Multi-objective Structural Optimization Research Articles

Multi-objective optimization of channel structure for a proton exchange membrane water electrolysis cell

The flow field dominates the process of mass transport and distribution inside the proton exchange membrane water electrolysis cell (PEMEC). Initially, a three-dimensional and non-isothermal PEMEC channel model was estimated to investigate the impact of channel height and width. Based on these results, a complete PEMEC model with a parallel flow-field pattern was developed, and the channel heights and widths of the model were optimized using a genetic algorithm (GA). Compared to the original model, the optimized model decreased the pressure drop by 34.97% at a lower voltage. In addition, because of the optimized flow-field pattern, the optimized model improves the current density on the proton exchange membrane as well as the gas holdup situation in a partial position in the cathode gas diffusion layer.

Multi-objective topology optimization design of truss structures based on evidence theory under limited information

Uncertainty information is often limited and has great discreteness, how to ensure the structure having good robustness under epistemic uncertainty becomes a technical problem for multi-objective topology optimization design. In this paper, the evidence theory is used to quantify the epistemic uncertainty; the plausibility measurement expressing upper limit of failure probability is applied to be a new evaluation of reliability. The total weight and the reliability of structures are taken as the optimization objectives, and a multi-objective robust topology optimization design model based on evidence theory is proposed. Parallelization technique based differential evolution for multi-objective optimization (DEMO) is preferable to search above robust Pareto front due to its merits of non-requirement of any gradient and superior mechanisms of non-dominate strategy. In order to verify the effectiveness of the proposed method, the multi-objective reliability optimization of a wood truss structure is implemented with considering elastic modulus and structural load as uncertain variables. According to the optimization results, six same truss specimens are made for the static random loading test. The failure probability of the truss structure is judged by the stress and node displacement obtained from the test, so as to verify the feasibility of the reliability optimization method based on evidence theory. The experimental results also indicate that the proposed method can avoid the deviation of the optimization results caused by the fluctuation of epistemic uncertainty, and provide a new method for designers to make the optimization results robust even when the data information is insufficient and the cognitive level is limited.

Multi-objective Optimization of a Novel Hybrid Structure for Co-generation of Ammonium Bicarbonate, Formic Acid, and Methanol with Net-Zero Carbon Emissions

Multi-objective Optimization of a Novel Hybrid Structure for Co-generation of Ammonium Bicarbonate, Formic Acid, and Methanol with Net-Zero Carbon Emissions

Crashworthiness analysis and multi-objective optimization of spatial lattice structure under dynamic compression

A spatial lattice structure is proposed to improve the structural crashworthiness and energy absorption. First, a single-cell structure is proposed via a bionic honeycomb, and then the single-cell structure is arrayed to form a spatial lattice structure. The finite element model of the spatial lattice structure for crashworthiness analysis is established. The theoretical model of the plateau stress of the lattice structure under compressive conditions is derived, and its accuracy is verified by the corresponding finite element analysis. After that, the effect of geometrical parameters of single-cell structure on crashworthiness is analyzed. Then, geometrical parameters of single-cell structure and number of single-cell in the X, Y, and Z directions are used as design variables, the mass, and overall size are used as constraints, and specific energy absorption and collision peak force are used as optimization objectives. The multi-objective crashworthiness optimization of spatial lattice structure is carried out, and the optimal lattice structure design is determined via the gray relational analysis coupling entropy weight method. The validity of the finite element model and optimal design is verified by the drop weight impact test. The crashworthiness optimization of spatial lattice structures has important guiding significance for the design of energy-absorbing structures.

