A Ship Reliability Assessment Method Based on Importance Sampling Method

Abstract

The present invention provides a ship reliability assessment method based on an important sampling method, which determines an initial proposed distribution, extracts samples from it, and calculates initial weights. According to previous samples and parameters, the proposed distribution is updated, and for each iterative step, samples are extracted from the updated proposed distribution. The weights of new samples are calculated by combining the weights of all previous proposed distributions, and then the mean of all estimated values ​​is taken as an unbiased estimate of the parameters to be estimated, so as to realize the assessment of ship reliability parameters. The adaptive multiple weighted important sampling method of the present method gradually adjusts the proposed distribution to make it closer to the target distribution, and distributes the error of a single important sampling to multiple sampling processes, and uses historically generated samples and weights to improve the stability and accuracy of the estimation. This adaptive sampling method not only solves the problem of the difficulty of constructing the proposed distribution, but also effectively reduces the variance and error of the estimation, which is an effective improvement on the traditional important sampling method.

Description

Technical Field

[0001] The present invention relates to the field of ship equipment, and more specifically, to a ship reliability assessment method based on an importance sampling method. Background Art

[0002] The form of the posterior distribution is relatively complex, and it is difficult to calculate directly through analytical methods. The Monte Carlo (MC) method approximates the complex distribution through numerical simulation, which enables effective parameter evaluation of the posterior distribution. In addition, for some problems, the analytical method may encounter data instability problems such as calculation overflow. The MC method can reduce the instability of numerical calculations based on the statistical properties of a large number of samples.

[0003] There are many sampling methods for MC simulation. Some scholars have pointed out that the importance sampling method has better sampling efficiency than other sampling methods. However, the importance sampling method has a proposed distribution The problem of constructing difficulties and how to further reduce the error of the important sampling method are also issues that need to be studied. Summary of the invention

[0004] In view of the technical problems existing in the prior art, the present invention provides a ship reliability assessment method based on an important sampling method, comprising:

[0005] Step 1: Construct the initial proposed distribution of ship reliability parameters based on Gaussian mixture distribution GMM , extract from Samples , and calculate the initial weight value of each sample , the ship reliability parameters include the life of ship spare parts;

[0006] Step 2: Update the initial proposal distribution based on the expectation maximization EM method Parameters of , get the updated proposal distribution ;

[0007] Step 3: In the tth iteration, from the proposal distribution Extract Samples , calculate the weight value of each sample , ;

[0008] Step 4, repeat steps 2 and 3 to iterate until the iteration termination condition is met, and then terminate the iteration;

[0009] Step 5: Based on the samples extracted from all iterations and the sample weight values, the posterior expected value of the proposed distribution is estimated to evaluate the reliability parameters of the ship.

[0010] The present invention provides a ship reliability assessment method based on an important sampling method. First, the initial proposed distribution of ship reliability parameters is constructed. Then, an adaptive multiple weighted important sampling method is used to gradually adjust the proposed distribution to make it closer to the target distribution. The error of a single important sampling is distributed to multiple sampling processes. The historically generated samples and weights are used to improve the stability and accuracy of the estimation. This adaptive sampling method not only solves the problem of the difficulty in constructing the proposed distribution, but also effectively reduces the variance and error of the estimation, which is an effective improvement on the traditional important sampling method. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 Schematic diagram of the posterior evaluation of the adaptive multi-weighted importance sampling method;

[0012] Figure 2 A flow chart of a ship reliability assessment method based on an important sampling method provided by the present invention;

[0013] Figure 3 This is the overall flow chart of the ship reliability assessment method based on the importance sampling method. DETAILED DESCRIPTION

[0014] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. In addition, the technical features in the various embodiments or single embodiments provided by the present invention can be arbitrarily combined with each other to form a feasible technical solution. This combination is not subject to the constraints of the sequence of steps and / or the structural composition mode, but must be based on the ability of ordinary technicians in this field to achieve. When the combination of technical solutions is contradictory or cannot be achieved, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0015] Aiming at the problems in the background technology, for the reliability parameters of ships, it is considered to use Gaussian Mixture Model (GMM) to construct the initial proposal distribution, and use expectation maximization (EM) to optimize the GMM parameters and update the proposal distribution. Through this adaptive method, the constructed proposal distribution is close to the optimal proposal distribution, and the multiple weighted idea is introduced to distribute the error to the multiple sampling process, thereby reducing the overall error, and finally realizing the estimation of ship reliability parameters, such as the evaluation of the life of ship spare parts, or the estimation of the failure rate index of ship spare parts.

