Flat wrecker structure multi-objective optimization method based on improved NSGA-II algorithm

Abstract

The invention provides a flat wrecker structure multi-objective optimization method based on an improved NSGA-II algorithm, and the method comprises the steps: carrying out the finite element static analysis of a to-be-optimized structure under all working conditions through ANSYS, and determining all optimizable parts and the most dangerous working conditions thereof; for each optimizable part, generating a. Wbpj file by using ANSYS, the. Wbpj file being used for determining a sample point of each optimizable part under the most dangerous working condition according to a design variable and a value range thereof; for each optimizable part, establishing an input file, an optimization file and an output file by using a numerical calculation and programming tool; for each optimizable component, ANSYS and numerical calculation and programming tools are integrated using a design and optimization integration platform. The invention provides a flat plate wrecker structure multi-objective optimization method based on an improved NSGA-II algorithm. The flat plate wrecker structure multi-objective optimization method is used for solving the problems that in the prior art, a flat plate wrecker is unreasonable in structural design, low in material utilization rate, large in self weight, not capable of achieving multi-objective optimization and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of structural optimization of flat wreckers, and particularly to a multi-objective optimization method for the structure of a flat wrecker based on an improved NSGA-II algorithm. Background Art

[0002] A wrecker is mainly a special vehicle used to clear road traffic obstacle vehicles. The flat wrecker has unique advantages in wrecking and rescue. Compared with other wreckers, it is safer and faster, and there is no secondary injury. At present, the domestic design and R & D capabilities for flat wreckers are relatively lagging behind, mainly achieved through imitation and reference of foreign products. Moreover, the selection of the cross-sectional dimensions of the upper structure mainly relies on experience, resulting in a large design redundancy. This makes the self-weight of light flat wreckers relatively large, unable to meet the normal operation requirements, and there will be serious safety hazards if forced to carry loads.

[0003] At present, most structural optimization technologies take a single objective as the optimization goal (such as structural mass, stiffness, and sound pressure, etc.), and then limit other parameters (such as the maximum equivalent stress and modal response frequency of the structure, etc.) to complete the optimization of the structure. There is no comprehensive consideration (such as optimizing the maximum equivalent stress, stiffness, modal response frequency, and maximum displacement while optimizing the structural mass). Therefore, the multi-objective optimization problem has become an urgent problem to be solved in structural optimization. Summary of the Invention

[0004] The present invention provides a multi-objective optimization method for the structure of a flat wrecker based on an improved NSGA-II algorithm to solve the problems of unreasonable structural design, low material utilization rate, heavy self-weight, and failure to achieve multi-objective optimization in the prior art for flat wreckers.

[0005] The present invention provides a multi-objective optimization method for the structure of a flat wrecker based on an improved NSGA-II algorithm, including:

[0006] Performing finite element static analysis on the structure to be optimized under various working conditions using ANSYS to determine all optimizable components and their most dangerous working conditions;

[0007] For each optimizable component, using ANSYS to generate a.wbpj file, the.wbpj file is used to determine the sample points of each optimizable component under its most dangerous working condition according to the design variables and their value ranges. The design variables are variables that affect the mass change of each optimizable component and have an optimization space, and the value ranges of the design variables are determined according to design requirements and actual production constraints. The sample points are used to construct an approximate model of the finite element model of each optimizable component;

[0008] For each optimizable component, an input file, an optimization file, and an output file are established using numerical calculation and programming tools. The input file is used to obtain the sample points from the output results of ANSYS. The optimization file is used to perform multi-objective optimization on the sample points based on the improved NSGA-II algorithm. The output file is used to determine and output the optimization scheme of the design variables based on the output results of the multi-objective optimization. The output results of ANSYS include the sample points and the stiffness and strength analysis results. The improved NSGA-II algorithm uses floating-point encoding, a normal distribution crossover operator, and an adaptive adjustment mutation operator. The mathematical model of the multi-objective optimization includes an objective function, the design variables, and constraint conditions. The objective function includes minimum mass and minimum maximum stress. The constraint conditions include static stiffness constraints and the value range of the design variables.

[0009] For each optimizable component, the ANSYS and numerical calculation and programming tools are integrated using a design and optimization integration platform. The design and optimization integration platform is used to receive and parse the output results of ANSYS and send the parsed output results of ANSYS to the numerical calculation and programming tools, receive the optimization results output by the numerical calculation and programming tools, and monitor the optimization process of the numerical calculation and programming tools in real time.

[0010] The above solution performs multi-objective optimization of the structure to be optimized based on the improved NSGA-II algorithm, ensuring that the structure to be optimized has better safety performance while achieving structural lightweighting. At the same time, the improved NSGA-II algorithm ensures the diversity and uniformity of the population, thereby strengthening the stability of the population; its strong global search ability effectively avoids the problem of premature convergence; and it improves the convergence speed and convergence stability.

[0011] Optionally, the ANSYS is used to perform finite element static analysis on the structure to be optimized under various working conditions to determine all optimizable components and their most dangerous working conditions, including:

[0012] Based on the mechanical analysis results of the structure to be optimized, loads are added to the finite element model of the structure to be optimized.

[0013] According to the connection relationship between the components in the structure to be optimized, constraints are applied to the structure to be optimized.

[0014] Under the above various working conditions, static analysis is performed to obtain the maximum stress of each component in the structure to be optimized. Based on the maximum stress of each component under the above various working conditions, all optimizable components and their most dangerous working conditions are determined. The optimizable component is a component whose maximum value of the maximum stress under the above various working conditions is less than 90% of the allowable stress. The most dangerous working condition of the optimizable component is the working condition where the maximum value of the maximum stress of the optimizable component is located among the above various working conditions.

[0015] Optionally, the steps for establishing the finite element model of the structure to be optimized include:

[0016] Create a 3D simplified model of the structure to be optimized using a 3D CAD design tool;

[0017] Define the material properties, connection relationships, and element types of the structure to be optimized using ANSYS, and perform mesh division on the structure to be optimized.

[0018] Optionally, the structure to be optimized is the working device of a flatbed wrecker, and the working device includes three components: a tray, a supporting beam, and a supporting arm.

[0019] Optionally, the mechanical analysis of the working device is based on the condition of normal full load.

[0020] Optionally, the working conditions include a horizontal backload condition, an inclined backload condition, and a full load braking condition.

[0021] Optionally, the determination of the sample points of each optimizable component under its most dangerous working condition according to the design variables and their value ranges includes:

[0022] Import the finite element model of each optimizable component under its most dangerous working condition into the DOE module;

[0023] Perform parametric processing on the finite element model according to the design variables and their value ranges;

[0024] Generate sample points using the design method in the DOE module.

[0025] Optionally, the floating-point encoding uses scientific notation based on binary encoding to convert binary numbers into floating-point numbers.

[0026] Optionally, the definition formulas for the mutation probability and fitness of the individual by the adaptive adjustment mutation operator are as follows:

[0027]

[0028]

[0029] Among them, M is the number of individuals, P m (X i ) and are the mutation probability and average mutation probability of individual X i respectively, e(X i ) and E(X i ) are the fitness of individual X i and the evaluation function of individual X i respectively.

