Structural Design Problems Research Articles

Truss sizing optimum design using a metaheuristic approach: Connected banking system

Several methods have been used to solve structural optimum design problems since the creation of a need for light weight design of structures and there is still no single method for solving the optimum design problems in structural engineering field that is capable of providing efficient solutions to all of the structural optimum design problems. Therefore, there are several proposed and utilized methods to deal with optimum design issues and problems, that sometimes give promising results and sometimes the solutions are quite unacceptable. This issue with metaheuristic algorithms, which are suitable approaches to solve these set of problems, is quite usual and is supported by the “No Free Lunch theorem”. Researchers try harder than the past to propose methods capable of presenting robust and optimal solutions in a wider range of structural optimum design problems, so that to find an algorithm that can cover a wider range of structural optimization problems and obtain a better optimum design. Truss structures are one of these problems which have extremely complex search spaces to conduct search procedures by metaheuristic algorithms. This paper proposes a method for optimum design of truss sizing problems. The presented method is used against 6 well-known benchmark truss structures (10 bar, 17 bar, 18 bar, 25 bar, 72 bar and 120 bar) and its results are compared with some of the available studies in the literature. The performance of the presented algorithm can be considered as very acceptable.

Historical evolution of structural optimization techniques for steel skeletal structures including industrial design applications

This study covers the review of algorithms developed for the optimum design of steel skeletal structures from the first article published in 1960 until to date. The paper initially describes the mathematical formulation of a simple truss structural design problem. The early optimum design algorithms that were based on mathematical programming techniques where the design variables are assumed to be continuous are reviewed. The optimum design of steel framed structures necessitates the selection of steel profiles from the standard list of discrete steel sections and requires the satisfaction of design code provisions. Both mathematical programming and optimality criteria techniques need more capability to produce solution to this type of optimum design problems. Soft computing techniques emerged recently provide solution directly without needing any approximation. These techniques are classified and reviewed and their use in obtaining the optimum solution of actual industrial steel design applications is given.

Optimization of truss structures using multi-objective cheetah optimizer

In this study, a multi-objective version of the recently proposed cheetah optimizer called multi-objective cheetah optimizer (MOCO) has been proposed. MOCO draws inspiration from the targeted hunting strategy employed by cheetahs, which involves a sequence of actions: searching for prey, patiently waiting for the right moment to attack, swiftly launching the attack, and then retreating from the prey and returning to their habitat. MOCO is the result of modification and enhancement from its single-objective counterpart, utilizing a Pareto dominance-based approach. This adaptation allows MOCO to efficiently handle multiple objectives, explores and exploits promising areas in the optimization landscape, and identifies non-dominated solutions, offering valuable tradeoff choices for decision-makers. To demonstrate its practical applications, the MOCO method has been employed to address five intricate structural design problems. These problems involve a pair of competing objectives: the minimization of structural weight and the reduction of maximum nodal displacement. To gauge the efficacy and efficiency of the proposed algorithm, a comparative analysis is conducted against three alternative state-of-the-art multi-objective algorithms. Furthermore, a rigorous evaluation is carried out utilizing hypervolume testing. The findings reveal that the MOCO algorithm surpasses the performance of the other algorithms, underscored by its capacity to uncover a diverse array of non-dominated solutions. To delve deeper into the experimental results, statistical analysis employing Friedman’s rank test is employed. The solutions generated and the convergence patterns exhibited by the MOCO approach underscore its exceptional proficiency in resolving intricate design problems.

Metaheuristic algorithm inspired by enterprise development for global optimization and structural engineering problems with frequency constraints

In this study, a novel metaheuristic optimization algorithm inspired by the enterprise development (ED) process was developed. This process encompasses tasks, structure, technology, and human interactions. A mechanism for switching activities was utilized to determine each step by updating the searched solutions. The ED optimizer underwent evaluation against 50 mathematical functions and 54 IEEE Congress on Evolutionary Computation (CEC) functions, and it was compared with six up-to-date algorithms, three winners of CEC 2020 in real-world single-objective constrained optimization, and ten well-known algorithms. The evaluation results revealed that the ED optimizer outperformed the algorithms in mathematical tests. Using finite element simulation, this novel method was applied to minimize steel structure component weights under various frequency constraints. The engineering designs included a 37-bar planar truss, a 52-bar dome, a 72-bar space truss, a 600-bar dome, and a 1,410-bar dome. Optimization results for these structures showed that the developed ED optimizer yielded the optimal solution and required fewer function evaluations. In conclusion, the ED optimizer is a superior metaheuristic algorithm that can effectively solve complex structural design problems.

