CN116050283B - Multi-objective optimal design method and equipment for composite flexible pipe layering - Google Patents
Multi-objective optimal design method and equipment for composite flexible pipe layering Download PDFInfo
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Abstract
The invention belongs to the technical field of ocean engineering design, and discloses a multi-objective optimization design method and equipment for a composite flexible pipe laying. Determining structural parameters and material parameters of RTPs, and setting an optimization target; selecting a homogenized optimal sample point; establishing an RTPs three-dimensional progressive damage failure model, and calling the three-dimensional progressive damage failure model through Matlab programming to calculate the bearing capacity and the tensile rigidity of each sample point of the optimal matrix; calculating the bearing capacity and the tensile rigidity of the test group through an interpolation proxy model; and establishing a two-stage multi-objective parallel optimization algorithm, and carrying out multi-angle multi-objective optimization design on RTPs by taking the RTPs bearing capacity and the tensile rigidity as targets. The parallel optimization algorithm is more suitable for complex engineering problems through the design of the inner stage and the outer stage, and has great potential and universal applicability in the multi-objective optimization problem.
Description
Technical Field
The invention belongs to the technical field of ocean engineering design, and particularly relates to a multi-objective optimization design method and equipment for a composite flexible pipe laying.
Background
The winding angle of the fiber reinforced thermoplastic flexible pipe reinforcing layer directly influences the mechanical property of the fiber reinforced thermoplastic flexible pipe reinforcing layer, and the multi-angle optimization method is a subject to be researched in the field of ocean engineering at present.
At present, the fiber winding flexible pipe adopts a single-angle design scheme of +/-55 degrees in the design process, so that the performance advantage of the flexible pipe cannot be exerted to the greatest extent, the application prospect of the flexible pipe is limited, and the cost waste is caused. In recent years, multi-angle optimization schemes have attracted attention in the industry, and related experiments and numerical simulation methods prove that the multi-angle winding schemes can enable the strength of the fiber reinforced layer to be more uniform, so that the mechanical properties of the flexible pipe are obviously improved.
However, the research results related to multi-angle winding are limited to a double-angle optimization scheme, and a multi-angle optimization theoretical model is not established yet.
Through the above analysis, the problems and defects existing in the prior art are as follows:
(1) The single-angle design method of the fiber-wound flexible pipe in the prior art is cost-consuming and cannot exert the performance advantages of the flexible pipe to the greatest extent.
(2) The multi-angle layering optimization design method for the fiber reinforced thermoplastic flexible pipe in the prior art is suitable for complex engineering effects, and the obtained product parameters are low in accuracy.
Disclosure of Invention
In order to overcome the problems in the related art, the disclosed embodiments of the present invention provide a multi-objective optimization design method and apparatus for composite flexible pipe lay-up.
The technical scheme is as follows: the multi-objective optimization design method for the composite flexible pipe laying is applied to an information data processing terminal and comprises the following steps:
s101, determining structural parameters and material parameters of a fiber reinforced thermoplastic composite pipe, and setting variables and optimization targets for flexible pipe layering optimization; wherein, the structural parameters of the fiber reinforced thermoplastic composite tube include: reinforcing layer number, test section tube length, outer protective layer thickness, inner liner thickness, inner diameter and outer diameter; the material parameters of the fiber reinforced thermoplastic composite tube include: an elastic constant in the reinforcing layer, a strength parameter in the reinforcing layer, an HDPE in the elastic constant, and an HDPE in the strength parameter;
s102, selecting an optimal sample point for layering homogenization of a fiber reinforced thermoplastic composite pipe;
s103, calculating the mechanical properties of sample points of the fiber reinforced thermoplastic composite pipe, according to the three-dimensional stress state of the fiber reinforced thermoplastic composite pipe, adopting an improved Hashin-Yeh failure criterion to be combined with a nonlinear stiffness degradation model, establishing a three-dimensional progressive damage failure model of the fiber reinforced thermoplastic composite pipe, and calling the three-dimensional progressive damage failure model through Matlab programming to calculate the bearing capacity and the tensile stiffness of each sample point of the optimal matrix of the fiber reinforced thermoplastic composite pipe;
s104, establishing an interpolation agent model; performing Kriging interpolation on the first 90% of sample points, taking the last 10% of sample points as a test group, and calculating the bearing capacity and the tensile rigidity of the test group through an interpolation proxy model;
s105, two-stage algorithm optimization; the traditional multi-objective optimization algorithm is improved by combining a rapid non-dominant ordering genetic algorithm with elite strategy, a two-stage multi-objective parallel optimization algorithm is established, and multi-angle multi-objective optimization design is carried out on the fiber reinforced thermoplastic composite pipe by taking the bearing capacity and the tensile rigidity of the fiber reinforced thermoplastic composite pipe as targets based on the two-stage multi-objective parallel optimization algorithm.
In step S101, the variable for optimizing the flexible pipe lay is set as the flexible pipe lay winding angle, and the winding angle distribution of the flexible pipe lay is wound by adopting two adjacent layers of positive and negative same angles, and the winding mode is as followsThe method comprises the steps of carrying out a first treatment on the surface of the And determining an optimization target according to the production capacity of the winding process, wherein the optimization target is a winding angle optimization range.