[0030] Optionally, the improved NSGA-II algorithm includes:

[0031] Step 401: Use the floating-point encoding for the design variables and the constraint conditions;

[0032] Step 402: Randomly generate an initial population containing N individuals, and perform fast non-dominated sorting on the initial population;

[0033] Step 403: Select N individuals as the parent generation P k , where k is the evolutionary generation number, k = 0;

[0034] Step 404: Use the normal distribution crossover operator and the adaptive adjustment mutation operator to perform crossover and mutation on the individuals in the parent generation P k to generate the offspring generation X k ;

[0035] Step 405: Combine the parent generation P k and the offspring generation X k to generate a new population Q k ;

[0036] Step 406: Perform the fast non-dominated sorting on the new population Q k , and use the crowded competition selection strategy to select N individuals to form a new parent generation P k+1 ;

[0037] Step 407: Increment the value of the evolutionary generation number k by 1, and determine whether the evolutionary generation number k is less than the evolutionary generation threshold. If so, execute Steps 403 - 407. If not, output the Pareto optimal solution set. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] To more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0039] Figure 1 is a schematic flowchart of a multi-objective optimization method for the structure of a flatbed wrecker based on an improved NSGA-II algorithm provided by an embodiment of the present invention;

[0040] Figure 2 is a schematic diagram of the three-dimensional structure of a domestic wrecker provided by an embodiment of the present invention, where

[0041] Chassis 1, tray 2, crossbeam 3, support arm 4, and hydraulic system 5;

[0042] Figure 3 It is a schematic diagram of the three-dimensional simplified model of the working device provided by the embodiment of the present invention. Among them,

[0043] A is the three-dimensional simplified model of the tray,

[0044] B is the three-dimensional simplified model of the crossbeam. Among them,

[0045] Welding point 6, slider position 7, hydraulic cylinder connecting shaft 8,

[0046] C is the three-dimensional simplified model of the support arm. Among them,

[0047] Pin shaft 9, hydraulic cylinder connection position 10;

[0048] Figure 4 It is a schematic diagram of the mesh model of the working device provided by the embodiment of the present invention. Among them,

[0049] A is the tray mesh model, B is the crossbeam mesh model, and C is the support arm mesh model;

[0050] Figure 5 It is a schematic diagram of the mechanical analysis of the working device of the flat wrecking truck provided by the embodiment of the present invention;

[0051] Figure 6 It is a schematic diagram of the stress and deformation nephogram of the tray and crossbeam under the most dangerous working conditions provided by the embodiment of the present invention. Among them,

[0052] A is the stress nephogram of the tray, B is the deformation nephogram of the tray, C is the stress nephogram of the crossbeam, and D is the deformation nephogram of the crossbeam;

[0053] Figure 7 It is a schematic diagram of the stress and deformation nephogram of the support arm under the full-load braking working condition provided by the embodiment of the present invention. Among them,

[0054] A is the stress nephogram of the support arm, and B is the deformation nephogram of the support arm;

[0055] Figure 8 It is a schematic diagram of the search space distribution of the binary crossover operator provided by the embodiment of the present invention;

[0056] Figure 9 It is a schematic diagram of the search space distribution of the normal distribution crossover operator provided by the embodiment of the present invention;

[0057] Figure 10 It is provided by the embodiment of the present invention that the average mutation probability is The schematic diagram of the change curve of the function value of the optimal individual with the increase of the number of evolutionary generations;

[0058] Figure 11 The function value curve of the optimal individual with the increase of the evolutionary generation number provided by the embodiment of the present invention, where the average mutation probability is A schematic diagram;

[0059] Figure 12 A schematic diagram of the flow of the improved NSGA-II algorithm provided by the embodiment of the present invention;

[0060] Figure 13 The change process of two objective functions of the tray provided by the embodiment of the present invention, where

[0061] A is the change process of the minimum tray mass, and B is the change process of the minimum maximum stress of the tray;

[0062] Figure 14 The change process of two objective functions of the joist provided by the embodiment of the present invention, where

[0063] A is the change process of the minimum joist mass, and B is the change process of the minimum maximum stress of the joist;

[0064] Figure 15 The Pareto solution sets of the tray and the joist provided by the embodiment of the present invention, where A is the Pareto solution set of the tray and B is the Pareto solution set of the joist;

[0065] Figure 16 The stress and deformation nephogram of the optimization scheme of the improved NSGA-II algorithm provided by the embodiment of the present invention, where

[0066] A is the stress nephogram of the tray, B is the deformation nephogram of the tray, C is the stress nephogram of the joist, and D is the deformation nephogram of the joist. Detailed implementation manners

[0067] In order to make the purpose, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0068] Figure 1 A schematic diagram of the flow of a multi-objective optimization method for the structure of a flatbed obstacle clearing vehicle based on an improved NSGA-II algorithm provided by the embodiment of the present invention is shown in detail, including:

[0069] Step 101: Use ANSYS to perform finite element static analysis on the structure to be optimized under various working conditions, and determine all optimizable components and their most dangerous working conditions.

[0070] In one example, ANSYS is used to perform finite element static analysis on the structure to be optimized under various working conditions, and all optimizable components and their most dangerous working conditions are determined, including:

[0071] Adding loads to the finite element model of the structure to be optimized based on the mechanical analysis results of the structure to be optimized;

[0072] Applying constraints to the structure to be optimized according to the connection relationship between components in the structure to be optimized;

[0073] Performing static analysis under various working conditions to obtain the maximum stress of each component in the structure to be optimized, and determining all optimizable components and their most dangerous working conditions based on the maximum stress of each component under various working conditions.

[0074] The analysis of optimizable components is mainly based on the fourth strength theory (i.e., the equivalent strength theory), and its relational expression is as follows;

[0075]

[0076] Among them, σ s is the maximum stress (or the maximum equivalent stress), and σ 1 , σ 2 , σ 3 are the principal stresses in the three coordinate axis directions;

[0077] The formula for the allowable stress is as follows:

[0078]

[0079] Among them, [σ] is the allowable stress, σ max is the ultimate stress of the material, and n is the safety factor of the structure;

[0080] The maximum stress and the allowable stress need to satisfy σ s ≤ [σ].

[0081] In structural optimization, it is usually allowed for the structure to approach the allowable stress in the high-stress area. However, to prevent local material failure or unforeseen load increase, the stress value of the structure cannot be too close to the allowable stress. When the maximum stress of the structure approaches 80% to 90% of the allowable stress, very careful optimization is required. Once it exceeds this range, further optimization may make the structure too weak, resulting in possible failure in actual applications. Therefore, when the maximum stress reaches about 90% of the allowable stress, further optimization should be stopped to ensure the safety and reliability of the structure.

[0082] Specifically, the optimizable components are those with the maximum value of the maximum stress in each working condition less than 90% of the allowable stress.

[0083] The optimization of the component to be optimized should be based on the most dangerous working conditions. Specifically, the most dangerous working condition of the component to be optimized is the working condition in which the maximum stress of the component to be optimized is the maximum value among all working conditions.

[0084] In one example, the steps for establishing the finite element model of the structure to be optimized include:

[0085] Create a three-dimensional simplified model of the structure to be optimized using a three-dimensional CAD design tool;

[0086] Define the material properties, connection relationships, and element types of the structure to be optimized using ANSYS, and perform mesh division on the structure to be optimized.

[0087] In one example, the structure to be optimized is the working device of a flatbed wrecker, and the working device includes three components: a tray, a supporting beam, and a supporting arm.

[0088] Specifically, Figure 2 Fig. shows the three-dimensional structure of a domestic wrecker. The flatbed wrecker includes a chassis 1, a working device, and a hydraulic system 5. The working device includes a tray 2, a supporting beam 3, and a supporting arm 4, where:

[0089] Chassis 1, most wreckers choose the second-class chassis of a general-purpose truck as the basic chassis. The second-class chassis has high load-bearing capacity and stability, and can meet the working requirements of the wrecker under various complex roads and environments, without room for optimization;

[0090] Tray 2, usually divided into front and rear parts. The sliding function of the tray 2 depends on the supporting beam subframe below, and the subframe enables the tray 2 to slide smoothly when needed;

[0091] Supporting beam 3, composed of a supporting beam subframe and legs, etc. Its main responsibility is to evenly disperse the concentrated load to the main frame. The design of the supporting beam 3 not only needs to meet the working requirements of components such as the tray 2 and the supporting arm 4, but also needs to consider the overall layout and configuration of the whole vehicle to ensure the stability and safety of the whole vehicle. In addition, the overall layout of the supporting beam 3 also needs to be carefully designed to avoid mutual interference between working components;

[0092] Supporting arm 4, mainly composed of inner and outer telescopic arms, a supporting arm crossbeam, and an L-arm. The outer arm is hinged to the end of the vehicle frame through a pin shaft, and the other end is connected to the subframe through a telescopic hydraulic cylinder. Therefore, the outer arm can be telescoped when needed to adapt to different vehicle models and repair requirements. The front end of the inner telescopic arm is hinged to the supporting arm crossbeam, and both ends of the crossbeam are fixedly connected to the L-arm, making the supporting arm 4 more stable during lifting and telescoping, and able to firmly hold parts such as wheels, girders, and leaf springs, thus ensuring safety during the operation process.

