Reliability-based Optimization Approach Research Articles

Revealing the impact of renewable uncertainty on grid-assisted power-to-X: A data-driven reliability-based design optimization approach

Designing a reliable power-to-X (PtX) process that uses renewable energy and grid electricity as backup power is challenging due to the uncertain nature of renewables and potential limits on grid usage. To address this challenge, this paper proposes a data-driven, reliability-based optimization approach for designing a grid-assisted PtX process and understanding how the uncertainty of time-series renewable profile affects its design and optimal sizing. This approach uses generative adversarial networks (GANs) to capture the complex patterns of renewables in temporal and spatial dimensions, rather than simply treating uncertainty as a probabilistic range as in conventional methods. The optimization considers both the mean and variance of production cost as objectives, while also taking into account the level of grid energy penetration as a probabilistic constraint through the reliability analysis. A power allocation and performance evaluation model is developed and used in conjunction with the optimization to assess uncertainty propagation through the PtX process and evaluate the impact of renewable uncertainty on process performance. A case study involving the production of methanol on Jeju Island in South Korea demonstrates how the mean and variance of production cost and other performance indicators can be balanced in the reliable design of PtX processes under renewable energy uncertainty, providing insights for decision-making in such situations.

Efficient decoupling approach for reliability-based optimization based on augmented Line Sampling and combination algorithm

This paper presents a novel decoupling approach to efficiently solve a class of reliability-based design optimization (RBDO) problems by means of augmented Line Sampling. The proposed approach can fully decouple the original RBDO by replacing the probabilistic constraint with the failure probability function (FPF), which is an explicit function of the design variables. One attractive feature is that the main numerical cost associated with this decoupling comes with only one implementation of augmented Line Sampling, which is actually highly efficient. And for the sake of accuracy, the proposed approach incorporates decoupling with the sequential optimization framework to solve the RBDO problem iteratively. On top of that, an optimal combination algorithm is proposed to reuse the information through aggregating the local estimates of FPF obtained in different iterations to produce an improved estimate, resulting in a more accurate and stable solution. Examples are given to show the effectiveness and efficiency of the proposed approach.

Ultimate Limit State Reliability-Based Optimization of MSE Wall Considering External Stability

We present reliability-based optimization (RBO) of the Mechanically Stability Earth (MSE) walls, using constrained optimization, considering the external stability, under ultimate limit state conditions of sliding, eccentricity, and bearing capacity. The design is optimized for a target reliability index of 3 that corresponds to an approximate failure probability of 1 in 1000. Reliability index is calculated by the first-order reliability method (FORM). The MSE wall, founded on cohesionless soil, with horizontal backfill and uniform live traffic surcharge, is studied. The RBO results are reported for the height of MSE wall ranging from 1.5 m to 20 m. For target reliability index of 3, the optimized length to height ratio, Lopt/H, of the MSE wall is greater than 0.7 (the minimum length to height ratio requirement of AASHTO) for H≤4.5 m, and then it decreases below the minimum required value of 0.7 for H>4.5 m. The RBO approach presented in this study will help practitioners to achieve cost-effectiveness in design.

Fatigue inspection and maintenance optimization: A comparison of information value, life cycle cost and reliability based approaches

Fatigue cracks increase structural failure risk and timely maintenance is very important. Maintenance planning is often formulated as a probabilistic optimization problem, considering uncertainties in structural and load modelling, material properties, damage measurements, etc. A decision rule or strategy, e.g. condition based maintenance (CBM), needs to be set up, and then an optimal maintenance criterion or threshold is derived via solving the optimization problem. This paper develops a probabilistic maintenance optimization approach exploiting value of information (VoI) computation and Bayesian decision optimization. The VoI based approach explicitly quantifies added values from future inspections, and gives an optimal decision (or strategy) by direct modelling decision alternatives and evaluating their expected outcomes, rather than a pre-defined strategy. A comparative study on VoI, life cycle cost (LCC) and reliability based optimization approaches is conducted. It is shown that the VoI based approach takes all available maintenance strategies into account (both with and without involving inspections), and can reliably yield optimal maintenance strategies, whether the VoI is larger than or equal to zero. When the VoI is equal to zero, LCC and reliability based CBM optimization can lead to suboptimal maintenance strategies. The differences in the approaches are illustrated on fatigue-sensitive components in a marine structure.

