CN113868765A - Ship main scale parameter optimization method based on approximate model - Google Patents
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Abstract
The invention relates to a ship main scale parameter optimization method based on an approximate model, which comprises the steps of S1, constructing a ship rapidity model test database; s2, selecting an approximate model type, establishing a corresponding approximate model function related to the mapping relation between the main scale, the ship type parameters and the residual resistance coefficient, and performing error analysis and validity check on the approximate model function; s3, selecting ship main scale and ship type parameter data outside a group of databases as input, forecasting resistance coefficients based on each approximate model, comparing the forecasting resistance coefficients with corresponding test values, and verifying the precision of the forecasting resistance of the established approximate model; and S4, optimizing the main scale parameters by using a single-target optimization algorithm of a self-adaptive simulated annealing algorithm based on the approximate model and taking the minimum resistance of the full-speed section as a target. The invention is based on the ASA single-target optimization algorithm, and can quickly realize the optimization selection of the main scale parameters of the ship by taking the minimum resistance at the full navigational speed as a target.
Description
Technical Field
The invention belongs to the technical field of optimization of ship main scale parameters, and particularly relates to a method for supporting ship main scale and ship type parameter demonstration optimization by using an optimization algorithm based on an approximate model and aiming at minimum resistance in a full navigational speed section.
Background
The modern ship overall design provides higher requirements for profile design optimization, in the process of demonstrating design, according to overall scheme requirements, a parent ship with excellent performance can carry out multi-round iterative design, a large number of schemes with different main scales and ship profile parameters are generated, the rapidity of the ship profile schemes needs to be evaluated through a large number of simulation calculations, the analysis workload is large, the timeliness is poor, the requirements of rapid design are difficult to adapt, and great inconvenience is brought to searching for the influence rule of profile parameter change and the profile optimization direction.
Disclosure of Invention
The invention aims to solve the technical problem that the optimization efficiency of the main scale parameters of the ship is low in the prior art, and provides a method for optimizing the main scale parameters of the ship based on an approximate model.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a ship main scale parameter optimization method based on an approximate model comprises the following steps:
s1, constructing a ship rapidity model test database: screening main hull resistance test data of different ship types under various water displacement, selecting a main scale, ship type parameters and rapidity parameters which mainly affect resistance, and constructing a main scale, ship type parameters and rapidity parameter database;
s2, approximate model construction: selecting an approximate model type based on the database sample points in S1, establishing a corresponding approximate model function related to the mapping relation between the main scale, the ship type parameters and the residual resistance coefficient, and performing error analysis and validity check on the approximate model function;
s3, resistance forecasting: selecting ship main scale and ship type parameter data outside a group of databases as input, calculating the frictional resistance by adopting a Prandtl-Schlichting formula, predicting resistance coefficients based on each approximate model established in S2, comparing the predicted resistance coefficients with corresponding test values, and verifying the accuracy of the predicted resistance of the established approximate model; finally, selecting a model with a more stable error range and a smaller error mean value as an approximate model for quickly forecasting the ship resistance;
s4, automatically optimizing the main scale parameters of the ship by using an optimization algorithm: based on the approximate model finally selected in S3, a main scale parameter is optimized by using an adaptive simulated annealing algorithm (ASA) single-target optimization algorithm and taking the minimum resistance at the full-speed section as a target.
In the above scheme, in step S1, the main scale mainly affecting the resistance includes a water line Length, a water line width Beam, a draft T, a displacement volume V, and a main hull wet surface area S, the ship-type parameters include a square coefficient Cb and a middle cross section coefficient Cm, and the rapidity parameters include a navigational speed Vs and a residual resistance coefficient 1000 Cr.
In the above-described embodiment, in step S1, when the database is constructed, the parameters are distributed as uniformly as possible within a reasonable range, and the upper and lower boundaries are as large as possible.
In the above solutions, in step S1, when the database is constructed, a ship model scheme with similar ship model characteristics is selected.
In the above scheme, in step S2, the approximate model includes a response surface model, where the response surface model takes Length, Beam, T, V, S, Cb, Cm, and Vs as input variables, and 1000Cr as output variables; corresponding approximate model functionComprises the following steps:
in the formula, xi、xjDesigning sample points for the ith and the j th, wherein k is the number of the sample points and alpha0、αi、αij、αii、αiii、αiiiiIs a fourth-order polynomial undetermined coefficient.
