Reliability-based Structural Optimization Research Articles

Aero-Structural Comprehensive Nonprobabilistic Reliability-Based Optimization Method for High Aspect Ratio Wings

An aero-structural comprehensive reliability-based optimization method is proposed to construct the optimization framework of designing the high aspect ratio wing. There are three parts included in this method. 1) The ideal cruising shape is obtained by optimizing the geometrical parameters in the cruising conditions, where only the aerodynamic shape optimization is involved and the structural deformation is not considered. 2) The jig-shape optimization method is presented, where the aerodynamic performance of the wing structure with deformation is improved by adjusting the twist angle along the span direction to make sure that the shape with the aeroelastic deformation approaches the ideal cruising shape. 3) A nonprobabilistic reliability-based structural optimization is conducted by updating the thickness of composite layer, where the dispersion of mechanical properties of composite materials is considered and a nonprobabilistic reliability index according to strength and stiffness constraints is established. The global stiffness of the wing structure is changed after jig-shape optimization and structural optimization, and the jig-shape and structural scheme are modified alternately. The previously mentioned process needs to be repeated until the changes in the jig-shape and structural scheme in the iterations can be ignored. Finally, the effectiveness of this method has been verified through the numerical example followed by some conclusions.

Comparative analysis of deterministic and reliability-based structural optimization methods

Optimization is the act of obtaining the best possible result under established conditions. Usually, the optimization of a structural design is done considering the structure's dimensions, the materials' properties, and the loads as deterministic values. This way, the optimization process can lead to a more economical design without guaranteeing that this structure is safe. In practice, there are always uncertainties about the final dimensions of the built structure, material properties, and loads. Then, the need arises to use design optimization techniques based on reliability to guarantee a project that is both economical and safe. This objective is achieved by including uncertainties in the optimization process. This article evaluates the parameters that determine the global minimum of the optimization methods DDO (Deterministic Design Optimization) and RBDO (Reliability-Based Design Optimization). This work aims to compare the structural optimization methods of DDO and RBDO through an example. The results are obtained through the codes of the methods implemented in the Python language and show that when comparing the two optimization methods, the presence of uncertainties alters the optimal solution.

Structural reliability-based design optimization with non-probabilistic credibility level

With the increasing diversity of performance requirements for engineering structures, credibility has become an essential prerequisite for ensuring structural safety. This article introduces a reliability-based structural optimization with non-probabilistic credibility (NCRSO) method, to characterize the credibility of the optimization process. First the concept of uncertainty quantification for credible set is introduced. By utilizing a limited number of sample points, structural parameters with a high level of credibility are obtained and maintained throughout the optimization procedure. Additionally, a reliability index is established based on area ratio and credible feature distance, and a credible sequential optimization strategy is developed. Implementation of the proposed method significantly enhances the overall computational efficiency of structural optimization. The reliability index can directly utilized as the translation distance for deterministic constraints in the sequential strategy, minimizing unnecessary calculations and leading to improved convergence. Three engineering examples are eventually presented to effectively illustrate and emphasize the necessity of considering credibility when utilizing the structural optimization method under complex uncertainty from different perspectives.

An efficient ranked Voronoi diagram-based hybrid method for reliability-based structural analysis and design optimization

An efficient ranked Voronoi diagram-based hybrid method for reliability-based structural analysis and design optimization

An Investigation of the Recent Developments in Reliability-based Structural Topology Optimization

Optimizing a structure's topology involves finding the best possible distribution of material and connections within a given design space. It has a significant effect on its performance, which is why there has been a meteoric rise in the number of articles published on the topic over the last two decades. This work offers an investigation of reliability-based topology optimization of structures, in light of the recent development of several topology optimization techniques for both linear and nonlinear systems. Therefore, the emphasis of this study is on the latest advancements, enhancements, and applications of reliability-based topology optimization. This paper's primary objective is to provide an overview of the latest advancements in the reliability-based topology optimization of structures, with a particular emphasis on the recent improvement of integrating reliability-based design into the bi-directional evolutionary structural optimization (BESO) method, which accounts for the topological optimization of geometric and material nonlinearity as well as thermoelastic problems.

