Multi-objective Structural Optimization Research Articles

A machine learning-based method for co-design and optimization of microwave-absorbing/load-bearing multifunctional structures

Simultaneously considering the absorption performance and load-bearing capability is a trend in the design of multifunctional structures. Nevertheless, the collaborative design and optimization involved in this process present a challenging problem. Herein, guided by multifunctionality, a lightweight microwave-absorbing/load-bearing multifunctional structure is intelligently inversely designed based on machine learning. A co-design scheme is developed to address the contradiction between the absorption performance and load-bearing performance. An approach for rapid inverse design of metamaterial absorbers containing multilayered frequency-selective surfaces is proposed. The simulation results obtained using multi-objective optimization based on surrogate models indicate that the optimized multifunctional structure achieves more than 90% absorption in the frequency range of 2.5 GHz–18.0 GHz and simultaneously exhibits superior load-bearing performance with an out-of-plane Young’s modulus of 334.8 MPa and an out-of-plane compressive strength of 4.95 MPa, demonstrating the effectiveness of the co-design scheme. Finally, the experimental results are analysed. This study provides a reference for co-design and multi-objective optimization of similar multifunctional structures.

A robust machine learning-based framework for handling time-consuming constraints for bi-objective optimization of nonlinear steel structures

In structural design, multi-objective optimization of nonlinear steel structures simultaneously considers various design (often conflicting) purposes during the stage of construction to the operation of projects. Such optimization generally requires excessive computational efforts for the evaluation of time-consuming constraints. To overcome this drawback, this paper presents an efficient machine learning-based (ML) method to perform bi-objective optimization of nonlinear steel structures describing two conflicting objectives, namely minimization of structural weight and nodal displacements, simultaneously. The proposed method combines a nondominated sorting genetic algorithm-II (NSGA2) with an extreme gradient boosting (XGBoost) surrogate-assisted model. Furthermore, a multi-objective comparison technique (MulCT) is implemented, where a safety parameter t is introduced to reduce errors in the predictive ML model. To demonstrate the efficiency of the proposed method, two robust design examples, including a planar 10-bar truss and 47-bar transmission tower structures, are provided. In comparison with various ML algorithms, numerical results illustrate that the XGBoost model is superior in performance and requires significantly less training time. The MulCT technique enhances computational efficiency, leading to a 20% reduction in computing resources as when it was implemented with NSGA2. The proposed method by integrating both MulCT and XGBoost models with NSGA2 can save more than 50% of computational efforts, while maintaining good accuracy, as can be achieved by NSGA2.

Multi-objective structural optimization and degradation model of magnesium alloy ureteral stent

BackgroundMg alloys have attractive properties, including biocompatibility, biodegradability, and ideal mechanical properties. Moreover, Mg alloys are regarded as one of the promising candidates for manufacturing ureteral stents. This study proposed a multi-objective optimization method based on the Kriging surrogate model, NSGA-Ⅲ, and finite element analysis to improve the degradation performance of Mg alloy ureteral stents. MethodsThe finite element model for the degradation of Mg alloy ureteral stents has been established to compare the degradation performance of the stents under different parameters. Latin hypercube sampling was adopted to generate train sample points in the design space. Meanwhile, the Kriging surrogate model was constructed between strut parameters and stent degradation behavior. The NSGA-Ⅲ was utilized to determine the optimal solution in the global design space. ResultsThe optimized stent achieved 5.52 ​× ​degradation uniformity (M), 10 ​× ​degradation time (DT), and 4 ​× ​work time (FT). The errors between the Kriging surrogate model and the finite element calculation results were less than 6%. ConclusionThe optimized stent achieved better degradation performance. The degradation behavior of stents was dependent on the design parameters. The multi-objective optimization method based on the Kriging surrogate model and finite element analysis was effective in stent design optimization problems.