Multi-objective structural profile optimization of ships based on improved Artificial Bee Colony Algorithm and structural component library

This paper addresses the multi-objective, design variables discrete problem of river boat profile structure optimization. The study considers not only the economic performance but also the stability of the boat to a certain extent when selecting the optimization objectives. First, the standard component library of the vessels is established and the discrete structural model is converted into a continuous optimization model based on the component library index. Second, to balance the global search and local search capability of the optimization algorithm, an adaptive Artificial Bee Colony Algorithm (I-ABC) is proposed. I-ABC uses a modified chaotic mapping to improve the diversity of nectar sources, and adaptive search and following mechanisms are adopted for the leading and following bee stages, respectively. Then, a Dominating Artificial Bee Colony Algorithm (D-ABC) is proposed for multi-objective optimization by introducing Pareto domination and considering the degree of individual crowding in terms of hypersphere neighborhood. Then, numerical simulations and comparative analysis of the proposed algorithm are performed using different test functions, and the results show that I-ABC and D-ABC have excellent performance in both single-objective and multi-objective optimization. Finally, using the component library established in this paper and the proposed improved Bee Colony Algorithm to optimize the profile structure of a chemical-liquid tanker, the optimization results show that the maximum reduction of the ship profile area is 5.08% and the maximum reduction of the vertical center height is 7.427%. The proposed optimization algorithm is also applicable to other river boats.

Application research in multi-objective constrained optimization of composite wing structure

In order to explore the optimization of composite wing structure, this paper reviews the past research works of optimization of composite wing structures worldwide and in China. It concludes that most optimization methods and calculations are useful but only applied with specified theoretic model. Then relevant composite optimization theories and strength constraints with composite lamination failure criteria, stability, aeroelasticity are sorts out. Optimizing algorithm and applied solution rounding strategy are also listed. Concentrating on weight-reduction analysis on the thickness, sequence, and angle of the composite stacking under multiple constraints, a practical model of a composite wing structure example with a large aspect ratio is completed, and the calculation is based on the finite element analysis tool Nastran and the genetic algorithm Matlab program. Two optimal solutions are given with detailed differences and the comparison of the composite structure parameters before and after calculation is also recorded. The application example indicates the feasibility of the optimization method and quadratic rounding process, the detail structure performance improvements with skin lamination change under the calculation are illustrated at the same time.

Finite Element Simulation and Structural Optimization of Structural Flow Sequential Field for Sequential Boost Switching Valve

Turbocharging technology is an important part of engine technology. Under the working condition of 730 °C and 0.5 MPa, the valve plate opening and closing will bear the high pressure of the internal fluid medium, resulting in the deformation of the switching valve. In this paper, ANSYS finite element simulation software is used to establish the valve fluid domain model, and the stress field and deformation law of the valve under the valve plate opening of 0 °~ 90 °are simulated and analyzed. Based on the fluid-solid coupling theory, the deformation and stress distribution of the valve plate structure are obtained by simulation analysis. The simulation results show that the smaller the opening of the valve plate, the more disordered the flow condition. As the opening increases, the flow tends to be stable. When the opening is 30 °, the negative pressure inside the valve is the largest; combined with the fluid-solid coupling analysis, the maximum stress load on the valve plate appears at the connection between the valve plate and the long valve shaft and the short valve shaft, and the maximum pressure appears at the opening of 60 °, which is 37.144 MPa; the maximum deformation occurs at the outer edge of the valve plate. Based on the results of this simulation analysis, the corresponding multi-objective structural optimization of the valve structure is carried out to provide technical reference for the structural design of similar valves.

Multi-objective optimization of PCM-fin structure for staggered Li-ion battery packs

Multi-objective optimization of PCM-fin structure for staggered Li-ion battery packs

Multi-Objective Structural Optimization of a Composite Wind Turbine Blade Considering Natural Frequencies of Vibration and Global Stability

