Reliability in Design and Analysis

Abstract

Tools and concepts of optimization are widespread in decision-making, design and planning. There is a moral imperative to ‘do our best’. Optimization underlies theories in physics and biology, and economic theories often presume that economic agents are optimizers. We argue that, in decisions under uncertainty, what should be optimized is robustness rather than performance. We discuss the equity premium puzzle from financial economics, and explain that the puzzle can be resolved by using the strategy of satisficing rather than optimizing. We discuss design of critical technological infrastructure, showing that satisficing of performance requirements – rather than optimizing them – is a preferable design concept. We explore the need for disaster recovery capability and its methodological dilemma. The disparate domains – economics and engineering – illuminate different aspects of the challenge of uncertainty and of the significance of robust-satisficing.

keywords

optimizing, satisficing, robustness, uncertainty, info-gap, financial investment, equity premium puzzle, technological infrastructure, moral hazard, disaster recovery

Abstract

Risk analysis is challenged in three ways by uncertainty. Our understanding of the world and its uncertainties is evolving; indeterminism is an inherent part of the open universe in which we live; and learning from experience involves untestable assumptions. We discuss several concepts of robustness as tools for responding to these epistemological challenges. The use of models is justified, even though they are known to err. A concept of robustness is illustrated in choosing between a conventional technology and an innovative, promising, but more uncertain technology. We explain that non-probabilistic robust decisions are sometimes good probabilistic bets. Info-gap and worst-case concepts of robustness are compared. Finally, we examine the exploitation of favorable but uncertain opportunities and its relation to robust decision making.

Keywords:

robustness, uncertainty, info-gap theory, satisficing, optimizing

Abstract

A novel Information-gap-based (Info-gap) damage detection method for uncertainty quantification is proposed in this study. The modal shapes of structures are selected as damage indices, and the uncertainty level of these indices caused by measurement errors and modal identification are described by Info-gap model. The decision function is defined as the distance of modal shape between health and unknown condition of structures, and then the solution of this function is translated into an optimization problem. The results from a numerical simulation and lab-scale structure show that the location and severity of damage can be successfully identified.

Author keywords

Damage detection; Distance function; Info-gap theory; Optimization; Uncertainty.

Indexed keywords

Optimization; Uncertainty analysis; Decision functions; Distance functions; Info-gap; Modal identification; Novel information; Optimization problems; Uncertainty; Uncertainty quantifications; Damage detection

Highlights

• IGDT is used to assess the robustness of an optimal input signal designing technique.
• The case of uncertainty affecting the parameters of a 2-DOF system is analyzed.
• It can be critical when affecting the masses or the linear stiffnesses values.
• Small influence is due to changes in the nonlinear stiffnesses or the damping ratios.
• The analyzed algorithm has shown to be robust to variations in the damage level.

Abstract

Info-Gap Decision Theory is adopted to assess the robustness of a technique aimed at identifying the optimal excitation signal to be used for active sensing approaches to damage detection. Here the term “active sensing” refers to procedures where a known input is applied to the structure to enhance the damage detection process. Given limited system response measurements and ever-present physical limits on the level of excitation, the ultimate goal of the mentioned technique is to improve the detectability of damage by increasing the difference between measured outputs of the undamaged and damaged systems. In particular, a two degree-of-freedom mass–spring–damper system characterized by the presence of a nonlinear stiffness is considered. Uncertainty is introduced to the system in the form of deviations of its parameters (mass, stiffness, damping ratio) from their nominal values. Variations in the performance of the mentioned technique are then evaluated both in terms of changes in the estimated difference between the responses of the damaged and undamaged systems and in terms of deviations of the identified optimal input signal from its nominal estimation. Finally, plots of the performances of the analyzed algorithm for different levels of uncertainty are obtained, enabling a clear evaluation of the risks connected with designing excitation signals for damage detection, when the parameters that dictate system behavior (e.g. stiffness, mass) are poorly characterized or improperly modeled.

Keywords

Info-Gap Decision Theory; Uncertainty; Structural health monitoring; Optimization

Abstract

A method is developed for experimental assessment of reliability of a system with a stringent safety requirement: explosive material. The focus is on analysis and management of both statistical variability of measurements and non-probabilistic uncertainty in probability distributions (distributional uncertainty). Info-gap theory is used to model the distributional uncertainty in the pdf of the threshold for actuation of the explosive material. The quantitative analysis and the qualitative judgments which accompany the certification of safety are studied. A proposition is proven asserting that the info-gap robustness function, for the class of problems examined, is independent of the experimental design over virtually all of its range.