Multi-objective optimization and theoretical analysis of re-entrant structure with enhanced mechanical properties

In response to the challenge of low stiffness and energy absorption capacity, various designs of negative Poisson's ratio (NPR) structures have emerged. However, these designs often lack a comprehensive analysis of other mechanical properties, leading to subpar mechanical performance. Previous studies have explored the mechanical properties response of enhanced re-entrant honeycombs (ERH) under impact conditions, revealing limitations in optimizing the structure's performance with a single objective. Therefore, this study aims to enhance ERH structural parameters to achieve superior mechanical performance through theoretical derivations and geometric optimizations. The results demonstrate that the proposed theoretical model is consistent with finite element analysis and response surface (RS) predictions. Expressions for Young's modulus, specific energy absorption, and compressive strength are proposed, facilitating the identification of structural parameters that meet specific requirements during reverse design. Furthermore, a multi-objective optimization approach optimizes the geometric parameters based on maximum energy absorption and compressive strength. The mechanical behavior of the optimized ERH is investigated using the finite element method, revealing the energy absorption capacity of 13.78 J/g while maintaining Poisson's ratio at -1.06. Additionally, the deformation mode of the optimized structure showcases enhanced stability compared to traditional honeycomb structures. The theoretical model and RS method were used to guide the design of ERH and promote the application of NPR structures.

Multi-objective optimization of composite sandwich structures using Artificial Neural Networks and Genetic Algorithm

Sandwich structures offer significant opportunities to improve the performance of many industrial applications such as aerospace, automotive, and marine. The design of a composite sandwich structure is often challenging because it is driven by the balance between the weight and cost of these structures. In this paper, a multi-objective optimization model using a Genetic Algorithm (GA) and an Artificial Neural Network (ANN) is presented to evaluate a new optimization approach in terms of weight and cost minimization for the composite sandwich structures. Classical lamination and beam bending theories were used, along with Monte Carlo simulation, to generate the design data for the proposed composite sandwich structure, which is applied as a floor panel for a high-speed train. Multilayer feedforward neural networks were used for predicting safety factors, cost, and weight of the designed structure based on the following inputs: core density, core thickness, face sheet materials’ combinations, and applied load. The trained Neural Network model was able to predict the considered results with a good performance metric, namely the coefficient of determination (R2 = 0.99) and the Mean Square Error (MSE = 1.3·10−5).Multi-objective optimization for cost and weight minimization was performed with a Genetic Algorithm using the derived ANN model. The obtained Pareto front provided several non-dominated optimal points leading to insights on the optimization process. The Finite Element Method (FEM) was used to model the key points of the optimal designs (i.e. the design with the lowest cost, weight, and Pareto optimal points). The FEM and optimization results had a maximum deviation of about 8.9%, indicating a good agreement between the two techniques.The newly elaborated methodology demonstrates a new approach for obtaining the optimum design of the investigated composite sandwich structure constructed from honeycomb core and laminated face sheets in terms the cost and weight. The study concluded that the use of Carbon Fiber-Reinforced Plastic (CFRP) or Fiber-Metal Laminate (FML) face sheets results in significant weight savings of about 59.5% and 48.6%, respectively, compared to an all-aluminum sandwich structure.

Multi-objective structure optimization and performance analysis of catalytic micro-reactor channel designed by an improved topology optimization model

Previous micro-reactor channel studies mainly focus on the limited design space or structure layout, rarely exploits design forms in which the procedural topology structure evolves freely. Therefore, a multi-objective topology optimization model are proposed for the inverse free evolution of micro-reactor channels, which can synergistically balance the effects among three objectives of reaction rate, flow loss and heat transfer to achieve optimal comprehensive performance. The topology optimization problem is formulated based on the material density-based design variable. The fluid dynamics response of design variables at each optimization iteration is updated by solving multi-physics governing equations, objective functions and variable constraints. Adjoint-based sensitivity analysis and GCMMA algorithm are used to obtain the gradient information of objective functions and update design variables, respectively. Additionally, the strict volume constraints and proposed pseudo-design-domain concept are introduced into the multi-objective function. In numerical examples, the influence of different Re conditions and different multi-objective weight-ratios on optimal designs is investigated, and their regular evolution mechanisms and the trade-off between performance optimization and structure evolution are analyzed. Then, the optimization principles for topology structure and performance parameters under the control of multi-objective functions are revealed. Finally, the comprehensive performance of micro-reactors under topology optimization method is compared with that of traditional micro-reactors to demonstrate the effectiveness of the improved method and reveal the physical mechanisms of multi-objective performance enhancement. The comparison results show that topology optimization designs can achieve 86.1% growth in reaction rate and 47.1% reduction in flow loss, and comprehensive performance coefficients have also been significantly optimized.