Aspects concerning resonance and global stability of a wind turbine blade must be carefully considered in its optimal design. In this paper, a composite wind turbine blade with an external geometry based on the NREL 5 MW model was subjected to multi-objective structural optimization considering these aspects. Four multi-objective structural optimization problems are formulated considering the blade mass, the maximum blade tip displacement, the natural frequencies of vibration, and the critical load factor as objective functions. The design variables are the number of plies, material, and fiber orientation. The design constraints are the materials’ margin of safety, the blade’s allowable tip displacement, and the minimum load factor. The blade model is submitted to the loads determined by the actuator lines theory and discretized in a finite element parameterized model using the Femap software according to geometric design variables. Among many multi-objective evolutionary algorithms available in the literature concerning evolutionary computation, the NSGA-II is the adopted evolutionary algorithm to solve the multi-objective optimization problems. Pareto fronts are obtained and performance indicators are used to evaluate the distribution of the non-dominated solutions. Multi-criteria decision-making is used to extract the solutions from the Pareto fronts according to the decision-maker’s preferences. The values of the objective functions, design variables, and constraints are presented for each extracted solution. The proposed study is expected to contribute to the multi-objective optimization and the structural design of wind turbine blades.

A two-archive multi-objective multi-verse optimizer for truss design

Multi-objective structure optimization is a complex design issue that involves dealing with multiple conflicting objectives and various constraints. Although metaheuristics have been successful in resolving such issues, their stochastic nature and limitations can make implementation challenging. To address this challenge, an efficient and powerful optimizer called the multi-objective multi-verse optimizer (MOMVO) has been proposed in this study. The MOMVO algorithm is based on a two-archive concept focused on convergence and diversity, respectively, and is termed MOMVO2arc. The effectiveness of MOMVO2arc was evaluated by applying it to five conventional planar and spatial real-world structural optimization problems. These problems had conflicting objectives, such as minimizing structural mass and minimizing maximum nodal deflection, while imposing safety and size constraints related to stress on components and discrete cross-sectional areas. The results were then compared with those of seven advanced optimization techniques, including MOEA/D and NSGA-II, using four globally accepted performance indicators, including Hypervolume, Inverted Generational Difference, Spacing to Extent matrices, and the qualitative behavior of the best Pareto-front plots that each algorithm can produce. The comparative analysis and average Friedman rank test revealed that MOMVO2arc was more effective in solving large structure optimization problems with less computation time. The suggested approach not only found and maintained more Pareto-optimal sets but also achieved good diversity and convergence in both the decision and objective spaces. Therefore, MOMVO2arc can be a promising tool for resolving complex multi-objective structure optimization problems.

Design optimization of a sandwich composite tube with auxetic core using multiobjective lichtenberg algorithm based on metamodelling

In this paper, the multi-objective optimization of a sandwich composite tube with an auxetic reentrant core was done. Five different responses of the model were considered: mass; critical buckling load; natural frequency; Poisson’s ratio; and failure load under compression effort. The Response Surface Methodology was applied, and a new meta-heuristic of optimization called the Multi-objective Lichtenberg Algorithm was used to find the optimized configuration of the structure. In addition, a parametric analysis was performed to verify how each of the design factors influenced each of the responses. It was found that the unit cell height is the most significant factor for failure load, natural frequency, and mass. On the other hand, unit cell height has no significance for Poisson's ratio. Furthermore, it was also verified that the Poisson's ratio has no correlation with any of the other responses studied (failure load, critical buckling load, mass, and natural frequency). Finally, it was possible to improve (reduce) the Poisson’s ratio by more than 56% in the optimization of the modal performance and improve the mass, the Poisson’s ratio, the failure load, and the critical buckling load in the static performance. Thus, this paper shows something unprecedented in the literature to date when evaluating the multi-objective design optimization of a tubular sandwich structure with an auxetic core.

