Ship long shafting centering optimization method based on proxy model

Abstract

The invention belongs to the technical field of ship power device design methods, and particularly relates to a ship long shafting alignment optimization method based on an agent model. Comprising the following steps: determining a host operation condition investigated by shafting alignment, and obtaining alignment input parameters according to an initial design scheme of a shafting; establishing a finite element centering calculation model of the shaft system, determining an optimization target, constraint conditions and variables of multi-target centering optimization, and determining an optimization target of centering; establishing an agent model; and carrying out multi-target centering optimization calculation to obtain an optimal shafting centering scheme. According to the method, on the premise that the prediction precision meets the requirement, the proxy model is adopted to replace a high-precision finite element model, and the multi-objective optimization algorithm is combined to perform shafting alignment optimization calculation, so that a more efficient and faster alignment optimization method is provided for the technical design of the long shafting, the design efficiency is improved, and the design period is shortened.

Description

Technical Field

[0001] The present application belongs to the technical field of ship power plant design methods, and in particular, relates to a ship long axis alignment optimization method based on an agent model. Background Art

[0002] The shaft system is an important part of the ship's power plant, and its design quality directly affects the safety and reliability of the ship's overall operation. Alignment calculation is an important part of the shaft system design process. The purpose is to make the shaft system alignment parameters such as bearing load, specific pressure, cross-sectional rotation angle and shaft bending stress meet the corresponding alignment requirements through calculation, verification and adjustment. The shaft system alignment calculation methods mainly include the three-moment method, transfer matrix method and finite element method. Among them, the finite element method has the advantages of high accuracy and good interactivity, and is currently the most widely used alignment calculation method. With the continuous development of modern optimization calculation methods, many scholars have studied the use of multi-objective optimization algorithms and finite element models to interact to carry out alignment calculations in order to obtain the optimal alignment results. However, the structure of the long shaft system of large ships is more complex, with the characteristics of multiple shaft system segments, long stern shaft span, and a large number of bearings. The alignment optimization calculation of this type of shaft system involves more design parameters, optimization objectives and constraints. If the multi-objective optimization algorithm is used to iterate the high-precision finite element alignment calculation model for multiple times, it will bring high calculation costs. Summary of the invention

[0003] The purpose of the present invention is to propose a method for optimizing the alignment of the long shaft system of a ship based on a proxy model. Under the premise that the prediction accuracy meets the requirements, the proxy model is used to replace the high-precision finite element model, and the shaft system alignment optimization calculation is performed in combination with a multi-objective optimization algorithm, so as to improve the efficiency and quality of the alignment optimization of the long shaft system of the ship.

[0004] To achieve the above purpose, the present invention adopts the following technical solution.

[0005] A method for optimizing the alignment of a ship's long axis system based on an agent model comprises the following steps:

[0006] Step 1: Obtain the input parameters for the alignment of a ship's long axis system

[0007] Specifically, it means: determining the main engine operating conditions to be investigated in the shaft system alignment, and obtaining the alignment input parameters according to the initial design plan of the shaft system; the alignment input parameters include spatial layout parameters, geometric parameters, material property parameters of each component of the shaft system, uniform load parameters, concentrated load parameters, bearing displacement parameters, and strength verification parameters;

[0008] Step 2: Establish the finite element centering calculation model of the shaft system

[0009] Specifically, according to the input parameters of the alignment, a finite element alignment calculation model of the shaft system is established; according to the overall layout and geometric parameters of the shaft system, a finite element model is established based on the Cartesian coordinate system, and each shaft section is modeled using beam units, whose internal density and elastic modulus are evenly distributed and free of defects; mass units are used to simulate the concentrated loads caused by the weight of the propeller and the large gear, and the gear meshing force under the investigated working conditions is added to the large gear; the model is meshed and the bearing fulcrum is set, the rear stern bearing fulcrum is taken at 1 / 3 of the bearing length from the rear end of the bearing to the bow end, and the support points of other bearings are taken at the midpoint of the bearing support length; the thermal displacement of the gear bearing is taken into account by means of forced displacement constraints;

[0010] Step 3: Determine the optimization objectives, constraints and optimization variables of multi-objective centering optimization;

[0011] Specifically, it means: based on the finite element alignment calculation model, firstly perform the linear alignment or reasonable alignment calculation of the shaft system, and determine the optimization target of the alignment according to the calculation results; the constraint conditions are determined according to the alignment standard requirements of the shaft system; the vertical displacement of the intermediate bearing is taken as the optimization variable. If it is a shaft system driven by a gearbox, the optimization variable should also include the vertical displacement of the gear bearing;

[0012] Step 4: Create a proxy model

[0013] A surrogate model for multi-objective centering optimization is constructed using response surface, Kriging model or neural network to predict the centering output parameters contained in the optimization objectives or constraints. The size of the sample set and the spatial correlation between sample points affect the prediction accuracy of the model. Latin hypercube sampling is used to extract sample points in the design space.

