Non-probabilistic Reliability-based Design Optimization Research Articles

A novel non-probabilistic reliability-based design optimization method using bilevel accelerated microbial genetic algorithm

A novel non-probabilistic reliability-based design optimization method using bilevel accelerated microbial genetic algorithm

Novel bootstrap-based ellipsoidal convex model for non-probabilistic reliability-based design optimization with insufficient input data

Performing reliability-based design optimization with insufficient input data is a significant and challenging issue as accurately quantifying epistemic uncertainty can be difficult in such scenarios. Non-probabilistic models can marginally alleviate the need for a large sample size by constructing the boundaries of uncertainty parameters. However, most of the existing non-probabilistic models account for only the available or known samples. For cases with insufficient data, the compact uncertainty domain may result in considerably hazardous results, particularly for the problems that require high reliability. Therefore, a novel bootstrap-based ellipsoidal convex model (BECM) is proposed herein to account for both known and unknown data. Herein, the bootstrap method is introduced to non-probabilistic convex models for the first time to quantify the ellipsoidal shape uncertainty caused by insufficient input data. Further, the proposed BECM is also integrated into non-probabilistic reliability-based design optimization. The entire framework of uncertainty quantification and reliability optimization design for insufficient input data is established. Marginally conservative results can finally be achieved in a rational and objective manner by partially sacrificing the ellipsoid volume. Comprehensive comparisons and detailed discussions on aspects, including the problem complexity, initial sample size, and distribution type, are also conducted. The numerical results show that the BECM displays the best performance in terms of accuracy and robustness. It can achieve an approximate balance between being conservative and taking risks. The significant advantages are also illustrated by an engineering example of linear buckling analysis of stiffened cylindrical shells.

Lightweight design process considering assembly connection and non-probabilistic uncertainty with its application to machine structural design

Owing to the complexity of machines, lightweight structural design needs to consider the influence of assembly connection and non-probabilistic uncertainty in material properties. This study suggests a novel lightweight design process that incorporates these two factors. In this process, the assembly connection was modelled with the finite element model and validated by experiments. The non-probabilistic uncertainty was described using the multidimensional parallelepiped model, and then the corresponding non-probabilistic reliability-based design optimization method was applied to ensure the safety of structures. The proposed design process was applied to the structural design of the upper beam of a forming machine. The results showed that ignoring the assembly connection and non-probabilistic uncertainty may lead to an unsafe structural design, and thus they should be considered in the lightweight structural design of machines. Moreover, the weight reduction by 30.43% for the upper beam achieved using the proposed method demonstrated its effectiveness.

An importance learning method for non-probabilistic reliability analysis and optimization

With the time-consuming computations incurred by nested double-loop strategy and multiple performance functions, the enhancement of computational efficiency for the non-probabilistic reliability estimation and optimization is a challenging problem in the assessment of structural safety. In this study, a novel importance learning method (ILM) is proposed on the basis of active learning technique using Kriging metamodel, which builds the Kriging model accurately and efficiently by considering the influence of the most concerned point. To further accelerate the convergence rate of non-probabilistic reliability analysis, a new stopping criterion is constructed to ensure accuracy of the Kriging model. For solving the non-probabilistic reliability-based design optimization (NRBDO) problems with multiple non-probabilistic constraints, a new active learning function is further developed based upon the ILM for dealing with this problem efficiently. The proposed ILM is verified by two non-probabilistic reliability estimation examples and three NRBDO examples. Comparing with the existing active learning methods, the optimal results calculated by the proposed ILM show high performance in terms of efficiency and accuracy.