In the above solution, in step S2, the approximation model includes a radial basis model, the radial basis model includes an input layer, a hidden layer, and an output layer, the input layer and the hidden layer present nonlinear transformation, the hidden layer and the output layer present linear transformation, and a Radial Basis Function (RBF) is a learning function from the input layer to the hidden layer of the neural network, and is a typical nonlinear function; the corresponding approximate model function is:
rk=R(||x-Tk||)
wherein x is [ x ]1,x2,…,xn]Representing an n-dimensional input vector, | | | | | is a Euclidean norm, TkIs the center of the kth hidden node (k 1, 2., N)T),NTFor training the number of sample points, R () is the RBF function, RkIs an output distance function.
In the above-described embodiment, in step S2, when performing the error analysis and the validity check of the approximation model function, the root mean square error R and the decision coefficient error R are used2The precision of the model is verified, R → 0 represents that the error of the model is small, the approximate precision is high, and R2→ 1 indicates that the similarity between the model and the original model is high.
In the above scheme, in step S3, the Prandtl-Schlichting formula is:
wherein Re is a Reynolds number,l is the characteristic length, V is the characteristic velocity, and V is the kinetic viscosity coefficient.
In the above scheme, in step S4, the objective function of the optimization algorithm is selected as the sum of the residual resistance coefficients of the full cruise, and the optimized mathematical model is as follows:
Min[SUM(Cr1,Cr2,…,Crn)]
in the optimization process, under the condition of satisfying the major scale constraint, the minimum objective function is the optimal solution, and the corresponding major scale parameter is the optimal major scale parameter combination.
In the above scheme, in step S4, the optimization process of the major-scale parameters specifically includes the following steps:
s4.1, providing initial values of design parameters of a main scale and a ship type of the ship by adopting an ASA optimization algorithm;
s4.2, calculating the residual resistance coefficient of each navigational speed based on the design parameters in the step S4.1 through the approximate model between the main scale, the ship shape parameter and the residual resistance coefficient constructed by the method to obtain a target function value;
s4.3, evaluating the target fitness according to the objective function value, updating design parameters according to the fitness evaluation result by the optimization algorithm, and iteratively performing S4.3 → S4.1 → S4.2 → S4.3 …; the optimization flow termination criteria are typically determined by the maximum number of iteration steps or by achieving an optimal solution (objective function minimum).
The invention has the beneficial effects that:
the method is based on the ship resistance test database, establishes an approximate model of the mapping relation between the abstract main scale and ship type parameters and the residual resistance coefficient, and performs resistance prediction by using the model, so that the workload and time of resistance prediction are greatly reduced compared with numerical calculation; based on an approximate model, the ASA single-target optimization algorithm is utilized, and the main scale parameter optimization selection of the ship can be quickly realized by taking the minimum resistance at the full navigational speed as a target.
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a comparison graph of fitting values of RSM model and original model in the embodiment of the present invention;
FIG. 2 is a graph comparing the fitting values of the RBF model with the original model in the embodiment of the present invention;
FIG. 3 is a diagram illustrating the comparison of the RSM model and the RBF model for predicting the actual ship resistance error according to the embodiment of the present invention;
FIG. 4 is a schematic view of the optimization process of the main scale parameters of the ship according to the present invention;
FIG. 5 is a schematic diagram of an objective function optimization process of the resistance at the full cruise speed section in the embodiment of the invention.
Detailed Description
For a more clear understanding of the technical features, objects and effects of the present invention, embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
The method for optimizing the main scale parameters of the ship based on the approximate model is specifically described below by taking a class of single square-stern ships (with the water displacement of 3000-10000 t) as a research object.
S1, constructing a ship rapidity model test database: screening main hull resistance test data of different ship types under various water displacement, selecting main scale, ship type parameters and rapidity parameters which mainly affect resistance, specifically water line Length, water line width Beam, draft T, water displacement volume V, main hull wet surface area S, square coefficient Cb, middle cross section coefficient Cm, navigational speed Vs and residual resistance coefficient 1000Cr, and constructing a main scale, ship type parameters and rapidity parameter database.
When the database is built, the parameters are uniformly distributed as much as possible in a reasonable range, the upper boundary and the lower boundary are as large as possible, because the parameter range of the database cannot be exceeded when the corresponding resistance of a certain main scale and ship type parameter is forecasted after an approximate model is built on the basis of the database, and extrapolation and calculation are not converged if the resistance is not exceeded. In addition, in order to improve the forecasting precision, a ship type scheme with similar ship type features is selected as much as possible when a database is constructed, so that sudden change of the ship type features and low fitting precision of an approximate model are avoided.