[0014] Step 5: Multi-objective shaft alignment optimization calculation based on the proxy model

[0015] Specifically, it means selecting a suitable multi-objective optimization algorithm to interact with the agent model, performing multi-objective centering optimization calculations, writing the algorithm's fitness function based on the determined optimization objectives and constraints, setting various parameters of the multi-objective optimization algorithm, and finally performing iterative optimization calculations within the range of optimization variables to obtain the Pareto solution set;

[0016] Step 6: Determine the plan

[0017] Specifically, after obtaining the Pareto solution set, the ideal solution corresponding to each optimization objective is found, and the optimal solution closest to the ideal solution is determined by the minimum distance method. This optimal solution is the optimal shaft alignment solution.

[0018] A further improvement or specific implementation method of the above-mentioned ship long shaft system alignment optimization method based on the proxy model, in the step one, the spatial layout parameters include the overall layout of the shaft system, the position of each bearing and the fulcrum; the geometric parameters include the length and inner and outer diameters of each shaft segment, the calculated reference points and reference lines; the material property parameters of each component of the shaft system include density, elastic model, Poisson's ratio, yield strength and tensile strength; the uniformly distributed load parameters include the weight of the shaft segment, bushing, flange and coupling; the concentrated load parameters are mainly the weight of the propeller. If it is a shaft system driven by a gearbox, it also includes the weight of the large gear and the gear meshing force under the examined working conditions; the bearing displacement parameters include the thermal displacement of the gearbox output flange under the examined working conditions, which is used to take into account the thermal displacement of the gear bearing when calculating; the strength verification parameters include the maximum thrust, tension and rated torque transmitted by the shaft system under the examined working conditions, as well as the additional bending moment, eccentric bending moment and stress concentration factor for alignment installation that need to be taken into account.

[0019] Further improvement or specific implementation of the above-mentioned ship long shaft alignment optimization method based on the proxy model, in the step three, the optimization objectives include minimizing the load on the rear stern bearing, minimizing the load difference between the front and rear stern bearings, and uniform distribution of loads on the same type or adjacent bearings;

[0020] The constraints include bearing load, stern bearing section angle, bearing specific pressure, gear bearing load difference within the allowable range, and shaft surface bending stress and safety factor of the dangerous section less than the specified value.

[0021] A further improvement or specific implementation of the above-mentioned ship long axis alignment optimization method based on the proxy model, in step 4, a sample point in the sample space is set as x i (i=1,2,3,…,n), its response value is y r (r=1,2,3,…,l), n is the total number of sample points, l is the total number of response values; then the mathematical expression of the Kriging surrogate model is:

[0022]

[0023] P(a ir ,x i )=a 1r p1(x i )+a 2r p2(x i )+…+a pr p p (x i )

[0024] Where p is the total number of polynomials; P(a ir ,x i ) is x i A polynomial function is used to capture the global approximate trend;

[0025] p p (x i ) is a basis function in polynomial form; a pr is the unknown coefficient; z r (x i ) is a random distribution error with mean 0; assuming x i Corresponding to one response value, that is, i=1, multiple response values ​​are analogous, and the above formula is simplified to:

[0026]

[0027] p T (x i )a=a1p1(x i )+a2p2(x i )+…+a p p p (x i )

[0028] z(x i ) is expressed as:

[0029] cov[z(x i ),z(x j ))]=σ 2 λ(x i ,x j )

[0030] Among them, p T (x i ) represents the row vector of basis functions; a represents the column vector of undetermined coefficients; z(x i ) represents a random distribution error with a mean of 0; a p represents the undetermined coefficient;

[0031] σ 2 is the variance; λ(x i ,x j ) represents the sample point x i , x j The Gaussian correlation function of the correlation between the two is expressed as:

[0032]

[0033] Among them, w is the dimension of the sample point; x ik represents the k-th dimension coordinate of the i-th sample point; x jk represents the k-th dimension coordinate of the j-th sample point; θ k is the correlation parameter; the predicted value of the Kriging proxy model for a certain predicted point x is expressed as:

[0034]

[0035] r T (x)=[λ(x,x1),λ(x,x2),...,λ(x,x n )] T

[0036] Among them, r T (x) represents the correlation between the predicted point and the sample point; Y = [y1(x1), y2(x2), ..., y n (x n )] T is a column vector containing the response values ​​of the sample set; P = [p1(x1), p2(x2), ..., p n (x n )] T is a column vector containing the basis functions of the sample set; is an estimate of a, obtained by generalized least squares estimation:

