Improved maximum entropy method for maximum a posteriori ship wave load reliability analysis

Abstract

The present invention discloses a maximum a posteriori ship wave load reliability analysis method of an improved maximum entropy method, which belongs to the technical field of ship wave load response and reliability assessment, including obtaining a function function of a ship profile load response, and obtaining variables and their distribution information that affect the function function of the ship profile load response; initially extracting a small number of samples based on a Sobol sequence in a sampling space to form a training set, and obtaining function values ​​according to the training set; on the basis of the training set, using a Gaussian random process, a neural network and other proxy model methods to construct a proxy model. The present invention uses the maximum a posteriori and proxy model methods, uses the proxy model method to obtain the mapping relationship of the function function, and uses the mapping relationship as a priori information based on the maximum a posteriori framework, effectively alleviating the problem that the prediction accuracy of the traditional integer-order moment maximum entropy method is not high due to insufficient information, thereby reducing the amount of function function calculation and improving the calculation accuracy.

Description

Technical Field

[0001] The invention belongs to the technical field of ship wave load response and reliability evaluation, and in particular relates to a maximum a posteriori ship wave load reliability analysis method with an improved maximum entropy method. Background Art

[0002] With the development of global trade, the safety and economy of ships sailing in the waves have attracted more and more attention. When ships sail in the sea, due to the non-straight side and large flared structure of the ship, slamming is prone to occur at high speed or high sea conditions, causing severe cross-sectional loads on the hull. In extreme sea conditions, the ship may even break, causing huge losses of life and property. Therefore, it is of great significance to accurately predict the wave loads of ships. In actual calculations, considering that the viscous flow theory requires a high calculation cost to predict the wave loads of ships, the potential flow theory is generally used to quickly predict the movement of ships. The deviation between the wave forecast and the actual sea conditions, the deviation between the ship structure size, and the material properties and theoretical properties indicate that there are many uncertain factors in the actual navigation of ships. The existing deterministic methods can only analyze the ship wave loads under certain sea conditions, but cannot reflect the characteristics of the ship wave loads under uncertain factors. For this reason, the influence of uncertain factors such as wave forecast, structure size, and material properties on the ship's motion posture is considered. However, there are many uncertain factors, and even if the potential flow theory is used for Monte Carlo simulation, it will take a lot of time and money. Therefore, using small sample information of ship wave loads to conduct overall reliability assessment has become a key issue in the current reliability analysis of ship wave loads.

[0003] At present, the reliability analysis field is mainly divided into random simulation method, approximate analysis method, proxy model method and moment method of reliability analysis. The representative method of random simulation method is Monte Carlo simulation method (MCS), which ensures the accuracy of calculation through a large number of random sampling. Therefore, although it can robustly estimate the reliability probability, it is difficult to afford the cost of test or calculation simulation in actual engineering problems. For this reason, approximate analysis method is proposed, represented by first-order reliability method and second-order reliability method, which analyzes reliability problems by calculating the maximum possible point and improves the calculation efficiency. However, for problems with strong nonlinearity, high dimension and multiple maximum possible points, the approximate analysis method represented by first-order reliability method and second-order reliability method has the problem of low accuracy. Due to the above problems of random simulation method and approximate analysis method, it is necessary to develop more new reliability analysis methods, among which the proxy model method has gradually become the mainstream of current research. The proxy model method uses a small number of samples and a black box model to fit the mapping relationship between the input and output of the actual function, thereby establishing a "proxy model" with less calculation to estimate the actual complex model. Currently, the more commonly used ones are polynomial response surface, artificial neural network, support vector machine, polynomial chaos expansion, Kriging model, etc. The moment method reconstructs the distribution of the limit state function by taking statistics as constraints, obtains the required probability density function, and then obtains the reliability probability. Commonly used parameterized models include Pearson system, Hermite model, saddle point estimation method, Johnson system and maximum entropy model. The maximum entropy method can avoid the use of false information, and is therefore regarded as the most unbiased estimation method for constructing probability density functions. However, it is difficult for the integer-order moment maximum entropy method to obtain high-precision results under the premise of small samples.