Parameter and Topology Optimization of Structures in the Frequency Domain under Nevanlinna–Pick Interpolation Constraints

The design optimization of structures can be conducted in either the time domain or the frequency domain. The frequency domain approach is advantageous compared to its time domain counterpart, especially if the degree of freedom is large, the objectives and/or constraints are formulated in the frequency domain, or the structure is subject to random loading. In this paper, an attempt is undertaken to obtain feasible optimal solutions by implementing the Nevanlinna–Pick (NP) interpolation theory across multi-objective structural optimization problems in the frequency domain. The NP equations introduce a trade-off that originates from the interpolation theory for complex variables. According to the NP theory, a complex function cannot have an independent amplitude from its derivative at a certain frequency. Consequently, the frequency response of a physical system cannot be shaped arbitrarily at discrete frequencies. Our objectives within this paper include calculating the weight, natural frequency, fatigue life, frequency domain response, and its derivative. To illustrate our claims, sample parameter and topology optimization problems were formulated and solved, both with and without the NP constraints. It was found that the inclusion of NP constraints induced a considerable improvement in the optimal solutions, while also causing the convergence to the optimal solution to become smoother.

Multiobjective optimization of an ionizer nozzle structure based on RSM and CFD

Multiobjective optimization of an ionizer nozzle structure based on RSM and CFD

Crashworthiness Design and Multi-Objective Optimization of Bionic Thin-Walled Hybrid Tube Structures

Crashworthiness Design and Multi-Objective Optimization of Bionic Thin-Walled Hybrid Tube Structures

Integrated shape-morphing and surrogate model-assisted multi-objective structural optimization of an automobile wheel made of lightweight materials to improve its impact resistance

To address the technical challenge that automobile wheels made of lightweight materials are prone to failure under dynamic impact loads, an integrated multi-objective optimization approach is proposed to determine the optimal design with enhanced impact resistance without reducing other structural performance. The shape-morphing technique, hybrid surrogate-based modelling approach, multi-objective particle swarm optimization algorithm, and a novel identification approach combining the modified technique for order preference by similarity to ideal solution and modified comprehensive objective weighting method are used separately to parameterize a model of the wheel, construct approximation models, solve the optimization process and determine the optimal trade-off design. The robustness and effectiveness of the identification method are demonstrated by analysing the effects of different optimization strategies on the optimal trade-off solutions. According to the optimized results, the impact resistance of the wheel is evidently enhanced while its total mass remains almost unchanged and other mechanical performance metrics are improved to varying degrees.

Multi-objective Topology Optimization of Sandwich Lattice Structures for Vibration Suppression: Numerical and Experimental Investigations

Multi-objective Topology Optimization of Sandwich Lattice Structures for Vibration Suppression: Numerical and Experimental Investigations

Memeplex-based memetic algorithm for the multi-objective optimal design of composite structures

Hybrid construction is proposed to decrease costs in lightweight structures using fiber-reinforced plastics (FRP) composite materials. Minimum weight, minimum strain energy (stiffness), and minimum energy variability of the structural system response are the objectives of the robust design optimization approach applied to composite shell structures with stiffeners. The trade-off depends on given stress, displacement, and buckling constraints imposed on composite structures considering non-linear geometric behavior. The design variables are ply angles and ply thicknesses of shell laminates, the cross-section dimensions of stiffeners, and the variables related to the selection of materials and their distribution at the laminate level and subsequently of the laminates along the structure. A Multi-Objective Memetic Algorithm (MOMA) applies multiple learning procedures exploring the synergy of different cultural transmission rules. An enlarged virtual population with a dual age-dominance nature captures and updates the Pareto curve. The concept of memeplex controls the meme selection and their propagation along the hybrid genetic and cultural evolution path. The success of memetic learning procedures is analyzed by measuring each meme's relative and absolute success events according to different approaches, depending on the reference time used in evolutionary history. Results show that MOMA is promising in multi-objective optimization of composite hybrid structures.