Reliability Analysis via an Optimal Covariance Matrix Adaptation Evolution Strategy: Emphasis on Applications in Civil Engineering

In this paper, a reliability-based optimization approach is applied using a recently proposed CMA-ES with optimal covariance update and storage complexity. Cholesky-CMA-ES gives a significant increase in optimization speed and reduces the runtime complexity of the standard CMA-ES. The reliability index is the shortest distance between the surface of Limit-State Function (LSF) and the origin of the standard normal space. Hence, finding the reliability index can be expressed as a constrained optimization problem. To verify the concept and test the feasibility of this algorithm, several numerical examples consisting of mathematical and highly nonlinear civil engineering problems are investigated. The reliability indexes obtained agree reasonably well with reported values from some existing approximation methods and Monte Carlo simulation.

A reliability-based optimization approach for material and thickness composition of multidirectional functionally graded plates

A reliability-based design optimization (RBDO) methodology is first proposed to simultaneously optimize material and thickness distribution of multidirectional functionally graded (MFG) plates for compliance minimization under uncertainties of design variables and system parameters. The modified sequential optimization and reliability assessment (MSORA) method is integrated into the recently suggested adaptive hybrid evolutionary firefly algorithm (AHEFA) to release a novel RBDO approach which is the so-called MSORA-AHEFA. The MSORA is refined from its original for computational cost savings by eliminating the iterative process of finding most probable points (MPPs). An isogeometric multimesh design (IMD) approach is presented to form two separate non-uniform rational B-spline (NURBS) surfaces via the k−refinement strategy. In which, a coarser design NURBS one is employed to define design variables of the ceramic volume fraction and z−axis coordinate of the top side coincidentally assigned at each of control points. A finer analysis NURBS one constructed by the isogeometric analysis (IGA) and a generalized shear deformation theory (GSDT) is used for bending analyses of MFG plates with arbitrary thickness. Applying such two separately defined surfaces dramatically lessens the number of design variables and the computational cost in optimization problems, yet still manifesting optimal profiles properly. Meanwhile, mechanical behavior of the plate in analysis ones is precisely simulated as well. For the validation of the suggested MSORA-AHEFA, its results for the benchmark welded beam are compared with those of formerly published work. Several numerical examples regarding RBDO of MFG plates are then executed to attest the effectiveness of the current paradigm.

A nonprobabilistic time-variant reliability-based optimization approach to the reliable active controller design of structural vibration considering convex uncertainties

It is observed that the controller, as the “brain” of the active control system, plays a vital role in the vibration-rejecting aspect, and thereby, techniques of the optimal controller design are attracting increasing attention in dynamical engineering recently. However, due to the existence of uncertainty effects originating from modeling parameters and environmental conditions, current design means based on the classical optimal control theory are no longer feasible. In view of this, a new nonprobabilistic time-variant reliability-based optimization (NTRBO) strategy considering convex uncertainties is presented in this study for the reliable controller design of structural vibration. Boundary rules and autocorrelation characteristics of dynamical responses under the linear quadratic regulator control are first determined using the state-space transformation and the convex process theory. Inspired by the out-crossing idea and the safety factor notation, a new piecewise function of the time-variant reliability index is defined, and the nonprobabilistic reliability constraint is then established. Weighing matrices in the Riccati equation, as the keys to construct the controller, are indeed optimized by solving the developed NTRBO model. The usage, validity, and efficiency of the presented reliable control methodology are eventually demonstrated by several example applications.