[0037]

[0038] The variance estimate of the response set Y is expressed as:

[0039]

[0040] Based on the above, we can see and Both with parameter θ k Related to; k It is obtained by the maximum likelihood estimation method, that is, to find the maximum value of the following likelihood function:

[0041]

[0042] Solve the above k-dimensional nonlinear unconstrained optimization problem, that is, find the Kriging model with the best fitting effect;

[0043] The construction process of the Kriging surrogate model combined with Latin hypercube sampling mainly includes the following steps:

[0044] a. Determine the sample space, that is, the value range of the optimization variable (bearing vertical displacement), then use LHS to obtain the sample set and interact with the shafting finite element model to obtain the true response value of each sample point;

[0045] b. Divide the sample set into training set and test set, and perform data normalization on each set;

[0046] c. Train the initial Kriging model, obtain the predicted response value of the test set, and perform denormalization on it;

[0047] d. Calculate the fitting determination coefficient between the predicted value and the true value To test the accuracy of the model; if it meets the requirements, the Kriging model is output; otherwise, the sample set is expanded and updated, and the model is trained again until the model accuracy meets the requirements; Calculated by the following formula:

[0048]

[0049] In the formula, y ij is the true value of the output parameter of the jth calibration for the i-th test set sample point, is the predicted value of the jth calibration output parameter for the i-th test set sample point, is the average value of the output parameter of the jth calibration center for the i-th test set sample point.

[0050] A further improvement or specific implementation method of the aforementioned surrogate model-based ship long axis alignment optimization method, wherein the parameters of the multi-objective optimization algorithm include the initial sample number, the maximum number of iterations, the Pareto percentage and the convergence tolerance.

[0051] As a further improvement or specific implementation of the above-mentioned ship long axis alignment optimization method based on the proxy model, the calculation formula of the minimum distance is as follows:

[0052]

[0053] Where D represents the distance between the optimal solution and the ideal solution, d = 2, 4, 6…, k is the number of optimization targets, and f ji is the value of the j-th Pareto solution for the ith optimization objective.

[0054] Its beneficial effects are:

[0055] The present invention proposes a method for optimizing the alignment of a ship's long shaft system based on a proxy model. On the premise that the prediction accuracy meets the requirements, the proxy model is used to replace the high-precision finite element model, and the shaft system alignment optimization calculation is performed in combination with a multi-objective optimization algorithm. The calculation cost can be significantly reduced while ensuring the accuracy, and technical support is provided for finding the optimal shaft system alignment solution. The proposed method can be applied to the technical design stage of the ship's long shaft system. Based on the multi-objective, multi-constraint and multi-variable characteristics of the ship's long shaft system alignment optimization, a more efficient and faster alignment optimization method is provided for the technical design of the long shaft system, which helps to improve the design efficiency and shorten the design cycle. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 A flow chart is provided for the implementation of the optimization method for the alignment of the ship's long axis based on the surrogate model;

[0057] Figure 2 Build a flow chart for the agent model;

[0058] Figure 3 This is the calculation model diagram of the shaft system finite element alignment;

[0059] Figure 4 This is the deflection distribution diagram of the shafting system under reasonable alignment;

[0060] Figure 5 This is a comparison chart of the predicted results of the calibration output parameters (bending stress on the shaft surface at the No. 4 bearing support);

[0061] Figure 6 Schematic diagram of Pareto solution set and optimal solution;

[0062] Figure 7 The deflection distribution diagram of the shafting after optimization for alignment. DETAILED DESCRIPTION

[0063] The present invention is described in detail below in conjunction with specific embodiments.

[0064] This application is a method for optimizing the alignment of a ship's long shaft system based on a proxy model, which is mainly used in the technical design stage of a ship's long shaft system. On the premise that the prediction accuracy meets the requirements, a proxy model is used to replace the high-precision finite element model, and a multi-objective optimization algorithm is combined to perform shaft system alignment optimization calculations to improve the efficiency and quality of the ship's long shaft system alignment optimization.