[0004] For the reliability analysis of ship wave loads using the integer-order maximum entropy method under small samples, it is necessary to mine more information. Effective information mining can improve the estimation accuracy of the reliability of ship wave loads using the integer-order maximum entropy method. Therefore, a maximum a posteriori ship wave load reliability analysis method with improved maximum entropy method is proposed. Through the surrogate model method, the input-output mapping relationship of the actual function function can be obtained under small samples as the prior information for the reliability analysis of ship wave loads. Based on the maximum a posteriori theory, the prior information of the mapping relationship is introduced, and the real small sample data is used as the likelihood information. The final probability density function is obtained through statistical inference, which is of great significance, especially in the field of ship wave load reliability analysis with small samples. Summary of the invention

[0005] The purpose of the present invention is to propose a maximum a posteriori ship wave load reliability analysis method based on an improved maximum entropy method, so as to achieve high-efficiency and high-precision estimation of the ship wave load reliability.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] The maximum a posteriori ship wave load reliability analysis method based on the improved maximum entropy method includes the following steps:

[0008] Step 1: Determine the functional functions and variables of the structure;

[0009] Step 2: Use the surrogate model method to obtain the potential mapping relationship between variables and responses;

[0010] Step 3: Use the integer-order moment maximum entropy method to further mine the prior information of the input-output mapping relationship hidden in the proxy model;

[0011] Step 4: Use the error discrimination formula to set the standard deviation of the prior distribution parameters;

[0012] Step 5: Use the maximum a posteriori method to obtain the final structural response probability density distribution and failure probability.

[0013] As a further description of the above technical solution: the step 1 specifically includes:

[0014] (1.1) Determine the variables that affect the ship's wave load response, such as ship mass distribution, speed, and wave conditions, based on design and analysis requirements;

[0015] (1.2) Using nonlinear potential flow theory to obtain the functional function corresponding to the ship wave load response , and obtain the variables that affect the function of the ship's wave load response and its distribution information, where represents a random variable, A function representing the response to wave loads.

[0016] As a further description of the above technical solution: the step 2 specifically includes:

[0017] (2.1) The sampling space obtained in step 1 using the Sobol sequence sampling method or other low-discrepancy sequence sampling methods Internal extraction A small number of samples constitute the training set , where space Variables that represent the function that affects the response of ships to wave loads space, training set Represented as the sampling space The set of combinations of random variables drawn from ;

[0018] (2.2) According to the performance function obtained in step 1 , get the training set The corresponding response value of the ship wave load function On this basis, we use Gaussian random process and based on the training set and the corresponding response value Building a proxy model , is the wave load response value of the training set;

[0019] (2.3) Using the Monte Carlo simulation method, in the variable space Extract Samples form the Monte Carlo sample set , and adopt the constructed proxy model generate The corresponding predicted response value ,in Represented as from variable space A set of samples randomly selected from the set can have a large sample size and can obtain a probability distribution that is statistically significant and can effectively approximate the structural response.

[0020] As a further description of the above technical solution: the step three specifically includes:

[0021] (3.1) The predicted value obtained in step 2 is calculated based on the integer-order moment maximum entropy method Perform probability distribution fitting to obtain predicted values Corresponding predicted probability density function ;

[0022] (3.2) Based on the predicted probability density function , obtain the mean of the prior information about the mapping relationship hidden in the proxy model ,in is the normalization parameter of the predicted probability density function, is the Lagrange multiplier that constitutes the predicted probability density function, .

[0023] As a further description of the above technical solution: the step 4 specifically includes:

[0024] (4.1) Setting prior information It obeys the normal distribution. Based on the mean of the prior information distribution obtained in step 3, the standard deviation of the distribution parameter is further obtained through the error discrimination formula to obtain the prior information The distribution of ;

[0025] (4.2) The wave load response values ​​of the training set based on the integer-order moment maximum entropy method Perform probability distribution fitting and obtain The corresponding probability density function ;

[0026] (4.3) Compare the training response values ​​obtained And step three to get the predicted , the difference between the two is obtained by the error discrimination formula , and ,in It is prior information The standard deviation of .

[0027] As a further description of the above technical solution: the step five specifically includes:

[0028] (5.1) Based on the maximum a posteriori method, construct the target optimization function considering the maximum a posteriori, and use the mean of the prior information obtained in step 4 and standard deviation And the training set wave load response value of step 2 As input parameters, the Lagrange multiplier that minimizes the maximum a posteriori objective optimization function is solved. ,in ;

[0029] (5.2) According to the maximum a posteriori Lagrange multiplier Construct the final probability density function and the probability distribution function , obtain the probability of extreme ship motion , the whole calculation process ends, where .

