Optimal Design Variables Research Articles

Fleet Design Optimization of Package Delivery Unmanned Aerial Vehicles Considering Operations

The conceptual design process of aircraft starts by deciding the representative mission requirements, followed by optimization of design variables to satisfy the given requirements. However, the appropriate mission requirements are not obvious, especially when designing package delivery unmanned aerial vehicles (UAVs; also called drones). The UAVs must accommodate various combinations of package weights and delivery distances. The complexity increases further when designing a heterogeneous fleet of UAVs that serves a large number of customers. This work addresses this problem by solving coupled design–operation optimization to find optimal mission requirements and optimal UAV designs simultaneously. We formulate this problem as a mixed-integer nonlinear optimization and propose a sequential heuristic algorithm to solve the coupled problem. The benchmark study of the proposed algorithm against a nonconvex branch-and-cut solver shows that the sequential heuristics are effective. We also demonstrate that the simultaneous UAV design and routing optimization reduces the UAV weight across the fleet by more than 12% on average compared to the conventional baseline.

A hybrid polynomial-based optimization method for underwater gliders with parameter uncertainty

As a type of enduring platform for ocean exploration, underwater glider usually contains some uncertain parameters in actual engineering applications, which are related to manufacturing errors, assembly errors, and sensor measurement errors. Uncertain parameters will make the glider performance show uncertain characteristics, so it is necessary to consider their effects in the design optimization process for an underwater glider. In this paper, a hybrid polynomial-based optimization method is proposed to solve optimization problems of underwater gliders with parameter uncertainty. The hybrid polynomial consists of power function terms and trigonometric function terms, and it is used for fitting surrogate models of the glider dynamic models. The fitted surrogate models are used for quickly calculating the performance evaluation parameters of underwater gliders. Specifically, power function terms and trigonometric function terms correspond to optimization design variables and uncertain parameters, respectively. The hybrid polynomial method covers the convenience of the traditional response surface method and the advantage of the Chebyshev polynomial in interval analysis. Based on surrogate models and interval analysis, we can estimate boundary functions of performance evaluation parameters, and they are employed to construct optimization objective functions. Then, the optimization iteration calculation can be carried out. Here, the proposed method is used for determining the optimal control parameter values of the Petrel-II glider with the uncertainty of some configuration and measurement parameters. The optimization objectives are to minimize the specific energy consumption and maximize the average advance velocity simultaneously. Finally, some laws of the glider performance are summarized.

A Multifunctional Reinforced Concrete Tuned Liquid Wall Damper with Optimal Design Variables

Dampers can be installed inside buildings to mitigate vibration and lateral displacement. Recently, a new type of tuned liquid wall damper (TLWD) was proposed, in which a reinforced concrete wall panel can contain various vertical openings, allowing internal water to flow to provide the damping effect. Generally, larger amounts of water lead to a better damping effect. However, this requires a larger opening area in the wall, which will reduce the strength of the wall. Therefore, a multiobjective optimization method, which considers both the strength and damping effects, was developed to accommodate the two conflicting design objectives in this work. The method starts with a local task (i.e., strength and damping). Once the individual objective is optimized, a global task accounts for all parameters. The optimal result is obtained by selecting the best solution from the global task. This approach achieves the optimal design of the TLWD system considering a wide range of size and number of the openings. It was concluded that, for optimal TLWD configuration, the panel has minor strength reduction while providing satisfactory damping capability for hazard mitigation. The method presented in this study can be used to design other types of structures with conflicting design objectives.

Explicit Tunnels and Cavities Control Using SIMP and MMA in Structural Topology Optimization

The topology of a 3D continuum structure is usually characterized by the number of independent connected component and holes in the structure, where the holes include tunnels (through holes) and cavities (interior holes). The number of these features can be measured by the topological invariants of the structure (e.g., Betti numbers and Euler characteristic). The quantitative control of structural topology is important in topology optimization design because of various considerations, including design freedom, manufacturability, structural performance, and manufacturing costs. However, effective control of the structural topology during the topology optimization process remains a challenge, particularly to control the structural tunnels. To simplify the problem, only the number of tunnels (NT) and cavities (NC) of the structure are controlled in this paper. To solve the aforementioned problems, this study calculates the characteristic information of the tunnels and cavities by introducing the tunnel loops of homology theory and fire-burning method (FBM), while proposing a method for quantitative control of the 3D structural tunnels and cavities within the framework of the solid isotropic material with penalty (SIMP) interpolation of the design variable and method of moving asymptotes (MMA) optimization algorithm. The method achieves unilateral constraints over the structural tunnels and cavities by establishing explicit relationships between the element design variables in the structural topology optimization and NT as well as NC in the structure. Numerical examples demonstrate that the proposed method can effectively control the tunnels and cavities of an optimized structure.