Abstract

In practical applications, there may exist a disparity between real values and optimal results due to uncertainties. This kind of disparity may cause violations of some probabilistic constraints in a reliability based design optimization (RBDO) problem. It is important to ensure that the probabilistic constraints at the optimum in a RBDO problem are insensitive to the variations of design variables. In this paper, we propose a novel concept and procedure for reliability based robust design in the context of random uncertainty and epistemic uncertainty. The epistemic uncertainty of design variables is first described by an info gap model, and then the reliability-based robust design optimization (RBRDO) is formulated. To reduce the computational burden in solving RBRDO problems, a sequential algorithm using shifting factors is developed. The algorithm consists of a sequence of cycles and each cycle contains a deterministic optimization followed by an inverse robustness and reliability evaluation. The optimal result based on the proposed model satisfies certain reliability requirement and has the feasible robustness to the epistemic uncertainty of design variables. Two examples are presented to demonstrate the feasibility and efficiency of the proposed method.

Keywords

epistemic uncertainty, info-gap models, feasible robustness index, sequential algorithm, shifting factor, reliabilitybased robust design optimization

Abstract

This paper first discusses the reliability-based design optimization (RDO) of structures under the mixture of random, interval and fuzzy variables. The sequential single-loop optimization method is applied for RDO with different combinations of uncertaities. Info-gap models are used to represent errors between “true” values and design results. A sequential algorithm for the robust reliability design is presented. Example 1 shows that the fuzzy reliability design can offer conservative result. The results of example 2 show there are different robust optimal solutions when the robustness index takes different values. When alpha_t is greater than 0.2, the robust optimal solution does not exist. After 1291 times computation of the objective function, the optimal result can be obtained by using the sequential algorithm for the robust reliability design, while 8107 times computation are needed by the conventional optimum algorithm.

Keywords

Incomplete information; Info-gap model; Possibility-based design; Reliability-based design; Robust design optimization

Abstract

This paper is concerned with the non-probabilistic methods to deal with uncertainties problems. First, this paper analyzes the difference between non-probabilistic reliability methods and traditional probabilistic reliability methods, which makes the comparative analysis on aspects of the application scope of methods, the use of processes and the complexity of employment. Second, this paper introduces the basic concept of the convex model, as the interval model, the ellipsoid model and the multidimensional ellipsoid model are briefly presented. Third, this paper analyzes the use of information gap model of uncertainty, including the basic application of the model and the way to use. Finally, numerical example is given to illustrate the validity and efficiency of non-probabilistic reliability method. The example used herein is reliability analysis of fatigue strength of turbine blade, but it is also an important reference of other types of uncertainties systems. Compared with the probability approach, the non-probabilistic information gap model only requires a small amount of samples to obtain the variation bounds of the imprecise parameters, and whereby makes the reliability analysis very convenient and economical.

Keywords

information gap model of uncertainty; non-probabilistic reliability method; the convex model

Abstract

A dispersion parameter was proposed and introduced in the info-gap (information gap) model. The info-gap model introduced dispersion parameter has more applicability for structural reliability analysis. A general non-probabilistic structural reliability model was established by using the info-gap model introduced dispersion parameter to describe the uncertainties based on the info-gap decision theory. The non-probabilistic reliability index defined in the new model can be obtained by solving a nonlinear programming problem. The mathematical deduction shows the relationship of the non-probabilistic structural reliability method based on info-gap model and the traditional probabilistic structural reliability method, which also shows the consistency of the two methods.

Keywords

Dispersion parameter; Info-gap(information-gap) model; Non-probabilistic reliability; Reliability index

Abstract

The difference of the dispersion style of the uncertainty quantities in the practical structural reliability problems was pointed out. The info-gap (information-gap) model with restriction was advanced by introducing a new parameter in the origin model. The new model could be degenerated into the origin model. The non-probabilistic structural reliability method with the info-gap model introducing restriction parameter could utilize the existing information thoroughly and estimate the structural reliability more reasonably. Comparing with the existing model the new non-probabilistic structural reliability model could reveal the influence of the restriction information on structural reliability. The numerical example shows that the non-probabilistic reliability index ignored the restriction of uncertainty quantities span would be too conservative.

Keywords

Info-gap(information-gap) model; Non-probabilistic reliability; Reliability index; Robust reliability; Set expansion

Abstract

Info-gap model is the foundation of the non-probabilistic reliability model. In this paper, ellipsoidal-bound model which is the most common Info-gap model has been updated by acquiring restriction information about uncertain quantities. The initial ellipsoidal-bound model can be degenerated from the updated model. A non-probabilistic structural reliability model based on the updated ellipsoidal-bound model was established. A non-probabilistic reliability index was proposed and the calculation method was also given. The example shows that the introduction of restriction information is valid, and the new non-probabilistic reliability model can reveal the influence of the span restriction of uncertain quantities on structural reliability.