New target performance approach for a super parametric convex model of non-probabilistic reliability-based design optimization

Non-probabilistic reliability-based design optimization (NRBDO) is an essential tool to deal with an optimization model with uncertain-but-bounded variables. A major disadvantage of NRBDO is that it conventionally suffers from excessively high computational costs. In the present study, a new target performance approach (TPA) is proposed to eliminate high computational cost incurred by complicated equality constraints in non-probabilistic reliability analysis in which the target performance constraint is applied to substitute for the non-probabilistic reliability index constraint. To further enhance the optimization efficiency, a new NRBDO algorithm is developed based on the proposed TPA in which the target performance iterative method (TPIM) is established to search for the target concern point while a convex approximate method is used to further improve the convergence. A mathematical example, three numerical examples, and two complex engineering examples, i.e., an axially compressed stiffened shell in a launch vehicle and a tower crane in civil engineering, are utilized to demonstrate the effectiveness of the proposed method in comparison with that of other existing methods. The results indicate that the proposed method is promising in terms of complicated engineering problems in the absence of prior knowledge of uncertain parameters.

Multiscale reliability-based topology optimization methodology for truss-like microstructures with unknown-but-bounded uncertainties

This paper introduces a new optimization framework to multiscale structures with unknown-but-bounded (UBB) uncertainties, where the optimal design is applied at two scales: the macroscale, i.e., the structural level, where the non-probabilistic reliability-based topology optimization (NRBTO) is conducted, and the microscale, i.e., the material level, where the non-probabilistic reliability-based design optimization (NRBDO) for truss-like cell dimensions is achieved. By combination of the homogenization method and interval mathematics, rules of macro–micro stiffness equivalence as well as interval bounds of macro displacement responses under specific micro structural settings can be first confirmed. For safety reasons, novel reliability definitions are respectively given for the double-level design, in which the offset factor with good differential properties is applied for the NRBTO and the matching factor derived from the improved rule of interval sorting is utilized for the NRBDO. To circumvent problems of large-scale variable updating in two-level optimization procedures, the adjoint-based vector in macro layout design as well as the particle swarm optimization (PSO) algorithm in micro parametric design are further discussed. The usage, effectiveness, and the superiority of the developed methodology are eventually demonstrated by two 3D engineering applications.

Super parametric convex model and its application for non-probabilistic reliability-based design optimization

• A general hyper parametric convex model is created. • The minimum volume method is developed to select the type of hyper parametric convex model properly. • Nominal value and advanced nominal value methods are proposed simultaneously to perform the non-probabilistic analysis effectively. • Effective non-probabilistic reliability-based design optimization approach is developed based on advanced nominal value method. In this study, we attempt to propose a new super parametric convex model by giving the mathematical definition, in which an effective minimum volume method is constructed to give a reasonable enveloping of limited experimental samples by selecting a proper super parameter. Two novel reliability calculation algorithms, including nominal value method and advanced nominal value method, are proposed to evaluate the non-probabilistic reliability index. To investigate the influence of non-probabilistic convex model type on non-probabilistic reliability-based design optimization, an effective approach based on advanced nominal value method is further developed. Four examples, including two numerical examples and two engineering applications, are tested to demonstrate the superiority of the proposed non-probabilistic reliability analysis and optimization technique.

An efficient adaptive-loop method for non-probabilistic reliability-based design optimization

For non-probabilistic reliability-based design optimization (NRBDO), existing methods cannot satisfy both efficiency and robustness requirements, especially for complex engineering problems. In this study, an efficient adaptive-loop (EAL) method for NRBDO is proposed based on an improved single loop method and enhanced chaos control method, aiming to enhance the optimization efficiency without sacrifice of numerical stability. The constraint function is reconstructed to improve the efficiency of reliability analysis. Moreover, a criteria condition is defined to guarantee the rationality of rough optimum and eliminate redundant constraints. The proposed EAL method can adaptively switch to a proper method, thus both high efficiency and robustness can be guaranteed. Nonlinear numerical examples and complex engineering problems are utilized to demonstrate the effectiveness of the proposed method by comparison with other existing methods.