Multi‐Objective Optimization for the Cross Brace of a Computer Numerical Control Gantry Machine Tool Based on Intelligent Algorithms

A multi‐objective optimization design method for the cross‐brace structure of a computer numerical control gantry machine tool is proposed to improve mechanical performance. Dynamic and static performance indexes of the cross brace are analyzed. On basis of sensitivity analysis, size parameters which have great influence on mass and dynamic and static performance indexes of the cross brace are selected as design variables for optimization. Objective values under design variables are obtained by orthogonal experimental method, and an objective function is fitted by response surface method. After verifying the fitting effect of the objective function, entropy weight method is used to calculate weight coefficient of each optimization objective, and a comprehensive performance optimization model of the cross brace is built. Accelerated particle swarm optimization (APSO) intelligent algorithm is used to solve the comprehensive performance optimization model. Comparison results before and after the optimization show that the mass of optimized cross brace is reduced by 8.377%, the maximum stress is reduced by 13.252%, and the first‐order natural frequency is increased by 2.183%. The proposed optimization method provides a new idea to improve the dynamic and static performance of the cross brace while reducing its mass.

An Improved Evolutionary Structure Optimization Method for Smooth Topology Design of Structures

To meet the needs of industrial production, an improved evolution structural optimization (ESO) method with high efficiency is proposed. The optimized design variables with intermediate density were designed using the windowed evolution structural optimization (WESO) method to increase the stability of the algorithm. The efficient calculation method of the element node sensitivity was established, which realizes the establishment of level set functions, smooth topological design of structures and the updating of design variables. The stability of the proposed algorithm was verified by the Zhou–Rozvany problem, two- and three-dimensional (3D) numerical results. The effectiveness and efficiency of the proposed algorithm was further verified by numerical comparison with other topology optimization frameworks. Lastly, the improved windowed ESO method was applied to the initial configuration design of the double-deck bridge structure, which not only provides guidance for its initial design but also demonstrates the applicability of the method in complex structural systems.

Adaptive ensemble surrogate-based optimization and analysis of forklift pallet racks

As an important part of the lifting platform of pallet forklift trucks, how to reduce the deformation of the pallet rack under working conditions while reducing the mass to ensure the safety performance of forklift trucks is the most concerning issue in the design of forklift truck structure. The pallet rack structure is complex, and optimizing simulation using traditional high-precision simulation models takes much time and effort. Therefore, this paper takes the lifting platform of an unmanned AVG forklift truck as the research object and establishes a parametric model of the pallet rack using the 3D modelling software SolidWorks and the finite element analysis software ANSYS to carry out static analysis of it. Optimization design variables are selected, a single surrogate model and ensemble surrogate model are chosen for various surrogate model techniques, a small number of sample points are used to construct a low-precision model, and adaptive infilling technology is used to improve the model accuracy, and the structure is optimized, and the results show that, while the pallet rack structure meets the requirements of light weight and strength, the mass is reduced by 1.2%, and the morphology is reduced by 17.2%. Moreover, a global sensitivity analysis of each design parameter was carried out under the guidance of the surrogate model, highlighting the most influential design variable as the height of the channel steel and establishing the design variables that should be taken into account in the structural design. This paper compares the performance of the mainstream single-surrogate model and ensemble-surrogate model as well as the adaptive infilling strategy in engineering design and proves that the surrogate model optimization method has a certain guiding significance for the structural optimization design of pallet racking.