[0093] The steps for establishing the finite element model of the working device of the flatbed wrecker include:

[0094] Step 201: Create a 3D simplified model of the working device using a 3D CAD design tool.

[0095] The 3D CAD design tool can be SolidWorks, Creo or UG. In this embodiment of the present invention, SolidWorks is used. SolidWorks provides powerful 3D modeling tools, supports rapid design from sketches to complex 3D models, and is suitable for mechanical design and product development.

[0096] In order to simplify the analysis model of the flatbed obstacle clearing vehicle working device, the following processing can be carried out:

[0097] Simplify the cross-sectional shape: Since there are often many adjacent components with no relative movement and similar functions in a complex mechanical system, merging these components into a single component can significantly reduce the computational workload during analysis;

[0098] Smooth the surface of the components: In actual engineering, there are often various details such as bosses, pin holes and wiring holes on the surface of the components. During finite element analysis or simulation, these details will increase the difficulty of mesh generation and the computational workload. Ignoring these details helps to improve the accuracy and efficiency of the analysis;

[0099] Transition arcs far from the stress concentration area and draft angles, chamfers, etc. that meet the technological requirements can also be appropriately simplified to reduce the number of meshes and the computational workload and improve the mesh quality.

[0100] Following the above processing principles, use Solidworks to create a 3D simplified model of the working device, as Figure 3 shown, where A is the 3D simplified model of the tray, B is the 3D simplified model of the supporting beam, and C is the 3D simplified model of the supporting arm.

[0101] Step 202: Use ANSYS to define the material properties, connection relationships and element types of the working device, and perform mesh division on the working device.

[0102] The main material used for the working device is high-strength steel of model 710L, which has strong tensile and bending resistance and is currently widely used in industries such as construction and vehicles. The material properties of 710L high-strength steel are shown in Table 1:

[0103] Table 1

[0104]

[0105] The connection relationships include weld connection, pin connection and contact pair connection, among which:

[0106] Weld connection: Since most parts are connected by welding in the actual production process, the weld is default defined as a bonded constraint in Workbench, which restricts the relative displacement between two nodes.

[0107] Pin connection: Pin connections are usually used to simulate the hinged or rotational connections between two components. Since the pin needs to bear the rotational motion and load force, and the conventional contact analysis method requires high-quality meshes, while the structural optimization problem of the flatbed wrecker does not involve contact motion, and the focus of the analysis is on non-contact motion, that is, to study the motion or force condition of the components under the influence of friction ignored, so a frictionless constraint is used to simulate the pin connection.

[0108] Contact pair connection: It is necessary to set contacts between the tray main beam and the beam slider in the working device, as well as between the inner and outer arms of the boom. Not only the force transfer needs to be ensured at these places, but also their relative sliding needs to be ensured. Therefore, it is necessary to select the surfaces in contact with each other, create target elements and contact elements, so as to form a contact pair.

[0109] When defining the element type, since shell elements can reduce the workload while maintaining the calculation accuracy compared with solid elements, for the thin plate structure of the tray main body and the arm structure of the boom, the middle surface is extracted and defined as shell elements, and for other structures, they are uniformly set as SOLID186 solid elements, and SOLID186 solid element is a kind of solid element.

[0110] The mesh model of the working device is as Figure 4 shown. Among them, A is the mesh model of the tray, B is the mesh model of the beam, C is the mesh model of the boom, the total number of meshes is 350,000, the number of nodes is 680,000, and the average mesh quality is 0.76.

[0111] Use ANSYS to perform finite element static analysis on the working device under various working conditions to determine all optimizable components and their most dangerous working conditions, including:

[0112] Step 301, add loads to the finite element model of the working device based on the mechanical analysis results of the working device.

[0113] The loads acting on the wrecker are divided into three categories: conventional loads, additional loads and special loads. Among them:

[0114] Conventional loads are the loads borne during normal operation. The mechanical analysis of the working device of the flatbed wrecker is as Figure 5 shown, mainly including its own gravity G, the back load F of the tray 1 and the load F carried by the boom 2 . Among them, the load F2 carried by the boom is decomposed into F2x and F2y in the horizontal and vertical directions;

[0115] The additional load mainly includes the additional weights of the toolbox and tires, etc.;

[0116] The special load mainly refers to the load generated under some complex conditions.

[0117] Since the additional load mainly depends on the vehicle chassis, and at the same time, special loads such as wind loads have little obvious effect on the flatbed wrecker. For the convenience of calculation, only the conventional load is considered in the embodiments of the present invention.

[0118] Under the condition of conventional full load, the load details of the working device are shown in Table 2:

[0119] Table 2

[0120]

[0121] Add the load borne by the working device in the workbench module according to Table 2.

[0122] Step 302: Apply constraints to the working device according to the connection relationship between the components in the working device.

[0123] Under normal working conditions, the towing beam is welded to the main chassis beam. Therefore, a full constraint is applied to the welding point 6 under the towing beam; the towing beam and the tray are connected by a slider and a hydraulic cylinder. Therefore, a constraint that retains its translational movement in the front and rear directions is applied to the position 7 of the slider, and a displacement constraint is applied to the position 8 of the hydraulic cylinder connecting shaft; the towing arm and the towing beam are connected by a pin shaft 9 and a hydraulic cylinder. Therefore, a displacement constraint is applied to the connection positions 10 of the pin shaft 9 and the hydraulic cylinder.

[0124] Step 303: Perform a static analysis under each working condition to obtain the maximum stress of each component in the working device, and determine all optimizable components and their most dangerous working conditions based on the maximum stress of each component under each working condition.

[0125] Analyze each working state according to the working process of the wrecker. Each working condition includes a horizontal backload condition, an inclined backload condition, and a full-load braking condition, where:

[0126] The horizontal backload condition is that the tray and the towing arm are fully loaded, stationary on the road surface, and there is no dynamic load coefficient;

[0127] The inclined backload condition is that the horizontal inclination angle of the tray is 17°, the tray is fully loaded while the towing arm is unloaded;

[0128] The full-load braking condition applies a dynamic load coefficient of 1.5 under the horizontal backload condition.

[0129] The maximum stress of each component in the working device under each working condition is shown in Table 3:

[0130] Table 3

[0131]

[0132] As can be seen from Table 3, when the flatbed obstacle-clearing vehicle is in the inclined back-loading condition, the maximum stresses of the tray and the supporting beam are the largest among all conditions, reaching 272.57 MPa and 166.93 MPa respectively. Moreover, the maximum values of the maximum stresses of the tray and the supporting beam are still some distance away from the allowable stress of 355 MPa (the threshold of the allowable stress is determined by the material. In the embodiment of the present invention, the allowable stress of the material used for the tray, supporting beam and supporting arm is 355 MPa), less than 90% of the allowable stress. Therefore, both the tray and the supporting beam are components that can be optimized, and the most dangerous condition for both the tray and the supporting beam is the inclined back-loading condition. It should be noted that under the inclined back-loading condition, the supporting arm is not stressed. The stress and deformation nephograms of the tray and the supporting beam under the most dangerous condition are as Figure 6 shown, where A is the stress nephogram of the tray, B is the deformation nephogram of the tray, C is the stress nephogram of the supporting beam, and D is the deformation nephogram of the supporting beam.