In step S102, selecting an optimal sample point for homogenizing a fiber reinforced thermoplastic composite tube layup includes:
(1) Determining the space dimension of the design variables of the Latin hypercube sampling method LHS according to the number N of the design variables, selecting M sample points, and selecting the following steps: dividing each dimension into M sections which are not overlapped with each other, so that each section has the same probability; randomly extracting M points in each interval in each dimension;
(2) Randomly extracting the points selected in the step (1) from each dimension, and forming sample vectors from the selected pointsM sample points form an N x M sample point matrix;
(3) Setting the sampling times as N, and establishing N N multiplied by M sample point matrixes; using a criterion of maximum and minimum distanceAnd the centralized deviation criterion->And carrying out homogenization evaluation on the established sample point matrix, and taking the matrix which is optimal in homogenization under two criteria as the sample point.
In one embodiment, for a maximum minimum distance criterion, the distance between any two sample points is calculated using the maximum minimum criterionSorting the obtained distances to obtain a distance function list，/>Is satisfied->The number of dot pairs of (1) by +.>Measuring sample uniformity;
for the centralized deviation criterionDefining the deviation of the point set at the point x, normalizing the sample points, and adopting the centralization deviation +.>The formula is as follows:
。
wherein, the liquid crystal display device comprises a liquid crystal display device,is->From the origin 0 andxrectangle of decision +.>Is->The point in (1) falls into->The number of (1)>The points in->When the walking of the Chinese medicine is uniform, the Chinese medicine is added>And->Is>Near (I)>Defined as the difference between the two, called the point set +.>Point(s)xError of (2); />And (5) designing the values of the test points in the matrix for the normalization test.
In step S103, the combination of the improved Hashin-Yeh failure criterion and the nonlinear stiffness degradation model is adopted, and before the three-dimensional progressive damage failure model of the fiber reinforced thermoplastic composite tube RTPs is established, the following steps are performed: according to the three-dimensional anisotropic elastic mechanics theory, according to interlayer stress, material nonlinearity, temperature stress and winding angle change factors of a flexible pipe layer, and by combining with the three-dimensional stress state of RTPs under a complex load working condition, constructing an RTPs three-dimensional constitutive model;
the improved Hashin-Yeh failure criteria include:
when the fiber is in tensile failure, the fiber is:
。
when the fiber compression fails, the fiber is: />。
The shear failure of the fiber matrix is as follows:。
when the matrix fails in tension, the matrix is:
。
when the matrix is in compression failure, the method comprises the following steps:
。
when the tensile delamination fails, the tensile delamination is:
。
when the compression delamination fails, the compression delamination is:
。
in the method, in the process of the invention,respectively positive stress and shear stress components in all directions; />Is the yield stress of HDPE; />Respectively the strength parameters of the glass fiber ribbon; />As a result of the failure factor,respectively, different types of failure modes, and when the failure factor is greater than 1, the type of failure mode starts to happen.
In the Kriging interpolation of the first 90% of the sample points in step S104, the correlation description function of the sample points is as follows:
。
。
wherein, the liquid crystal display device comprises a liquid crystal display device,representing the number of known design variables, +.>Training sample points +.>And->Is the first of (2)kA component;
the gaussian correlation function is selected as follows:
taking the last 10% of sample points as a test group, calculating the bearing capacity and the tensile rigidity of the test group through an interpolation proxy model, and verifying the quality of the interpolation proxy model according to a root mean square error and a complex correlation coefficient formula;
the mean square error is:
。
the complex correlation coefficients are:
。
the interpolation proxy model is built as follows:
(1) The optimization targets are to improve the bearing capacity and the tensile rigidity of the fiber reinforced thermoplastic composite pipe, and simultaneously perform multi-target optimization on the bearing capacity and the tensile rigidity of the fiber reinforced thermoplastic composite pipe;
(2) The winding angle distribution of the flexible pipe adopts adjacent two layers of positive and negative winding at the same angle, and the winding mode is thatThe design variables are two；
(3) Determining the optimal range of the winding angle to be +/-40 degrees to +/-80 degrees;
(4) The built interpolation proxy model is expressed as follows:
。
。
wherein the method comprises the steps ofRespectively represents an optimized winding angle, function->And (5) interpolating proxy models corresponding to the two objective functions.
In step S105, the two-stage multi-objective parallel optimization algorithm includes:
establishing a plurality of parallel initial islands in an inner stage, and realizing design variable optimization in each island through an elite strategy NSGA-II algorithm sequence comprising an initialization stage, an fitness evaluation stage, a selection stage, a crossing stage and a mutation stage;
defining migration conditions at an outer stage, selecting samples with the same proportion from the good population and the poor population in each island as random migration samples, exchanging migration samples in the rest parallel islands, and then carrying out a re-optimization cycle; and screening and sequencing the optimized sample set to obtain a final Pareto optimal solution.
Another object of the present invention is to provide a computer apparatus comprising: at least one processor, a memory, and a computer program stored in the memory and executable on the at least one processor, which when executed implements the composite flexible pipe lay-up multi-objective optimization design method described above.