[0065] like Figure 1 As shown, the ship long axis alignment optimization method based on the proxy model of the present application mainly includes the following basic steps:

[0066] Step 1. Obtain the alignment input parameters of a ship's long shaft system. Specifically, it means determining the main engine operating conditions to be investigated in the alignment of the shaft system, and obtaining the alignment input parameters based on the initial design plan of the shaft system, where the spatial layout parameters include the overall layout of the shaft system, the positions of each bearing and the fulcrum, etc.; the geometric parameters include the length and inner and outer diameters of each shaft section, the calculated reference points and reference lines, etc.; the material property parameters of each component of the shaft system include density, elastic model, Poisson's ratio, yield strength and tensile strength, etc.; the uniformly distributed load parameters include the weight of the shaft section, bushing, flange and coupling, etc.; the concentrated load parameters are mainly the weight of the propeller. If it is a shaft system driven by a gearbox, it also includes the weight of the large gear and the gear meshing force under the investigated working conditions; the bearing displacement parameters include the thermal displacement of the output flange of the gearbox under the investigated working conditions, which is used to take into account the thermal displacement of the gear bearing during calculation; the strength verification parameters include the maximum thrust, tension and rated torque transmitted by the shaft system under the investigated working conditions, as well as the additional bending moment, eccentric bending moment, stress concentration factor, etc. required for alignment installation;

[0067] Step 2, establish a finite element alignment calculation model for the shaft system. Specifically, according to the alignment input parameters obtained in step 1, establish a finite element alignment calculation model for the shaft system. According to the overall layout and geometric parameters of the shaft system, a finite element model is established based on the Cartesian coordinate system. Each shaft section is modeled using beam units, and its internal density, elastic modulus, etc. are evenly distributed and free of defects; mass units are used to simulate the concentrated loads caused by the weight of the propeller (wet weight in water) and the weight of the large gear, and the gear meshing force under the investigated working conditions is added to the large gear; the model is meshed, and the bearing fulcrum is set. The stern bearing fulcrum is taken at 1 / 3 of the bearing length from the rear end of the bearing to the bow end, and the support points of other bearings are taken at the midpoint of the bearing support length; the thermal displacement of the gear bearing is taken into account by means of forced displacement constraints;

[0068] Step 3: Determine the optimization objectives, constraints and optimization variables of multi-objective centering optimization. Based on the finite element centering calculation model established in step 2, first perform linear centering or reasonable centering calculation of the shaft system, and determine the optimization objectives of the centering according to the calculation results, mainly including the minimum load on the rear stern bearing, the minimum load difference between the front and rear stern bearings, and the uniform distribution of loads on the same type or adjacent bearings;

[0069] The constraint conditions are mainly determined according to the requirements of shaft alignment and calibration, including that the bearing load, stern bearing section angle, bearing specific pressure, gear bearing load difference, etc. are within the allowable range, and the shaft surface bending stress and safety factor of the dangerous section are less than the specified value;

[0070] The vertical displacement of the intermediate bearing is usually taken as the optimization variable in the centering optimization. If it is a shaft system driven by a gearbox, the optimization variable should also include the vertical displacement of the gear bearing.

[0071] Step 4: Establishing a proxy model. The proxy model for multi-objective centering optimization can be constructed by using a response surface, a Kriging model or a neural network. The present invention uses a Kriging model to replace the shafting finite element centering calculation model to predict the centering output parameters contained in the optimization objectives or constraints, but is not limited to this model.

[0072] Assume that a sample point in the sample space is x i (i=1,2,3,…,n), its response value is y r (r=1,2,3,…,l), then the mathematical expression of the Kriging surrogate model is:

[0073]

[0074] P(a ir ,x i )=a 1r p1(x i )+a 2r p2(xi )+…+a pr p p (x i )

[0075] Among them, p p (x i ) is a basis function in polynomial form; a pr is the unknown coefficient; z r (x i ) is a random distribution error with mean 0. Assume x i Corresponding to one response value, that is, l = 1 (multiple response values ​​can be deduced in this way), the above formula can be simplified to:

[0076]

[0077] p T (x i )a=a1p1(x i )+a2p2(x i )+…+a p p p (x i )

[0078] z(x i ) can be expressed as:

[0079] cov[z(x i ),z(x j ))]=σ 2 λ(x i ,x j )

[0080] Among them, σ 2 is the variance; λ(x i ,x j ) represents the sample point x i , x j The Gaussian correlation function of the correlation between the two can be expressed as:

[0081]

[0082] Among them, w is the dimension of the sample point; θ k is the correlation parameter. The predicted value of the Kriging proxy model for a certain predicted point x can be expressed as:

[0083]

[0084] r T (x)=[λ(x,x1),λ(x,x2),...,λ(x,x n )] T

[0085] Among them, r T (x) represents the correlation between the point to be predicted and the sample point;

[0086] Y=[y1(x1),y2(x2),...,y n (x n )] T is a column vector containing the response values ​​of the sample set;

[0087] P=[p1(x1),p2(x2),...,p n (x n )] T is a column vector containing the basis functions of the sample set; It can be obtained by generalized least squares estimation:

[0088]