Efficiency of air classifiers in dry separation of nometallic mineral fines

The article analyzes dry separation of nometallic mineral fines with a view to enhance the process efficiency owing to optimized choice of equipment design variables and operating conditions. The earlier studies neglected the separation process capacity and energy intake, which weakened representativity of the research findings. It is possible to improve the quality and quantity characteristics of air separation using the specific effect criteria which define the perfection rate of the test machines and determine their optimal design variables. The main specific effect criterion is assumed to be a criterion which provides such choice of design variables that the operational factors with respect to the other criteria are the best. In the air classifier efficiency evaluation, the main criterion is a criterion which takes into account both the mechanical energy intake and the processing time. The analysis of the criteria used to assess the classification machines finds out that the main optimization criterion for air classifiers is a criterion that takes into account the quantity of pollutants in separation products, while the main optimization criterion for vibratory air classifiers is a criterion that takes into account the mechanical energy intake of separation. This study also adjusts parameters of air classification machines using their earlier recommended ranges: the grid incline angle αgrid = 8–9 deg, the vibration amplitude Ас = 2.5 mm and the vibration frequency ωc = 100 s–1 of the vibratory air classifier body. The obtained results enable recommending choosing design variables and operating conditions in air classification and vibratory air classification in dry separation of granite by the size of 10 mm and in dry separation of carbonate minerals by the size of 1 mm.

Mechanical property analysis and design parameter optimization of a novel nitinol nasal stent based on numerical simulation.

Background: A novel braided nasal stent is an effective alternative to nasal packing after septoplasty that can be used to manage the mucosal flap after septoplasty and expand the nasal cavity. This study aimed to investigate the influence of design parameters on the mechanical properties of the nasal stent for optimal performance. Methods: A braided nasal stent modeling method was proposed and 27 stent models with a range of different geometric parameters were built. The compression behavior and bending behavior of these stent models were numerically analyzed using a finite element method (FEM). The orthogonal test was used as an optimization method, and the optimized design variables of the stent with improved performance were obtained based on range analysis and weight grade method. Results: The reaction force and bending stiffness of the braided stent increased with the wire diameter, braiding density, and external stent diameter, while wire diameter resulted as the most important determining parameter. The external stent diameter had the greatest influence on the elongation deformation. The influence of design parameters on von-Mises stress distribution of bent stent models was visualized. The stent model with geometrical parameters of 25mm external diameter, 30° braiding angle, and 0.13mm wire diameter (A3B3C3) had a greater reaction force but a considerably smaller bending stiffness, which was the optimal combination of parameters. Conclusion: Firstly, among the three design parameters of braided stent models, wire diameter resulted as the most important parameter determining the reaction force and bending stiffness. Secondly, the external stent diameter significantly influenced the elongation deformation during the compression simulation. Finally, 25mm external diameter, 30° braiding angle, and 0.13mm wire diameter (A3B3C3) was the optimal combination of stent parameters according to the orthogonal test results.

Reduced-order modeling of supersonic fuel–air mixing in a multi-strut injection scramjet engine using machine learning techniques

Dual-mode ramjet/scramjet engines promise extended flight speed range and are the commonly preferred air-breathing propulsion system from within the family of hypersonic aircraft concepts. One of the main challenges that should be hurdled in their design is modeling the fuel–air mixing process to provide optimal fuel distribution and yield the best engine performance. Injecting fuel into high-speed air stream along multiple parallel struts can augment the fuel penetration and improve mixing efficiency. Mixing intensity is increased with turbulence by the shock-expansion waves in post-strut regions. However, this enhancement in mixing can bring about detrimental effects on the aerodynamic performance by increasing losses on total pressure. Designing the optimal working configuration requires testing the interaction between many design variables. This can be a tedious and computationally costly task. Machine learning models thus appear well-suited for multi-objective optimization of design variables that can be elusive to designers. In particular, non-linear regression models can be built over the available sparse simulation data to predict unseen mixing conditions. In the present work, we carry out a detailed investigation of the effect of multi-strut configuration parameters on three objective functions: mixing efficiency, mixing length, and the total pressure recovery (TPR) factor. These objective functions are linked with the most relevant physical phenomena in the supersonic fuel–air mixing flow field. We first generate a CFD database by solving compressible, non-reactive, Reynolds-averaged Navier–Stokes (RANS) filtered flow equations in a 2D scramjet engine domain with three varying design variables: struts location, strut wedge angle and strut V-settlement angle. We then apply various regression models – artificial neural network (ANN), Gaussian process regression (GPR), and kernel regression – to this database and formulate a surrogate model relevant for fuel injection that can be utilized in reduced-order modeling studies that estimate the hypersonic engine performance. We find that regression is generally more difficult in the vicinity of fuel struts (due to turbulence/shock effects) and easier further downstream from the struts, but ANN performs generally better than other regression models. Thus, our reduced-order tool incorporates a mixing efficiency model predicted by the ANN. It computes the thrust of a hypersonic engine with less than 10% error. We also present a detailed discussion of the physical insights gained from our CFD database; we link this discussion with the earlier findings from the machine learning tools. In our sensitivity study, we find the strut wedge angle to be the most influencing parameter on the mixing properties and aerodynamic losses.