[0133] Meanwhile, when the flatbed vehicle is in the full-load braking condition, the maximum stress of the supporting arm is the largest among all conditions, reaching 348.08 MPa. Since it is very close to the allowable stress of 355 MPa and has exceeded 98% of the allowable stress, the supporting arm is no longer optimized. The stress and deformation nephogram of the supporting arm under the full-load braking condition are as Figure 7 shown, where A is the stress nephogram of the supporting arm and B is the deformation nephogram of the supporting arm.

[0134] In summary, it is determined that the tray and the supporting beam are components that can be optimized, the most dangerous condition for both the tray and the supporting beam is the inclined back-loading condition, and the supporting arm is a component that cannot be optimized.

[0135] Step 102: For each component that can be optimized, use ANSYS to generate a.wbpj file, and the.wbpj file is used to determine the sample points of each component that can be optimized under its most dangerous condition according to the design variables and their value ranges.

[0136] Specifically, the design variables are the variables that affect the mass change of each component that can be optimized and have an optimization space. The value ranges of the design variables are determined according to the design requirements and actual production constraints. The sample points are used to construct an approximate model of the finite element model of each component that can be optimized.

[0137] In one example, determining the sample points of each component that can be optimized under its most dangerous condition according to the design variables and their value ranges includes:

[0138] Import the finite element model of each component that can be optimized under its most dangerous condition into the DOE module;

[0139] Perform parametric processing on the finite element model according to the design variables and their value ranges;

[0140] Use the design method in the DOE module to generate sample points.

[0141] For the pallet, the parameters that have a major impact on the quality change include the thickness of the flat plate, the main beam, the tail cross beam, the reinforcing rib, and the tail beam, etc. Among them, the thickness of the flat plate has the greatest impact on the quality. Since the current thickness of the flat plate is only 1.8 mm, but it has reached the limit of design and actual production and cannot be thinned further, so the remaining thicknesses of the main beam, the tail cross beam, the reinforcing rib, and the tail beam are selected as design variables, and their value ranges are determined according to the design requirements and the actual production constraints of the steel. The actual production constraints of steel refer to various limitations and conditions encountered in the steel production process. Possible constraints include:

[0142] Raw material constraints: Steel production requires raw materials such as iron ore, coke, and scrap steel. The supply stability, quality, cost, and availability of raw materials are all constraint factors. For example, if the supply of iron ore is tight or the price rises, it will directly affect the production cost and output of steel;

[0143] Technical constraints: The production technology level and equipment capacity are key factors affecting steel production. Backward technology or equipment may not be able to produce high-quality or specific specification steel, restricting product diversity and market competitiveness.

[0144] The design variables of the pallet and their value ranges are shown in Table 4, where the initial value is the original value of the pallet design variable:

[0145] Table 4

[0146]

[0147] Import the finite element model of the pallet under the inclined backload condition into the DOE module, parameterize the finite element model of the pallet according to the design variables of the pallet and their value ranges, and use the Central Composite Design (CCD) method in the DOE module to generate sample points.

[0148] The parameterization process includes:

[0149] Define the design variables;

[0150] Set the value range of the design variables;

[0151] Parameterized model construction: Use the defined design variables to construct the model, which means that the geometric shape, size, material properties, boundary conditions, and loads of the model are determined by the design variables;

[0152] Parameterized analysis settings: Set the analysis type (such as static analysis) and ensure that the analysis steps refer to the design variables;

[0153] Perform parametric analysis: When running the analysis, ANSYS automatically conducts multiple analyses based on the value ranges of the design variables. After each analysis is completed, ANSYS saves the analysis results.

[0154] Key results (such as stress, displacement, frequency, etc.) corresponding to the design variables can be extracted from the analysis results saved by ANSYS for easy comparison and analysis. The analysis results can help determine the parameters that have the greatest impact on the structural performance and the parameter combinations that can provide the optimal design.

[0155] The reasons for choosing to use the central composite design method to generate sample points for the tray include:

[0156] The central composite design method is a commonly used design method in response surface methodology, especially suitable for constructing quadratic models (i.e., polynomial models containing quadratic terms). There is a non - linear relationship in the response of the tray, and the quadratic response surface can capture this non - linearity. Therefore, using the central composite design method helps to construct a more accurate response surface model;

[0157] Compared with other design methods, such as the full factorial design, the central composite design method requires relatively fewer experimental runs and can provide sufficient sample points to fit the quadratic model;

[0158] High flexibility: The central composite design method can control the flexibility of the design by adjusting the positions of different types of sample points (such as the positions of the center point and star points). For complex tray working devices, this flexibility can help optimize the design parameters and improve the system performance;

[0159] Choosing to use the central composite design method to generate sample points helps to construct an accurate response surface model with a limited number of experimental runs, thereby effectively optimizing the design parameters of the tray of the flatbed obstacle - clearing vehicle.

[0160] The number of generated sample points mainly depends on the number of design variables, that is, the number of factors, usually denoted as k. The number of sample points generated by the central composite design method includes:

[0161] Full factorial points: The full factorial points are distributed at the corner points of the design space. For k design variables, the number of points in the full factorial design is 2 k ;

[0162] Center points: The center points are located at the center of the design space. The number of center points is usually set according to the experimental requirements, and they help to estimate the experimental error;

[0163] Axial Points / Star Points: Axial points are located at a certain distance from the center point along the axis of each design variable, and the number is 2k.

[0164] The number of sample points generated by the central composite design method can be expressed as:

[0165] Num = 2 k + 2k + n c

[0166] where Num is the number of sample points, and n c is the number of center points. For the case of 4 design variables, the number of full factorial design points is 2 4 = 16, the number of axial points is 2×4 = 8, the number of center points is 21, and the number of sample points is 45.

[0167] Based on all sample points, an approximate model of the finite element model of the tray can be constructed, and subsequent optimization is carried out for this approximate model (i.e., all sample points).

[0168] Based on the value range of the tray design variables, multiple sizes are set, and the stiffness and strength analysis are carried out for 45 sample points of each size. The maximum deformation and maximum stress of 45 sample points of some sizes are shown in Table 5:

[0169] Table 5

[0170]

[0171] For the joist, the parameters that have a major impact on the mass change include the main beam thickness, slider thickness, cross beam thickness, etc. The main beam thickness, slider thickness, and cross beam thickness are selected as design variables, and their value ranges are determined according to the design requirements and the actual production constraints of the steel. The design variables of the joist and their value ranges are shown in Table 6, and the initial values are the original values of the joist design variables:

[0172] Table 6

[0173]

[0174] Import the finite element model of the joist under the inclined backload condition into the DOE module, parameterize the finite element model of the joist according to the design variables of the joist and their value ranges, and use the Box-Behnken experimental design method in the DOE module to generate sample points.

[0175] The reasons for choosing to use the Box-Behnken experimental design method to generate sample points for the joist include:

[0176] Avoid extreme conditions: The structure of the joist may exhibit complex non-linear behavior under extreme stress or strain conditions. The Box-Behnken experimental design method does not generate sample points when all factors are at their maximum or minimum values, which can avoid potential structural failure problems caused by design variables simultaneously being at extreme values and improve experimental safety;

[0177] The distribution of sample points generated by the Box-Behnken experimental design method can effectively fit the quadratic response model, which is crucial for capturing the non-linear characteristics of the joist response. The quadratic model can describe the interaction and quadratic effects between factors, thus more accurately predicting the performance of the joist under different design conditions;

[0178] Uniform distribution of sample points: The sample points of the Box-Behnken experimental design method are uniformly distributed near the middle levels of the factors, reducing the risk of errors generated at the boundaries of the design space. This can provide more stable experimental data and improve the accuracy of the response surface model;

[0179] Simplify model construction and verification: Since the sample points generated by the Box-Behnken experimental design method are not at the extreme positions of the design space, the complex non-linear effects under extreme conditions are reduced, making the model construction and verification process relatively simplified and easier to analyze and optimize the model.