[0089] The variance estimate of the response set Y can be expressed as:

[0090]

[0091] Based on the above, it can be seen and Both with parameter θ k Related. k It can be obtained by the maximum likelihood estimation method, that is, to find the maximum value of the following likelihood function:

[0092]

[0093] By solving the above k-dimensional nonlinear unconstrained optimization problem, the Kriging model with the best fitting effect can be found. The scale of the sample set and the spatial correlation between sample points affect the prediction accuracy of the model. The present invention uses Latin Hypercube Sampling (LHS) in the experimental design to extract sample points in the design space. The sample points obtained by this method are more evenly distributed, which can improve the fitting accuracy of the model. The construction process of the Kriging proxy model combined with LHS is as follows: Figure 2 As shown, it mainly includes the following steps:

[0094] a. Determine the sample space, that is, the value range of the optimization variable (bearing vertical displacement), then use LHS to obtain the sample set and interact with the shafting finite element model to obtain the true response value of each sample point;

[0095] b. Divide the sample set into training set and test set, and perform data normalization on each set;

[0096] c. Train the initial Kriging model, obtain the predicted response value of the test set, and perform denormalization on it;

[0097] d. Calculate the fitting determination coefficient between the predicted value and the true value To test the accuracy of the model. If it meets the requirements, the Kriging model is output. Otherwise, the sample set is expanded and updated, and the model is trained again until the model accuracy meets the requirements. It can be calculated by the following formula:

[0098]

[0099] In the formula, y ij is the true value of the output parameter of the jth calibration for the i-th test set sample point, is the predicted value of the jth calibration output parameter for the i-th test set sample point, is the average value of the output parameter of the jth calibration center for the i-th test set sample point;

[0100] Step 5: Perform multi-objective alignment optimization calculations on the shaft system based on the proxy model. Specifically, it means selecting a suitable multi-objective optimization algorithm to interact with the proxy model to perform multi-objective alignment optimization calculations. First, write the fitness function of the algorithm based on the determined optimization objectives and constraints; then, set the various parameters of the multi-objective optimization algorithm, including the initial sample size, maximum number of iterations, Pareto percentage, and convergence tolerance; finally, perform iterative optimization calculations within the range of optimization variables to obtain the Pareto solution set;

[0101] Step 6: Determine the solution. Specifically, after iterative calculation, the Pareto solution set is obtained, and the ideal solution corresponding to each optimization target is found. The optimal solution closest to the ideal solution is determined by the minimum distance method. This optimal solution is the optimal shaft alignment solution. The calculation formula for the minimum distance is as follows:

[0102]

[0103] Where D represents the distance between the optimal solution and the ideal solution, d = 2, 4, 6…, k is the number of optimization targets, and f ji is the value of the j-th Pareto solution for the ith optimization objective.

[0104] The following is an explanation of the research method of the present invention in conjunction with a long shaft system of a certain ship, and the alignment status of the shaft system before and after optimization is compared to verify the feasibility of the alignment optimization method based on the proxy model. The example is based on a long shaft system, which contains a total of 9 sets of bearings (numbered 1 to 9 from the stern to the bow), of which bearings 1 to 3 are stern bearings, and bearings 8 and 9 are gear bearings.

[0105] According to step 1, the input parameters of the shaft system alignment are obtained, and then the shaft system finite element alignment calculation model is established according to step 2, such as Figure 3 shown.

[0106] According to step 3, based on the finite element alignment calculation model, the shaft system linear alignment calculation is first performed. Under the linear alignment state, the gear bearing load difference is greater than the specified value, so further reasonable alignment is performed. After reasonable alignment, the state parameters of each bearing are shown in Table 1, the strength verification results of each dangerous section are shown in Table 2, and the shaft system deflection distribution is shown in Table 3. Figure 4 shown.

[0107] Table 1 State parameters of each bearing under reasonable alignment

[0108] Bearing No. Vertical displacement / mm Section angle / rad Load / kN <![CDATA[Specific pressure / (N / mm 2 )]]> <![CDATA[Allowable bearing pressure / (N / mm 2 )]]> 1 0.00 5.0012e-04 491.48 0.266 0.800 2 0.00 -1.4070e-04 148.56 0.155 0.800 3 0.00 5.9103e-05 197.94 0.206 0.300 4 0.00 1.9042e-07 103.26 0.177 0.600 5 0.00 3.0376e-05 90.50 0.155 0.600 6 0.00 -5.4220e-05 95.81 0.164 0.600 7 -1.30 -3.1500e-04 132.17 0.226 0.600 8 -4.30 -6.515e-05 481.08 1.091 3.000 9 -4.30 5.7785e-05 498.82 1.131 3.000