Topology Optimal Design of NRD Guide Devices Using Function Expansion Method and Evolutionary Approaches

In order to increase communication capacity, the use of millimeter-wave and terahertz-wave bands are being actively explored. Non-radiative dielectric waveguide known as NRD guide is one of promising platform of millimeter-wave integrated circuits thanks to its non-radiative and low loss nature. In order to develop millimeter wave circuits with various functions, various circuit components have to be efficiently designed to meet requirements from application side. In this paper, for efficient design of NRD guide devices, we develop a topology optimal design technique based on function-expansion-method which can express arbitrary structure with arbitrary geometric topology. In the present approach, recently developed two-dimensional full-vectorial finite element method (2D-FVFEM) for NRD guide devices is employed to improve computational efficiency and several evolutionary approaches, which do not require appropriate initial structure depending on a given design problem, are used to optimize design variables, thus, NRD guide devices having desired functions are efficiently obtained without requiring designer's special knowledge.

On the tradeoffs between embodied and operational carbon in building envelope design: The impact of local climates and energy grids

The building envelope has a substantial influence on a building’s life cycle operational and embodied carbon emissions. Window-to-wall ratios, wall assemblies, shading and glazing types, have been shown to have a significant impact on total emissions. This paper provides building designers, owners, and policy makers with actionable guidance and a prioritization framework for establishing co-optimized lifecycle carbon performance of facade assembly components in a broad spectrum of climate contexts and energy carbon intensities. A large parametric study of building envelopes is conducted using building performance simulation and cradle-to-gate embodied carbon calculations in 6 US cities. The authors derive the total carbon emissions optimization for commercial office and residential space types using standard code-reference models and open-source lifecycle data. Comparisons between optimal total carbon solutions and (i) optimal operational carbon and (ii) minimum required assemblies, show the impact of under and over investing in envelope-related efficiency measures for each climate. Results show how the relationship between embodied and operational carbon is highly localized, that optimal design variables can vary significantly. In low carbon intensity energy grids, over investment in envelope embodied carbon can exceed as 10 kgCO2e/m2, while under investment in high carbon intensity grids can be higher than 150 kgCO2e/m2.

Influence of integer design variables in topology optimization of incompressible turbulent flow

• Optimize incompressible turbulent flow at bidimensional and tridimensional domains employing the continuous adjoint approach • Analyze the influence of integer design variables in topology optimization of incompressible turbulent fluids • Develop the adjoint near wall distance calculation to treat the adjoint spalart allmaras turbulence model Turbulent fluid flow is a challenging physical problem to be addressed with topology optimization due to the vortex generation and the near wall distance calculation that difficult the calibration of topology optimization parameters when continuous design variables based-optimizers are used. The intrinsic nature of topology optimization inverse permeability interpolation clashes with the accuracy requirements from turbulent fluid flow dynamics. To solve the mentioned challenge, the present paper investigates the influence of an integer continuous variable-based-optimizer, i.e. a [0, 1] binary behaviour, that avoids grey regions during the optimization process. Its influence on the near wall distance calculation is analyzed as it affects the permeability of the fluid domain. The turbulence phenomenon is treated via the Spalart-Allmaras model and its near wall distance calculation is approached by the Hamilton-Jacobi formulation. Permeability independence on the topology optimization formulation constraints is proposed firstly at the continuous adjoint approach to avoid miscalculations in the fluid cells. The finite volume method is employed to solve the Reynolds Averaged Navier-Stokes governing equations and 2D and 3D tests are developed, where discussions on the solid-fluid boundaries definition, the material penalization dependence, objective function comparisons and accuracy of the CFD analysis and the wall distance calculation are presented.