By combining all the technical schemes, the invention has the advantages and positive effects that:
first, aiming at the technical problems existing in the prior art and the difficulty of solving the problems, the technical problems solved by the technical scheme of the invention to be protected, results and data in the research and development process and the like are closely combined, the technical problems solved by the technical scheme of the invention are analyzed in detail and deeply, and some technical effects with creativity brought after the problems are solved are specifically described as follows:
the invention discloses a multi-angle layering optimization design method of a fiber reinforced thermoplastic flexible pipe, which constructs a two-stage multi-objective parallel optimization algorithm and establishes a special island model to realize parallel operation of the algorithm model. In order to improve the convergence speed of the optimization algorithm and maintain the solution diversity in the convergence process, an approximate interpolation proxy model is introduced, migration criteria are established between parallel islands, and the search domain of the optimal solution is enlarged. And the combined action of different convergence criteria, optimization mechanisms and the like can be realized in each parallel island at the inner stage so as to improve the flexibility and the application range of the algorithm. Meanwhile, the final screening and sorting mechanism at the outer stage realizes 'optimal-middle-optimal-selection' and effectively avoids the problems that the optimal solution is lost and falls into local optimal. The parallel optimization algorithm is more suitable for complex engineering problems through the design of the inner stage and the outer stage, and has great potential and universal applicability in the multi-objective optimization problem.
Secondly, the technical proposal is regarded as a whole or from the perspective of products, and the technical proposal to be protected has the technical effects and advantages as follows:
along with the gradual improvement of the production capacity of the flexible pipe, the fine control of the winding angle of each layer of the enhancement layer can be realized, so that a three-dimensional multi-angle optimization model of RTPs needs to be established to furthest improve the mechanical properties of the RTPs.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the disclosure and together with the description, serve to explain the principles of the disclosure;
FIG. 1 is a flow chart of a multi-objective optimization design method for a composite flexible pipe lay-up provided by an embodiment of the invention;
FIG. 2 is a schematic diagram of the establishment of a three-dimensional progressive damage failure model for RTPs provided by an embodiment of the present invention;
FIG. 3 is a NSGA-II flowchart provided by an embodiment of the present invention;
FIG. 4 is a flow chart of a parallel optimization algorithm provided by an embodiment of the present invention;
fig. 5 is a schematic diagram of a sample distribution latin square matrix according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of an optimized solution set for 4-layer RTPs provided by an embodiment of the present invention;
FIG. 7A is a population distribution diagram of the 1 st generation to the 9 th generation in the Pareto optimal solution set convergence step according to the embodiment of the invention;
FIG. 7B is a population distribution diagram from generation 50 to generation 200 in the Pareto optimal solution set convergence step provided by an embodiment of the invention;
FIG. 8 is a schematic diagram of a progressive failure process for a composite material provided by an embodiment of the present invention;
fig. 9 is a theoretical model calculation flowchart provided by an embodiment of the present invention.
Detailed Description
In order that the above objects, features and advantages of the invention will be readily understood, a more particular description of the invention will be rendered by reference to the appended drawings. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. The invention may be embodied in many other forms than described herein and similarly modified by those skilled in the art without departing from the spirit or scope of the invention, which is therefore not limited to the specific embodiments disclosed below.
1. The embodiments are explained.
Example 1.
As shown in fig. 1, the multi-objective optimization design method for the composite flexible pipe pavement provided by the embodiment of the invention comprises the following steps:
s101, setting flexible pipe laying optimization variables and optimization targets:
firstly, determining structural parameters and material parameters of fiber reinforced thermoplastic composite tubes RTPs (Reusable Thermal Protection System, RTPS), and setting a flexible tube layering optimization target; the design variable is the flexible pipe layer winding angle, and the flexible pipe needs to resist torsion working conditions, so that adjacent two layers of positive and negative same-angle winding are adopted for the flexible pipe layer winding angle distribution, namely the winding mode is thatThe method comprises the steps of carrying out a first treatment on the surface of the And determining the optimal range of the winding angle according to the production capacity of the winding process.
Wherein, structural parameters of the fiber reinforced thermoplastic composite tube RTPs include: the number of the reinforcing layers is 4; the length of the test section tube is 993mm; the thickness of the outer protective layer is 2mm; the thickness of the lining layer is 4mm; the inner diameter is 48mm; the outer diameter is 62mm;
the material parameters of the fiber reinforced thermoplastic composite tube RTPs include: the elastic constants in the reinforcement layer are:
。
。
HDPE (High Density Polyethylene HDPE) in the elastic constant is:
。
the strength parameters in the enhancement layer are:
。
。
among the strength parameters, HDPE is:
。
s102, selecting an optimal sample point for layering homogenization of a fiber reinforced thermoplastic composite pipe;
first according to the number of design variablesNDetermining the space dimension of a design variable of a Latin hypercube sampling method LHS, selecting M sample points, and selecting the following steps: dividing each dimension into M sections which are not overlapped with each other, so that each section has the same probability; randomly extracting M points in each interval in each dimension; randomly extracting the points selected in the previous step from each dimension, and forming the points into sample vectorsThe M sample points form an nxm sample point matrix.
Setting the sampling times as N, and establishing N N multiplied by M sample point matrixes; using a criterion of maximum and minimum distanceAnd the centralized deviation criterion->And carrying out homogenization evaluation on the established sample point matrix, and taking the matrix which is optimal in homogenization under two criteria as the sample point.