[0109] Table 2 Strength verification results of the cross sections at each bearing support and dangerous cross sections after reasonable alignment

[0110]

[0111]

[0112] From the reasonable alignment results, it can be seen that the specific pressure of each bearing, the cross-sectional rotation angle, the gear bearing load difference, etc. are all less than the specified values. Inspecting the cross-sections and dangerous cross-sections at each bearing support, the bending stress on the shaft surface is less than the maximum allowable value of 41.00MPa, and the safety factor is also within the allowable range. However, the load difference between bearings 1 and 2 is still large, and the load difference of the other bearings is also large. Therefore, the vertical displacement of bearings 4 to 5 is taken as the optimization variable, and the optimization goals are set to minimize the load on bearing 1, minimize the load difference between bearings 1 and 2, and make the load distribution of the same type or adjacent bearings more uniform, so as to further optimize the alignment state of the shaft system. According to the requirements of the shaft system alignment standard, the constraints that need to be considered in the optimization include the allowable range of the load of each bearing, the load difference of the gear bearing, the cross-sectional rotation angle of the stern bearing, the cross-sectional bending stress on the shaft surface of the cross-section at each bearing support and the dangerous cross-section, and the safety factor.

[0113] According to step four, a proxy model is established to predict the calibration output parameters contained in the above optimization objectives or constraints. During the optimization process, the bending stresses of the first two sections shown in Table 2 remain basically unchanged, so no prediction is required. Assume that the vertical displacements of bearings 4 to 6 are Δh4, Δh5, Δh6, and the value range is [-3.00, 3.00] mm. 900 sample points are extracted using the LHS method, 20 of which are randomly selected as the test set, and the remaining points are used as the training set. After training and adjustment, the final output Kriging model can be obtained. Comparing the predicted values ​​and true values ​​of the test set samples, the comparison of some calibration output parameters is as follows. Figure 5The fitting determination coefficient between the predicted value and the true value of the output parameter in each school was calculated, and the results are shown in Table 3.

[0114] Table 3 Fitting determination coefficients of output parameters in each school

[0115]

[0116] The larger the fitting determination coefficient, the more accurate the proxy model's prediction of the parameter. In engineering, it is believed that the model accuracy meets the requirements when its value is greater than 0.99. As shown in Table 3, the established Kriging model has good fitting accuracy and can be used to replace the high-precision shaft system finite element alignment calculation model.

[0117] According to step 5, a multi-objective genetic algorithm is used to interact with the agent model to perform multi-objective axis alignment optimization calculation. According to step 3, the optimization objective is written in the algorithm fitness function:

[0118] min{f R ,f ΔR ,f S}

[0119] f R =R1

[0120] f ΔR =|R1-R2|

[0121]

[0122] Among them, f R is the objective function to characterize the degree of load reduction of the rear stern bearing, f ΔR is the objective function that characterizes the degree of reduction of the load difference between the front and rear stern bearings, f S To characterize the objective function of the load uniformity between adjacent bearings, it is written in the form of standard deviation; R1 is the load of bearing No. 1, R2 is the load of bearing No. 2, and R i is the load of bearing No. i, is the average load of adjacent bearings.

[0123] According to step 3, add the following constraints to the algorithm fitness function:

[0124] st0.2G i ≤R i ≤R imax

[0125] ΔR 89 ≤[ΔR 89 ]

[0126]

[0127] σj ≤[σ j ]

[0128] n j ≤[n j ]

[0129] Among them, G i is the total weight of the two adjacent spans of the i-th bearing, R i and R imax are the i-th bearing load and the maximum allowable load respectively; and are the cross-sectional rotation angle and allowable rotation angle of bearing No. 1 respectively; σ j and [σ j ] are the bending stress and allowable stress of the shaft surface of the jth shaft section respectively; n j and [n j ] are the safety factor and allowable safety factor of the j-th shaft section respectively.

[0130] Set the initial sample size of the algorithm to 200, the maximum number of iterations to 100, the Pareto percentage to 10%, the convergence tolerance to 0.001, and perform optimal solution within the range of optimization variables based on the surrogate model. Figure 6 The Pareto solution set is shown.

[0131] According to step 6, the minimum distance method is used to screen out the optimal solution in the Pareto solution set. Figure 6 The optimal shaft alignment solution is the point marked in the middle. Table 4 shows the state parameters of each bearing after alignment optimization, and Table 6 shows the strength verification results of the cross-sections and dangerous cross-sections of each bearing support after alignment optimization. Figure 7 Shown is the shafting deflection distribution after alignment optimization.

