability. For sample points The model predicts the failure probability. It is a set consisting of multiple sample points extracted from clusters. For sample pool The highest model prediction failure probability.

[0042] minimum normalized distance Calculated using Formula 5: Formula Six; in, To account for the normalized distance of the variable scale, P For the current stage of the Kriging model's training sample set, for random variables For interval variables, the shortest interval length with a confidence level of 95% is given. The interval length is... n For the dimensions of the variable, Let be the input sample point, and y be a single sample point in the current stage of the Kriging model training sample set. Let j be the j-th sample in the training sample set of the Kriging model at the current stage. To calculate the original distance, To maximize the calculation of the original distance, This represents the number of samples in the first training set.

[0043] In this embodiment, the first learning function integrates prediction uncertainty, failure probability, and spatial distance information, and can proactively identify the sample points most effective in improving the boundary prediction accuracy of the Kriging model. This guidance mechanism achieves a balance between "exploration" and "utilization," efficiently driving the model to converge toward the failure boundary with minimal sample increments, significantly reducing the number of expensive simulations required.

[0044] S3-3: Combine the sample points corresponding to the minimum set number of the first learning values ​​to form the first training set.

[0045] In this embodiment, the number is set to 4. According to experiments, adding 4 sample points with smaller first learning values ​​to the first training set each time can balance training efficiency and training accuracy.

[0046] S4: Train the first Kriging model to be trained using the first training set to obtain the first Kriging model; the first Kriging model to be trained is initially the initial Kriging model, and the subsequent models are the first Kriging models obtained in the previous first loop. S5: If the first kriging model obtained in the first cycle satisfies the first convergence criterion, then proceed to steps S6 to S7; otherwise, repeat the first cycle, including steps S2 to S5. Furthermore, the first convergence criterion is: The average prediction bias of the first Kriging model is less than the first set value, and the number of sample points in the existing training sample set is greater than the second set value.

[0047] In this embodiment, the first setting value is 0.2, and the second setting value is 28.

[0048] The first set value is calculated as follows: Formula 7; in, excursion The first set value, This represents the number of sample points in the first sample pool. For model-predicted failure indication functions, Predict the failure probability for the model.

[0049] Satisfying Formula Eight: Formula 8; Here, else indicates otherwise. This represents the model's predicted mean.

[0050] The first convergence criterion, by setting both an upper limit for the average prediction bias and a lower limit for the minimum sample size, enables intelligent judgment and control of the first-stage model training process. Its technical effect is that, while ensuring the prediction accuracy of the Kriging model, it effectively prevents underfitting or insufficient stability due to insufficient samples. This criterion, as an automatic stopping criterion for the iterative loop, avoids meaningless overtraining, significantly improves the convergence efficiency and reliability of the optimization process, and provides a stable and accurate input foundation for the second-stage model update.

[0051] S6: Update the first kriging model based on the current first sample pool to obtain the second kriging model, including: S6-1: Initialize or update the first sample pool, and generate new sample points based on the updated first sample pool; Furthermore, new sample points are generated based on the updated first sample pool, including: Match interval variables for each sample point in the current first sample pool to maximize the model prediction failure probability of the maximum strain of the solid rocket motor propellant grain; Multiple sample points and their corresponding interval variables are input into the second learning function to calculate multiple second learning values; the second learning function is used to assist in selecting effective sample points to improve the prediction accuracy of the second Kriging model to be trained. The sample point corresponding to the smallest second learning value is taken as the new sample point.

[0052] Furthermore, the second learning function is: Formula Nine; in, m This represents the predicted mean of the Kriging model. Let be the standard deviation of the Kriging model's predictions, and e be the natural index. error This is the deviation index; This represents the minimum normalized distance between the Kriging model's predictions and the actual results.

[0053] Deviation Index error Equation 10 represents: Formula 10; in, It is a symbolic function.

[0054] S6-2: Add the new sample points to the training sample set to obtain the second kriging model; the second kriging model is initially the first kriging model when it is to be trained, and the subsequent model is the second kriging model obtained in the previous second cycle. S6-3: If the second Kriging model obtained in this second cycle satisfies the second convergence criterion, then proceed to step S7; otherwise, repeat the second cycle, including steps S6-1 to S6-3.

[0055] In this embodiment, the second convergence criterion is represented by Formula 11: Formula 11; in, This represents the predicted failure indicator function of the current second Kriging model. This represents the predicted failure indicator function of the second Kriging model in the previous second cycle. This represents the predicted failure indicator function of the second Kriging model for the first two second cycles. The specific value of the predicted failure indicator function can be calculated using Equation 8.

[0056] In this embodiment, step S6, based on the Kriging model and sample pool that converged in the first stage, uses a second learning function to select the most informative sample points from the entire sample pool, constructing more comprehensive new sample points to drive the model for refined learning. The stability of the model's predictions is judged by a second convergence criterion, ensuring that the update process automatically terminates when the prediction results become consistent. The second loop effectively eliminates any prediction fluctuations that may remain from the first loop, significantly improving the robustness and accuracy of the final failure probability calculation, and providing a high-confidence reliability assessment result for engineering decisions.

[0057] S7: Calculate the failure probability of the solid rocket motor propellant grain with maximum strain using the second Kriging model.

[0058] After the Kriging model is constructed, the specific values ​​of the actual geometric parameters of the propellant grain can be substituted into the Kriging model to calculate the failure probability of the maximum strain.

[0059] Based on the above steps, a well-trained high-precision surrogate model is used to replace the expensive finite element simulation, achieving efficient and robust calculation of failure probability. At the same time, by actively searching for the most unfavorable interval variable combination, it is ensured that the reliability assessment results correspond to the most dangerous situation in the project, significantly improving the engineering practicality and conservative reliability of the assessment results, and providing a direct and reliable quantitative basis for the structural safety design and life assessment of solid rocket motor propellant grains.