[0016] The present invention uses Gaussian distribution as the proposed distribution, but a single Gaussian distribution can only describe a unimodal and symmetrical distribution. For a posterior distribution with complexity, a single Gaussian distribution is usually not able to effectively describe it. Therefore, for the proposed distribution, a mixed Gaussian distribution (Gaussian Mixture Model, GMM) composed of a weighted sum of multiple Gaussian components is considered, and its expression is:

[0017] (1);

[0018] in, is the number of components of GMM, indicating that the mixed Gaussian distribution is composed of Gaussian distribution weighted sum, For the proposed distribution The weight of the Gaussian components, also called the mixing coefficient, and Respectively The mean and variance of a Gaussian distribution.

[0019] From formula (1), we can see that the Gaussian mixture model GMM can better describe the complex, multimodal, and asymmetric target posterior distribution through the combination of multiple weighted Gaussian distributions, and can more accurately approximate the target distribution, thereby improving the efficiency and accuracy of important sampling. Although the mixed Gaussian distribution model can better represent the target posterior distribution than the single Gaussian distribution model, its optimal proposal distribution still has a certain gap in reducing the estimation variance. In order to make the mixed Gaussian proposal distribution model closer to the optimal proposal distribution, it is considered to use historical sampling samples and weights to update the parameters of the mixed Gaussian proposal distribution, so that the proposal distribution gradually approaches the target posterior distribution, thereby improving the accuracy of the estimation.

[0020] See also Figure 1 , the basic idea of ​​posterior evaluation based on adaptive multi-weighted importance sampling is:

[0021] Constructing the initial proposed distribution of ship reliability parameters based on Gaussian mixture model GMM , and extract from it Samples , and calculate the initial weight of each sample . Update the proposed distribution based on previous samples and parameters , For each iteration step, and from the updated proposal distribution Extract Samples , combined with the weights of all previous proposed distributions, calculate the weight of the new sample , and then take the mean of all estimated values ​​as the unbiased estimate of the parameter to be estimated.

[0022] See also Figure 2 , provides a ship reliability assessment method based on the importance sampling method, see Figure 2 and Figure 3 , the method mainly includes the following steps:

[0023] Step 1: Construct the initial proposed distribution of ship reliability parameters based on Gaussian mixture distribution GMM , extract from Samples , and calculate the initial weight value of each sample .

[0024] Among them, for ship reliability parameters, such as the life of ship spare parts and the stability of ship spare parts, the initial proposed distribution is constructed based on the Gaussian mixture distribution GMM composed of the weighted sum of multiple Gaussian components , whose expression is:

[0025] (2);

[0026] in, is the number of components of GMM, indicating that the mixed Gaussian distribution is composed of Gaussian distribution weighted sum, The initial proposed distribution No. The weight of the Gaussian components, also called the mixing coefficient, and They are the initial proposal distributions No. The mean and variance of a Gaussian distribution.

[0027] From the initial proposal distribution Extract Samples Then calculate the sample weight, the initial sample weight The calculation method is:

[0028] (3);

[0029] in, is the initial target posterior distribution The i-th sample distribution of The initial proposed distribution The i-th sample distribution of .

[0030] Step 2: Update the initial proposal distribution based on the expectation maximization EM method Parameters of , get the updated proposal distribution .

[0031] Among them, after constructing the initial proposal distribution, the parameters of the initial proposal distribution are updated. For the proposal distribution generated in each iteration, the expectation maximization EM algorithm is used to update the proposal distribution parameters: mixing coefficient , mean and variance Update and obtain the proposed distribution for the next iteration.

[0032] The parameters of the proposed distribution are updated using historical sampling samples and weights, so that the mixed Gaussian proposal distribution model is closer to the optimal proposal distribution and gradually approaches the target posterior distribution. For this type of iterative parameter estimation problem, the EM algorithm (Expectation-Maximization) is widely used in this field, especially in problems involving mixed models, hidden Markov models and Gaussian mixture models, the effect of the EM algorithm is more significant. The present invention uses the EM algorithm to estimate the parameters of GMM: , and , updating the proposal distribution in each iteration.