[0030] As a further description of the above technical solution: the method is divided into four stages, namely, a proxy model construction stage, a priori information mean acquisition stage, an error discrimination formula stage, and a maximum a posteriori stage, wherein the proxy model construction stage includes steps one and two; the priori information acquisition stage includes step three; the error discrimination formula stage includes step four; the maximum a posteriori stage includes step five, wherein the step one acquires a functional function, that is, through a program, automatically modifies the variables that affect the ship wave load response, forms an input parameter file required by the software, automatically calls a commercial software calculation program, and finally passes the results calculated by the software to the ship wave load reliability analysis program of steps three to five.

[0031] As a further description of the above technical solution: the specific formula of the integer-order moment maximum entropy method in step 2 and step 3 can be written as: ,in is the response value, is the normalization parameter of the probability density function, is the Lagrange multiplier of the probability density function, is the order of the moment, is the total number of moments, and , .

[0032] As a further description of the above technical solution: the specific formula of the error discrimination formula in step 4 is as follows:

[0033] ;

[0034] in is the total number of discretized probability density function values, is the predicted probability density function, is the probability density function corresponding to the training set response, The index corresponding to the function value of the discretized probability density function.

[0035] As a further description of the above technical solution: the maximum a posteriori objective optimization function obtained in step 5 is specifically expressed as:

[0036] ;

[0037] in is the total number of response values, is the total number of moments, is the response value, is the Lagrange multiplier, is the order of the moment, and , is the mean of the prior information, is the standard deviation of the prior information, is the index corresponding to the response value of the function, The index corresponding to the order value of the moment.

[0038] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0039] 1. The present invention uses Sobol sequence in the variable adoption space Generate candidate sample points to ensure that the candidate sample points are in the sampling space Uniform distribution: Uniformly distributed candidate sample points effectively avoid the problem of sparse sample points in low probability areas and high crowding of candidate sample points in high probability areas, which leads to poor accuracy of the constructed proxy model.

[0040] 2. The present invention introduces a proxy model method to establish a mapping relationship between the input and output of the function, thereby providing a way to obtain more prior information under small sample conditions. Traditional methods are usually difficult to fully utilize prior information under small sample conditions. However, the present invention combines the maximum a posteriori method to accurately process the input-output mapping relationship introduced in the proxy model. By optimizing the training set response The constructed likelihood function and the regularization term constructed by the mapping prior information can be used to obtain the probability density function that takes into account the mapping prior information. This process significantly improves the calculation accuracy of the integer-order maximum entropy method and greatly improves the processing ability of small samples and complex mapping relationships compared to traditional methods.

[0041] 3. The present invention constructs an error discrimination formula, which automatically sets the standard deviation of the prior parameters by estimating the difference between the probability density function predicted by the estimated proxy model and the probability density function predicted by the estimated initial sample points, effectively considering the weight of the prior information and ensuring the accuracy of the optimization process as much as possible. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 A flow chart of the maximum a posteriori ship wave load reliability analysis method of the improved maximum entropy method proposed in the present invention;

[0043] Figure 2 Schematic diagram of an undamped single-degree-of-freedom oscillation system in Example 1 of the present invention;

[0044] Figure 3 : is a comparison diagram of the probability density function PDF of the method of the present invention and the typical method in Example 1 of the present invention;

[0045] Figure 4 A comparison diagram of the probability distribution function CDF of the method of the present invention and the typical method in Example 1 of the present invention;

[0046] Figure 5 This is a schematic diagram of a panel model of a ship sailing in waves in Example 2 of the present invention;

[0047] Figure 6 : is a comparison diagram of the probability density function PDF of the method of the present invention and the typical method in Example 2 of the present invention;

[0048] Figure 7 4 is a comparison diagram of the probability distribution function CDF of the method of the present invention and the typical method in Example 2 of the present invention. DETAILED DESCRIPTION

[0049] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in 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. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0050] Please see attached Figure 1 -Attached Figure 7The present invention provides a technical solution: a maximum entropy ship motion reliability analysis method based on maximum a posteriori and proxy model comprises the following steps:

[0051] Step 1: Determine the functional functions and variables of the structure;

[0052] 1.1 According to the design and analysis requirements, the variables affecting the ship's wave load response are determined, such as ship mass distribution, speed and wave conditions. The variables affecting the ship's wave load response can be expressed as: ,in, ;and Dimension expressed as a function of the ship's wave load;

[0053] 1.2 Using nonlinear potential flow theory to obtain the functional function corresponding to the ship wave load response , and obtain the variables that affect the function of the ship's wave load response and its distribution information, where represents a random variable, A function representing the response to wave loads;

[0054] Step 2: Use the surrogate model method to obtain the potential mapping relationship between variables and responses;

[0055] 2.1 The sampling space obtained in step 1 using the Sobol sequence sampling method or other low-discrepancy sequence sampling methods Internal extraction A small number of samples constitute the training set ;

[0056] The sampling space Variables that represent the function that affects the response of ships to wave loads The space can be expressed as ,and Expressed as the joint probability density function of the variables The inverse function of Represented as a variable The amount The marginal probability density function of The inverse function of Expressed as the cumulative probability density function of the normal distribution, the training set Represented as from variable space The set of combinations of random variables drawn from .