[0060] The above description is merely a preferred embodiment of the present invention and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention is not limited to the specific combination of the above-described technical features, but also includes other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions disclosed in this invention.

Claims

1. A reliability assessment method for the structural integrity of a solid rocket motor propellant grain, characterized in that, include: S1: Obtain the initial Kriging model; the Kriging model is used to calculate the failure probability of the propellant grain at maximum strain in a solid rocket motor. S2: Initialize or update the first sample pool; the first sample pool contains multiple combinations of geometric parameters of the drug column; S3: Cluster all sample points in the first sample pool to obtain multiple clusters; extract multiple sample points according to the clusters; obtain the first training set based on the multiple sample points; the number of sample points in the first training set is less than the number of sample points in the first sample pool, and is used for training the first Kriging model in this first loop; S4: Train the first Kriging model to be trained using the first training set to obtain the first Kriging model; the first Kriging model to be trained is initially the initial Kriging model, and the subsequent models are the first Kriging models obtained in the previous first loop. S5: If the first kriging model obtained in the first cycle satisfies the first convergence criterion, then proceed to steps S6 to S7; otherwise, repeat the first cycle, including steps S2 to S5. S6: Update the first kriging model based on the current first sample pool to obtain the second kriging model; S7: Calculate the failure probability of the solid rocket motor propellant grain with maximum strain using the second Kriging model.

2. The reliability assessment method for the structural integrity of a solid rocket motor propellant grain according to claim 1, characterized in that, Obtain the initial kriging model, including: S1-1: Obtain the distribution function of various geometric parameters of the propellant grain; the geometric parameters of the propellant grain include: star hole depth, corner radius, and propellant grain inner diameter; S1-2: Generate the initial sample pool based on the distribution function of each geometric parameter; S1-3: Construct an initial kriging model using a portion of the sample points in the initial sample pool.

3. The reliability assessment method for the structural integrity of a solid rocket motor propellant grain according to claim 2, characterized in that, The method for initially setting up or updating the first sample pool is as follows: multiple sample points are drawn from the initial sample pool without repetition using a simple rejection sampling method to form a new first sample pool.

4. The reliability assessment method for the structural integrity of a solid rocket motor propellant grain according to claim 1, characterized in that, The first training set is obtained based on multiple sample points, including: For each sample point extracted from the cluster, an interval variable is matched to maximize the model prediction failure probability of the maximum strain of the solid rocket motor propellant grain; the interval variable includes equilibrium modulus, Poisson's ratio, and expansion coefficient. Multiple sample points extracted from the cluster and their corresponding interval variables are input into the first learning function to calculate multiple first learning values; the first learning function is used to assist in selecting sample points that are effective in improving the prediction accuracy of the first Kriging model to be trained. The sample points corresponding to the minimum set number of the first learning values ​​are combined to form the first training set.

5. The reliability assessment method for the structural integrity of a solid rocket motor propellant grain according to claim 4, characterized in that, For each sample point extracted from the cluster, an interval variable is matched to maximize the model prediction failure probability of the maximum strain of the solid rocket motor propellant grain, including: The first expression for the failure probability of the maximum strain of the solid rocket motor propellant grain for each sample point extracted from the cluster is calculated using the first Kriging model; the first expression contains unknown interval variables; The interval variable that corresponds to each sample point and maximizes the probability of model prediction failure is calculated based on the first expression.

6. The reliability assessment method for the structural integrity of a solid rocket motor propellant grain according to claim 4, characterized in that, The first learning function is: in, For the first learning function ， e is the natural index. The model predicts the failure probability for the normalized maximum strain of the propellant grain in a solid rocket motor. The standard deviation of the Kriging model's predictions. The minimum normalized distance between new samples added to the Kriging model and the existing training sample set.

7. The reliability assessment method for the structural integrity of a solid rocket motor propellant grain according to claim 1, characterized in that, The first convergence criterion is: The average prediction bias of the first Kriging model is less than the first set value, and the number of sample points in the existing training sample set is greater than the second set value.

8. The reliability assessment method for the structural integrity of a solid rocket motor propellant grain according to claim 1, characterized in that, The first kriging model is updated based on the current first sample pool to obtain the second kriging model, including: S6-1: Initialize or update the first sample pool, and generate new sample points based on the updated first sample pool; S6-2: Use the newly added sample points to train the second kriging model to obtain the second kriging model; the second kriging model to be trained is initially the first kriging model, and then the second kriging model obtained in the previous second loop. S6-3: If the second Kriging model obtained in this second cycle satisfies the second convergence criterion, then proceed to step S7; otherwise, repeat the second cycle, including steps S6-1 to S6-3.

9. The reliability assessment method for the structural integrity of a solid rocket motor propellant grain according to claim 8, characterized in that, New sample points are generated based on the updated first sample pool, including: Match interval variables for each sample point in the current first sample pool to maximize the model prediction failure probability of the maximum strain of the solid rocket motor propellant grain; Multiple sample points and their corresponding interval variables are input into the second learning function to calculate multiple second learning values; the second learning function is used to assist in selecting effective sample points to improve the prediction accuracy of the second Kriging model to be trained. The sample point corresponding to the smallest second learning value is taken as the new sample point.

10. A reliability assessment method for the structural integrity of a solid rocket motor propellant grain according to claim 9, characterized in that, The second learning function is: in, μ This represents the predicted mean of the Kriging model. Let be the standard deviation of the Kriging model's predictions, and e be the natural index. error This is the deviation index; The minimum normalized distance between newly added sample points in the Kriging model and the existing training sample set.

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