The database construction format is as follows:
length | Beam | T | V | S | Cb | Cm | Vs | 1000Cr |
L1 | B1 | T1 | V1 | S1 | Cb1 | Cm1 | Vs1 | 1000Cr1 |
L2 | B2 | T2 | V2 | S2 | Cb2 | Cm2 | Vs2 | 1000Cr2 |
… | … | … | … | … | … | … | … | … |
s2, approximate model construction: and selecting an approximate model type based on the database sample points in the S1, establishing a corresponding approximate model function related to the mapping relation between the main scale, the ship type parameters and the residual resistance coefficient, and performing error analysis and validity check on the approximate model function.
The process of establishing the approximate model mainly comprises the following steps:
1) selecting a sample point for input;
2) selecting a model function type to express and fit the sample data;
3) and (5) checking the validity.
In this embodiment, two approximation models, namely a fourth-order Response Surface Model (RSM) and a Radial Basis Function (RBF), are created for comparison.
(a) RSM model
The response surface model adopts a nonlinear polynomial with higher fourth-order accuracy as a response surface approximation function, and the response surface model is created by applying methods such as fitting, regression and the like on a plurality of groups of sample points and output values. For the sample point database selected and constructed in the embodiment, length, Beam, T, V, S, Cb, Cm, and Vs are input variables, 1000Cr is output variables, and for the selected 8 variables, at least 61 sample points are required for constructing the fourth-order response surface model, and the number of the sample points in the database constructed herein is 162, which meets the requirement.
The RSM approximation function is of the form:
in the formula (I), the compound is shown in the specification,as a response function xi、xjDesigning sample points for the ith and the j th, wherein k is the number of the sample points and alpha0、αi、αij、αii、αiii、αiiiiIs a fourth-order polynomial undetermined coefficient.
Judging the effectiveness of the fitted response surface model, wherein the common error indexes comprise maximum absolute value error, square sum error, root mean square error and decision coefficient error R2Etc., the present embodiment employs the root mean square R and the decision coefficient error R2The precision of the model is checked, R → 0 represents that the RSM model has small error, R2→ 1 indicates that the RSM model and the original model have high similarity.
In the RSM model constructed in this example, R ═ 0.0224, R2=0.9976。
Randomly selecting 4 sample points in a database for verification, wherein the sample point data comprises main scale and ship type parameter input values and 1000Cr test values, fitting the sample points based on the constructed response surface model, and indicating the result that the RSM model fitting value and the test value 1000Cr corresponding to the sample point are shown in figure 1, and combining R, R2The RSM model constructed in the method has high precision.
(b) RBF model
The Radial Basis Function (RBF) is a learning function from the input layer to the hidden layer of the neural network and is a typical nonlinear function. The corresponding approximate model function is:
rk=R(||x-Tk||)
wherein x is [ x ]1,x2,…,xn]Represents an n-dimensional input vector, |, | | | | is a Euclidean norm, TkIs the center of the kth hidden node (k 1, 2., N)T),NTFor training the number of sample points, R () is the RBF function, RkIs an output distance function.
Determining the validity of the fitted radial basis model, again using the root mean square R and the determinant error (R)2) The precision of the model is checked, R → 0 represents that the RSM model has small error, R2→ 1 indicates that the RSM model and the original model have high similarity.
In the RBF model constructed in this example, R is 0.002112=0.99996。
Randomly selecting 5 sample points for verification, wherein the sample point data comprises main scale and ship type parameter input values and 1000Cr test values, fitting the sample points based on the constructed radial basis model, and comparing the result with the test value 1000Cr corresponding to the sample points, wherein the result shows that the RBF model fitting value is shown in figure 2. Bond R, R2In value, the RBF model constructed in this embodiment is higher than the RSM model.
S3, resistance forecasting: selecting ship main scale and ship type parameter data outside a group of databases as input, calculating the frictional resistance by adopting a Prandtl-Schlichting formula, predicting resistance coefficients based on each approximate model established in S2, comparing the predicted resistance coefficients with corresponding test values, and verifying the accuracy of the predicted resistance of the established approximate model; and finally, selecting a model with a more stable error range and a smaller error mean value as an approximate model for quickly forecasting the ship resistance.