Combined Subset Simulation and Comprehensive Learning Particle Swarm Optimization in Reliability-Based Structural Optimization

Reliability-based design optimization (RBDO) addresses the cost-effective integrity design of structures in the presence of inherent uncertain parameters. Processing this class of problem is challenging from the computational burden to determine the failure probability of structures violating the limit-state function. This paper proposes an efficient decoupling RBDO method that advantageously couples a comprehensive learning particle swarm optimization (CLPSO) algorithm with a subset simulation (SS), termed as SS-CLPSO approach. In essence, the proposed method iteratively performs the CLPSO assuming deterministic parameters based on the most probable point underpinning limit-state functions updated within the reliability evaluation process. Based on the CLPSO design data, the SS approximates the spectrum of limit-state functions under uncertain parameters, and hence enables the significant reduction of Monte-Carlo simulations for the failure probability prediction. The SS map outs the failure probability from the conditional samples constructed at each intermediate event. The proposed SS-CLPSO terminates the optimal solution to the RBDO problem as when the resulting failure probability converges to the permissible threshold. The applications of the present approach are illustrated through the steel truss design under probabilistic uncertain parameters and constraints.

Global Decoupling for Structural Reliability-Based Optimal Design Using Improved Differential Evolution and Chaos Control

This paper presents a new method for performing reliability-based design optimization (RBDO) of structures based on sequential optimization and reliability assessment (SORA). SORA is an effective method for solving RBDO that separates uncertainty analysis from optimization loops for reducing computational cost. However, SORA has some limitations, such as an inability to deal with problems involving discrete design variables or discontinuity in a domain, the dependency of solutions on the starting point of numerical solutions, and the lack of guarantee that global optimum solutions will be found. In this paper, a global decoupling method is proposed to tackle these limitations and improve the performance of SORA. This method links SORA enhanced with modified chaos control (ESORA) to an improved differential evolution (IDE) to perform RBDO. To deal with RBDO problems with discrete design variables, a rounding method is integrated into IDE. IDE also utilizes an adaptive selection scheme in a mutation step and an elitist strategy in the selection phase. To improve the efficiency of the method for RBDO problems with highly nonlinear performance functions and nonnormal random variables, a modified chaos control is employed to assess reliability constraints. Five numerical examples are considered to investigate the strength of the proposed method, illustrating its appropriate efficiency and accuracy. The proposed method is also extendable to more complex problems such as system reliability-based structural optimization and RBDO of nonlinear structures.

Reliability-based structural design optimization: hybridized conjugate mean value approach

The efficiency and robustness of reliability techniques are important in reliability-based design optimization (RBDO). Commonly, advanced mean value (AMV) is utilized in reliability loop of RBDO but unstable solutions using AMV may be obtained for highly concave performance functions. Owing to the challenges of commonly reliability methods, the conjugate gradient analysis (CGA) is proposed as a robust methodology but it shows inefficient results for convex constraints. In this research, hybrid conjugate mean value (HCMV) method is proposed using sufficient condition for the enhancement of efficiency and robustness of RBDO. The CGA and AMV are dynamically utilized for simple solution of convex/concave constraints using sufficient descent criterion in HCMV. The HCMV is used to evaluate the convergence performances and is compared with numerous existing reliability methods through three reliability problems (two concave/convex mathematical examples and one applicable structure) and four RBDO problems. From the numerical results, the HCMV exhibited the better efficiency, and robustness compared to other studied formulations in reliability and RBDO problems.

Metamodels of optimal quality for stochastic structural optimization

Metamodels or response surface models are frequently chosen to reduce computational cost for structural optimization problems. These methods are also very popular for structural reliability analysis. It is therefore not surprising that response surface models are very attractive for reliability-based structural optimization. The paper discusses strategies to obtain a suitable response surface model, to assess its quality concerning prediction, and to use the response surface mode to identify important and unimportant variables. Several mathematical and structural examples illustrate the applicability of the presented approach.

Comparación de algoritmos de optimización para optimización estructural basada en confiabilidad

El diseno de estructuras confiables requiere de herramientas robustas que permitan analizar el comportamiento del sistema sometido a variabilidad en su resistencia y cargas aplicadas. Para esto, se disponen de diversas formulaciones y algoritmos computacionales que permiten modelar el comportamiento estructural bajo incertidumbres. Bajo estos requerimientos, la metodologia de diseno optimo mas popular y confiable es la optimizacion basada en confiabilidad (RBO, reliability based optimization), que puede implementarse a traves de la combinacion de modelos matematicos o computacionales de alta fidelidad, e.g. modelos de elementos finitos, metodos eficientes y precisos de estimacion de la confiabilidad, y algoritmos eficientes y eficaces de optimizacion en ingenieria. La mayoria de aplicaciones de RBO para optimizacion estructural cuenta con los ultimos desarrollos de tecnicas computacionales eficientes para simulacion y calculo de confiabilidad, sin embargo, a pesar de que existe una gran variedad de metodos de optimizacion, generalmente no realizan una seleccion del algoritmo de optimizacion mas apropiado para cada aplicacion. En este contexto, la contribucion principal de este articulo es la realizacion de un estudio comparativo del desempeno computacional de algoritmos de optimizacion aplicados en optimizacion estructural por RBO. El estudio realizado comparo el desempeno numerico de algoritmos de optimizacion en tres problemas. Los algoritmos comparados corresponden a algoritmos basados en derivadas, algoritmos de busqueda directa, y algoritmos bioinspirados; incluyendo los algoritmos mas representativos de cada categoria. Los resultados del estudio comparativo senalan ventajas y desventajas del uso de los diferentes tipos de algoritmos y permiten concluir sobre los criterios que deben considerarse para la seleccion de un algoritmo que favorezca el rendimiento computacional.