[0180] An approximate model of the finite element model of the joist can be constructed based on all sample points, and subsequent optimization is carried out for this approximate model (i.e., all sample points).

[0181] In the Box-Behnken experimental design method, first determine the main beam thickness H 5 , slider thickness H 6 and cross beam thickness H 7 three influencing factors, and set three different levels for each factor. The influencing factors and their level settings are shown in Table 7:

[0182] Table 7

[0183]

[0184] Conduct stiffness, strength analysis and mass analysis for all sample points at different levels. The maximum deformation, maximum stress and mass of all sample points at some levels are shown in Table 8:

[0185] Table 8

[0186]

[0187] Step 103: For each optimizable component, use numerical calculation and programming tools to establish an input file, an optimization file, and an output file. The input file is used to obtain sample points from the output results of ANSYS. The optimization file is used to perform multi-objective optimization on the sample points based on the improved NSGA-II algorithm. The output file is used to determine and output the optimization scheme of the design variables based on the output results of the multi-objective optimization.

[0188] The numerical calculation and programming tools can be MATLAB or Python. In this embodiment of the present invention, MATLAB is used. MATLAB has a rich mathematical function library and can quickly perform matrix operations, numerical calculations, data analysis, and algorithm development. The language of MATLAB is concise and intuitive, and its graphical interface is powerful, making it suitable for rapid prototyping development and algorithm testing.

[0189] Specifically, the output results of ANSYS include sample points and rigid strength analysis results.

[0190] Since the traditional NSGA-II algorithm cannot guarantee the diversity and uniformity of the population, the stability of the population is weak; its global search ability is poor, and it is prone to premature convergence; the convergence speed is slow and the convergence is unstable. In view of the above problems, combined with the characteristics of the multi-objective optimization of the flatbed wrecker structure, including the large span of the cross-sectional dimensions of the flatbed wrecker structure, high dimensional accuracy requirements, and complex and continuous dimensional data, this embodiment of the present invention provides an improved NSGA-II algorithm. This improved NSGA-II algorithm can optimize specific components or the scheduling system and belongs to an optimization method.

[0191] Specifically, the improved NSGA-II algorithm uses floating-point encoding, normal distribution crossover operator, and adaptive adjustment mutation operator.

[0192] The encoding method of the traditional NSGA-II algorithm is binary encoding. This method converts the vector of each individual in the population from decimal to a binary string, which is called a chromosome. Subsequent selection, crossover, and mutation operations are all performed on this chromosome. Its encoding method is as follows:

[0193]

[0194] This method is simple and easy to understand. However, during the specific operation of the genetic algorithm, continuous encoding and decoding are required, which greatly increases the amount of calculation and calculation time. At the same time, discontinuity will occur during the crossover and mutation operations of binary encoding. For example, a chromosome is 110101, and its decoded value is 53. When the second bit is mutated to 100101, its decoded value will become 37, showing a large jump.

[0195] The floating-point encoding is based on binary encoding and uses scientific notation to convert binary numbers into floating-point numbers. A floating-point number consists of a sign bit, an exponent, and a mantissa. The formula is as follows:

[0196] N float =(1S + 8E + 23M)

[0197] Where N float is the floating-point number, S is the sign bit, indicating positive or negative, occupying 1 bit, 0 represents a positive number, 1 represents a negative number, E is the exponent, that is, the binary number of the exponent in binary scientific notation plus the intermediate number (or offset) 127, occupying 8 bits, and M is the mantissa, that is, the binary code after the decimal point when the binary number moves the decimal point to the left (or right) until the first 1. The functional relationships between the sign bit, exponent, and mantissa in the decimal number and the encoded floating-point number are as follows:

[0198] N 10 =[(-1) S M′2 E-127 2

[0199] Where N 10 is the decimal number, and M′ is the binary number after adding "1." in front of the mantissa M.

[0200] For example, the binary number of the decimal number 53 is 110101. Then the sign bit S is 0, the exponent is 5, the exponent E is the binary number of 5 + 127 = 133, that is, 10000101, and the mantissa M is 10101000...0. Therefore, the floating-point encoding chromosome of 53 is 01000010110101000...0. This chromosome has better continuity during crossover and mutation and will not undergo large mutations. At the same time, due to the larger number of bits of the floating-point number, its precision is higher.

[0201] Therefore, the floating-point encoding has significant advantages in solving optimization problems. It exhibits higher precision and stronger robustness, which means that when searching in a larger range of space, the floating-point encoding can more accurately approach the optimal solution and effectively resist the influence of various noises and interferences. Choosing the floating-point encoding method is more convenient for accurately and effectively encoding design variables and constraint conditions.

[0202] To improve the space search ability of the traditional NSGA-II algorithm, the normal distribution crossover operator (NDX: Normal Distribution Crossover) is selected to replace the simulated binary crossover operator (SBX: Simulated Binary Crossover) in the traditional NSGA-II algorithm. The normal distribution crossover operator is a crossover strategy based on the characteristics of the normal distribution.​

[0203] In the crossover operation, the normal distribution crossover operator is used to generate offspring from the selected parents. For the i-th variable, the crossover process is as follows:

[0204] First, a random number t is generated. The random number t is uniformly distributed between [0, 1] and determines how the parental genes are passed on to the offspring;

[0205] Next, the random number t is compared with the preset crossover probability α. If t is less than or equal to α, the following operations are performed:

[0206]

[0207] where, x 1,i is the value of the offspring x 1 at the i-th variable, x 2,i is the value of the offspring x 2 at the i-th variable, p 1,i is the value of the parent p 1 at the i-th variable, p 2,i is the value of the parent p 2 at the i-th variable, |N(0, 1)| is a normally distributed random variable, and the normally distributed random variable determines the difference between the offspring genes and the parental genes;

[0208] If t is greater than α, the following operations are performed:

[0209]

[0210] Due to the randomness of the normally distributed random variable, the algorithm can explore more widely in the search space, thus avoiding premature convergence to local optimal solutions.

[0211] In the one-dimensional search space, a detailed comparison of the normal distribution crossover operator and the binary crossover operator is carried out as follows:

[0212] First, the positions of two parents are selected in the experiment;

[0213] Next, the positions of the two parents are calculated 5000 times each to generate 10000 offspring individuals;

[0214] Then, the distribution of the offspring individuals in the search space is observed and statistical analysis is performed on it.

[0215] To more intuitively show the distribution of the offspring individuals in the search space in the experimental results, Figure 8 the search space distribution of the binary crossover operator is shown. Among them, the spatial search range of the binary crossover operator is only between 0.1 and 0.8, which is relatively narrow; Figure 9The search space distribution of the normal distribution crossover operator is shown. Among them, the spatial search range of the normal distribution crossover operator is between -1.8 and 3.3, covering the entire experimental area. This means that the normal distribution crossover operator can explore the solution space more comprehensively during the search process, thereby increasing the probability of finding the Pareto optimal solution. At the same time, due to the relatively wide spatial search range of the normal distribution crossover operator, the algorithm can more easily break free from the bondage of local optimal solutions during the search process. In contrast, the spatial search range of the binary crossover operator is relatively narrow, making it prone to falling into local optimal solutions and reducing the overall search efficiency.