For the maximum and minimum distance criterion, calculating the distance between any two sample points by adopting the maximum and minimum criterionOrdering the obtained distances to obtain a distance function list +.>，/>Is satisfied->The number of dot pairs of (1) by +.>Measuring sample uniformity;
for the centralized deviation criterionDefining the deviation of the point set at the point x, carrying out normalization processing on the sample points, and adopting a centralized deviation for improving the timeliness of deviation calculation>As formula (1):
。
wherein, the liquid crystal display device comprises a liquid crystal display device,is->From the origin 0 andxrectangle of decision +.>Is->The point in (1) falls into->The number of (1)>The points in->When the walking of the Chinese medicine is uniform, the Chinese medicine is added>And->Is>Near (I)>Defined as the difference between the two, called the point set +.>Point(s)xError of (2); />And (5) designing the values of the test points in the matrix for the normalization test.
S103, calculating the mechanical properties of the sample points of the fiber reinforced thermoplastic composite tube:
as shown in fig. 2, according to the three-dimensional anisotropic elastic mechanics theory, on the basis of considering factors such as interlayer stress, material nonlinearity, temperature stress, winding angle change and the like, the three-dimensional stress state of the RTPs under the complex load working condition is described in detail, and the three-dimensional constitutive model of the RTPs of the fiber reinforced thermoplastic composite pipe is constructed. According to the three-dimensional stress state description of the RTPs of the fiber reinforced thermoplastic composite pipe, an improved Hashin-Yeh failure criterion is combined with a nonlinear stiffness degradation model, a three-dimensional progressive damage failure model of the RTPs of the fiber reinforced thermoplastic composite pipe is established, and the bearing capacity and the tensile stiffness of each sample point of the optimal matrix are calculated by calling the three-dimensional progressive damage failure model through Matlab programming.
Wherein the improved Hashin-Yeh failure criteria comprises:
when the fiber is in tensile failure, the fiber is:
。
when the fiber compression fails, the fiber is:
。
the shear failure of the fiber matrix is as follows:
。
when the matrix fails in tension, the matrix is:
。
when the matrix is in compression failure, the method comprises the following steps:
。
when the tensile delamination fails, the tensile delamination is:
。
when the compression delamination fails, the compression delamination is:
。
in the method, in the process of the invention,respectively positive stress and shear stress components in all directions; />Is the yield stress of HDPE; />Respectively the strength parameters of the glass fiber ribbon; />As a result of the failure factor,respectively, different types of failure modes, and when the failure factor is greater than 1, the type of failure mode starts to happen.
S104, establishing an interpolation agent model:
kriging interpolation is carried out on the first 90% of sample points, and the correlation description function of the sample points is as follows:
。
wherein, the liquid crystal display device comprises a liquid crystal display device,representing the number of known design variables, +.>Training sample points +.>And->Is the first of (2)kA component;
since the formula (2) has high nonlinearity, the gaussian correlation function is selected as follows:
（3）
and taking the last 10% of sample points as a test group, calculating the bearing capacity and the tensile rigidity of the test group through the interpolation proxy model, and verifying the quality of the interpolation proxy model according to the root mean square error and the complex correlation coefficient as shown in the formula (4) and the formula (5), wherein the smaller the root mean square error is, the larger the complex correlation coefficient is, and the higher the accuracy of the interpolation proxy model is.
Mean square error:
（4）
complex correlation coefficient:
（5）
s105, two-stage algorithm optimization:
the flow of the two-stage multi-objective parallel optimization algorithm is shown in fig. 4, and the interpolation agent model established by the previous step is combined with a special island model to realize the two-stage multi-objective parallel optimization algorithm, so that the advantage is that a Pareto front is solved, a decision maker can select a final solution according to actual engineering needs, and the solution is not easy to fall into local optimum due to the design of the inner stage and the outer stage.
First, a parallel initial island group is established in an inner stage, and design variable optimization is realized in each island through an elite strategy NSGA-II algorithm sequence comprising the steps of initialization, fitness evaluation, selection, crossover and mutation, as shown in figure 3.
An independent convergence criterion or adaptation method (such as execution time, iteration times or adaptation value) is defined in the operation process on each island, and different NSGA-II algorithms can be adopted between different islands, so that the optimization method can be suitable for single-target optimization.
In the outer stage, firstly defining migration conditions, selecting samples with the same proportion from the good population and the poor population in each island as random migration samples, exchanging migration samples in the rest parallel islands, and then carrying out a re-optimization cycle.
The two-stage multi-objective parallel optimization algorithm adopts a full-communication structure, so that samples can be conveniently and directly migrated between the communication islands, and different convergence criteria or adaptation methods can be selected from different parallel islands. And the two-stage parallel model stores each generation of optimized samples in each parallel island in a memory, and screens and sorts the optimized sample set to obtain a final Pareto optimal solution set.
Example 2.
The multi-objective optimization design method for the composite flexible pipe pavement provided by the embodiment 1 of the invention can design a composite flexible pipe pavement.
Example 3.
The multi-objective optimization design method for the composite flexible pipe laying provided by the embodiment of the invention is applied to an information data processing terminal and comprises the following steps:
firstly, according to the three-dimensional anisotropic elastic mechanics theory, on the basis of considering factors such as interlayer stress, material nonlinearity, temperature stress, winding angle change and the like, describing the three-dimensional stress state of RTPs under a complex load working condition, and constructing a three-dimensional constitutive model of the fiber reinforced thermoplastic composite pipe RTPs (Reusable Thermal Protection System, RTPS).