[0033] The EM algorithm consists of two main steps: the expectation step (E-step) and the maximization step (M-step). In each iteration, these two steps are performed alternately until the parameters converge.

[0034] The basic steps for updating the proposal distribution using the EM algorithm are as follows:

[0035] (1) Initialization parameters. Initialize GMM parameters, GMM parameters: mixing coefficient , mean and variance .

[0036] (2) Expectation step (E-step). In the expectation step, the “responsibilities” of each sample belonging to each Gaussian component under the current parameters are calculated, which represents the probability that a given sample belongs to a certain component. Samples ,Element Responsibility Calculated as:

[0037] (4);

[0038] in It is The probability density function of the Gaussian components is:

[0039] (5);

[0040] (3) Maximization step (M-step): In the maximization step, the “responsibility” calculated in the expectation step is used to re-estimate the parameters of the GMM.

[0041] Mixing coefficient Updated to:

[0042] (6);

[0043] in It is The number of effective samples of each component is is the number of samples drawn from the proposal distribution at each iteration.

[0044] Mean Updated to:

[0045] (7);

[0046] variance Updated to:

[0047] (8).

[0048] Step 3: In the tth iteration, from the proposal distribution Extract Samples , calculate the weight value of each sample , .

[0049] It is understandable that, in each iteration process, after the parameters of the proposed distribution are updated to obtain the proposed distribution of the next iteration, it is determined whether the iterative process meets the iteration termination condition.

[0050] The iteration termination condition is that the number of iterations reaches the maximum number of iterations T or the parameters of the proposed distribution converge; judging whether the parameters of the proposed distribution converge, including: comparing whether the maximum absolute difference of the parameters of the proposed distribution before and after each iterative update is less than a preset tolerance tol, if so, the parameters of the proposed distribution converge; if not, the parameters of the proposed distribution do not converge.

[0051] It is understandable that if the current number of iterations has not reached the maximum number of iterations T, but the parameters of the proposed distribution have converged, the iteration process is terminated in advance to obtain the optimal proposed distribution. If the parameters of the proposed distribution corresponding to the current number of iterations have not converged, then the iteration continues until the number of iterations reaches the maximum number of iterations T. At this time, regardless of whether the parameters of the proposed distribution of the Tth iteration have converged, the iteration process is terminated to obtain the optimal proposed distribution.

[0052] In each iteration, a certain number of samples are drawn from the proposed distribution and the weight value of each sample is calculated. For example, in the tth iteration, Extract Samples , calculate the weight value of each sample , ,include:

[0053] Based on all the proposal distributions from the 1st iteration to the tth iteration , calculate the weight of each sample extracted in the tth iteration , which is calculated as:

[0054] ;

[0055] in, is the target posterior distribution in the tth iteration The i-th sample distribution of Propose distribution for the jth iteration The i-th sample distribution of .

[0056] Step 4: Repeat steps 2 and 3 to iterate until the iteration termination condition is met.

[0057] It can be understood that the iterative process is repeated. In each iteration, a certain number of samples are extracted from the proposed distribution of this iteration, and the weight value of each sample is calculated. Based on the extracted samples, the parameters of the proposed distribution are updated, and the iteration is continued until the iteration termination condition is met to obtain the optimal proposed distribution.

[0058] Step 5: Based on the samples extracted in all iterations and the sample weight values, the posterior expected value of the proposed distribution is estimated to evaluate the reliability parameters of the ship spare parts.

[0059] After the iteration is completed, the expected value of the posterior distribution is estimated based on the samples and sample weights extracted in each iteration. , which is the evaluation value of the reliability parameters of ship spare parts:

[0060] ;

[0061] Where T is the number of the last iteration, is the number of samples drawn in the jth iteration, the function For sample to the reliability parameters, is the reliability parameter of the i-th sample in the j-th iteration. is the ship life sample, then the ship life index is , for the exponential distribution, the ship failure rate index is .

[0062] It is understandable that the above method can be used to evaluate the reliability parameters of the ship, such as the life and stability of the ship's spare parts. The life and stability of the ship's spare parts can be calculated based on the iteration of the proposed distribution.