An optimized economic-environmental model for a proposed flare gas recovery system

Iran is the second largest oil and gas producer among the Persian Gulf states, with 13.26 billion m3 gas flaring in 2020, approximately 9.34% of the global gas flaring. To reduce pollutants emissions and energy loss, an accurate feasibility study of flare gas recovery technologies is needed as the first step. Multi-objective optimization of process structure for the development of a comprehensive flare gas recovery system based on process simulation has not attracted much attention in the literature. In this study, a process structure for a flare gas recovery system was proposed using a multi-objective optimization approach to decrease associated gas flaring in southern Iran with a current flaring capacity of 279.7 MMSCFD. In the proposed structure, associated gas goes through sweetening and Natural Gas Liquids (NGL) units. After separating the liquid and vapor products, the NGL outlet gas is allocated to different units, including reinjection of gas to oil wells, gas pipelines, Liquefied Natural Gas, Compressed Natural Gas, Gas to Liquid, Gas to Power, and Desalination units. These units were simulated in Aspen HYSYS, providing an accurate economic and environmental analysis. Afterward, the shares of NGL outlet gas allocated to downstream units were considered optimization variables. The process structure was optimized by maximizing the economic (net present value) and environmental (greenhouse gas emission) objective functions. Results show that in the optimized process structure, 93.4% of the NGL outlet gas is allocated to gas injection and 6.6% to the power generation unit, resulting in a reduction of 6.22 million tons of CO2 emissions per year in this oilfield. The net present value of the flare gas recovery system is approximately 1.504 billion dollars, with a payback period of 1.60 years, suggesting the feasibility of the process.

Numerical optimization-based design studies on biaxial tensile tests

Biaxial tensile tests are of great significance for the characterization of materials. For ductile materials, they allow the representation of the yield strength curve separating elastic and plastic material behavior. Contrary demands regarding the specimen design arise, if a biaxial stress state with the equivalent stress equal or close to the yield strength shall be obtained. On one hand, the specimen shall be of constant thickness and stiffness, in order to allow an unconstrained deformation without undesired lateral strains. On the other hand, stress concentrations arising from the load introduction make a thickened border region necessary, in order to avoid a premature failure of the specimen. The present paper addresses this problem by a multi-objective structural optimization using Evolutionary Algorithms. Well-defined parametric models of biaxial tensile test specimens allow to systematically investigate the influence of the thickness distribution and the sizing of the border region. Additionally, the influence of actuators of constant force compared to actuators of constant displacement are quantified. In all cases, the minimization of the stress difference as well as the actuation effort are considered as objectives. The results allow a deep insight to the optimal definition of biaxial tensile test specimens and are summed up in well-defined design proposals.

Multi-objective performance optimization of target surface of bionic blue whale-skin impinged by array jet

Jet impingement cooling technology is usually applied to combustor liner with large heat load. With the continuous improvement of high capacity and low emission of heavy-duty gas turbines,the research on low resistance and high cooling efficiency cooling technology is particularly important. To meet these urgent needs, based on the blue whale skin structure, a new array impingement target surface cooling structure was proposed from the perspective of bionics. The flow and heat transfer characteristics of the array impingement bionic target surface cooling structure were numerically simulated under high Reynolds number (Re) and high Heat flux density (q) conditions. The influence of groove depth (H, 1 to 3 mm), radius ratio (R/H, 1 to 3) and spacing ratio (P/H, 10 to 20) on the cooling performance of impingement target surface was analyzed. Multi-objective performance optimization of the bionic structure was carried out by using the second-order response surface approximation model (RSM) and the second-generation non-inferior sequencing genetic algorithm (NSGA-II), and the performance of the optimized structure was tested. The results show that the above optimization method is accurate and effective, and the optimal bionic structure is H = 1.212 mm, R/H = 1.132, P/H = 12.078. Compared with the plane target surface, the average Nusselt number (Nuave), flow friction factor (f), and comprehensive thermal coefficient (F) of the optimal bionic groove structure increased by 14.5%, 1.1% and 14.1%，respectively. The structure and multi-objective optimization method proposed in this paper can provide a certain reference for the design of new efficient cooling structure of heavy-duty gas turbines combustor liner.