Reliability-based optimization of steel truss arch bridges

A reliability-based optimization approach is developed and applied to minimize the weight of steel truss arch bridges subject to probabilistic (the overall probability failure of the structure) and deterministic (stress and deflection) constraints. The method intelligently integrates the genetic algorithm (GA), the finite element method and the first order reliability method. A real-coded/integer-coded method is used to realistically represent the values of the design variables. Three GA operators consisting of constraint aggregate selection procedure, arithmetic crossover, and non-uniform mutation are proposed. The finite element method (FEM) and the first order reliability method are used to compute the value of the probabilistic and deterministic constraint functions. A numerical example involving a detailed computational model of a long span steel arch bridge with a main span of 550 m is presented to demonstrate the applicability and merits of the present method. Finally, several important parameters in the present method are discussed.

Reliability-based design: Artificial neural networks and double-loop reliability-based optimization approaches

Two advanced optimization approaches to solving a reliability-based design problem are presented. The first approach is based on the utilization of an artificial neural network and a small-sample simulation technique. The second approach considers an inverse reliability task as a reliability-based optimization task using a double-loop optimization method based on small-sample simulation. Both techniques utilize Latin hypercube sampling with correlation control. The efficiency of both approaches is tested using three numerical examples of structural design – a cantilever beam, a reinforced concrete slab and a post-tensioned composite bridge. The advantages and disadvantages of the approaches are discussed.

Reliability-based assessment/design of floor isolation systems

Floor isolation systems have been becoming increasingly popular as a protective measure for critical structural contents such as computer servers or museum artifacts. Supplemental dampers, working in tandem with the isolation system, are also frequently considered in this context for reducing the isolated floor displacement or enhancing vibration suppression. This paper discusses a reliability-based optimization approach for this kind of applications that adequately addresses at the design stage the variability related to the earthquake hazard as well as the nonlinear dynamics of the coupled structure/isolation system. The floor isolation system is optimized based on reliability criteria, where the reliability of the system is quantified by the plausibility that the acceleration of the protected contents will not exceed an acceptable performance bound, and is calculated using stochastic simulation. The latter facilitates the adoption of complex numerical models for the coupled system. A stochastic ground motion model is utilized to characterize the seismic hazard, and an efficient stochastic optimization approach, called non-parametric stochastic subset optimization, is adopted for performing the associated design optimization. Near-fault directivity pulses are explicitly addressed within this modeling context and their effect on the optimal design is investigated in detail. Also, a global sensitivity analysis is integrated within the framework to investigate the importance of the different uncertain model parameters (risk factors) towards the system failure probability. For demonstrating the proposed framework, the protection of a computer server placed at different floors within a four-story structure is considered.

Efficient approach for reliability-based optimization based on weighted importance sampling approach

An efficient methodology is presented to perform the reliability-based optimization (RBO). It is based on an efficient weighted approach for constructing an approximation of the failure probability as an explicit function of the design variables which is referred to as the ‘failure probability function (FPF)’. It expresses the FPF as a weighted sum of sample values obtained in the simulation-based reliability analysis. The required computational effort for decoupling in each iteration is just single reliability analysis. After the approximation of the FPF is established, the target RBO problem can be decoupled into a deterministic one. Meanwhile, the proposed weighted approach is combined with a decoupling approach and a sequential approximate optimization framework. Engineering examples are given to demonstrate the efficiency and accuracy of the presented methodology.

Bayesian Reliability-Based Optimization Design of Torsion Bar

Based on bayesian statistics theory and reliability-based optimization design, the research presents a new reliability-based optimization design approach that solves the form of finite test samples. In the article, the bayesian reliability-based optimization mathematical model is established and the bayesian reliability-based optimization approach of torsion bar is proposed. The method adopts a bayesian inference technique to estimate reliability, gives definition of bayesian reliability. The results illustrates the method presented is an efficient and practical reliability-based optimization approach of torsion bar.

A survey on approaches for reliability-based optimization

Reliability-based Optimization is a most appropriate and advantageous methodology for structural design. Its main feature is that it allows determining the best design solution (with respect to pre...