Combining an improved Hashin-Yeh failure criterion with a nonlinear stiffness degradation model according to RTPs three-dimensional stress state description, establishing an RTPs three-dimensional progressive damage failure model,
for RTPs reinforcing layer glass fiber belts, the RTPs reinforcing layer glass fiber belts have high anisotropism, and for reinforcing layers formed by bonding multiple layers of glass fiber belts, the influence of damage has a certain limitation due to the load sharing and restraining actions between adjacent glass fiber belts, which also leads to the fact that the reinforcing layers are subjected to complex damage before reaching the ultimate strength to cause final failure, and the damage evolution rule is shown in figure 8. Therefore, in the damage failure prediction process, the instantaneous damage theory is adopted to reduce the material property, namely, the calculation result is inaccurate and the numerical calculation convergence difficulty is increased. In order to improve the accuracy of composite damage prediction, the evolution rule of the composite damage must be simulated by considering the progressive damage theory.
In the view of figure 8 of the drawings,σ eq andδ eq is the stress and strain of the composite material;σ 0 eq is the ultimate strength of the composite material；αIs the damage coefficient of the material. The damage path corresponding to the instantaneous damage theory is OBCD, and the damage path corresponding to the progressive damage theory is OBD. When the composite material is damaged, the degradation factor is utilizedd i Establishing a nonlinear stiffness degradation model whenαLinear degradation when=0, whenα=1,2,3…nAnd correspondingly, the index is degraded.
（6）
The progressive damage model currently in common use defines damage coefficients for linear failures, or only one failure mode uses progressive degradation modeling, while the other failure modes use transient degradation modeling, and such progressive damage theory cannot accurately simulate the progressive damage history. The embodiment of the invention adopts a nonlinear index degradation mode, comprehensively considers an intrinsic coupling mechanism among failure modes, and has the material damage coefficient of the nonlinear degradation modeαTaking 1, the flexibility matrix of the damaged glass fiber ribbon under the material coordinate system can be obtained:
（7）
in the method, in the process of the invention,is the parameters of the glass fiber band flexibility matrix under the material coordinate system.
Whereas different failure modes may occur simultaneously in the same layer, the damage parameters are definedTo determine the primary failure mode, the expression is as follows:
。
。
。
。
。
。
。
。
（8）
in the actual calculation process, the change of the damage parameters presents complex nonlinearity due to the complexity of the stress field distribution and the winding angle change. According to the formulas (6) to (8), the influence of different failure modes can be converted into the rigidity degradation of the RTPs reinforcing layer, so that the coupling effect of the different failure modes is comprehensively considered.
According to the above, the RTPs three-dimensional progressive damage model is constructed, and the stress analysis and failure prediction of the RTPs under different load working conditions are carried out. The theoretical model solving process is realized by adopting Matlab mathematical software to program a calculation program, and failure mechanisms of RTPs under different load working conditions are analyzed. The loading process is simulated in a successive iteration mode, the model calculation process is shown in fig. 9, and the detailed processes of iteration and matrix calculation are shown in a flow chart. First, inputting RTPs initial geometric parameters and material properties, and establishing a compliance matrix of each layer in a material coordinate system. Before iteration starts, a damage state matrix is definedInitial loadFIncremental step of loadF i And limit loadF_loadAnd establishing an RTPs global compliance matrix under a cylindrical coordinate system. From a given initial loadFStarting iteration, predicting stress distribution of each layer for failure evaluation, and determining material nonlinearity and winding angle change according to stress state. And updating the input parameters of the RTPs according to the calculation result of the previous iteration for the next iteration. If it isF<F_loadThenF = F+F i The iterative computation continues; when (when)F ≥ F_loadWhen iteration is finished, outputting limit loadF_loadCalculation result under action. Judging failure factors while iterative calculationR i Whether or not is greater than 1, when the failure factorR i And when the number is greater than 1, recording failure positions and failure modes, storing failure information in a failure state matrix, outputting the failure information, judging the progressive damage process of RTPs according to the outputted failure state matrix, and updating a flexibility matrix, wherein the construction of a complete theoretical model is shown in a detailed view in figure 2.
Establishing an interpolation proxy model of a progressive damage failure model based on Latin hypercube sampling simulation and a spatial local interpolation method (Kriging method);
in order to concentrate the optimization result in the Pareto dominant region, the embodiment of the invention combines a rapid non-dominant ordering genetic algorithm (NSGA-II) with elite strategy to improve the traditional multi-objective optimization algorithm, provides a two-stage multi-objective parallel optimization algorithm, establishes a special island model for parallel calculation of the two-stage multi-objective parallel optimization algorithm model, and carries out multi-angle multi-objective optimization design on RTPs by taking the bearing capacity and tensile rigidity of the RTPs as targets.
In the foregoing embodiments, the descriptions of the embodiments are emphasized, and in part, not described or illustrated in any particular embodiment, reference is made to the related descriptions of other embodiments.
The content of the information interaction and the execution process between the devices/units and the like is based on the same conception as the method embodiment of the present invention, and specific functions and technical effects brought by the content can be referred to in the method embodiment section, and will not be described herein.