Reliability-based structural optimization of 300 × 300 mm2 dye-sensitized solar cell module

Dye-sensitized solar cell (DSC) is a promising candidate for the application in building-integrated photovoltaics (BIPV). At higher temperature above 85°C, the reliability of the module has remained a major challenge yet. A large DSC module, sized 300×300mm2, is developed. In the preliminary module design, the width of cell is 11mm and the coefficients of temperature expansion (CTE) for sealant and electrolyte are 699 and 807ppm/°C, respectively. The modules are stored in 85°C. The power conversion efficiency of the modules drops rapidly in 100h during the test. To analyze and enhance the module design in view of reliability, finite element model is developed for the module. Stress analysis reveals that high stresses in electrode cause the breakage of electrode and sealant in succession and the loss of electrolyte finally. From a parameter sensitivity analysis with the finite element model, it is identified that the maximum stress in electrode can decrease when the cell width increases. CTEs of sealant and electrolyte can be also optimized as analysis confirms that the maximum stress in electrode drops when the CTEs of sealant and electrolyte decrease. Based on the studies, new module design is formulated, which have the cell width of 18mm and the CTEs of 277 and 656ppm/°C for sealant and electrolyte, respectively. The new modules are tested in 85°C and show much better lifetime than the preliminary one without the leakage of electrolyte.

Robust and Reliability-Based Structural Topology Optimization Using a Continuous Adjoint Method

AbstractA unified framework for robust and reliability-based structural topology optimization, considering structural model and loading uncertainties, is presented using a continuous adjoint formulation. The topology optimization is formulated for objective functions related to uncertainty measures of the compliance or displacements of the structure. Uncertainty measures, such as mean, standard deviation, and level exceedance probability or failure probability, involve the estimation of multidimensional integrals over the uncertain parameter space. These integrals are evaluated using (1) sparse grid quadrature techniques for the mean and standard deviation and (2) the approximate first-order reliability method (FORM) for failure probability. A unified continuous adjoint formulation is presented for the different objective function formulations. Simplifications are proposed that result in increased computational efficiency and accuracy for special cases of uncertainties and structural performance measures....

Symmetry analysis for structural optimization problems involving reliability measure and bi-modulus materials

In the present work, some symmetry theorems for structural optimization problems involving reliability measure and bi-modulus materials are established. In the first part of this paper, two types of symmetric reliability-based structural optimization problems are discussed. It is proved that, for the first type symmetric RBDO problems, the existence of symmetric global optimal solutions can be guaranteed even through the probability density function (PDF) is non-symmetric. While for the second type symmetric RBDO problems, more severe conditions on PDF are required to ensure the existence of symmetric global optimal solutions. In the second part of the paper, the convexity of the compliance of truss structures involving bi-modulus materials is confirmed firstly. Based on this result, it is found that for both deterministic and robust symmetric compliance minimization of truss structures involving bi-modulus materials, symmetric global optima always exist. The theoretical results are also demonstrated through some academic examples.

Reliability-Based Optimal Design of Steel Box Structures. I: Theory

AbstractA steel box structural design has been traditionally used for bridges and surface marine vessels and is on the basis of engineering experience/judgment and deterministic approaches, such as working stress design. Recent developments in reliability-based design have lead to the development and application of the load and resistance factor design (LRFD) approach, in which inherent uncertainties are accounted for in an indirect manner. Structural optimization algorithms and tools have also seen an increased application in the area of structural design in the context of weight reduction, cost savings, and other design improvements. A three-step strategy for the design of such structures is proposed in this paper, which combines the innovative aspects of both reliability-based methods and structural optimization theories and algorithms. After selecting an initial design as a starting point, the methodology then improves on this through deterministic optimization, in which design variables, objectives, ...