Tool Failure Analysis and Multi-Objective Optimization of a Cutting-Type Energy-Absorbing Structure for Subway Vehicles

This paper aims to provide essential guidance for the crashworthiness design of cutting energy-absorbing structures for subway vehicles. By investigating tool failure with experiment and numerical approaches, a new energy-absorbing tube structure was proposed and optimized to improve the crashworthiness and reliability of the cutting energy-absorption structure. The impact test results revealed that multiple failure modes occurred in the tool. Mechanical wear occurs mainly in the middle of the cutting edge, while the tool’s tip failure is primarily due to thermal wear. Impact forces were no longer stable due to tool failure. The simulation results of the established tool-tube thermal–structural coupling finite element model were consistent with the tests. The temperature distribution indirectly validated the failure modes in different tool areas. By eliminating the tearing-type fracture mode, the proposed new structure effectively reduced the high temperature of the tool’s tip, better maintained the uniform temperature of the cutting edge, and smoothed changing of the cutting force. Finally, the Kriging surrogate model and NSGA-II algorithm were utilized to obtain the tool’s minimum steady-state temperature (STT) and maximum mean average cutting force (MCF). The optimal solution determined by the minimum distance method is STT = 514 K, MCF = 131 kN.

Performance analysis and multi-objective optimization of bionic dendritic furcal energy-absorbing structures for trains

Rail vehicles offer the characteristics of large carrying capacity and high running speed. Train accidents usually result in substantial personal casualties and economic losses. Energy-absorbing structures can efficiently and quickly absorb and disperse the energy generated during collisions. In this paper, the performances with different cross-sections and partings of the bionic dendritic furcal structure (BDFS) inspired by the furcal branch and bifurcation structure of neurons are analyzed and compared by numerical simulation. The simplified super folding element theory and experiments verify that the finite element models are effective. A hybrid multi-stage optimization decision system, i.e., multi-criteria decision-making (MCDM)- multi-objective optimization (MOP)- MCDM, which integrates the VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method, the multiple objective particle swarm optimization-crowding distance (MOPSO-CD) evolutionary algorithm and repetitive VIKOR method, is proposed to find the optimal structure and obtain the optimal parameter alternative of the structure. Comparisons and analyses of experiments and simulations are carried out to verify the effectiveness of the proposed method. The results show that BDFS with six furcal ribs and 3rd-order parting display the best comprehensive crashworthiness under the working condition of 10 m/s specified in EN15227 standard. When the single target requirement is considered, specific energy absorption (SEA) can be increased by 16.18%, peak crushing force (PCF) can be decreased by 67.07%, and undulation of the load-carrying capacity (ULC) can be decreased by 14.02%. This study provides an effective tool for the analysis and optimization of energy-absorbing structures.

Energy absorption characteristic and crashworthiness optimization design of VRB-VCS structures under manufacturing constraints

After fully understanding the limitations of traditional variable rolled blank (VRB) and variable cross-sectional (VCS) double-hat shaped beam structures on the energy absorption ability and collision safety optimal design, we propose a variable rolled blank and variable cross-sectional (VRB-VCS) double-hat shaped beam structure with piecewise exponential function. Firstly, the thickness distribution function and the mathematical model of constraint conditions are derived under the constraints of manufacturing rollability. The corresponding finite element (FE) model of the VRB-VCS structure is validated by the dropping hammer impact axial crush experiments, which can predict the crushing process with high fidelity. Secondly, the parametric researches of the energy absorption characteristic of VRB-VCS structure are carried out based on the FE model. The reasonable range of each parameter is obtained by analyzing the influence of the thickness distribution and other key cross-sectional parameters on the energy absorption characteristic and deformation mode of VRB-VCS structure. Finally, the Pareto frontier solutions of the linear and piecewise exponential function VRB-VCS structures are obtained by the multi-objective optimization of the corresponding structures. In comparison to VCS, VRB and linear VRB-VCS structures, the proposed VRB-VCS structure has a higher energy absorption capacity and greater crashworthiness.