Automated circuit sizing with multi-objective optimization based on differential evolution and Bayesian inference

Manual sizing of analog circuit specifications has become challenging owing to their ever-increasing complexity. Especially for innovative, large-scale circuit designs with numerous design variables, operating conditions, and conflicting objectives to optimize, analog designers must run time-consuming simulations for several weeks to find the optimum configuration. Recently, machine learning and optimization techniques have been applied in the field of analog circuit design, wherein evolutionary algorithms and Bayesian models have shown good results for circuit sizing tasks. In this context, we introduce multi-objective optimization based on differential evolution and Bayesian inference (MODEBI)—a design optimization method based on generalized differential evolution 3 (GDE3) and Gaussian processes (GPs). The proposed method can perform sizing for complex circuits that require optimization of many design variables and conflicting objectives. Although state-of-the-art methods reduce multi-objective problems to single-objective optimization and potentially induce a priori bias, the proposed method searches directly over the multi-objective space using Pareto dominance and ensures that designers are provided with diverse solutions to choose from. To reduce optimization time, we propose using GPs to model the circuit and employing this surrogate model to preselect candidates. However, this results in a more complex offspring selection process, and the diversity in population survival must be specifically addressed. This paper proposes several solutions to these problems, resulting in multiple MODEBI variations. To the best of our knowledge, this is the first method that specifically addresses solution diversity and simultaneously focuses on minimizing the number of simulations required to obtain feasible configurations. The evaluation performed on two voltage regulators with different complexity levels showed that the proposed offspring selection method and survival policy can obtain highly diverse feasible solutions considerably faster than GDE3 or Bayesian optimization-based algorithms.

Shape Optimization of the Streamlined Train Head for Reducing Aerodynamic Resistance and Noise

Aiming to improve the comprehensive aerodynamic performance of a high-speed train, a multi-objective shape optimization method for a streamlined train head is proposed in this work. The shape of the streamlined train head is parameterized with some spline curves. The optimization design variables are uniformly sampled using the optimal Latin hypercube design method. The aerodynamic resistance and dipole noise sources are chosen as the optimization objectives, which can be obtained through the computational fluid dynamics (CFD) method. An approximate calculation model is established by the radial basis function neural network so as to effectively predict the values of optimization objectives. The error between the predicted values and actual values of the aerodynamic resistance is less than 1%, and that of the dipole noise source is less than 3 dB, which demonstrate the validity of the approximate calculation model. In the optimization process, the algorithm NSGA-II is adopted to update the values of the optimization design variables, and the approximate calculation model is used to calculate the optimization objectives, which greatly reduces the optimization computation time of the streamlined head shape. Through iterative computation of the optimization algorithm in the design space, each optimized design variable shows a trend of convergence, and the aerodynamic resistance and dipole noise source generally show a decreasing trend. The Pareto front is corrected by the CFD method after optimization. The aerodynamic resistance can be reduced by up to 4.5%, and the dipole noise source can be reduced by up to 3.9 dB.

Development and validation of an improved model for Dye-sensitized solar cell and estimation of the optimum design parameters for maximum performance

ObjectiveThe performance of a Dye-Sensitized Solar Cell (DSSC) mainly depends on specific surface area, dye loading, pore-volume, thickness of the semiconductor layer, and electron lifetime. The optimization of these set of parameters is crucial in obtaining the best performance. The experimental optimization of the above parameters is often expensive and time consuming, therefore the present study aims for validation of an improved mathematical model and extraction of these set of parameters using the mathematical model. MethodThe current work proposes an improved mathematical model and an optimal design for Degussa P25 (DP25) based DSSC after optimizing the mathematical model formulated using continuity and transport equations. The proposed model describes the charge transport and recombination process of a DSSC. A metaheuristic-based optimization algorithm is used to extract the optimal design parameters for the DP25 based DSSC. ResultsThe J-V characteristics produced by the proposed model are qualitatively analyzed against the different reported experimental results using TiO2 (DP25), SnO2, and ZnO as photoanodes. The model results are in well agreement with the published experimental results and can be used to further optimize the performance of the DSSC. The proposed model using the extracted parameters reveals that the performance of the DSSC can be further enhanced by using optimal design variables during the development. AdvancementThis study opens a new era of research for fabricating efficient DSSCs at low cost through the combined approach of theoretical modeling and experimentation.