[0216] Therefore, the normal distribution crossover operator has advantages in terms of the uniformity and extensiveness of the spatial search range, making it more efficient in finding the Pareto optimal solution set. This advantage stems from its larger search range, enabling the algorithm to find the global optimal solution faster during the search process. In practical applications, the normal distribution crossover operator has higher optimization ability and search efficiency compared to the binary crossover operator, and can better solve complex optimization problems.

[0217] To address the problem of excessive subjectivity and randomness in the mutation method of the traditional NSGA-II algorithm, an adaptive adjustment mutation operator is selected to replace the polynomial mutation operator in the NSGA-II algorithm. By introducing an adaptive adjustment mechanism, the mutation process can adjust the mutation amplitude and probability according to the fitness of the individual, thereby improving the convergence speed and stability of the algorithm.

[0218] The definition formulas for the mutation probability and fitness of the individual by the adaptive adjustment mutation operator are as follows:

[0219]

[0220]

[0221] Among them, M is the number of individuals, P m (X i ) and are the mutation probability and average mutation probability of individual X i respectively, e(X i ) and E(X i ) are the fitness of individual X i and the evaluation function of individual X i respectively. Fitness represents the superiority or fitness of an individual under a certain evaluation criterion. The larger the value, the better the individual performs in the current environment.

[0222] According to the definition formula of the mutation probability, it can be known that the mutation probability is obtained by subtracting the fitness from the average mutation probability, which means that the higher the fitness of an individual, the lower its mutation probability. During the evolution process, individuals with high fitness indicate that their gene combinations are more adaptable to the environment. Therefore, reducing the mutation probability of these individuals can protect their excellent genes from being damaged. On the other hand, individuals with low fitness may carry some genes that are not conducive to survival, and increasing their mutation probability helps to explore new gene combinations, thereby finding individuals that are more adaptable to the environment.

[0223] Sum over i according to the definition formula of fitness, that is:

[0224]

[0225] And That is:

[0226]

[0227] Then the definition formula of fitness is simplified to:

[0228]

[0229] Take the average of i according to the definition formula of the mutation probability, that is:

[0230]

[0231] Expand the right side of the above formula, that is:

[0232]

[0233] Among them, Is a constant, that is:

[0234]

[0235] According to the simplified result of the definition formula of fitness, simplify the definition formula of the mutation probability to:

[0236]

[0237] In order to fully verify the advantages and effectiveness of the algorithm improvement, traditional polynomial mutation method and improved adaptive adjustment mutation method are respectively used to conduct simulation experiments on solving the minimum value problem of nonlinear functions.

[0238] Suppose the expression of the nonlinear function is:

[0239]

[0240] Among them, f(x i ) is the function value, and x i Is the design variable of the function.

[0241] In the evolutionary computing process, a real-number coding method, a deterministic sampling selection method, and an arithmetic crossover method are adopted. To ensure the fairness of the experiment, other parameters are set to the same values in both methods. The population size is set to 100, the crossover probability is 0.9, and the evolutionary generation threshold is 1000. Among them, the population size is the number of individuals, and the evolutionary generation refers to the number of generations experienced by the entire population in the genetic algorithm. Through simulation experiments, Figure 10 shows that the average mutation probability is the change curve of the function value of the optimal individual with the increase of the evolutionary generation, Figure 11 shows that the average mutation probability is the change curve of the function value of the optimal individual with the increase of the evolutionary generation. From Figure 10 and Figure 11 it can be seen that the improved adaptive adjustment mutation method has achieved remarkable results in solving the contradiction problem in the selection of the mutation probability. The function values of the optimal individuals obtained by the improved method are all smaller than those of the traditional polynomial mutation method. This advantage is largely attributed to the dynamic adjustment of the mutation probability by the improved adaptive adjustment mutation method, enabling the algorithm to more flexibly handle different situations during the search process. In addition, the solution distribution of the improved algorithm is more uniform, which means that the algorithm has higher stability and reliability during the process of finding the optimal solution. At the same time, the convergence speed is also improved. The experimental results fully verify the effectiveness and performance advantages of the improved adaptive adjustment mutation method in the optimization algorithm.

[0242] Specifically, the mathematical model of multi-objective optimization includes an objective function, design variables, and constraint conditions. The objective function includes minimizing mass and minimizing maximum stress, and the constraint conditions include static stiffness constraints and the value range of design variables.

[0243] The goals pursued by the multi-objective optimization design of the flat obstacle clearing vehicle structure are the lightest metal structure and the best safety performance. A lighter structure means lower costs, but its safety also needs to be considered while reducing costs, so the maximum stress should be as small as possible. Therefore, minimizing its mass and minimizing the maximum equivalent stress are selected as the goals of the optimization design. The formulas for minimizing mass and minimizing maximum stress are as follows:

[0244]

[0245] Among them, W is the mass function, M(x) is minimizing mass, x is the design variable, S is the maximum stress function, and σ(x) is minimizing maximum stress. According to engineering experience, the weights of minimizing mass and minimizing maximum stress can be set in numerical calculation and programming tools, and the weight ratio is 2:1.

[0246] The design variables are mainly the thicknesses of the structural parts in the components that can be optimized. The formula for the design variables of the tray is as follows:

[0247] H = [H 1 , H 2 , H 3 , H 4 T

[0248] The formula for the design variables of the joist is as follows:

[0249] H = [H 5 , H 6 , H 7 T

[0250] The constraint conditions for the design of the flat obstacle removal vehicle include static stiffness constraints and the value range of design variables. The static stiffness constraint mainly considers that the maximum deformation does not exceed the allowable deformation, that is:

[0251] y ≤ y L

[0252] where y is the maximum deformation, and y L is the allowable deformation, and y L = 0.003L, where L is the length of the working device and can take a value of 15.5 mm;

[0253] The value range of the design variables is:

[0254]

[0255] where and are the lower limit and upper limit of the r-th design variable H r respectively.

[0256] In one example, the process of improving the NSGA-II algorithm is as Figure 12 shown, including:

[0257] Step 401: Use floating-point coding for the design variables and constraint conditions.

[0258] Step 402: Randomly generate an initial population containing N individuals, and perform fast non-dominated sorting on the initial population.

[0259] In the fast non-dominated sorting method, a dominated individual is an individual that is inferior to another individual in multiple objective functions; the set of individuals dominated by an individual is the set composed of all individuals that are inferior to this individual in multiple objective functions; a non-dominated individual is an individual that is not dominated by other individuals; the number of dominating individuals is the number of individuals that dominate a certain individual; the number of dominated individuals is the number of individuals dominated by a certain individual. The multiple objective functions in the embodiments of the present invention are the minimum mass and the minimum maximum stress.

[0260] ​​The main steps of the fast non-dominated sorting method are as follows:

[0261] First, save all non-dominated individuals in the population to the current front to screen out excellent individuals in the population, providing a basis for subsequent sorting and selection;

[0262] Secondly, calculate the set S of individuals dominated by each individual A in the current front. Subtract 1 from the number of dominating individuals of each individual B in the set S. If the number of dominating individuals of a certain individual B is reduced to 0, it means that it is not dominated by any other individual and becomes a non-dominated individual. Store it in another set H to find the non-dominated individuals in the set S and prepare for the next-level sorting;

[0263] Finally, let the set of non-dominated individuals in the first level be F1, and so on. Sort the individuals in the set H according to the number of dominating individuals, and ensure that all individuals in the population are sorted, so as to stratify the individuals in the population according to the non-dominated relationship. Individuals in each layer have the same non-dominated rank.

[0264] The fast non-dominated sorting method can not only ensure the diversity of the population, but also effectively screen out excellent individuals for selection and inheritance. Through multi-level sorting, it can ensure that each generation of the population contains multiple possible excellent solutions, thus improving the global search ability of the algorithm. In addition, the fast non-dominated sorting method also has high computational efficiency, enabling the algorithm to still maintain good performance when dealing with large-scale optimization problems.