MOAAA/D: a decomposition-based novel algorithm and a structural design application

When real-world engineering challenges are examined adequately, it becomes clear that multi-objective need to be optimized. Many engineering problems have been handled utilizing the decomposition-based optimization approach according to the literature. The performance of multi-objective evolutionary algorithms is highly dependent on the balance of convergence and diversity. Diversity and convergence are not appropriately balanced in the decomposition technique, as they are in many approaches, for real-world problems. A novel Multi-Objective Artificial Algae Algorithm based on Decomposition (MOAAA/D) is proposed in the paper to solve multi-objective structural problems. MOAAA/D is the first multi-objective algorithm that uses the decomposition-based method with the artificial algae algorithm. MOAAA/D, which successfully draws a graph on 24 benchmark functions within the area of two common metrics, also produced promising results in the structural design problem to which it was applied. To facilitate the design of the "rectangular reinforced concrete column" using MOAAA/D, a solution space was derived by optimizing the rebar ratio and the concrete quantity to be employed.

Buckling mode constraints for topology optimization using eigenvector aggregates

Buckling-constrained structural design problems have conventionally prioritized optimizing the buckling load factor with less consideration given to the buckling mode shape. In this work, mode shape constraints are imposed within a topology optimization problem using an eigenvector aggregate constraint that is a weighted sum of homogeneous quadratic functions of the linearized buckling eigenvectors. A generalized formulation of the eigenvector aggregate is introduced, extending previous work. A new adjoint-based derivative evaluation technique is derived that is valid even in the presence of repeated eigenvalues. Numerical examples, including a clamped beam, a compressed column, and a square plate, demonstrate the effectiveness of the proposed approach. The results show the ability of the eigenvector aggregate to handle repeated eigenvalues, enable design space exploration, and capture mode shape switching.

State estimation and structure identification of complex networks with time‐varying delays and model uncertainty based on probabilistic graph neural network

SummaryIn this paper, the state estimation problem and structure identification problem are investigated for an array of complex networks with time‐varying delays and model uncertainty. Model uncertainty is generated by uncertain connections between nodes in complex networks. Combining probabilistic graph model and graph neural network, a probabilistic graph neural network is proposed to deal with the uncertainty, and the multiple linear terms of the errors between nodes are estimated. The purpose of the addressed state estimation problem is to design a state estimator such that, in the presence of the model uncertainty, the estimation error to converge to zero can be guaranteed and the explicit expression of the estimator parameters is given. Based on a Lyapunov function, the parameters of the estimator and the updating laws of the weights of probabilistic graph neural network can be obtained by the solutions to linear matrix inequalities. The purpose of the addressed structure identification problem is to infer a definite graph structure model based on Bayes' theorem in the presence of a stable probabilistic graph neural network and state estimator. Finally, an illustrative example is provided to demonstrate the feasibility and effectiveness of the developed state estimation and structure identification scheme.

Structural Optimization of Trusses in Building Information Modeling (BIM) Projects Using Visual Programming, Evolutionary Algorithms, and Life Cycle Assessment (LCA) Tools

The optimal structural design is imperative in order to minimize material consumption and reduce the environmental impacts of construction. Given the complexity in the formulation of structural design problems, the process of optimization is commonly performed using artificial intelligence (AI) global optimization, such as the genetic algorithm (GA). However, the integration of AI-based optimization, together with visual programming (VP), in building information modeling (BIM) projects warrants further investigation. This study proposes a workflow by combining structure analysis, VP, BIM, and GA to optimize trusses. The methodology encompasses several steps, including the following: (i) generation of parametric trusses in Dynamo VP; (ii) performing finite element modeling (FEM) using Robot Structural Analysis (RSA); (iii) retrieving and evaluating the FEM results interchangeably between Dynamo and RSA; (iv) finding the best solution using GA; and (v) importing the optimized model into Revit, enabling the user to perform simulations and engineering analysis, such as life cycle assessment (LCA) and quantity surveying. This methodology provides a new interoperable framework with minimal interference with existing supply-chain processes, and it will be flexible to technology literacy and allow architectural, engineering and construction (AEC) professionals to employ VP, global optimization, and FEM in BIM-based projects by leveraging open-sourced software and tools, together with commonly used design software. The feasibility of the proposed workflow was tested on benchmark problems and compared with the open literature. The outcomes of this study offer insight into the opportunities and limitations of combining VP, GA, FEA, and BIM for structural optimization applications, particularly to enhance structural efficiency and sustainability in construction. Despite the success of this study in developing a workable, user-friendly, and interoperable framework for the utilization of VP, GA, FEM, and BIM for structural optimization, the results obtained could be improved by (i) increasing the callback function speed between Dynamo and RSA through specialized application programming interface (API); and (ii) fine-tuning the GA parameters or utilizing other advanced global optimization and supervised learning techniques for the optimization.