[0132] Table 5 Bearing status parameters after alignment and optimization

[0133]

[0134]

[0135] Table 6 Strength verification results of the cross sections and dangerous cross sections at each bearing support after centering optimization

[0136]

[0137] It can be seen from the alignment optimization results that, under the premise that parameters such as bearing load, specific pressure, cross-sectional angle, shaft surface bending stress and safety factor meet the requirements of shaft alignment, compared with the reasonable alignment state, the load of bearing No. 1 of the optimized shaft system is reduced by 1.74kN, the load difference between bearings No. 1 and No. 2 is reduced by 13.51kN, the load distribution of adjacent bearings is also more uniform, and the alignment state of the shaft system is significantly improved.

[0138] This embodiment uses the Kriging model as a proxy model for centering optimization, but is not limited to this model. Under the premise that the accuracy meets the requirements, designers can use other types of proxy models according to actual conditions. In addition, due to hardware conditions, the optimization target value range selected in this embodiment and the number of sample populations set in the optimization algorithm are limited, and only the effectiveness of the method proposed in this invention is verified. Faced with different long axis systems, designers can expand the optimization variable value range according to actual conditions and set a larger population size to obtain a better axis centering design solution.

[0139] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention, rather than to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the essence and scope of the technical solution of the present invention.

Claims

1. A method for optimizing the alignment of a ship's long axis based on an agent model, characterized in that: The steps include: Step 1: Obtain the input parameters for the alignment of a ship's long axis system Specifically, it means: determining the main engine operating conditions to be investigated in the shaft system alignment, and obtaining the alignment input parameters according to the initial design plan of the shaft system; the alignment input parameters include spatial layout parameters, geometric parameters, material property parameters of each component of the shaft system, uniform load parameters, concentrated load parameters, bearing displacement parameters, and strength verification parameters; Step 2: Establish the finite element centering calculation model of the shaft system Specifically, according to the input parameters of the alignment, a finite element alignment calculation model of the shaft system is established; according to the overall layout and geometric parameters of the shaft system, a finite element model is established based on the Cartesian coordinate system, and each shaft section is modeled using beam units, whose internal density and elastic modulus are evenly distributed and free of defects; mass units are used to simulate the concentrated loads caused by the weight of the propeller and the large gear, and the gear meshing force under the investigated working conditions is added to the large gear; the model is meshed and the bearing fulcrum is set, the rear stern bearing fulcrum is taken at 1 / 3 of the bearing length from the rear end of the bearing to the bow end, and the support points of other bearings are taken at the midpoint of the bearing support length; the thermal displacement of the gear bearing is taken into account by means of forced displacement constraints; Step 3: Determine the optimization objectives, constraints and optimization variables of multi-objective centering optimization; Specifically, it means: based on the finite element alignment calculation model, firstly perform the linear alignment or reasonable alignment calculation of the shaft system, and determine the optimization target of the alignment according to the calculation results; the constraint conditions are determined according to the alignment standard requirements of the shaft system; the vertical displacement of the intermediate bearing is taken as the optimization variable. If it is a shaft system driven by a gearbox, the optimization variable should also include the vertical displacement of the gear bearing; Step 4: Create a proxy model A surrogate model for multi-objective centering optimization is constructed using response surface, Kriging model or neural network to predict the centering output parameters contained in the optimization objectives or constraints. The size of the sample set and the spatial correlation between sample points affect the prediction accuracy of the model. Latin hypercube sampling is used to extract sample points in the design space. Step 5: Multi-objective shaft alignment optimization calculation based on the proxy model Specifically, it means selecting a suitable multi-objective optimization algorithm to interact with the agent model, performing multi-objective centering optimization calculations, writing the algorithm's fitness function based on the determined optimization objectives and constraints, setting various parameters of the multi-objective optimization algorithm, and finally performing iterative optimization calculations within the range of optimization variables to obtain the Pareto solution set; Step 6: Determine the plan Specifically, after obtaining the Pareto solution set, the ideal solution corresponding to each optimization objective is found, and the optimal solution closest to the ideal solution is determined by the minimum distance method. This optimal solution is the optimal shaft alignment solution.

2. The method for optimizing the alignment of a ship's long axis system based on a proxy model according to claim 1, characterized in that: In the step one, the spatial layout parameters include the overall layout of the shaft system, the positions of each bearing and the fulcrum; the geometric parameters include the length and inner and outer diameters of each shaft segment, the calculated reference points and reference lines; the material property parameters of each component of the shaft system include density, elastic model, Poisson's ratio, yield strength and tensile strength; the uniformly distributed load parameters include the weight of the shaft segment, bushing, flange and coupling; the concentrated load parameters are mainly the weight of the propeller. If it is a shaft system driven by a gearbox, it also includes the weight of the large gear and the gear meshing force under the examined working conditions; the bearing displacement parameters include the thermal displacement of the gearbox output flange under the examined working conditions, which is used to take into account the thermal displacement of the gear bearing during calculation; the strength verification parameters include the maximum thrust, tension and rated torque transmitted by the shaft system under the examined working conditions, as well as the additional bending moment, eccentric bending moment and stress concentration factor for centering installation that need to be taken into account.