[0057] 2.2 Functional function obtained according to step 1 , get the training set The corresponding response value of the ship wave load function On this basis, we use Gaussian random process and based on the training set and the corresponding response value Building a proxy model , is the wave load response value of the training set;

[0058] 2.3 Using the Monte Carlo simulation method, in the variable space Extract Samples form the Monte Carlo sample set , and adopt the constructed proxy model generate The corresponding predicted response value ,in It is represented as a set of samples randomly drawn from the variable space. The sample size is large, and a probability distribution that is statistically significant and can effectively approximate the structural response can be obtained.

[0059] Step 3: Use the integer-order moment maximum entropy method to further mine the prior information of the input-output mapping relationship hidden in the proxy model;

[0060] 3.1 Prediction of the value obtained in step 2 based on the maximum entropy method of integer moments Perform probability distribution fitting to obtain predicted values Corresponding predicted probability density function ;

[0061] The integer-order moment maximum entropy method used can be expressed as: ;

[0062] , is the functional response value of the ship wave load response, , is the coefficient of the integer-order maximum entropy method, is the order of the moment, is the total number of moments, and , .

[0063] 3.2 Based on the predicted probability density function , obtain the mean of the prior information about the mapping relationship hidden in the proxy model ,in is the normalization parameter of the predicted probability density function, is the Lagrange multiplier that constitutes the predicted probability density function, ;

[0064] Step 4: Use the error discrimination formula to set the standard deviation of the prior distribution parameters;

[0065] 4.1 Setting Prior Information It obeys the normal distribution. Based on the mean of the prior information distribution obtained in step 3, the standard deviation of the distribution parameter is further obtained through the error discrimination formula to obtain the prior information The distribution of ;

[0066] 4.2 Analysis of wave load response values ​​of training set based on integer-order moment maximum entropy method Perform probability distribution fitting and obtain The corresponding probability density function ;

[0067] 4.3 Comparison of training response values ​​obtained And step three to get the predicted , the difference between the two is obtained by the error discrimination formula , and ,in It is prior information The standard deviation of ;

[0068] The error discrimination formula is expressed as: ,in is the total number of discretized probability density function values, is the predicted probability density function, is the probability density function corresponding to the training set response, is the index corresponding to the function value of the discretized probability density function;

[0069] Step 5: Use the maximum a posteriori method to obtain the final sample distribution and failure probability;

[0070] 5.1 Based on the maximum a posteriori method, construct the target optimization function considering the maximum a posteriori, and use the mean of the prior information obtained in step 4 and standard deviation And the training set wave load response value of step 2 As an input parameter, the Lagrange multiplier that minimizes the maximum a posteriori objective optimization function is solved. ,in .

[0071] The maximum a posteriori objective optimization function is specifically expressed as:

[0072] ;

[0073] in is the total number of response values, is the total number of moments, is the response value, is the Lagrange multiplier, is the order of the moment, and , is the mean of the prior information, is the standard deviation of the prior information, is the index corresponding to the response value of the function, The index corresponding to the order value of the moment.

[0074] 5.2 Lagrange multipliers obtained from maximum a posteriori Construct the final probability density function and the probability distribution function , obtain the probability of extreme ship motion , the whole calculation process ends.

[0075] Among them, the typical method is the integer-order moment maximum entropy method, which is a general technology and will not be described in detail here.

[0076] Embodiment 1:

[0077] This embodiment 1 further illustrates the present invention by taking an undamped single-degree-of-freedom oscillation system as an example. Figure 2 As shown, this example is a common engineering example in the field of reliability analysis.

[0078] Step 1: Determine the functional functions and variables of the structure;

[0079] 1.1According to the design and analysis requirements, obtain the variables that affect the functional functions and its distribution,

[0080] ,in, ;and Dimensions expressed as a function of events;

[0081] In this embodiment, the random variable is expressed as , with a dimension of 6, where represents the mass of the slider of the oscillator system, and is expressed as the elastic stiffness of the spring of the oscillator system, It represents the resistance of the oscillator system. represents the magnitude of the force on the oscillator system, The time that represents the force on the oscillator system.

