Efstratios Nikolaidis

A Single-Loop Approach for System Reliability-Based Design Optimization

An efficient single-loop approach for series system reliability-based design optimization problems is presented in this paper. The approach enables the optimizer to apportion the system reliability among the failure modes in an optimal way by increasing the reliability of those failure modes whose reliability can be increased at low cost. Furthermore, it identifies the critical failure modes that contribute the most to the overall system reliability. A previously reported methodology uses a sequential optimization and reliability approach. It also uses a linear extrapolation to determine the coordinates of the most probable points of the failure modes as the design changes. As a result, the approach can be slow and may not converge if the location of the most probable failure point changes significantly. This paper proposes an alternative system RBDO approach that overcomes the above difficulties by using a single-loop approach where the searches for the optimum design and for the most probable failure points proceed simultaneously. An easy to implement active set strategy is used. The maximum allowable failure probabilities of the failure modes are considered as design variables. The efficiency and robustness of the method is demonstrated on three design examples involving a beam, an internal combustion engine and a vehicle side impact. The results are compared with deterministic optimization and the conventional component RBDO formulation.Copyright

Comparison of Probability and Possibility for Design Against Catastrophic Failure Under Uncertainty

This paper compares probabilistic and possibility-based methods for design under uncertainty. It studies the effect of the amount of data about uncertainty on the effectiveness of each method. Only systems whose failure is catastrophic are considered, where catastrophic means that the boundary between success and failure is sharp. First, the paper examines the theoretical foundations of probability and possibility, focusing on the impact of the differences between the two theories on design. Then the paper compares the two theories on design problems. A major difference between probability and possibility is in the axioms about the union of events. Because of this difference, probability and possibility calculi are fundamentally different and one cannot simulate possibility calculus using probabilistic models. Possibility-based methods tend to underestimate the risk of failure of systems with many failure modes. For example, the possibility of failure of a series system of nominally identical components is equal to the possibility of failure of a single component. When designing for safety, the two methods try to maximize safety in radically different ways and consequently may produce significantly different designs. Probability minimizes the system failure probability whereas possibility maximizes the normalized deviation of the uncertain variables from their nominal values that the system can tolerate without failure. In contrast to probabilistic design, which accounts for the cost of reducing the probability of each failure mode in design, possibility tries to equalize the possibilities of failure of the failure modes, regardless of the attendant cost. In many safety assessment problems, one can easily determine the most conservative possibilistic model that is consistent with the available information, whereas this is not the case with probabilistic models. When we have sufficient data to build accurate probabilistic models of the uncertain variables, probabilistic design is better than possibility-based design. However, when designers need to make subjective decisions, both probabilistic and possibility-based designs can be useful. The reason is that large differences in these designs can alert designers to problems with the probabilistic design associated with insufficient data and tell them that they have more flexibility in the design than they may have known.

New Approach for System Reliability-Based Design Optimization

An efficient approach for reliability-based design optimization (RBDO) of series systems is presented. A modified formulation of the RBDO problem is employed in which the reliabilities of the failure modes of a system are included in the set of the design variables. This allows for an optimal apportionment of the reliability of a system among its failure modes. A sequential optimization and reliability assessment method is used to efficiently determine the optimum design. Here, the constraints on the reliabilities of the failure modes of the RBDO problem are replaced with approximate deterministic constraints. The proposed approach is demonstrated on two example problems that have been solved in previous studies without optimizing the required reliability levels of the failure modes. The first example performs RBDO to a cantilever beam with a rectangular cross section under lateral and vertical loads. The constraints are on the strength and the maximum allowable displacement. The second example performs RBDO to a cable-stayed box girder with five failure modes. Compared to the designs found by previous studies, the new approach finds designs with lower mass but without reducing the system reliability.