It will be apparent to those skilled in the art that, for convenience and brevity of description, only the above-described division of the functional units and modules is illustrated, and in practical application, the above-described functional distribution may be performed by different functional units and modules according to needs, i.e. the internal structure of the apparatus is divided into different functional units or modules to perform all or part of the above-described functions. The functional units and modules in the embodiment may be integrated in one processing unit, or each unit may exist alone physically, or two or more units may be integrated in one unit, where the integrated units may be implemented in a form of hardware or a form of a software functional unit. In addition, the specific names of the functional units and modules are only for distinguishing from each other, and are not used for limiting the protection scope of the present invention. For specific working processes of the units and modules in the system, reference may be made to corresponding processes in the foregoing method embodiments.
2. Application example.
Application example 1.
The multi-objective optimization design method for the composite material flexible pipe layering provided by the embodiment of the invention is applied to the preparation of fiber reinforced thermoplastic flexible pipes in the fields of ocean engineering, aviation and chemical industry.
Application example 2.
The embodiment of the invention also provides a computer device, which comprises: at least one processor, a memory, and a computer program stored in the memory and executable on the at least one processor, which when executed by the processor performs the steps of any of the various method embodiments described above.
Embodiments of the present invention also provide a computer readable storage medium storing a computer program which, when executed by a processor, performs the steps of the respective method embodiments described above.
The embodiment of the invention also provides an information data processing terminal, which is used for providing a user input interface to implement the steps in the method embodiments when being implemented on an electronic device, and the information data processing terminal is not limited to a mobile phone, a computer and a switch.
The embodiment of the invention also provides a server, which is used for realizing the steps in the method embodiments when being executed on the electronic device and providing a user input interface.
Embodiments of the present invention provide a computer program product which, when run on an electronic device, causes the electronic device to perform the steps of the method embodiments described above.
The integrated units, if implemented in the form of software functional units and sold or used as stand-alone products, may be stored in a computer readable storage medium. Based on such understanding, the present application implements all or part of the flow of the method of the above embodiments, and may be implemented by a computer program to instruct related hardware, where the computer program may be stored in a computer readable storage medium, where the computer program, when executed by a processor, may implement the steps of each of the method embodiments described above. Wherein the computer program comprises computer program code which may be in source code form, object code form, executable file or some intermediate form etc. The computer readable medium may include at least: any entity or device capable of carrying computer program code to a photographing device/terminal apparatus, recording medium, computer Memory, read-Only Memory (ROM), random access Memory (Random Access Memory, RAM), electrical carrier signals, telecommunications signals, and software distribution media. Such as a U-disk, removable hard disk, magnetic or optical disk, etc.
In the foregoing embodiments, the descriptions of the embodiments are emphasized, and in part, not described or illustrated in any particular embodiment, reference is made to the related descriptions of other embodiments.
3. Evidence of example related effects:
taking 4 RTPs as an example, calculating Pareto optimal solution sets of bearing capacity and tensile rigidity under different winding angles, and the structural parameters and material parameters of the RTPs sample tube are shown in tables 1 and 2.
TABLE 1 parameters of sample tube structure
。
TABLE 2 parameters of sample tube materials
。
And (5) performing multi-angle optimization on the RTPs winding angle. The interpolation proxy model is built as follows:
(1) The optimization targets are to improve the bearing capacity and the tensile rigidity of RTPs, and the multi-target optimization is carried out on the two targets at the same time.
(2) The winding angle distribution of the flexible pipe adopts adjacent two layers of positive and negative winding with the same angle, namely the winding mode is [ [φ 1 , -φ 1 , φ 2 , -φ 2 ]. The design variables are two.
(3) The production capacity of the current winding process is +/-40 degrees to +/-80 degrees, so that the optimal range of the winding angle is +/-40 degrees to +/-80 degrees.
(4) The built interpolation proxy model may be expressed as follows:
。/>
。
wherein the method comprises the steps ofRepresents an optimized winding angle in units of degrees; function->And (5) interpolating proxy models corresponding to the two objective functions.
And selecting sample points by using a Latin hypercube sampling method, selecting 50 sample points, wherein the Latin square sampling number is 5000, namely randomly establishing 5000 sample point matrixes with the 2-factor 50 level. And carrying out homogenization evaluation on the established sample point matrix, and extracting the matrix with optimal homogenization as a sample point. Fig. 5 is a latin square matrix of the determined sample points, and the calculated response values of the RTPs progressive damage failure model are summarized in table 3, which is used as a basis for the subsequent Kriging interpolation.
TABLE 3 Kriging interpolation sample points
。
Table 3 Kriging interpolation sample points (continuations)
。
And extracting 50 optimal sample points by Latin hypercube sampling, and calling the established three-dimensional damage failure model to calculate the corresponding bearing capacity and tensile rigidity. And carrying out kriging interpolation on the first 45 samples, taking the number of the last 5 groups of samples as a test group, and verifying the advantages and disadvantages of the established interpolation model through a comparison result. And (3) establishing an interpolation proxy model by selecting a Gaussian function suitable for the nonlinear problem, calculating response values of 5 groups of samples according to the established proxy model, and correspondingly calculating the response values as shown in a table 4.
According to the formula (4) and the formula (5), establishing an interpolation proxy model quality evaluation method, taking the bearing capacity and the tensile rigidity obtained by calculation of the samples 46-50 as test points, and calculating the corresponding root mean square error and complex correlation coefficient, wherein the calculation results are shown in the table 5. According to the calculation result, the root mean square error corresponding to the calculation result of the interpolation proxy model is very small, and meanwhile, the complex correlation coefficient is close to 1, so that the established interpolation proxy model can be proved to have good quality, and the requirement of subsequent optimization calculation is met.