[0265] Step 403: Select N individuals as the parent generation P using the crowding tournament selection strategy k , where k is the evolutionary generation number and k = 0.

[0266] The main difference between the NSGA-II algorithm and the NSGA algorithm lies in the crowding tournament selection method it adopts. The crowding tournament selection method jointly determines which individual will be preferentially selected based on two core attributes: dominance rank and crowding distance.

[0267] The dominance rank ensures the selection of individuals on better non-dominated fronts. An individual is said to dominate another individual if it is not worse than another individual in all objectives and is better than another individual in at least one objective. In this way, the individuals in the population can be divided into different dominance ranks, and individuals with lower dominance ranks are preferentially selected.

[0268] When two individuals are on the same non-dominated front, the dominance rank cannot distinguish their advantages and disadvantages, and it is necessary to introduce crowding distance to further evaluate individuals. The crowding distance refers to the distance between an individual and its adjacent individuals, which is used to evaluate the distribution of individuals in the solution space. An individual with a larger crowding distance means that its search range in the objective space is wider and it is more likely to find new solutions. Therefore, in the selection process, when the dominance ranks of two individuals are the same, the individual with the larger crowding distance is preferentially selected.

[0269] The calculation method of the crowding distance is as follows:

[0270] Set the number of individuals in the population, initialize the crowding distance of each individual in the population, and the initial value can be 0 or other appropriate values;

[0271] Determine the number of objective functions, and sort the individuals in the population in the order from good to bad according to each objective function. In the embodiment of the present invention, the objective functions are the minimum mass and the minimum maximum stress, and the number is 2;

[0272] Since the boundary individuals have the widest search range in the objective space and the largest crowding distance, the crowding distance of the boundary individuals is set to infinity. For other individuals, their crowding distances are calculated according to the differences in the objective function values of adjacent individuals, and the calculation formula is as follows:

[0273]

[0274] Where, is the index number of the individual in the sorting, I 1 and I n are the minimum value and the maximum value of the objective function respectively, and are the objective function values between two adjacent individuals respectively, and are the maximum value and the minimum value of the population for the m-th objective respectively.

[0275] It should be noted that on different objective functions, the same two individuals are not necessarily adjacent. Therefore, when calculating the crowding distance, it is necessary to sort the individuals according to each objective function, find the index vector of the sorting, and then calculate the crowding distance between each individual and its adjacent individuals on each objective function. This distance is normalized to [0, 1], and the crowding distances of each individual on all objective functions are accumulated as the final crowding distance of each individual. In the selection process, individuals with a lower dominance rank and a larger crowding distance are preferentially selected. This method not only ensures the diversity of selection but also effectively avoids the algorithm falling into a local optimal solution.

[0276] Step 404: Use the normal distribution crossover operator and the adaptive adjustment mutation operator successively to perform crossover and mutation on the individuals in the parent generation P k to generate the offspring generation X k .

[0277] Step 405: Combine the parent generation P k and the offspring generation X k to generate a new population Q k .

[0278] Step 406: Perform fast non-dominated sorting on the new population Q k and use the crowded tournament selection strategy to select N individuals to form a new parent generation P k+1 .

[0279] Step 407: Increment the value of the evolution generation k by 1, and determine whether the evolution generation k is less than the evolution generation threshold. If so, execute Steps 403 - 407. If not, output the Pareto optimal solution set.

[0280] The value-taking rules for the steel plate thickness in the national standard "GB / T 708 - 2019" are as follows:

[0281] For steel plates with a thickness less than or equal to 4 mm, the thickness should be taken as a multiple of 0.1 mm. Taking the value range of 2 - 4 as an example, the thickness should be an integer multiple of 0.1 mm, that is, 2.1 mm, 2.2 mm, 2.3 mm, etc., up to 4.0 mm;

[0282] For steel plates with a thickness greater than 4 mm, the thickness should be taken as a multiple of 0.5 mm. Taking the value range of 4 - 5 as an example, the thickness should be an integer multiple of 0.5 mm, that is, 4.5 mm, 5.0 mm.

[0283] Based on the output Pareto optimal solution set, referring to the value-taking rules for the steel plate thickness in the above national standard "GB / T 708 - 2019", round the optimization results of each design variable according to the value range of each design variable to obtain the optimization scheme of the design variables.

[0284] On the premise of balancing the calculation amount and the optimization performance, the example of the present invention selects a moderate initial population size of 60 as the basis for subsequent experiments; sets the evolution generation threshold to 50 to ensure that the algorithm achieves a better optimization effect within a reasonable time; on the basis of weighing the global search and local search capabilities, selects 0.8 as the value of the crossover probability; after comprehensively considering the exploration ability and development ability of the algorithm, sets the crossover distribution index and the mutation distribution index to 10 and 20 respectively.

[0285] Step 104: For each component to be optimized, use the Design and Optimization Integration Platform to integrate ANSYS and numerical calculation and programming tools. The Design and Optimization Integration Platform is used to receive and parse the output results of ANSYS, send the parsed output results of ANSYS to the numerical calculation and programming tools, receive the optimization results output by the numerical calculation and programming tools, and monitor the optimization process of the numerical calculation and programming tools in real time.

[0286] The Design and Optimization Integration Platform can be Isight or Optimus. In this embodiment of the invention, Isight is used. Isight can integrate multiple simulation tools and design tools together to achieve interdisciplinary optimal design. Isight can seamlessly integrate multiple simulation tools and automatically execute the workflow.

[0287] It should be noted that before integrating ANSYS using the Design and Optimization Integration Platform, a static analysis file, such as qingzhangche.wbpj, needs to be prepared. This file not only contains all the processes of the finite element static analysis of the operation device of the flatbed obstacle clearing vehicle, but also lists the input design variables and the output rigid strength analysis results. These variables are the key parameters in the optimization process. At the same time, this file also contains the sample points of the operation device. Before integrating the numerical calculation and programming tools using the Design and Optimization Integration Platform, all necessary input files, optimization files, and output files of the numerical calculation and programming tools need to be prepared.

[0288] During the optimization process, use the Design and Optimization Integration Platform to monitor the optimization process in real time, so that the historical optimization process of each step can be clearly displayed in the window. Finally, at the end of the iteration, the final optimization result can be displayed in an intuitive window form.

[0289] Perform multi-objective optimization on the tray and the supporting beam based on the improved NSGA-II algorithm. The optimization solution is completed after 3000 iterations of calculation. Finally, the optimization results are output from the post-processing part of the Design and Optimization Integration Platform software. Among them, the number of iterations usually refers to the number of operations in each generation during the operation of the algorithm. Specifically, the number of iterations can include the frequent update times of the individuals in the population in operations such as selection, crossover, and mutation. The improved NSGA-II algorithm takes about 5 hours, which greatly shortens the optimization design cycle. Figure 13 Shows the change process of two objective functions of the tray. Among them, A is the change process of the minimum tray mass, B is the change process of the minimum maximum stress of the tray. The area where the black dots gather usually represents the Pareto front, that is, the set of non-dominated solutions searched by the algorithm. The blue dots represent the convergence points, which refer to the points where the algorithm tends to be stable after multiple iterations and the distribution of solutions no longer changes significantly. Figure 14The change processes of two objective functions of the joist are shown, where A is the change process with the minimum mass of the joist, and B is the change process with the minimum maximum stress of the joist.

[0290] The NSGA-II algorithm aims to find the Pareto solution set in the design variables. By running the optimization model, the Pareto solution sets with the minimum mass and the minimum maximum stress of the obstacle clearing vehicle tray and joist can be obtained to improve the NSGA-II algorithm. Figure 15 The Pareto solution sets of the tray and the joist are shown, where A is the Pareto solution set of the tray and B is the Pareto solution set of the joist. It can be seen that after optimization, the curve formed by the obtained non-dominated solutions (Pareto solution sets) is smooth. Therefore, it can be considered that the quality of the solution set is good.