Multi-objective optimization of truss structure using multi-agent reinforcement learning and graph representation

This paper presents a novel method for multi-objective optimization of truss design utilizing multi-agent reinforcement learning and graph representation. The agents are trained to modify solutions to increase the hypervolume and spread the distribution of the non-dominated solutions. This iterative modification is modeled as a Markov game where multiple agents interact with the environment by changing the state of the environment, i.e., the solution and the current non-dominated solutions. Agents observe data representations of the state, modify each solution in the current non-dominated solutions, and receive their reward based on the improvement of the current non-dominated solutions. Each agent is modeled by the multi-agent deep deterministic gradient consisting of a policy function that predicts actions from its observation data and a value function that estimates rewards from the observation data, its action, and the actions of the other agents. The non-dominated solutions are represented as graph data and observed by the agents as the observation data through graph representation. The proposed method is applied to three multi-objective optimization problems: (1) a simple mathematical problem, (2) a 10-bar truss problem to minimize the structural volume and the displacement, and (3) trade-off designs of trusses to minimize the structural volume and bring the shape closer to the target shape. These numerical examples show the versatility of the trained agents to obtain superior solutions in practical structural optimization problems, compared to a conventional method.

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.

Multi-objective optimization of gradient gas diffusion layer structures for enhancing proton exchange membrane fuel cell performance based on response surface methodology and non-dominated sorting genetic algorithm-III

The gas diffusion layer structure has a significant impact on water and gas transport in proton exchange membrane fuel cell (PEMFC). In this study, a multi-objective optimization (MOO) method is applied to optimize the PEMFC gas diffusion layer (GDL) structures for performance enhancement. Nine design parameters are studied to analyses the output performance of the fuel cell and the average water content of the membrane, oxygen concentration non-uniformity, power density and system efficiency are used as performance indexes. The MOO forms the response surface regression model based on the three-dimensional numerical model of PEMFC, and the response surface methodology after processing through the non-dominated sorting genetic algorithm-III (NSGA-III) to obtain the Pareto frontier, and prioritizes the best operating conditions and structures based on technique for order preference by similarity to an ideal solution (TOPSIS). Compared with the reference point, the performance indexes of the decision point obtained by the NSGA-III algorithm and TOPSIS algorithm is enhanced by 0.45 %, 42.06 %, 2.99 % and 0.25 %, respectively. This study presents a new multi-objective optimization method for optimizing operating conditions combine with GDL structures for building efficient PEMFC, which provides a solution for achieving higher performance. The optimal results in this paper can provide some guidance for fuel cell performance improvement and control optimization.

Multi-objective structural optimization for the automatic member grouping of truss structures using evolutionary algorithms

This paper aims to formulate the multi-objective structural optimization problem to find the best member grouping of truss structures. The weight of the structure and the different number of discrete cross-sectional areas are the conflicting objective functions to be minimized simultaneously, generating a Pareto front presenting the non-dominated solutions. Sixteen multi-objective evolutionary algorithms are adopted to solve the proposed optimization problems. Several benchmark problems and a new proposed optimization problem are analyzed. Even though original groupings based on symmetry are defined, it is possible to discover other competitive structural member configurations that can interest decision-makers regarding manufacturing, cutting, transportation, checking, and welding.

Multi-objective design optimization of reentrant auxetic model using Lichtenberg algorithm based on metamodel

PurposeThe present paper aims at the multi-objective optimization of a reentrant hexagonal cell auxetic structure. In addition, a parametric analysis will be carried out to verify how each of the design factors impact each of the responses.Design/methodology/approachThe multi-objective optimization of five different responses of an auxetic model was considered: mass, critical buckling load under compression effort, natural frequency, Poisson's ratio and failure load. The response surface methodology was applied, and a new meta-heuristic of optimization called the multi-objective Lichtenberg algorithm was applied to find the optimized configuration of the model. It was possible to increase the failure load by 26.75% in compression performance optimization. Furthermore, in the optimization of modal performance, it was possible to increase the natural frequency by 37.43%. Finally, all 5 responses analyzed simultaneously were optimized. In this case, it was possible to increase the critical buckling load by 42.55%, the failure load by 28.70% and reduce the mass and Poisson's ratio by 15.97 and 11%, respectively. This paper addresses something new in the scientific world to date when evaluating in a multi-objective optimization problem, the compression and modal performance of an auxetic reentrant model.FindingsIt was possible to find multi-objective optimized structures. It was possible to increase the critical buckling load by 42.82%, and the failure load in compression performance by 26.75%. Furthermore, in the optimization of modal performance, it was possible to increase the natural frequency by 37.43%, and decrease the mass by 15.97%. Finally, all 5 responses analyzed simultaneously were optimized. In this case, it was possible to increase the critical buckling load by 42.55%, increase the failure load by 28.70% and reduce the mass and Poisson's ratio by 15.97 and 11%, respectively.Originality/valueThere is no work in the literature to date that performed the optimization of 5 responses simultaneously of a reentrant hexagonal cell auxetic structure. This paper also presents an unprecedented statistical analysis in the literature that verifies how the design factors impact each of the responses.