Benchmark problems in optimum structural design of 3D reinforced concrete frames

Benchmarking goes hand in hand with the development and establishment of efficient and robust optimization methodologies in various scientific fields. Nevertheless, benchmark problems, with known global optima, are currently missing in the optimum structural design of reinforced concrete (RC) frames. In the present study, for first time, benchmark case studies in the optimum design of RC frames are presented. The aim is that these benchmarks are used for the calibration, tuning, improvement and development of optimization algorithms to address the efficient design of concrete frames. More particularly, six three-dimensional concrete building frames are optimally designed to Eurocodes. First, exhaustive search is conducted to identify the global optimum solutions and Pareto fronts. Useful conclusions are also made with respect to the properties of the optimal solutions. Moreover, all candidate designs results are provided in an supplementary file so that they can be used in future optimization studies. Next, the performance of several well-known, single- and multi-objective optimization algorithms is assessed against the global optima to examine their efficiency and applicability in this class of optimization problems. Closing, the need for further and larger in scale benchmark case studies in the optimum design of concrete frames is emphasized.

Bayesian Updating for Random Tensile Force Identification of Ancient Tie Rods Using Modal Data

Tie rods play a crucial role in civil engineering, particularly in controlling lateral thrusts in arches and vaults, and enhancing the structural integrity of masonry buildings, both historic and contemporary. Accurately assessing the tensile axial forces in tie rods is challenging due to the limitations of existing methodologies. These methodologies often rely on indirect measurements, computational models, and optimization procedures, resulting in single-point solutions and neglecting both modeling and measurement uncertainties. This study introduces a novel Bayesian updating framework to effectively address these limitations. The framework aims to accurately identify the structural parameters influencing tie rod behavior and estimate uncertainties using natural frequencies as references. A key innovation lies in the mathematical formulation of Bayesian updating, which is founded upon the definition of computational models integrating uncertain updating parameters and latent random variables derived from a rigorous sensitivity analysis aimed at quantifying the impact of the updating parameters on the natural frequencies. Notably, the application of Bayesian updating to the structural identification problem of ancient tie rods represents a significant advancement. The framework provides a comprehensive description of the uncertainties associated with computational models, offering valuable insights for practitioners and researchers alike. Moreover, the results of the sensitivity analysis serve as a valuable tool for setting up inverse problems geared towards accurately identifying tensile axial forces.

A T-splines-oriented isogeometric topology optimization for plate and shell structures with arbitrary geometries using Bézier extraction

Recently, the non-uniform rational B-splines (NURBS) have been considerably employed in modeling plate and shell structures, or developing the related size, shape or topology optimization methods for their design. However, the NURBS with the tensor product feature strongly hinders the effectiveness of the optimization on complex structures. The primary intention of the current research is to propose a new T-splines-oriented Isogeometric Topology Optimization (T-ITO) method and then address the critical design problem of plate and shell structures with arbitrary shapes in practical applications. Firstly, the Bézier extraction is utilized in the T-splines to map the geometrical model into a family of Bézier elements, each of which is presented by a local Density Distribution Function (DDF) for elementary topology. A global DDF is constructed by an assembly of all local DDFs with a natural connection to the present structural topology. Secondly, the T-splines-based IsoGeometric Analysis (T-IGA) formulation with the Bézier extraction for complex plate and shell structures is developed using the Kirchhoff-Love theory, where a universal numerical implementation framework is constructed, including the Rhino, MATLAB, export modules with all geometric information and import modules for the analysis. Thirdly, a mathematical formulation for plate and shell structures with arbitrary geometries is developed using the T-ITO method to improve structural loading-capability, and the sensitivity analysis with respect to design variables is rigorously derived in detail. Finally, several numerical examples of plate and shell structures with both regular and elaborate geometries are tested to demonstrate the validity, effectiveness, superiorities and indispensability of the T-ITO method.