Table 4 interpolation proxy model calculations
。
Table 5 interpolation proxy model quality assessment
。
Performing multi-angle optimization by combining a two-stage multi-objective parallel optimization model with an NSGA-II algorithm, wherein the final optimization result is shown in figure 6, and the distribution range of the bearing capacity is 12.20-31.91 MPa; the tensile stiffness distribution ranges from 2023.12 to 2648.43 kN. Further analysis shows that the influence of the winding angle on the bearing capacity and the tensile rigidity is opposite, so that the winding angle is required to be preferentially selected according to the actual engineering requirement, and the sufficient bearing capacity is ensured, and too much tensile rigidity cannot be sacrificed. The pressure bearing capacity obtained by the existing single-angle winding scheme is 23.63 MPa, the tensile rigidity is 2088.66 kN, and the single-angle winding scheme is far away from the Pareto front, so that the structural advantages of RTPs cannot be fully exerted by the single-angle winding scheme; the weight coefficient method multi-objective optimization scheme incorporates human control factors, is solved into a part of the Pareto front, and the optimization result cannot provide a wide reference value; according to the analysis, the phase multi-objective parallel optimization algorithm provided by the invention improves the optimization precision of the optimization model to the greatest extent, avoids the problem of optimal solution loss or local optimization, and has a wide reference value for engineering practice.
The convergence process of the multi-angle optimal solution set is shown in fig. 7A-7B, the objective function is rapidly converged to the vicinity of the optimal solution after the first few generations of scattered distribution, the optimal solution is already approximate to the 50 generations, and the subsequent few generations only carry out fine tuning.
While the invention has been described with respect to what is presently considered to be the most practical and preferred embodiments, it is to be understood that the invention is not limited to the disclosed embodiments, but on the contrary, is intended to cover various modifications, equivalents, and alternatives falling within the spirit and scope of the invention.
Claims (7)
1. The multi-objective optimization design method for the composite flexible pipe laying is characterized by being applied to an information data processing terminal, and comprises the following steps:
s101, determining structural parameters and material parameters of a fiber reinforced thermoplastic composite pipe, and setting variables and optimization targets for flexible pipe layering optimization; wherein, the structural parameters of the fiber reinforced thermoplastic composite tube include: reinforcing layer number, test section tube length, outer protective layer thickness, inner liner thickness, inner diameter and outer diameter; the material parameters of the fiber reinforced thermoplastic composite tube include: an elastic constant in the reinforcing layer, a strength parameter in the reinforcing layer, an HDPE in the elastic constant, and an HDPE in the strength parameter;
s102, selecting an optimal sample point for layering homogenization of a fiber reinforced thermoplastic composite pipe;
s103, calculating the mechanical properties of sample points of the fiber reinforced thermoplastic composite pipe, according to the three-dimensional stress state of the fiber reinforced thermoplastic composite pipe, adopting an improved Hashin-Yeh failure criterion to be combined with a nonlinear stiffness degradation model, establishing a three-dimensional progressive damage failure model of the fiber reinforced thermoplastic composite pipe, and calling the three-dimensional progressive damage failure model through Matlab programming to calculate the bearing capacity and the tensile stiffness of each sample point of the optimal matrix of the fiber reinforced thermoplastic composite pipe;
s104, establishing an interpolation agent model; performing Kriging interpolation on the first 90% of sample points, taking the last 10% of sample points as a test group, and calculating the bearing capacity and the tensile rigidity of the test group through an interpolation proxy model;
s105, two-stage algorithm optimization; the traditional multi-objective optimization algorithm is improved by combining a rapid non-dominant ordering genetic algorithm with elite strategy, a two-stage multi-objective parallel optimization algorithm is established, and multi-angle multi-objective optimization design is carried out on the fiber reinforced thermoplastic composite pipe by taking the bearing capacity and the tensile rigidity of the fiber reinforced thermoplastic composite pipe as targets based on the two-stage multi-objective parallel optimization algorithm;
the two-stage multi-objective parallel optimization algorithm comprises the following steps:
establishing a plurality of parallel initial islands in an inner stage, and realizing design variable optimization in each island through an elite strategy NSGA-II algorithm sequence comprising an initialization stage, an fitness evaluation stage, a selection stage, a crossing stage and a mutation stage;
defining migration conditions at an outer stage, selecting samples with the same proportion from the good population and the poor population in each island as random migration samples, exchanging migration samples in the rest parallel islands, and then carrying out a re-optimization cycle; and screening and sequencing the optimized sample set to obtain a final Pareto optimal solution.
2. The multi-objective optimization design method for the flexible pipe pavement of the composite material according to claim 1, wherein in the step S101, the variable of the flexible pipe pavement optimization is set as the flexible pipe pavement winding angle, and two adjacent layers of positive and negative same-angle winding are adopted for the flexible pipe pavement winding angle distribution, and the winding mode is thatAnd determining an optimization target according to the production capacity of the winding process, wherein the optimization target is a winding angle optimization range.