Reliability-Based Structural Optimization of Wave Energy Converters

More and more wave energy converter (WEC) concepts are reaching prototypelevel. Once the prototype level is reached, the next step in order to further decrease thelevelized cost of energy (LCOE) is optimizing the overall system with a focus on structuraland maintenance (inspection) costs, as well as on the harvested power from the waves.The target of a fully-developed WEC technology is not maximizing its power output,but minimizing the resulting LCOE. This paper presents a methodology to optimize thestructural design of WECs based on a reliability-based optimization problem and the intentto maximize the investor’s benefits by maximizing the difference between income (e.g., fromselling electricity) and the expected expenses (e.g., structural building costs or failure costs).Furthermore, different development levels, like prototype or commercial devices, may havedifferent main objectives and will be located at different locations, as well as receive varioussubsidies. These points should be accounted for when performing structural optimizationsof WECs. An illustrative example on the gravity-based foundation of the Wavestar deviceis performed showing how structural design can be optimized taking target reliability levelsand different structural failure modes due to extreme loads into account.

Reliability analysis of structures with complex limit state functions using probability density evolution method

In reliability-based structural analysis and design optimization, there exist some limit state functions exhibiting disjoint failure domains, multiple design points and discontinuous responses. This study addresses this type of challenging problem of reliability assessment of structures with complex limit state functions based on the probability density evolution method (PDEM). Probability density function (PDF) of stochastic structures under static and dynamic loads can be acquired, which is independent of the specific form of limit state functions. Numerical results of several typical examples illustrate that, the time-invariant and instantaneous PDF curves and failure probabilities of stochastic structures with disjoint failure domains, multiple design points and discontinuous responses are calculated effectively and accurately. Moreover, the PDEM is validated to be more efficient than the Monte Carlo simulation and the subset simulation, and is a feasible and general approach to tackle the reliability analysis of complicated problems. In addition, the influence of random design parameters of structures on uncertainty propagation is also scrutinized.

Reliability-Based Structural Optimization Using Hybrid High Dimensional Model Representation

A design method of reliability-based structural optimization has a powerful advantage because some random variables can be considered. However, the sensitivity analysis of reliability with respect to random variables is very complicated and its computational cost is very expensive. Thus, in this paper, based on hybrid high dimensional model representation (HDMR) and first order second moment (FOSM) method, a new method for the reliability-based structural optimization is proposed. A numerical example is presented to demonstrate the computational efficiency of the proposed method. It is shown that the proposed method can reduce the number of finite element calculation and has the high efficiency.

An efficient response surface method and its application to structural reliability and reliability-basedoptimization

In structural reliability analysis, the response surface method is widely used to reduce the computational efforts of engineering analyses. However, in order to reduce the number of finite element analysis and ensure the accuracy of evaluation, the locations of experimental points used to form a response surface function must be selected in a judicious way. Therefore, in this study, the control point of experimental points is constructed. The new center point of experimental points is chosen by using the control point instead of the design point. The control point can guarantee that the center point of experimental points lies exactly on the failure surface and is close to the actual design point. Two improved methods are proposed based on the control point and the moving technique of experimental points considering the compromise between the accuracy and the efficiency. Five examples are given to demonstrate the efficiency and the accuracy of the proposed method for both structural reliability and reliability-based structural optimization.

Non-probabilistic reliability-based structural design optimization based on the interval analysis method

Using interval variables to describe uncertain parameters in structural systems and their complex environments, a non-probabilistic reliability-based optimization model, which can give optimized design to meet certain reliability requirements, is proposed based on the interval reliability analysis method. Two levels are included in the non-probabilistic reliability optimization process for structures. The outer layer uses different global optimization algorithms according to the characteristics of the specific issues. The inner layer evaluates the upper and the lower bounds of the structural responses using the interval analysis method based on the Taylor expansion or the collocation interval analysis method according to the sensitivities of the responses with respect to the uncertainties. The optimization process which has strong portability, can not only avoid the two nested optimization which reduces the computational efficiency, but also take full advantage of existing mature optimization algorithms. Two different improved practical interval reliability models, which named 1-formula model based on interval possibilistic method and 2-formula chart-based model, are used in the optimization model. Two numerical examples in the paper show the effectiveness of the proposed method.

Reliability-Based Structural Optimization Using Sequential Response Surface Method

A design method of reliability-based structural optimization has a powerful advantage because some random variables can be considered. However, the sensitivity analysis of reliability with respect to random variables is very complicated and its computational cost is very expensive. Thus, a response surface method is adopted for approximating the limit state function to improve computational efficiency. An iterative strategy is used to determine a response surface that is able to fit the limit state function in the neighborhood of the design point. A sequential response surface method is performed to satisfy the demand of accuracy in the process of reliability-based structural optimization. A numerical example is presented to demonstrate the computational efficiency of the proposed method.