Research on Key Problems and Optimization Based on Structural Design of Super High-rise Buildings

At present, complex super high-rise buildings and super high-rise buildings are emerging all over China, but there are still many problems to be solved in the design of super high-rise structures. For example, the wind pressure and earthquake risk of high-rise buildings, fire safety issues and personnel evacuation issues, earthquake will produce greater inertia force and bending force in high-rise buildings, wind load and wind pressure effect will be more significant, these are the parts that need to be carefully considered to ensure the safety and stability of the building structure. Therefore, it is necessary to analyze and optimize the problem of high-rise buildings. Taking a super high-rise building in Luohu District of Shenzhen City as an example, this paper analyzes the basic structure of super high-rise building, analyzes the key problems of structural design, and discusses the optimization method. This paper puts forward the optimization design method of building structure for seismic problem of super high-rise building structure, puts forward the solution to wind resistance problem, and puts forward the optimization layout method of building fire protection.

Robust optimization of a closed-loop supply chain network based on an improved genetic algorithm in an uncertain environment

Aiming at the network structure design problems of facility location, path planning, and flow distribution in an e-commerce closed-loop supply chain network under an uncertain environment, the uncertainties of both the forward and reverse logistics demands and the impact of facility disruptions are analyzed. A robust optimization model is established using the robust peer-to-peer optimization method. An algorithm is designed that combines the minimum spanning tree algorithm with a two-layer adaptive genetic algorithm (Prim-DMGA) to solve the model. The results show that the Prim-DMGA not only requires less computation time, but also generates solutions of higher quality. In addition, the application of the robust optimization model reduces the adverse effects of uncertain factors on the e-commerce closed-loop supply chain network, thereby improving its robustness.

Piezoelectric impedance-based high-accuracy damage identification using sparsity conscious multi-objective optimization inverse analysis

Two elements are essential in structural health monitoring utilizing dynamic responses: response measurement with high-frequency contents, i.e., small characteristic wavelengths, that can adequately reflect damage features, and effective inverse identification analysis that is however oftentimes under-determined. The advancement of smart structure integration has led to active interrogation through frequency-sweeping piezoelectric impedance measurement at high frequency range. In this research we develop a multi-objective optimization formulation for the identification of damage location and severity utilizing piezoelectric impedance. While one optimization objective is to match the response measurement with finite element model prediction in the damage parametric space, the other is the number of locations of damage, i.e., the sparsity of damage index as the solution vector, since damage usually occurs within a small number of locations. This multi-objective formulation fits well the under-determined nature of damage identification, as it naturally provides multiple solutions as basis for further elucidation. The challenge remaining is how to find a small solution set that can include the actual damage scenario. Here we develop a novel inverse identification framework utilizing the intelligent swarm optimizer which possesses flexibility for enhancement. We first embed a sparsity enforcement process into the population generation of the optimizer, which yields a solution repository intrinsically possessing sparsity. We then apply reinforcement learning so the agents can adaptively opt for local strategies with the aim of enriching the searching patterns to diversify the solutions. Through the incorporation of a Q-table, searching toward more promising directions will be rewarded. Our case analyses employing experimental data indicate that this sparsity-conscious multi-objective particle swarm optimization technique can lead to a small solution set which generally encompasses the true damage scenario. This effectively solves the structural damage identification problem with piezoelectric impedance measurement.

The effect of generative design and topology optimization on the design and manufacturing of components in additive manufacturing

Additive manufacturing, has shown great promises, offering unexpectable design freedom and manufacturing flexibility. but traditional design methodologies cannot fully exploit the functionality of am. this study explores the impact of generative design and topology optimization in the design and production of parts in additive production. by using these advanced design tools, we aim to optimize the case study performance, minimize material usage, and unlock design opportunities. The case study is a gripper arm which is part of a robot deputed to the handle meteors is presented to demonstrate the application of these methods. additionally, it offers a useful description of Autodesk’s generative design, a software, used in our case, that uses generative design to generate a series of potential solutions to a static structural design problem. the finding reveal how generative design and topology optimization can significantly enhance component performance, reduce mass, and enable complex geometries that are difficult or impossible when using traditional methods. additionally, the paper highlights the importance of taking manufacturability constraints into account during the design process.

A controller design method based on the integration of structure search and parameter optimization

For the controller structure design problem, a controller design method based on the integration of structure search and parameter optimization is proposed with the idea of ENAS, which automates the controller structure design work, and searches for the most suitable controller structure and completes the parameter optimization in a relatively short time. The simulation study with the galvano scanner as the controlled plant shows that the number of iterations and the consumption time of the method are only 15% of the traditional method in achieving the same performance compared with the traditional design method.