Genetic Algorithms for Reliability-Based Optimization of Water Distribution Systems

A new approach for reliability-based optimization of water distribution networks is presented. The approach links a genetic algorithm (GA) as the optimization tool with the first-order reliability method (FORM) for estimating network capacity reliability. Network capacity reliability in this case study refers to the probability of meeting minimum allowable pressure constraints across the network under uncertain nodal demands and uncertain pipe roughness conditions. The critical node capacity reliability approximation for network capacity reliability is closely examined and new methods for estimating the critical nodal and overall network capacity reliability using FORM are presented. FORM approximates Monte Carlo simulation reliabilities accurately and efficiently. In addition, FORM can be used to automatically determine the critical node location and corresponding capacity reliability. Network capacity reliability approximations using FORM are improved by considering two failure modes. This research demonstrates the novel combination of a GA with FORM as an effective approach for reliability-based optimization of water distribution networks. Correlations between random variables are shown to significantly increase optimal network costs.

Reliability-Based Optimal Design of Water Distribution Networks

A new approach for reliability-based optimization of water distribution networks is presented. The approach is capable of recognizing the uncertainty in nodal demands and pipe capacity as well as the effects of mechanical failure of system components. A probabilistic hydraulic model is used in the model to account for uncertainty in nodal demands and pipe capacity. The primary innovation of the model is the use of a first-order reliability-method-based algorithm to compute approximate values of the capacity reliability of water distribution networks. Capacity reliability is defined as the probability that the nodal demand is met \Iat or over\N the prescribed minimum pressure for a fixed network configuration under random nodal demands and random pipe roughnesses. The model also incorporates a strategy for identifying the critical nodes on which the reliability constraints are imposed in the cost minimizing step. The computational efficiency of the optimization is shown to be enhanced by deriving the first-order derivatives analytically using a sensitivity-analysis-based technique. The efficiency and capacity of the proposed algorithm are illustrated by application to two sample networks.

Deterministic and reliability-based optimization of truss bridges

This paper reports analytical investigations into both deterministic and reliability-based optimization of bridges. In the first part of this paper, the effects of component material behavior on the optimum weight of deterministic truss bridge systems are studied, with a 65-bar truss bridge being used to demonstrate such effects. In the second part of this paper, a reliability-based optimization approach to design truss bridges with uncertain correlated strengths, acted upon by random correlated loads, is presented. The importance of such correlations, and of some of the other statistical parameters such as the variabilities in strengths and loadings, is demonstrated by an example of sensitivity studies on the reliability-based optimum solution.

Incorporation of corrosion effects in reliability-based optimization of composite hybrid plate girders

Available data suggest that corrosion may have significant effects on the reliability of structural components and systems including highway bridges, offshore platforms, and hydraulic structures. Therefore, reliability-based design and/or optimization of a structure or component placed during its intended service life in a corrosive environment must take the effects of this environment into account. A reliability-based optimization approach to the design of composite hybrid plate girders under corrosion effects is developed herein. The proposed approach incorporates all constraints specified in the AASHTO bridge code considering time-dependent corrosion effects. Numerical examples illustrate the application of the proposed approach to time-dependent reliability-based optimum design of both unstiffened and stiffened composite hybrid plate girders for highway bridges.

Design of composite hybrid plate girder bridges based on reliability and optimization

A practical and efficient reliability-based optimization approach to the design of both unstiffened and stiffened composite hybrid plate girders for highway bridges is presented. The steel weight of the built up plate girder is adopted as the objective to be minimized and all constraints specified in the AASHTO bridge code are considered in the optimization process. The solution is obtained by coupling an optimization program with a reliability analysis program. Numerical examples illustrate the application of the approach to reliability-based optimum design of unstiffened and stiffened composite plate girders. Sensitivity analyses are also performed for finding the rates of change of the optimum solution with respect to changes in problem preassigned parameters.