Dynamic Response and Optimal Design of Radio Telescope Structure under Wind Load Excitation

The dynamic response of a radio telescope structure under wind load excitation significantly impacts the accuracy of signal reception. To address this issue, this study established a parametric finite element model of a radio telescope to simulate its dynamic response under wind load excitation. An improved Latin hypercube sampling method was applied in the design of experiments (DOEs) to optimize the structural dimensional parameters of various components of the radio telescope with the aim of reducing the dynamic response to wind load. A response surface model and multi-objective genetic algorithm (MOGA) were employed for multi-objective structural optimization of the radio telescope structure. The findings reveal that the thickness of the stiffening ribs, the length of the side of the square hollow pole, the thickness of the middle pole, and the inner diameter of the thin pole are the most influential structural parameters affecting the first-order frequency (F1), second-order frequency (F2), maximum deformation in the x-direction (DX), and maximum deformation in the z-direction (DZ) of the radio telescope, respectively. Optimizing the radio telescope results in a 40.00% improvement in F1 and a 24.16% enhancement in F2, while reducing DX by 43.94% and DZ by 64.25%. The study outcomes offer a comprehensive scheme for optimizing the structural dimensional parameters of various radio telescope components in regions characterized by multiple wind fields.

Design, analysis and optimization of a hybrid fluid flow magnetorheological damper based on multiphysics coupling model

Magnetorheological (MR) dampers are widely used in industrial applications due to its simple structure, fast response and adjustable damping performance. However, the volume of the MR damper will be limited by the installation space, which hinders the application to some extent. In this paper, a hybrid fluid flow MR damper which can be used in antiseismic building is designed to achieve better damping performance under constrained volume size. The multiphysics coupling simulation model and circuit simulation model are also established. Numerical results show the output damping force is 6.367 kN, the dynamic adjustable range is 50.768, and the current input time is 31 ms under the applied current of 2.0 A. In order to improve the dynamic performance of the designed MR damper under constrained volume size, a multi-objective structural optimization method based on theoretical calculation model is proposed. Experiments are also conducted to investigate the dynamic performance of the initial and optimal MR damper. Compared with the initial MR damper, the output damping force and the dynamic adjustable range of the optimal damper are improved by 6.6 % and 46.3 %, while the energy consumption is reduced by 10.7 %, respectively.

Multi-Objective Optimization of Thin-Walled Composite Axisymmetric Structures Using Neural Surrogate Models and Genetic Algorithms.

Composite shells find diverse applications across industries due to their high strength-to-weight ratio and tailored properties. Optimizing parameters such as matrix-reinforcement ratio and orientation of the reinforcement is crucial for achieving the desired performance metrics. Stochastic optimization, specifically genetic algorithms, offer solutions, yet their computational intensity hinders widespread use. Surrogate models, employing neural networks, emerge as efficient alternatives by approximating objective functions and bypassing costly computations. This study investigates surrogate models in multi-objective optimization of composite shells. It incorporates deep neural networks to approximate relationships between input parameters and key metrics, enabling exploration of design possibilities. Incorporating mode shape identification enhances accuracy, especially in multi-criteria optimization. Employing network ensembles strengthens reliability by mitigating model weaknesses. Efficiency analysis assesses required computations, managing the trade-off between cost and accuracy. Considering complex input parameters and comparing against the Monte Carlo approach further demonstrates the methodology's efficacy. This work showcases the successful integration of network ensembles employed as surrogate models and mode shape identification, enhancing multi-objective optimization in engineering applications. The approach's efficiency in handling intricate designs and enhancing accuracy has broad implications for optimization methodologies.