The Prandtl-Schlichting formula is as follows:
wherein Re is a Reynolds number,l is the characteristic length, V is the characteristic velocity, and V is the kinetic viscosity coefficient.
The following table shows the predicted drag coefficient of the present embodiment and the error value of the real ship drag.
Because the absolute value of the residual resistance coefficient is small, the Cr forecasting error of the RSM model reaches 12 percent at most, and the Cr forecasting error of the RBF model reaches 7 percent at most; the actual ship resistance is forecasted, the forecasting error of the RSM model is about 5%, and the forecasting error of the RBF model is about 3%.
As shown in FIG. 3, it can be seen that the error range of the RBF model is more stable in the full-speed range, and the mean value is smaller than that of the RSM model, and compared with the actual ship resistance test value, the error is controlled within 3%. Therefore, the present embodiment selects the RBF model as an approximate model for rapidly forecasting the ship resistance.
S4, automatically optimizing the main scale parameters of the ship by using an optimization algorithm: based on the finally selected approximate model in S3, a single-target optimization algorithm of a self-adaptive simulated annealing algorithm is utilized, and the main scale parameter is optimized by taking the minimum full-flight-speed resistance as a target.
In the embodiment, based on the established RBF approximate model, an Adaptive Simulated Annealing (ASA) single-target optimization algorithm is utilized, and an objective function is selected as the sum of residual resistance coefficients of a full navigational speed section (10-32 kn). In the optimization process, under the condition of meeting the main scale constraint, the objective function is the optimal solution when being the minimum, the corresponding main scale parameter is the optimal main scale parameter combination, and through the optimization process, quick and favorable support can be provided for main scale demonstration work of the overall design of the ship. The optimized mathematical model is as follows:
Min[SUM(Cr1,Cr2,…,Crn)]
as shown in fig. 4, the optimization process specifically includes the following steps:
s4.1, providing initial values of design parameters of a main scale and a ship type of the ship by adopting an ASA optimization algorithm;
s4.2, calculating the residual resistance coefficient of each navigational speed based on the parameters in the step S4.1 through the approximate model between the main scale, the ship shape parameters and the residual resistance coefficient constructed by the method to obtain a target function value;
and S4.3, evaluating the target fitness according to the objective function value, updating the design parameters according to the evaluation result by the optimization algorithm, and iterating to carry out S4.3 → S4.1 → S4.2 → S4.3 …. The optimization flow termination criteria are typically determined by the maximum number of iteration steps or by achieving an optimal solution (objective function minimum).
The optimization process of the embodiment is shown in fig. 5, in the optimization process, as the iteration step increases, the objective function tends to converge and approach to the minimum value, the optimization target is reached, the combination of the main scale with the minimum resistance at the full navigational speed section and the ship type parameter is found through optimization, and quick and effective support is provided for ship main scale demonstration.
The method of the invention has the following advantages:
1. a ship rapidity model test database is established, sample data with excellent performance is selected, two approximate models of the mapping relation of the main scale, ship type parameters and residual resistance coefficients are established, and the accuracy of model fitting degree errors is over 99%; and selecting a better approximate model through verification.
2. The method takes the main scale and the ship type parameters of the ship as input, realizes the rapid prediction of the resistance of the main hull in the full navigational speed section based on an approximate model, has an error of about 3 percent compared with the actual ship resistance test value, greatly saves the solving time compared with the CFD numerical calculation, and provides an efficient response capability for the prediction of the ship resistance with approximate ship type characteristics.
3. Based on the established approximate model, the main scale parameters are optimized by using a self-adaptive simulated annealing optimization algorithm and aiming at the minimum resistance of the full navigational speed section, and reasonable main scale parameters are effectively and objectively selected.