A novel non-probabilistic reliability-based design optimization algorithm using enhanced chaos control method

In this study, an efficient and robust algorithm of non-probabilistic reliability-based design optimization (NRBDO) is proposed based on convex model. In this double-nested optimization model, the inner loop concerns a Min–max problem for the evaluation of reliability index, where the target performance approach is applied to substitute the Min–max problem. To improve the convergence rate, an enhanced chaos control (ECC) method is developed on the basis of chaotic dynamics theory, which can check and re-update the control factor by the Wolfe–Powell criterion. To further enhance the optimization efficiency, a novel NRBDO algorithm is developed based on the proposed ECC, where HL–RF algorithm is applied at the initial stage of this algorithm, while ECC is used to improve the robustness once the oscillation or chaotic behavior is identified. Three mathematical examples, one numerical example and one complex engineering problem, i.e. axially compressed stiffened shells in launch vehicles, are utilized to demonstrate the robustness and efficiency of the proposed method by comparison with other existing methods. Results indicate that the proposed method is particularly suitable for complicated engineering problems without prior knowledge of uncertainty distributions, which is expected to be utilized in the structural design of future launch vehicles.

A decoupled approach for non-probabilistic reliability-based design optimization

Non-probabilistic reliability-based design optimization (NRBDO) offers a powerful tool for structural design when uncertain-but-bounded parameters are considered. Like the reliability-based design optimization (RBDO), the NRBDO application for practical engineering structure is hindered by the huge computational effort involved in the repeated evaluation of non-probabilistic constraints. The decoupled strategy is one of the most efficient RBDO strategies. However, whether it is widely applicable for NRBDO problem remains unknown. In this paper, we make attempts to develop a decoupled strategy for NRBDO convex models based on the concerned performance approach, and propose a sequential optimization approach to handle the deterministic optimization and non-probabilistic reliability analysis sequentially. A new feasibility-checking criterion is further proposed, and the non-probabilistic constraints are divided into active, inactive and violated categories. Since only concerned points of active and violated constraints are calculated accurately, the computational cost associated with non-probabilistic constraint is decreased significantly. Four examples are tested to envelop representative NRBDO problems based on interval set, single-ellipse or multi-ellipse convex model. This way, we show that the decoupled strategies could be promising for a large variety of engineering NRBDO problems.

Non-probabilistic reliability-based design optimization of stiffened shells under buckling constraint

Stiffened shells are affected by numerous uncertainty factors, such as the variations of manufacturing tolerance, material properties and environment aspects, etc. Due to the expensive experimental cost of stiffened shell, only a limited quantity of statistics about its uncertainty factors are available. In this case, an unjustified assumption of probabilistic model may result in misleading outcomes of reliability-based design optimization (RBDO), and the non-probabilistic convex method is a promising alternative. In this study, a hybrid non-probabilistic convex method based on single-ellipsoid convex model is proposed to minimize the weight of stiffened shells with uncertain-but-bounded variations, where the adaptive chaos control (ACC) method is applied to ensure the robustness of search process of single-ellipsoid convex model, and the particle swarm optimization (PSO) algorithm together with smeared stiffener model are utilized to guarantee the global optimum design. A 3m-diameter benchmark example illustrates the advantage of the proposed method over RBDO and deterministic optimum methods for stiffened shell with uncertain-but-bounded variations.

On non-probabilistic reliability-based design optimization of structures with uncertain-but-bounded parameters

This paper investigates the formulation and numerical solution of reliability-based optimization of structures exhibiting grouped uncertain-but-bounded variations. Based on the multi-ellipsoid convex model description for grouped uncertain-but-bounded parameters, the mathematical definition of a non-probabilistic reliability index is presented for quantified measure of the safety margin. The optimal design is then formulated as a nested optimization problem. A method based on concerned performance is proposed for regularization of the reliability index constraints. The expensive computation of the non-probabilistic reliability index and its derivative is thus avoided. Numerical examples are given to illustrate the validity and efficiency of the present method.