[0082] In this embodiment, the distribution information of all variables is as shown in Table 1 below:

[0083] Table 1 Distribution of variables in Example 1

[0084]

[0085] 1.2 Use mechanical theory or finite element simulation methods to obtain the functional function of the required analysis structure.

[0086] In this embodiment 1, the functional function of the structure is expressed as:

[0087] ;

[0088] in ;

[0089] Step 2: Use the surrogate model method to obtain the potential mapping relationship between variables and responses;

[0090] 2.1 The sampling space obtained in step 1 using the Sobol sequence sampling method or other low-discrepancy sequence sampling methods Internal extraction A small number of samples constitute the training set ;

[0091] Among them, sampling Indicates the variables that affect the function The set of can be expressed as ,and Expressed as the joint probability density function of the variables The inverse function of Represented as a variable The amount The marginal probability density function of The inverse function of Expressed as the cumulative probability density function of the normal distribution, the training set Represented as from variable space The set of combinations of random variables drawn from .

[0092] In this embodiment 1, the Sobol sequence sampling method is used to extract Initial random sample points form the training set ;

[0093] 2.2 Functional function obtained according to step 1 , get the training set The response value of the corresponding function On this basis, we use Gaussian random process and based on the training set and the corresponding response value Building a proxy model , The training set response value, using Gaussian random process to establish a proxy model is a prior art, and the present invention will not repeat it;

[0094] 2.3 Using the Monte Carlo simulation method, in the variable space Extract Samples form the Monte Carlo sample set , and adopt the constructed proxy model generate The corresponding predicted response value ,in It is represented as a set of samples randomly drawn from the variable space. The sample size is large, and a probability distribution that is statistically significant and can effectively approximate the structural response can be obtained.

[0095] In this embodiment 1, the Monte Carlo method is used to generate Monte Carlo sample points;

[0096] Step 3: Use the integer-order moment maximum entropy method to further mine the prior information of the input-output mapping relationship hidden in the proxy model;

[0097] 3.1 Prediction of the value obtained in step 2 based on the maximum entropy method of integer moments Perform probability distribution fitting to obtain predicted values Corresponding predicted probability density function ;

[0098] The integer-order moment maximum entropy method used can be expressed as: ;

[0099] , is the functional response value of the ship wave load response, , is the coefficient of the integer-order maximum entropy method, is the order of the moment, is the total number of moments, and , .

[0100] 3.2 Based on the predicted probability density function , obtain the mean of the prior information about the mapping relationship hidden in the proxy model ,in is the normalization parameter of the predicted probability density function, is the Lagrange multiplier that constitutes the probability density function of the prediction, where ;

[0101] Step 4: Use the error discrimination formula to set the standard deviation of the prior distribution parameters;

[0102] 4.1 Prior Information Based on Empirical Information Assuming that it obeys normal distribution, based on the mean of the prior information distribution obtained in step 3, the standard deviation of the distribution parameter is further obtained through the error discrimination formula to obtain the prior information The distribution of ;

[0103] 4.2 Analysis of wave load response values ​​of training set based on integer-order moment maximum entropy method Perform probability distribution fitting and obtain The corresponding probability density function ;

[0104] 4.3 Comparison of training response values ​​obtained And step three to get the predicted , the difference between the two is obtained by the error discrimination formula , and ,in It is prior information The standard deviation of ;

[0105] The error discrimination formula is expressed as: ,in is the total number of discretized probability density function values, is the predicted probability density function, is the probability density function corresponding to the training set response, is the index corresponding to the function value of the discretized probability density function;

[0106] Step 5: Use the maximum a posteriori method to obtain the final sample distribution and failure probability;

[0107] 5.1 Based on the maximum a posteriori method, construct the maximum a posteriori objective optimization function and use the mean of the prior information obtained in step 4 and standard deviation And the training set wave load response value of step 2 As input parameters;

[0108] Through this input parameter, the Lagrange multiplier that minimizes the maximum a posteriori objective optimization function is solved. , .

[0109] The maximum a posteriori objective optimization function is specifically expressed as:

[0110] ;

[0111] in is the total number of response values, is the total number of moments, is the response value, is the Lagrange multiplier, is the order of the moment, and , is the mean of the prior information, is the standard deviation of the prior information, is the index corresponding to the response value of the function, The index corresponding to the order value of the moment.

