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This paper aims to tackle the challenge topic of continuum structural layout in the presence of random loads and to develop an efficient robust method.

An innovative robust topology optimization approach for continuum structures with random applied loads is reported. Simultaneous minimization of the expectation and the variance of the structural compliance is performed. Uncertain load vectors are dealt with by using additional uncertain pseudo random load vectors. The sensitivity information of the robust objective function is obtained approximately by using the Taylor expansion technique. The design problem is solved using bi-directional evolutionary structural optimization method with the derived sensitivity numbers.

The numerical examples show the significant topological changes of the robust solutions compared with the equivalent deterministic solutions.

A simple yet efficient robust topology optimization approach for continuum structures with random applied loads is developed. The computational time scales linearly with the number of applied loads with uncertainty, which is very efficient when compared with Monte Carlo-based optimization method.

Meta-model method has been widely used in structural reliability optimization design. The main limitation of this method is that it is difficult to quantify the error caused by the meta-model approximation, which leads to the inaccuracy of the optimization results of the reliability evaluation. Taking the local high efficiency of the proxy model, this paper aims to propose a local effective constrained response surface method (LEC-RSM) based on a meta-model.

The operating mechanisms of LEC-RSM is to calculate the index of the local relative importance based on numerical theory and capture the most effective area in the entire design space, as well as selecting important analysis domains for sample changes. To improve the efficiency of the algorithm, the constrained efficient set algorithm (ESA) is introduced, in which the sample point validity is identified based on the reliability information obtained in the previous cycle and then the boundary sampling points that violate the constraint conditions are ignored or eliminated.

The computational power of the proposed method is demonstrated by solving two mathematical problems and the actual engineering optimization problem of a car collision. LEC-RSM makes it easier to achieve the optimal performance, less feature evaluation and fewer algorithm iterations.

This paper proposes a new RSM technology based on proxy model to complete the reliability design. The originality of this paper is to increase the sampling points by identifying the local importance of the analysis domain and introduce the constrained ESA to improve the efficiency of the algorithm.

The present study is based on finding the structural response of a tensile membrane structure (TMS) through deformation. The intention of the present research is to develop a basic understanding of reliability analysis and deflection behavior of a pre-tensioned TMS. The mean value first-order second-moment method (MVFOSM) method is used here to evaluate stochastic moments of a performance function with random input variables. Results suggest the influence of modulus of elasticity, the thickness of the membrane, and edge span length are significant for reliability based TMS design.

A simple TMS is designed and simulated by applying external forces (along with prestress), as a manifestation of wind and snow load. A nonlinear analysis is executed to evaluate TMS deflection, followed by calculating the reliability index. Parametric study is done to consider the effect of membrane material, thickness and load location. First-order second moment (FOSM) is used to evaluative the reliability. A comparison of reliability index is done and deflection variations from μ − 3s to μ + 3s are accounted for in this approach.

The effectiveness of deflection is highlighted for the reliability assessment of TMS. Reliability and parametric study collectively examine the proposed geometry and material to facilitate infield design requirements. The estimated β value indicates that most suitable fabric material for a simple TMS should possess an elasticity modulus in the range of 1,000–1,500 MPa, the thickness may be considered to be around 1.00 mm, and additional adjustment of around 5–10 mm is suggested for edge length. The loading position in case of TMS structures can be a sensitive aspect where the rigidity of the surface is dependent on the pre-tensioning of the membrane.

The significance of the parametric study on material and loading for deflection of TMS is emphasized. Due to the lack of consolidated literature in the field combining reliability with deflection limits of a TMS, this work can be very useful for researchers.

The present work outcome may facilitate practitioners in determining effective design methodology and material selection for TMS construction.

The significance of parametric study for serviceability criteria is emphasized. Parameters like pre-stress can be included in future parametric studies to witness in depth behavior of TMS. Due to lack of consolidated literature in the field combining reliability with deflection limits of a TMS, this work can be very useful for the researchers. The present work outcome may facilitate practitioners in determining effective design methodology and material selection for TMS construction.

The purpose of this paper is to analyse fatigue-life prediction based on a reliability assessment for coil springs of vehicle suspension systems using different road excitations under random loading.

In this study, a reliability assessment was conducted to predict the fatigue life of an automobile coil spring during different road data surfaces. Campus, urban and highway road surfaces were considered to capture fatigue load strain histories using a data acquisition system. Random loadings are applied on top of a coil spring where coil is fixed from down. Fatigue reliability was established as a system of correlated events during the service life to predict the probability of fatigue life using Coffin–Manson, Morrow and Smith–Watson–Topper (SWT) models.

Fatigue-life prediction based on a reliability assessment revealed that the Morrow model can predict a safe region of a life data point for the three road surfaces. Highway road data indicated the highest rate of reliability at 0.8 for approximately 1.69 × 10⁵ cycles for the SWT model.

Reliability assessment of the fatigue life of vehicle coil springs is vital for safe operation. The reliability analysis of a coil spring under random loading excitations can be used for fatigue-life prediction.

This paper aims to present a new physically inspired meta-heuristic algorithm, which is called Plasma Generation Optimization (PGO). To evaluate the performance and capability of the proposed method in comparison to other optimization methods, two sets of test problems consisting of 13 constrained benchmark functions and 6 benchmark trusses are investigated numerically. The results indicate that the performance of the proposed method is competitive with other considered state-of-the-art optimization methods.