Efficient one-dimensional turbomachinery design method based on transfer learning and Bayesian optimization

Aerodynamic optimization is a powerful approach used in turbomachinery design to shorten design cycles and reduce manual intervention. The design task is to find the optimal design variables with optimal efficiency. However, most design optimization algorithms must start from scratch for each new design task because they cannot reuse previous design experience, in contrast to human experts, who can identify a near-optimal solution based on prior design experience. To address this issue, this paper proposes a transfer optimization learning method for one-dimensional (1D) turbine aerodynamic design. It can transfer the knowledge from the samples accumulated from past design optimizations (source tasks) to accelerate the target design optimization (target task). For each task, a Gaussian process-based surrogate model is established. These models are combined by a probability weighting strategy to build an ensemble model that achieves knowledge transfer. The method is validated on a 1D design case of a single-stage turbine. The results show that, compared with other state-of-the-art optimization algorithms that do not use prior design experience, the proposed method can reduce the computational cost by more than 30% while maintaining the same aerodynamic performance. This paper demonstrates an efficient transfer optimization method for the high-nonlinear 1D turbine design problem.

Multiobjective Optimization of a Dual Stator Brushless Hybrid Excitation Motor Based on Response Surface Model and NSGA 2

This article proposes a multiobjective optimization design framework for a double stator brushless hybrid excitation motor (DSBHEM) to provide high torque, wide flux regulation ability and low torque ripple. The design variables are divided into sensitive level and insensitive level by sensitivity analysis. The response surface model (RSM) and nondominated sorting genetic algorithm 2 (NSGA2) are organically combined to generate a set of Pareto solutions for the sensitive level variables, from which the optimal values of the sensitive level variables are obtained. In addition, the optimal values of insensitive variables are obtained through single parameter scanning optimization, and a set of final optimal design variables are obtained. The electromagnetic performance of the initial design and the optimal design are compared with finite element analysis. Finally, a prototype is manufactured to verify the proposed concepts.

Assessment of emission and environmental parameters of different commercial high by‐pass turbofan engines throughout landing and take‐off cycle

AbstractAchieving more eco‐friendly aircraft propulsion systems is of paramount importance in the aerospace industry since their exhaust emissions possess an important influence on the depletion of ozone layer. In this work, 24 turbofan engines having the close thrust ranging from 117 to 133 kN are examined using energetic, exergetic, and exergo‐environmental tools throughout the LTO cycle involving take‐off, climb‐out, approach, and taxi‐out phases. According to emission findings, the highest CO emission indexes (CO EIs) of the engines vary from 13.77 to 40.1 g/kg fuel in the idle phase; whereas the highest NOx EIs change from 18.4 to 64.36 g/kg fuel at take‐off phase. Moreover, the highest exergy efficiency (ExEFF) of the turbofan engines vary between 15.88% and 24.31% at the climb‐out phase whilst the lowest ExEFF change between 4.59% and 7.46% at the idle phase. Moreover, the idle phase is observed to have the highest wasted exergy ratio (WExR) varying from 18.5% to 19%; whereas the climb‐out phase enjoys the lowest WExR changing from 15.11% to 16.8%. As a new index, specific irreversibility production (SIP) of the engines is observed to range from 0.297 to 0.497 MW/kN at the taxi‐out phase; while SIP becomes the minimum at the climb‐out phase, changing from 0.138 to 0.269 MW/kN. It could be deduced that since by‐pass ratio and compressor pressure ratio of the engines have significant influences on exergetic and emission values, increasing the thrust of the engine does not mean raising its emission value or wasted exergy ratio. It is thought that this study helps find optimum design variables leading to the lowest environmental effect.

Optimization of Shearer Drum Based on Multi-Objective Bat Algorithm with Grid (MOBA/G)

The shearer drum undertakes the main function of coal falling and loading, and picks distributed on it have a great impact on the performance of the drum. However, few studies have optimized the pick and drum at the same time. In this paper, parameters of pick and drum are considered as design variables, and the response functions of design variables are established based on the central composite experiment method. The optimal structural and working parameters of the pick and the drum of MG500/1130-WD shearer are obtained by using the multi-objective bat algorithm and multi-objective bat algorithm with grid, respectively. Comparing results of the two algorithms, the multi-objective bat algorithm with grid is more effective in improving the comprehensive performance of the drum. According to the optimized design variables, a coal mining test is carried out to verify the optimization effect of the algorithm. The result provides some theoretical references for the design and production of the drum and has some engineering application value.