Managing the staffing process of the Samara region oil industry

The problem of constructing dynamic models in the form of differential equations or transfer functions linking the performance indicators of the oil industry of the Samara region with the performance indicators of a regional university with a large institute of oil and gas technologies, considered as the controlling factors of staffing the oil industry, is solved. The input factors of the model are the normative performance indicators of the Samara State Technical University (SamSTU). The effectiveness of the regional oil cluster of the Samara region is assessed by indicators established by the Federal State Statistics Service (Rosstat), in particular, the amount of oil received for processing. For the algorithm of personnel management of the oil industry of the region, the problem of structural and parametric identification of the personnel training process at the university based on statistical characteristics as experimental data is solved. Using the library of typical linear models of management objects by N.S. Raibman, mathematical models of the process of staffing the industry in the form of transfer functions are constructed. Verification of mathematical models is carried out by comparison with official statistical data. On the basis of the obtained transfer functions, the synthesis of algorithms for automatic management of the personnel management process of the regulatory industry in the management decision support system is carried out.

Bayesian optimization-based topology optimization using moving morphable bars for flexible structure design problems

This paper presents a Bayesian optimization (BO) based topology optimization to solve flexible structure design problems in highly nonlinear design spaces. Our primary interest is to avoid topology optimization’s strong dependency on initial designs, which is inevitable when employing gradient-based optimizers. In order to do this, BO is used as a gradient-free optimizer that uses a probabilistic model to trade off exploration and exploitation in order to balance global and local search with a minimal number of iterations. Because of the curse of dimensionality in BO, a moving morphable bar (MMB) is used as a primitive member for a low-dimensional surrogate. We verified that BO could handle dozens of design parameters using the MMB through mean compliance minimization problems with known global optimum layouts. The effect of the BO trade-off parameter in the acquisition function, balancing the optimizer’s exploration, is also investigated. Numerical examples show that the proposed BO-based topology optimization method has suggested better optimum solutions for flexible structures than the MMA-based topology optimization. The performance of the proposed method is also compared with other global optimization methods, showing better performance in terms of minimized objective functions as well as the number of analyses for convergence.

Numerical design optimization of real size complex steel space frame structures using a novel adaptive cuckoo search method

AbstractIn this study, real size complex steel space frame structures are numerically designed to achieve optimal design weight. For this aim, standard cuckoo search algorithm is rectified through a newly proposed adaptive method over two fundamental algorithmic parameters of alien egg probability detection (Pa) and step size control (α) to overcome incompetency of trapping into local optima. Besides, to strengthen exploitation phase of newly proposed algorithm, it is boosted with greedy selection (GS). So, novel algorithm has more promising exploration and exploitation capabilities. An 8‐story, 1024‐member and a 20‐story, 1860‐member real size complex steel space frame structures are selected as design examples. Also, initially to verify the supremacy of novel algorithm, a well‐known welded beam is optimized as a benchmark structural design problem. Afterwards, the steel space frame structures are optimally designed via novel algorithm. Since ready steel section lists are utilized as selection pool for design variables, discrete programming problem is come into existence. The dead, live, snow, and wind design loads acting on frame structures are calculated in direction of ASCE 7‐05 provisions. Furthermore, the structural design constraints are determined from LRFD‐AISC specifications. Eventually, the newly proposed adaptive cuckoo search algorithm boosted with GS presents outstanding algorithmic performance.

On the Advantages of Searching Infeasible Regions in Constrained Evolutionary-Based Multi-Objective Engineering Optimization

Abstract Solving a multiple-criteria optimization problem with severe constraints remains a significant issue in multi-objective evolutionary algorithms. The problem primarily stems from the need for a suitable constraint handling technique. One potential approach is balancing the search in feasible and infeasible regions to find the Pareto front efficiently. The justification for such a strategy is that the infeasible region also provides valuable information, especially in problems with a small percentage of feasibility areas. To that end, this paper investigates the potential of the infeasibility-driven principle based on multiple constraint ranking-based techniques to solve a multi-objective problem with a small feasibility ratio. By analyzing the results from intensive experiments on a set of test problems, including the realistic multi-objective car structure design and actuator design problem, it is shown that there is a significant improvement gained in terms of convergence by utilizing the generalized version of the multiple constraint ranking techniques.