[0112] 5.2 Lagrange multipliers obtained from maximum a posteriori Construct the final probability density function and the probability distribution function , obtain the probability of extreme ship motion , the whole calculation process ends.

[0113] Figure 3 The comparison between the probability density function PDF of the method proposed in the present invention in Example 1 and the real distribution and the typical method is given;

[0114] Figure 4 The comparison between the probability distribution function CDF of the method proposed in the present invention and the real distribution and typical methods is shown;

[0115] More detailed results are shown in Table 2.

[0116] Table 2 Comparison of the results of the method of the present invention and the typical method in Example 1

[0117]

[0118] Among them, the typical method is the integer-order moment maximum entropy method, which is a general technology and will not be described in detail here.

[0119] According to the results in Table 2, compared with the Monte Carlo simulation results, the maximum entropy reliability analysis method based on the maximum a posteriori and surrogate model proposed in the present invention can achieve the estimation of the failure probability of a certain event with high efficiency and accuracy. Compared with the typical method, under the same small sample, the relative error with the Monte Carlo simulation is significantly reduced. Figure 3 and Figure 4 The PDF and CDF curves shown show that the Monte Carlo simulation method proposed by the present invention has a better fit. Furthermore, the method proposed by the present invention achieves similar accuracy to the Monte Carlo method under small samples, indicating the efficiency of the method.

[0120] Embodiment 2:

[0121] In order to further demonstrate the effectiveness of the method proposed in the present invention, a wave load problem in the field of ships is proposed as an example to explain the method proposed in the present invention in detail.

[0122] Example 2 is a case of a ship sailing in waves. The ship panel model is as follows: Figure 5 As shown, the ship sails against the waves at a fixed speed. It is assumed that the ship is only affected by the waves during navigation, and the effects of wind, current, etc. on the ship load are not considered.

[0123] Step 1: Determine the functional functions and variables of the structure:

[0124] 1.1 According to the design and analysis requirements, the variables affecting the ship's wave load response are determined, such as ship mass distribution, speed and wave conditions. The variables affecting the ship's wave load response can be expressed as: ,in, ;and Dimension expressed as a function of the ship's wave load;

[0125] In this embodiment;

[0126] The random variable is represented by , the dimension is 21, Represents the section moment of inertia of each section of the ship;

[0127] In this embodiment 2, the distribution information of all variables is as shown in Table 2 below:

[0128] Table 2 Distribution of variables in implementation 2:

[0129]

[0130] 1.2 Using nonlinear potential flow theory to obtain the functional function corresponding to the ship wave load response , and obtain the variables that affect the function of the ship's wave load response and its distribution information, where represents a random variable, A function representing the response to wave loads;

[0131] In this embodiment 2, the functional function of the structure is expressed as:

[0132] ;

[0133] in is the vertical bending moment amidships.

[0134] Step 2: Use the surrogate model method to obtain the potential mapping relationship between variables and responses

[0135] 2.1 The sampling space obtained in step 1 using the Sobol sequence sampling method or other low-discrepancy sequence sampling methods Internal extraction A small number of samples constitute the training set ;

[0136] The sampling space Variables that represent the function that affects the response of ships to wave loads The space can be expressed as ,and Expressed as the joint probability density function of the variables The inverse function of Represented as a variable The amount The marginal probability density function of The inverse function of Expressed as the cumulative probability density function of the normal distribution, the training set Represented as from variable space The set of combinations of random variables drawn from .

[0137] In this embodiment 2, the Sobol sequence sampling method is used to extract Initial random sample points form the training set ;

[0138] 2.2 Functional function obtained according to step 1 , get the training set The corresponding response value of the ship wave load function On this basis, we use Gaussian random process and based on the training set and the corresponding response value Building a proxy model , is the wave load response value of the training set;

[0139] 2.3 Using the Monte Carlo simulation method, in the variable space Extract Samples form the Monte Carlo sample set , and adopt the constructed proxy model generate The corresponding predicted response value ,in It is represented as a set of samples randomly drawn from the variable space. The sample size is large, and a probability distribution that is statistically significant and can effectively approximate the structural response can be obtained.