3. The method for multi-objective optimal design of a composite flexible pipe lay-up according to claim 1, wherein in step S102, selecting an optimal sample point for homogenizing a fiber reinforced thermoplastic composite pipe lay-up comprises:
(1) Determining the space dimension of the design variables of the Latin hypercube sampling method according to the number N of the design variables, selecting M sample points, and selecting the following steps: dividing each dimension into M sections which are not overlapped with each other, so that each section has the same probability; randomly extracting M points in each interval in each dimension;
(2) Randomly extracting the points selected in step (1) from each dimension, and combining the selected points into a sample vector (1, 2 … N) T M sample points form an N x M sample point matrix;
(3) Setting the sampling times as N, and establishing N N multiplied by M sample point matrixes; using a criterion of maximum and minimum distanceAnd a centralization deviation criterion CL 2 And carrying out homogenization evaluation on the established sample point matrix, and taking the matrix which is optimal in homogenization under two criteria as the sample point.
4. A composite flexible pipe lay-up multi-objective optimization design method according to claim 3, characterized by a maximum and minimum distance criterionComprising the following steps: calculating the distance between any two sample points +.>The obtained distances are ordered to obtain a distance function list (d i -J i )，J i Is satisfied d i By the number of pairs of pointsMeasuring sample uniformity;
centralizing deviation criterion CL 2 Comprising the following steps: defining the deviation of the point set at the point x, carrying out normalization processing on the sample points, and adopting a centralized deviation CL 2 The formula is as follows:
wherein x= (x) 1 ，…，x s )∈C s ，[0，x 1 )×[0，x 2 )×…×[0，x s ) Is C s In the rectangle defined by the origin 0 and x, M (P n [0, x) ] is P n The number of points falling into [0, x), when P n The point in (C) s When the walking is uniform, N (p n Volume x of [0, x))/n and [0, x ] 1 ，…，x s Near, D (x) = |n (P) n (0, x)) -Vol ([ 0, x)) | is defined as the difference between the two, referred to as the point set at P n Error of point x; x is x ij And (5) designing the values of the test points in the matrix for the normalization test.
5. The method for multi-objective optimization design of a composite flexible pipe lay-up according to claim 1, wherein in step S103, the combination of the modified Hashin-Yeh failure criterion and the nonlinear stiffness degradation model is adopted, and before the three-dimensional progressive damage failure model of the fiber reinforced thermoplastic composite pipe is established, the following steps are performed: according to the three-dimensional anisotropic elastic mechanics theory, according to interlayer stress, material nonlinearity, temperature stress and winding angle change factors of a flexible pipe layer, and by combining the three-dimensional stress state of the fiber reinforced thermoplastic composite pipe under a complex load working condition, a three-dimensional constitutive model of the fiber reinforced thermoplastic composite pipe is constructed;
the improved Hashin-Yeh failure criteria include:
σ 1 and when the tensile failure of the fiber is more than or equal to 0, the tensile failure of the fiber is as follows:
σ 1 at < 0, the fiber compression failure is:
the shear failure of the fiber matrix is as follows:
σ 2 and when the tensile failure of the matrix is more than or equal to 0, the tensile failure of the matrix is as follows:
σ 2 when less than 0, the matrix compression failure is as follows:
σ 3 and when the tensile delamination is not less than 0, the tensile delamination failure is as follows:
σ 3 when less than 0, the compression delamination fails as follows:
in sigma 1 ，σ 2 ，σ 3 ，τ 12 ，τ 13 ，τ 23 Respectively positive stress and shear stress components in all directions; sigma (sigma) s Is the yield stress of HDPE; x is X T ，X C ，Y T ，Y C ，Z T ，Z C ，X 12 ，X 13 ，X 23 Respectively the strength parameters of the glass fiber ribbon; r is R i For the failure factor, i=ft, fc, mt, mc, s, td, cd are respectively different types of failure modes, which start to occur when the failure factor is greater than 1.
6. The composite flexible pipe lay-up multi-objective optimization design method according to claim 1, wherein in step S104, in Kriging interpolation of the first 90% of sample points, a correlation description function of the sample points is as follows:
wherein n is v Representing the number of known design variables,respectively training sample points x i And x j Is the kth component of (2);
the gaussian correlation function is selected as follows:
taking the last 10% of sample points as a test group, calculating the bearing capacity and the tensile rigidity of the test group through an interpolation proxy model, and verifying the quality of the interpolation proxy model according to a root mean square error and a complex correlation coefficient formula;
the mean square error is:
the complex correlation coefficients are:
the interpolation proxy model is built as follows:
(1) The optimization targets are to improve the bearing capacity and the tensile rigidity of the fiber reinforced thermoplastic composite pipe, and simultaneously perform multi-target optimization on the bearing capacity and the tensile rigidity of the fiber reinforced thermoplastic composite pipe;
(2) The winding angle distribution of the flexible pipe layer is that two adjacent layers are wound at the same positive and negative angles, and the winding mode is thatThe design variables are two;
(3) Determining the optimal range of the winding angle to be +/-40 degrees to +/-80 degrees;
(4) The built interpolation proxy model is expressed as follows:
wherein the method comprises the steps ofRespectively represents an optimized winding angle, a function f 1 ，f 2 And (5) interpolating proxy models corresponding to the two objective functions.
7. A computer device, the computer device comprising: at least one processor, a memory and a computer program stored in the memory and executable on the at least one processor, which processor, when executing the computer program, implements the composite flexible pipe lay-up multi-objective optimization design method according to any one of the preceding claims 1-6.
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