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (10)
1. A ship main scale parameter optimization method based on an approximate model is characterized by comprising the following steps:
s1, constructing a ship rapidity model test database: screening main hull resistance test data of different ship types under various water displacement, selecting a main scale, ship type parameters and rapidity parameters which mainly affect resistance, and constructing a main scale, ship type parameters and rapidity parameter database;
s2, approximate model construction: selecting an approximate model type based on the database sample points in S1, establishing a corresponding approximate model function related to the mapping relation between the main scale, the ship type parameters and the residual resistance coefficient, and performing error analysis and validity check on the approximate model function;
s3, resistance forecasting: selecting ship main scale and ship type parameter data outside a group of databases as input, calculating the frictional resistance by adopting a Prandtl-Schlichting formula, predicting resistance coefficients based on each approximate model established in S2, comparing the predicted resistance coefficients with corresponding test values, and verifying the accuracy of the predicted resistance of the established approximate model; finally, selecting a model with a more stable error range and a smaller error mean value as an approximate model for quickly forecasting the ship resistance;
s4, automatically optimizing the main scale parameters of the ship by using an optimization algorithm: based on the approximate model finally selected in S3, a main scale parameter is optimized by using an adaptive simulated annealing algorithm (ASA) single-target optimization algorithm and taking the minimum resistance at the full-speed section as a target.
2. The approximate model based ship main scale parameter optimization method according to claim 1, wherein in step S1, the main scales mainly affecting the resistance include a water line Length, a water line width Beam, a draft T, a displacement volume V, a main hull wet surface area S, the ship type parameters include a square coefficient Cb and a middle cross section coefficient Cm, and the rapidity parameters include a navigational speed Vs and a residual resistance coefficient 1000 Cr.
3. The method for optimizing main-scale parameters of a ship based on an approximate model according to claim 2, wherein in step S1, when constructing the database, the parameters are distributed as uniformly as possible within a reasonable range and the upper and lower boundaries are as large as possible.
4. The method for optimizing main scale parameters of ships according to claim 2, wherein in step S1, a ship type scheme with similar ship type characteristics is selected when the database is constructed.
5. The approximate model-based ship main scale parameter optimization method according to claim 2, wherein in step S2, the approximate model comprises a response surface model, the response surface model takes Length, Beam, T, V, S, Cb, Cm, Vs as input variables, and 1000Cr as output variables; corresponding approximate model functionComprises the following steps:
in the formula, xi、xjDesigning sample points for the ith and the j th, wherein k is the number of the sample points and alpha0、αi、αij、αii、αiii、αiiiiIs a fourth-order polynomial undetermined coefficient.
6. The method for optimizing main scale parameters of ships according to claim 2, wherein in step S2, the approximate model comprises a radial basis model, the radial basis model comprises an input layer, a hidden layer and an output layer, the input layer and the hidden layer exhibit nonlinear transformation, the hidden layer and the output layer exhibit linear transformation, and a Radial Basis Function (RBF) is a learning function from a neural network input layer to the hidden layer, and is a typical nonlinear function; the corresponding approximate model function is:
rk=R(||x-Tk||)
wherein x is [ x ]1,x2,…,xn]Representing an n-dimensional input vector, | | | | | is a Euclidean norm, TkIs the center of the kth hidden node (k 1, 2., N)T),NTFor training the number of sample points, R () is the RBF function, RkIs an output distance function.
7. The method for optimizing main scale parameters of ships according to claim 5 or 6, wherein in step S2, the root mean square R and the decision coefficient error R are used for the analysis of the function error of the approximate model and the validity check2The precision of the model is verified, R → 0 represents that the error of the model is small, the approximate precision is high, and R2→ 1 indicates that the similarity between the model and the original model is high.
9. The method for optimizing main scale parameters of ships according to claim 1, wherein in step S4, the objective function of the optimization algorithm is selected as the sum of the residual drag coefficients of the full-speed section, and the optimized mathematical model is as follows:
Min[SUM(Cr1,Cr2,…,Crn)]
in the optimization process, under the condition of satisfying the major scale constraint, the minimum objective function is the optimal solution, and the corresponding major scale parameter is the optimal major scale parameter combination.
10. The approximate model-based ship main-scale parameter optimization method according to claim 9, wherein in step S4, the main-scale parameter optimization process specifically includes the following steps:
s4.1, providing initial values of design parameters of a main scale and a ship type of the ship by adopting an ASA optimization algorithm;
s4.2, calculating the residual resistance coefficient of each navigational speed based on the design parameters in the step S4.1 through the approximate model between the main scale, the ship shape parameter and the residual resistance coefficient constructed by the method to obtain a target function value;
s4.3, evaluating the target fitness according to the objective function value, updating design parameters according to the fitness evaluation result by the optimization algorithm, and iteratively performing S4.3 → S4.1 → S4.2 → S4.3 …; the optimization flow termination criteria are typically determined by the maximum number of iteration steps or by achieving an optimal solution (objective function minimum).
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