In this paper, a new physically-based metaheuristic algorithm called plasma generation optimization (PGO) algorithm is developed for solving constrained optimization problems. PGO is a population-based optimizer inspired by the process of plasma generation. In the proposed algorithm, each agent is considered as an electron. Movement of electrons and changing their energy levels are based on simulating excitation, de-excitation and ionization processes occurring through the plasma generation. In the proposed PGO, the global optimum is obtained when plasma is generated with the highest degree of ionization.

A new physically-based metaheuristic algorithm called the PGO algorithm is developed that is inspired from the process of plasma generation.

The results indicate that the performance of the proposed method is competitive with other state-of-the-art methods.

To survey the approaches to design optimization based on possibility theory and evidence theory comparatively, as well as their prominent characteristics mainly for epistemic uncertainty.

Owing to uncertainties encountered in engineering design problems and limitations of the conventional probabilistic approach in handling the impreciseness of data or knowledge, the possibility‐based design optimization (PBDO), evidence‐based design optimization (EBDO) and their integrated approaches are investigated from the viewpoints of computational development and performance improvement. After that, this paper discusses the fusion technologies and an example of integrated approach in reliability to reveal the qualitative value and efficiency.

It is recognized that more conservative results are obtained with both PBDO and EBDO, which may be appropriate for design against catastrophic failure compared with the probability‐based design. Furthermore, the EBDO design may be less conservative compared with the PBDO design.

How to perfect already‐existing integration approaches in a more generally analytical framework is still an active domain of research.

The paper is a holistic reference for design engineers and industry managers.

The paper is focused on decomposition strategies and fusion technologies, especially addressing epistemic uncertainty for large‐scale and complex systems when statistical data are scarce or incomplete.

The purpose of this paper is to report a study in which the feasibility of conducting probabilistic finite element analysis (FEA) for crane hook design has been explored.

This paper presents the results of probabilistic analysis, where in the input random variables are varied and corresponding variations in the output parameters were observed. In this study, material properties and load have been considered as random input variables and the maximum stress, maximum deflection variations were considered as output random variables.

The probability of occurrence of output variation and the sensitivity of output variables on the input variables are the important results generated from this analysis. By performing this probabilistic analysis, the random selection of factor of safety could be avoided.

The implementation study has been carried out for a single product.

The usage of the approach will indicate the importance of probabilistic analysis in product design and development process. This process will enable the organization to compete in the global market.

A case study has been reported to indicate the feasibility of performing probabilistic FEA for crane hook design. Hence, the contributions are original.

This study aims to research the influence of non-probabilistic design variables on interval robust optimization of electric multiple units (EMU) brake module, therefore obtain the reasonable of design variables of the EMU brake module.

A robust optimization model of the EMU brake module based on interval analysis is established. This model also considers the dimension tolerance of design variables, and it uses symmetric tolerance to describe the uncertainty of design variables. The interval order relation and possibility degree of interval number are employed to deal with the uncertainty of objective function and constraint condition, respectively. On this basis, a multiobjective robust optimization model in view of interval analysis is established and applied to the robust optimization of the EMU brake module.

Compared with the traditional method and the method proposed in the reference, the maximum stress fluctuation of the EMU brake module structure is smaller after using the method proposed in this paper, which indicates that the robustness of the maximum stress of the structure has been improved. In addition, the weight and strength of the structure meet the design requirements. It shows that this method and model introduced in this research have certain feasibility.

This study is the first attempt to apply the robust optimization model based on interval analysis to the optimization of EMU structure and obtain the optimal solution set that meets the design requirements. Therefore, this study provides an idea for nonprobabilistic robust optimization of the EMU structure.

The paper aims to apply numerical optimization to the aircraft design procedures applied in the airspace industry.

It is harder than ever to achieve competitive construction. This is why numerical optimization is becoming a standard tool during the design process. Although optimization procedures are becoming more mature, yet in the industry practice, fairly simple examples of optimization are present. The more complicated is the task to solve, the harder it is to implement automated optimization procedures. This paper presents practical examples of optimization in aerospace sciences. The methodology is discussed in the article in great detail.

Encountered problems related to the numerical optimization are presented. Different approaches to the solutions of the problems are shown, which have impact on the time of optimization computations and quality of the obtained optimum. Achieved results are discussed in detail with relation to the used settings.

Investigated different aspects of handling optimization problems, improving quality of the obtained optimum or speeding-up optimization by parallel computations can be directly applied in the industry optimization practice. Lessons learned from multidisciplinary optimization can bring industry products to higher level of performance and quality, i.e. more advanced, competitive and efficient aircraft design procedures, which could be applied in the industry practice. This can lead to the new approach of aircraft design process.

Introduction of numerical optimization methods in aircraft design process. Showing how to solve numerical optimization problems related to advanced cases of conceptual and preliminary aircraft design.

This chapter develops a methodology to assist critical facility operators in designing physical protection systems to defend against a single adversary (thief, saboteur, terrorist, etc.) attack. The developed methodology utilizes a multicriteria decision-making approach that balances the competing goals of minimal security system cost and maximum system performance. The methodology utilizes a network-based approach to facility security system design and analysis, which locates physical protection (detection, delay, and response) elements throughout a facility. These elements enable the facility owner to prevent attacks through deterrence and to defeat the adversary if he or she chooses to attack. The developed approach results in the ability for the facility operator to assess relative facility and/or infrastructure safety, and make decisions regarding how to optimally allocate resources for physical protection elements to balance cost and performance. A hypothetical example is discussed which demonstrates the usefulness of the developed methodology.