[0291] To verify the optimization effect of the improved NSGA-II algorithm, the optimization scheme of the design variables obtained based on the improved NSGA-II algorithm for all optimizable components is compared with the initial values, as shown in Table 9:

[0292] Table 9

[0293]

[0294]

[0295] The optimization scheme of the design variables obtained by the improved NSGA-II algorithm is used for model reconstruction, and its finite element simulation is carried out through ANSYS. After static analysis simulation, the stress and deformation nephograms of the tray and the joist can be obtained. Figure 16 The stress and deformation nephograms of the optimization scheme of the improved NSGA-II algorithm are shown, where A is the stress nephogram of the tray, B is the deformation nephogram of the tray, C is the stress nephogram of the joist, and D is the deformation nephogram of the joist. The maximum stress and deformation obtained by simulation are compared with the maximum stress and deformation obtained by the improved NSGA-II algorithm, so as to verify the effectiveness of the improved NSGA-II algorithm. The comparison and verification of the simulation values and the optimization results are shown in Table 10:

[0296] Table 10

[0297]

[0298] As can be seen from Table 10, the errors of the maximum stress and deformation obtained by the improved NSGA-II algorithm compared with the results obtained by simulation are both within 5%, and the average error is 2.02%. Therefore, the effectiveness of the optimization of the improved NSGA-II algorithm is verified.

[0299] The optimization results of the improved NSGA-II algorithm obtained in this example are compared with the initial values, as shown in Table 11:

[0300] Table 11

[0301]

[0302]

[0303] By comparing the data in Table 9 and Table 11, it can be obtained that through the optimization of the improved NSGA-II algorithm, the respective dimensions of the wrecker structure have basically been reduced. This reduction not only optimizes the shape of the structure but also reduces the material usage, thereby reducing the total mass of the structure, making the structural mass decrease by 15.15%. It effectively reduces the self-weight of the whole vehicle, thus reducing the energy consumption and wear during the operation of the vehicle and improving the usage efficiency of the vehicle, indicating the effectiveness and superiority of the improved NSGA-II algorithm in dealing with the multi-objective optimization problem of the flatbed wrecker structure.

[0304] Although the preferred embodiments of the present invention have been described, those skilled in the art can make additional changes and modifications to these embodiments once they learn the basic creative concept. Therefore, the appended claims are intended to be construed as including the preferred embodiments and all changes and modifications falling within the scope of the present invention.

[0305] Obviously, those skilled in the art can make various changes and modifications to this application without departing from the spirit and scope of this application. Thus, if these modifications and variations of this application fall within the scope of the claims of this application and their equivalent technologies, this application also intends to include these changes and modifications.

Claims

1. A multi-objective optimization method for flatbed tow truck structure based on improved NSGA-II algorithm, characterized in that: include: Use ANSYS to perform finite element static analysis of the optimized structure under various working conditions to determine all components that can be optimized and their most dangerous working conditions; For each optimizable component, ANSYS is used to generate a .wbpj file, wherein the .wbpj file is used to determine sample points of each optimizable component under its most dangerous working condition according to design variables and their value ranges, wherein the design variables are variables that have an impact on the mass change of each optimizable component and have optimization space, and the value range of the design variables is determined according to design requirements and actual production constraints, and the sample points are used to construct an approximate model of the finite element model of each optimizable component; For each of the optimizable components, an input file, an optimization file and an output file are established using numerical calculation and programming tools, wherein the input file is used to obtain the sample points from the output results of ANSYS, the optimization file is used to perform multi-objective optimization on the sample points based on an improved NSGA-II algorithm, and the output file is used to determine and output an optimization scheme for the design variables based on the output results of the multi-objective optimization. The output results of ANSYS include the sample points and stiffness analysis results. The improved NSGA-II algorithm uses floating-point encoding, a normal distribution crossover operator and an adaptive adjustment mutation operator. The mathematical model of the multi-objective optimization includes an objective function, the design variables and constraints. The objective function includes minimum mass and minimum maximum stress, and the constraints include static stiffness constraints and the value range of the design variables. For each of the optimizable components, ANSYS and the numerical calculation and programming tool are integrated using a design and optimization integrated platform. The design and optimization integrated platform is used to receive and parse the output results of ANSYS and send the parsed output results of ANSYS to the numerical calculation and programming tool, receive the optimization results output by the numerical calculation and programming tool, and monitor the optimization process of the numerical calculation and programming tool in real time.

2. The method according to claim 1, characterized in that: The finite element static analysis of the optimized structure under various working conditions using ANSYS is used to determine all the components that can be optimized and their most dangerous working conditions, including: Adding loads to a finite element model of the structure to be optimized based on a mechanical analysis result of the structure to be optimized; Applying constraints to the structure to be optimized according to the connection relationship between the components in the structure to be optimized; Static analysis is performed under the various working conditions to obtain the maximum stress of each component in the structure to be optimized. Based on the maximum stress of each component under the various working conditions, all the optimizable components and their most dangerous working conditions are determined. The optimizable components are components whose maximum value of the maximum stress under the various working conditions is less than 90% of the allowable stress. The most dangerous working condition of the optimizable component is the working condition where the maximum stress of the optimizable component under the various working conditions has the maximum value.

3. The method according to claim 2, characterized in that: The steps of establishing the finite element model of the structure to be optimized include: Using a three-dimensional CAD design tool to create a three-dimensional simplified model of the structure to be optimized; ANSYS is used to define the material properties, connection relationships and unit types of the structure to be optimized, and to perform mesh division on the structure to be optimized.

4. The method according to claim 1, characterized in that: The structure to be optimized is an operating device of a flatbed tow truck, and the operating device includes three components: a pallet, a support beam and a support arm.

5. The method according to claim 4, characterized in that: The mechanical analysis of the working device is performed based on a normal fully loaded condition.

6. The method according to claim 4, characterized in that: The various working conditions include a horizontal back-loading working condition, an inclined back-loading working condition and a full-load braking working condition.

7. The method according to claim 1, characterized in that: Determining the sample points of each optimizable component under its most dangerous working condition according to the design variables and their value ranges includes: Importing the finite element model of each optimizable component under its most dangerous working condition into the DOE module; Performing parameterization processing on the finite element model according to the design variables and their value ranges; Generate sample points using the design method in the DOE module.

8. The method according to claim 1, characterized in that: The floating point number encoding is to convert the binary number into a floating point number by using scientific notation based on the binary encoding.

9. The method according to claim 1, characterized in that: The definition formula of the adaptive adjustment mutation operator for the mutation probability and fitness of an individual is as follows: Where M is the number of individuals, P m (X i )and Individual X i The mutation probability and average mutation probability, e(X i ) and E(X i ) are individual X i The fitness and individual X i The evaluation function of .

10. The method according to claim 1, characterized in that: The improved NSGA-II algorithm includes: Step 401: Use the floating point number encoding for the design variables and the constraint conditions; Step 402: randomly generate an initial population including N individuals, and perform fast non-dominated sorting on the initial population; Step 403: Use the crowding competition selection strategy to select N individuals as the parent generation P k , where k is the evolutionary generation, k = 0; Step 404: Use the normal distribution crossover operator and the adaptive adjustment mutation operator to perform the parent generation P k The individuals in the crossover and mutation generate offspring X k ; Step 405: Merge the parent generation P k and the offspring X k Generate a new population Q k ; Step 406: k Perform the fast non-dominated sorting and use the crowded competition selection strategy to select N individuals to form a new parent generation P k+1 ; Step 407, add 1 to the value of the evolutionary generation k, and determine whether the evolutionary generation k is less than the evolutionary generation threshold. If yes, execute steps 403 to 407; if not, output the Pareto optimal solution set.

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