[0140] In this embodiment 2, the Monte Carlo method is used to generate Monte Carlo sample points;

[0141] Step 3: Use the integer-order moment maximum entropy method to further mine the prior information of the input-output mapping relationship hidden in the proxy model

[0142] 3.1 Prediction of the value obtained in step 2 based on the maximum entropy method of integer moments Perform probability distribution fitting to obtain predicted values Corresponding predicted probability density function ;

[0143] The integer-order moment maximum entropy method used can be expressed as: ;

[0144] , is the functional response value of the ship wave load response, , is the coefficient of the integer-order maximum entropy method, is the order of the moment, is the total number of moments, and , .

[0145] 3.2 Based on the predicted probability density function , obtain the mean of the prior information about the mapping relationship hidden in the proxy model ,in is the normalization parameter of the predicted probability density function, is the Lagrange multiplier that constitutes the predicted probability density function, ;

[0146] Step 4: Use the error discrimination formula to set the standard deviation of the prior distribution parameters

[0147] 4.1 Prior Information Based on Empirical Information Assuming that it obeys normal distribution, based on the mean of the prior information distribution obtained in step 3, the standard deviation of the distribution parameter is further obtained through the error discrimination formula to obtain the prior information The distribution of ;

[0148] 4.2 Analysis of wave load response values ​​of training set based on integer-order moment maximum entropy method Perform probability distribution fitting and obtain The corresponding probability density function ;

[0149] 4.3 Comparison of training response values ​​obtained And step three to get the predicted , the difference between the two is obtained by the error discrimination formula , and ,in It is prior information The standard deviation of ;

[0150] The error discrimination formula is expressed as: ,in is the total number of discretized probability density function values, is the predicted probability density function, is the probability density function corresponding to the training set response, is the index corresponding to the function value of the discretized probability density function;

[0151] Step 5: Use maximum a posteriori to obtain the final sample distribution and failure probability

[0152] 5.1 Based on the maximum a posteriori method, construct the maximum a posteriori objective optimization function and use the mean of the prior information obtained in step 4 and standard deviation And the training set wave load response value of step 2 As an input parameter. Through this input parameter, the Lagrange multiplier that minimizes the maximum a posteriori objective optimization function is solved. , .

[0153] The maximum a posteriori objective optimization function is specifically expressed as:

[0154] ;

[0155] in is the total number of response values, is the total number of moments, is the response value, is the Lagrange multiplier, is the order of the moment, and , is the mean of the prior information, is the standard deviation of the prior information, is the index corresponding to the response value of the function, The index corresponding to the order value of the moment.

[0156] 5.2 Lagrange multipliers obtained from maximum a posteriori Construct the final probability density function and the probability distribution function , obtain the probability of extreme ship motion , the whole calculation process ends.

[0157] Figure 5 The computational ship panel model is shown. Figure 6 The comparison between the probability density function PDF of the method proposed in the present invention in Example 1 and the real distribution and typical methods is given. Figure 7The comparison between the probability distribution function CDF of the proposed method and the real distribution and the typical method is shown. More detailed results are shown in Table 3.

[0158] Table 3 Comparison of the results of the method of the present invention and the typical method in Example 2

[0159]

[0160] Among them, the typical method is the integer-order moment maximum entropy method, which is a general technology and will not be described in detail here.

[0161] According to the results in Table 3, compared with the Monte Carlo simulation results, the maximum entropy method for ship motion reliability analysis based on the maximum a posteriori and surrogate model proposed in the present invention can efficiently and accurately estimate the failure probability of Case 2. Compared with the typical method, it can achieve a smaller relative error than the Monte Carlo simulation, and further, the method proposed in the present invention can achieve similar accuracy to the Monte Carlo method under small samples, indicating the efficiency of this method.

[0162] The following are specific embodiments of the present invention, which are not intended to limit the present invention.