3. The method for optimizing the alignment of a ship's long axis system based on a proxy model according to claim 2, characterized in that: In step 3, the optimization objectives include minimizing the load on the rear stern bearing, minimizing the load difference between the front and rear stern bearings, and uniformly distributing the loads on the same type or adjacent bearings. The constraints include bearing load, stern bearing section angle, bearing specific pressure, gear bearing load difference within the allowable range, and shaft surface bending stress and safety factor of the dangerous section less than the specified value.

4. The method for optimizing the alignment of a ship's long axis based on a proxy model according to claim 3 is characterized in that: In step 4, let a sample point in the sample space be x i (i=1,2,3,…,n), its response value is y r (r=1,2,3,…,l), n is the total number of sample points, l is the total number of response values; then the mathematical expression of the Kriging surrogate model is: P(a ir ,x i )=a 1r p1(x i )+a 2r p2(x i )+…+a pr p p (x i ) Where p is the total number of polynomials; p p (x i ) is a basis function in polynomial form; P(a ir ,x i ) is x i A polynomial function is used to capture the global approximate trend; a pr is the unknown coefficient; z r (x i ) is a random distribution error with mean 0; assuming x i Corresponding to one response value, that is, i=1, and multiple response values ​​are analogous, the above formula is simplified to: p T (x i )a=a1p1(x i )+a2p2(x i )+…+a p p p (x i ) z(x i ) is expressed as: cov[z(x i ),z(x j ))]=σ 2 λ(x i ,x j ) Among them, σ 2 is the variance; λ(x i ,x j ) represents the sample point x i , x j The Gaussian correlation function of the correlation between the two is expressed as: Among them, w is the dimension of the sample point; x ik represents the k-th dimension coordinate of the i-th sample point; x jk represents the k-th dimension coordinate of the j-th sample point; θ k is the correlation parameter; the predicted value of the Kriging proxy model for a certain predicted point x is expressed as: r T (x)=[λ(x,x1),λ(x,x2),...,λ(x,x n )] T Among them, r T (x) represents the correlation between the predicted point and the sample point; Y = [y1(x1), y2(x2), ..., y n (x n )] T is a column vector containing the response values ​​of the sample set; P = [p1(x1), p2(x2), ..., p n (x n )] T is a column vector containing the basis functions of the sample set; is an estimate of a, obtained by generalized least squares estimation: The variance estimate of the response set Y is expressed as: Based on the above, we can see and Both with parameter θ k Related to; k It is obtained by the maximum likelihood estimation method, that is, to find the maximum value of the following likelihood function: Solve the above k-dimensional nonlinear unconstrained optimization problem, that is, find the Kriging model with the best fitting effect; The construction process of the Kriging surrogate model combined with Latin hypercube sampling mainly includes the following steps: a. Determine the sample space, that is, the value range of the optimization variable (bearing vertical displacement), then use LHS to obtain the sample set and interact with the shafting finite element model to obtain the true response value of each sample point; b. Divide the sample set into training set and test set, and perform data normalization on each set; c. Train the initial Kriging model, obtain the predicted response value of the test set, and perform denormalization on it; d. Calculate the fitting determination coefficient between the predicted value and the true value To test the accuracy of the model; if it meets the requirements, the Kriging model is output; otherwise, the sample set is expanded and updated, and the model is trained again until the model accuracy meets the requirements; Calculated by the following formula: In the formula, y ij is the true value of the output parameter of the jth calibration for the i-th test set sample point, is the predicted value of the jth calibration output parameter for the i-th test set sample point, is the average value of the output parameter of the jth calibration center for the i-th test set sample point.

5. The method for optimizing the alignment of a ship's long axis based on a proxy model according to claim 4, characterized in that: The parameters of the multi-objective optimization algorithm include the initial sample size, the maximum number of iterations, the Pareto percentage, and the convergence tolerance.

6. The method for optimizing the alignment of a ship's long axis based on a proxy model according to claim 5, characterized in that: The minimum distance is calculated as follows: Where D represents the distance between the optimal solution and the ideal solution, d = 2, 4, 6…, k is the number of optimization targets, and f ji is the value of the j-th Pareto solution for the ith optimization objective.

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