Multi-objective crashworthiness design optimization of a rollover protective structure by an improved constraint-handling technique

<abstract> <p>This study proposes a multi-objective optimization (MOO) strategy with an improved constraint-handling technique to improve the crashworthiness of an excavator rollover protective structure (ROPS). First, the experimental test under the ISO 12117 criteria is conducted and the developed numerical model is verified. Then, the amounts of energy absorption and the cross-sectional forces of components in the ROPS are analyzed. The main energy absorbing and load carrying components are identified. Finally, the thicknesses of the identified components are considered as the design variables. A multi-objective crashworthiness optimization process aims at improving the safety distance and reducing the total mass is designed by the finite element analysis-based surrogate model technique and a modified MOO algorithm. The proposed algorithm modifies the objective function values of an individual with its constraint violations and the true objective function values, of which adaptive penalty weights fed back from the constraint violations are used to keep the balance. Compared with the existing methods, it is found that the optimal solutions obtained by the proposed algorithm show superiority on convergence rate and diversity of distribution. The optimal results show that the safety distance is 27.42% higher while the total mass is 7.06% lower than those of the baseline design when it meets the requirements of ISO 12117. This study provides an alternative crashworthiness design route for the ROPS of the construction machines.</p> </abstract>

Bionic design and multi-objective optimization of thin-walled structures inspired by conchs

<abstract> <p>Thin-walled structures have been widely used in various parts of vehicle subsystems because of their high-efficiency impact energy absorption and lightweight characteristics. However, the impact deformation mode of conventional thin-walled structures is unstable and the energy absorption efficiency is low. Therefore, a series of novel bionic conch structures (BCS) are proposed to find a more excellent crashworthiness design in this study. First, the finite element simulation model of BCS verified by experiments is established. Then, the energy absorption characteristics of bionic conch structures, and conventional single-cell and multi-cell tubes under axial loading are compared by employing finite element simulation. The results show that the thin-walled structures inspired by conchs have a higher energy absorption efficiency than the other two structures with the same mass. In addition, the influence of main design parameters (wall thickness, inner and outer ring diameter, and the number of inner and outer panels) on the crashworthiness of BCS is studied through parameter design and factor significance analysis. Finally, the optimal geometric configuration is found by combining the approximation model and multi-objective particle swarm optimization, and the crashworthiness of BCS is further optimized. The bionic crashworthiness design and optimization framework proposed in this study can also provide a reference for other engineering protective structures.</p> </abstract>

Experimentally informed structure optimization of amorphous TiO2 films grown by atomic layer deposition.

Amorphous titanium dioxide TiO2 (a-TiO2) has been widely studied, particularly as a protective coating layer on semiconductors to prevent corrosion and promote electron-hole conduction in photoelectrochemical reactions. The stability and longevity of a-TiO2 is strongly affected by the thickness and structural heterogeneity, implying that understanding the structure properties of a-TiO2 is crucial for improving the performance. This study characterized the structural and electronic properties of a-TiO2 thin films (∼17 nm) grown on Si by atomic layer deposition (ALD). Fluctuation spectra V(k) and angular correlation functions were determined with 4-dimensional scanning transmission electron microscopy (4D-STEM), which revealed the distinctive medium-range ordering in the a-TiO2 film. A realistic atomic model of a-TiO2 was established guided by the medium-range ordering and the previously reported short-range ordering of a-TiO2 film, as well as the interatomic potential. The structure was optimized by the StructOpt code using a genetic algorithm that simultaneously minimizes energy and maximizes the match to experimental short- and medium-range ordering. The StructOpt a-TiO2 model presents improved agreements with the medium-range ordering and the k-space location of the dominant 2-fold angular correlations compared with a traditional melt-quenched model. The electronic structure of the StructOpt a-TiO2 model was studied by ab initio calculations and compared to the crystalline phases and experimental results. This work uncovered the medium-range ordering in a-TiO2 thin films and provided a realistic a-TiO2 structure model for further investigation of structure-property relationships and materials design. In addition, the improved multi-objective optimization package StructOpt was provided for structure determination of complex materials guided by experiments and simulations.