[0163] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. The maximum a posteriori ship wave load reliability analysis method based on the improved maximum entropy method is characterized by: The following steps are involved: Step 1: Determine the functional function of the ship structure and the random variables that affect the ship's wave load response; Step 2: Use the surrogate model method to obtain the potential mapping relationship between variables and responses; Step 3: Use the integer-order moment maximum entropy method to further mine the prior information of the input-output mapping relationship hidden in the proxy model; Step 4: Use the error discrimination formula to set the standard deviation of the prior distribution parameters; Step 5: Use the maximum a posteriori method to obtain the final structural response probability density distribution and failure probability; The step 2 specifically includes: (2.1) Using the Sobol sequence sampling method, the sampling space obtained Internal extraction A small number of samples constitute the training set , where space Variables that represent the function that affects the response of ships to wave loads space, training set Represented as the sampling space The set of combinations of random variables drawn from ; (2.2) According to the performance function obtained in step 1 , get the training set The corresponding response value of the ship wave load function On this basis, we use Gaussian random process and based on the training set and the corresponding response value Building a proxy model , is the wave load response value of the training set; (2.3) Using the Monte Carlo simulation method, in the variable space Extract Samples form the Monte Carlo sample set , and adopt the constructed proxy model generate The corresponding predicted response value ,in Represented as from variable space A set of samples randomly selected from the sample with a large sample size can obtain a probability distribution that is statistically significant and can effectively approximate the structural response; The step three specifically includes: (3.1) The predicted value obtained in step 2 is calculated based on the integer-order moment maximum entropy method Perform probability distribution fitting to obtain predicted values Corresponding predicted probability density function ; (3.2) Based on the predicted probability density function , obtain the mean of the prior information about the mapping relationship hidden in the proxy model ,in is the normalization parameter of the predicted probability density function, is the Lagrange multiplier that constitutes the predicted probability density function, ; The step 4 specifically includes: (4.1) Setting prior information It obeys the normal distribution. Based on the mean of the prior information distribution obtained in step 3, the standard deviation of the distribution parameter is further obtained through the error discrimination formula to obtain the prior information The distribution of ; (4.2) The wave load response values ​​of the training set based on the integer-order moment maximum entropy method Perform probability distribution fitting and obtain The corresponding probability density function ; (4.3) Compare the training response values ​​obtained And step three to get the predicted , the difference between the two is obtained by the error discrimination formula , and ,in It is prior information The standard deviation of ; The step five specifically includes: (5.1) Based on the maximum a posteriori method, construct the target optimization function considering the maximum a posteriori, and use the mean of the prior information obtained in step 4 and standard deviation And the training set wave load response value of step 2 As an input parameter, the Lagrange multiplier that minimizes the maximum a posteriori objective optimization function is solved. ,in ; (5.2) According to the maximum a posteriori Lagrange multiplier is obtained Construct the final probability density function and the probability distribution function , obtain the probability of extreme ship motion , the whole calculation process ends, where .

2. The maximum a posteriori ship wave load reliability analysis method based on the improved maximum entropy method according to claim 1 is characterized in that: The step 1 specifically includes: (1.1) Determine the variables that affect the ship's wave load response, ship mass distribution, speed and wave conditions according to design and analysis requirements; (1.2) Using nonlinear potential flow theory to obtain the functional function corresponding to the ship wave load response , and obtain the variables that affect the function of the ship's wave load response and its distribution information, where represents a random variable, A function representing the response to wave loads.

3. The maximum a posteriori ship wave load reliability analysis method based on the improved maximum entropy method according to claim 1 is characterized in that: The method is divided into four stages, namely, a proxy model construction stage, a priori information mean acquisition stage, an error discrimination formula stage, and a maximum a posteriori stage, wherein the proxy model construction stage includes steps one and two; the priori information acquisition stage includes step three; the error discrimination formula stage includes step four; and the maximum a posteriori stage includes step five. The step one acquires a functional function, that is, automatically modifies the variables affecting the ship wave load response through a program, forms an input parameter file required by the software, automatically calls a commercial software calculation program, and finally passes the results calculated by the software to the ship wave load reliability analysis program of steps three to five.

4. The maximum a posteriori ship wave load reliability analysis method based on the improved maximum entropy method according to claim 1 is characterized in that: The specific formula of the integer-order moment maximum entropy method in step 2 and step 3 can be written as: ,in is the response value, is the normalization parameter of the probability density function, is the Lagrange multiplier of the probability density function, is the order of the moment, is the total number of moments, and , .

5. The maximum a posteriori ship wave load reliability analysis method based on the improved maximum entropy method according to claim 1 is characterized in that: The specific formula of the error discrimination formula in step 4 is as follows: ； in is the total number of discretized probability density function values, is the predicted probability density function, is the probability density function corresponding to the training set response, The index corresponding to the function value of the discretized probability density function.

6. The maximum a posteriori ship wave load reliability analysis method based on the improved maximum entropy method according to claim 1 is characterized in that: The maximum a posteriori objective optimization function obtained in step 5 is specifically expressed as: ； in is the total number of response values, is the total number of moments, is the response value, is the Lagrange multiplier, is the order of the moment, and , is the mean of the prior information, is the standard deviation of the prior information, is the index corresponding to the response value of the function, is the index corresponding to the order value of the moment. For the maximum entropy method of integer-order moments, the order of the moment The corresponding index value equal.

Images