[0063] The present invention provides a ship reliability assessment method based on an important sampling method, which uses a mixed Gaussian distribution to construct an initial proposed distribution of the ship's reliability parameters, and uses an adaptive multiple weighted important sampling method to gradually adjust the proposed distribution to make it closer to the target distribution, and distributes the error of a single important sampling to multiple sampling processes, and uses historically generated samples and weights to improve the stability and accuracy of the estimation, thereby improving the assessment accuracy of the reliability parameters of ship spare parts. This adaptive sampling method not only solves the problem of the difficulty of constructing the proposed distribution, but also effectively reduces the variance and error of the estimation, and is an effective improvement on the traditional important sampling method.

[0064] It should be noted that in the above embodiments, the description of each embodiment has its own emphasis, and for parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0065] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0066] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A ship reliability assessment method based on importance sampling method, characterized in that: include: Step 1: Construct the initial proposed distribution of ship reliability parameters based on Gaussian mixture model GMM , extract from Samples , and calculate the initial weight value of each sample , the ship reliability parameters include the life of ship spare parts; Step 2: Update the initial proposal distribution based on the expectation maximization EM method Parameters of , get the updated proposal distribution ; Step 3: In the tth iteration, from the proposal distribution Extract Samples , calculate the weight value of each sample , ; Step 4, repeat steps 2 and 3 to iterate until the iteration termination condition is met, and then terminate the iteration; Step 5: Based on the samples extracted from all iterations and the sample weight values, the posterior expected value of the proposed distribution is estimated to evaluate the reliability parameters of the ship; The step 1 is to construct an initial proposed distribution of ship reliability parameters based on the Gaussian mixture model GMM ,include: Construct the initial proposal distribution based on the Gaussian mixture model GMM composed of multiple Gaussian components weighted and composed , whose expression is: ； in, is the number of components of GMM, indicating that the mixed Gaussian distribution is composed of Gaussian distribution weighted sum, The initial proposed distribution No. The weight of the Gaussian components, also called the mixing coefficient, and They are the initial proposal distributions No. The mean and variance of a Gaussian distribution; In each iteration, the parameters of the proposed distribution of this iteration are updated based on the expectation maximization EM method, including: In the expectation step, we compute the probability of sampling from the proposal distribution The responsibility of each sample of samples belonging to each Gaussian component represents the probability that a given sample belongs to a given Gaussian component. Samples ,Element Responsibility Calculated as: ； in It is The probability density function of the Gaussian components is: ； In the maximization step, the parameters of the GMM are re-estimated using the "responsibility" calculated in the expectation step, where: Mixing coefficient Updated to: ； in It is The number of effective samples of each component, is the number of samples drawn in each iteration; Mean Updated to: ； variance Updated to: 。 2. The ship reliability assessment method according to claim 1, characterized in that: In step 1, the initial weight value of each sample is calculated ,include: ； in, is the initial target posterior distribution The i-th sample distribution of The initial proposed distribution The i-th sample distribution of , i=1,2,...,N1.

3. The ship reliability assessment method according to claim 1, characterized in that: In step 3, in the tth iteration, from the proposal distribution Extract Samples , calculate the weight value of each sample , ,include: Based on all the proposal distributions from the 1st iteration to the tth iteration , calculate the weight of each sample extracted in the tth iteration , which is calculated as: ； in, The target posterior distribution at iteration t The i-th sample distribution of Propose distribution for the jth iteration The i-th sample distribution of .

4. The ship reliability assessment method according to claim 1, characterized in that: The method further comprises: After each iteration, determine whether the current iteration meets the iteration termination condition, where the iteration termination condition is that the number of iterations reaches the maximum number of iterations or the parameters of the proposed distribution converge; Determine whether the parameters of the proposed distribution converge, including: By comparing whether the maximum absolute difference of the parameters of the proposed distribution before and after each iterative update is less than the preset tolerance tol, if so, the parameters of the proposed distribution converge; if not, the parameters of the proposed distribution do not converge.

5. The ship reliability assessment method according to claim 1, characterized in that: The step 5 estimates the posterior expected value of the proposed distribution based on the samples extracted in all iterations and the sample weight values, and evaluates the reliability parameters of the ship, including: After the iteration is completed, the expected value is estimated based on the samples and sample weights extracted in each iteration : ； Where T is the number of the last iteration, is the number of samples drawn in the jth iteration, the function For sample to the reliability parameters, is the reliability parameter of the i-th sample in the j-th iteration.

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