An Efficient Re-Analysis Methodology for Probabilistic Vibration of Large-Scale Structures

Probabilistic analysis and design of large-scale structures requires repeated finite-element analyses of large models, and each analysis is expensive. This paper presents a methodology for probabilistic analysis and reliability-based design optimization of large-scale structures that consists of two re-analysis methods, one for estimating the deterministic vibratory response and another for estimating the probability of the response exceeding a certain level. The deterministic re-analysis method can analyze efficiently large-scale finite-element models consisting of tens or hundreds of thousand degrees of freedom and design variables that vary in a wide range. The probabilistic re-analysis method calculates very efficiently the system reliability for different probability distributions of the random variables by performing a single Monte Carlo simulation of one design. The methodology is demonstrated on probabilistic vibration analysis and reliability-based design optimization of a realistic vehicle model. It is shown that the computational cost of the proposed re-analysis method for a single reliability analysis is about 1/20 of the cost of the same analysis using MSC/NASTRAN. Moreover, the probabilistic re-analysis approach enables a designer to perform reliability-based design optimization of the vehicle at a cost almost equal to that of a single reliability analysis. Without using the probabilistic re-analysis approach, it would be impractical to perform reliability-based design optimization of the vehicle.

Effects of isolators internal resonances on force transmissibility and radiated noise

Abstract Vibration isolators have been extensively used to reduce the vibration and noise transmitted between the components of mechanical systems. Although some previous studies on vibration isolation considered the inertia of isolators, they only examined its effects on the vibration of single degree-of-freedom (d.o.f.) systems. These studies did not emphasize the importance of the isolators’ inertia, especially from the perspective of noise reduction. This paper shows that the internal dynamics of the isolator, which are also known as internal resonances (IRs) or wave effects , can significantly affect the isolator performance at high frequencies. To study the IR problem, a model of a primary mass connected to a flexible foundation through three isolators is used. In this model, the isolator is represented as a one-dimensional continuous rod that accounts for its internal dynamics. The primary mass is modelled as a rigid body with three d.o.f.s. The effects of the IRs on the force transmissibility and the radiated sound power from the foundation are examined. It is shown that the IRs significantly increase the force transmissibility and the noise radiation level at some frequencies. These effects cannot be predicted using a traditional model that neglects the inertia of the isolator. The influence of the foundation flexibility on the IRs is also investigated. It is shown that the foundation flexibility greatly affects the noise radiation level but it affects only slightly the force transmissibility, especially at high frequencies where the IRs occur.

Reliability-Based Structural Optimization of an Elastic-Plastic Beam

The application of reliability-based optimization to an elastic-plastic beam is studied. The objective is to demonstrate the benefits of reliability-based optimization over the deterministic optimization in such applications where the design requirements of the member tolerate some plastic behavior. Also, some of the difficulties that one might encounter while performing reliability-based optimization of elastic-plastic beams are addressed. A graphical method was used here to avoid the problems of high nonlinearity and derivative discontinuity of the reliability function. The method starts by obtaining a deterministic optimum design that has the lowest possible weight for a prescribed safety factor, and, based on that design, the method obtains an improved optimum design that has either a higher reliability or a lower weight or cost. In this application three failure modes are considered for an elastic-plastic beam of T cross section under combined axial, bending, and shear loads. The failure modes are based on the beam total plastic failure in a section, buckling, and maximum allowable deflection. The results show that it is possible to get improved optimum designs (more reliable or lighter) using reliability-based optimization as compared to the design given by deterministic optimization. Also, the results show that the reliability function can be highly nonlinear with respect to the design variables with discontinuous derivatives.

PROBABILISTIC SYSTEM IDENTIFICATION OF TWO FLEXIBLE JOINT MODELS

The flexibility of welded joints is an important issue in structural analysis and design of car bodies. Two three-dimensional, design-oriented models (uncoupled and coupled) are developed to represent the complaint behavior of multibranch flexible joints. The uncoupled model consists of torsional springs restraining the relative rotation of the joint branches in the three planes, while all branches are assumed to be rigidly connected in translation. Coupling between motions in different planes is neglected. The coupled model accounts for such coupling. A statistical system identification method is proposed for inferring the model parameters from the static response of the structure. The method is demonstrated by applying it to a simple cube frame structure and a car body. Finally, the two models are compared in terms of their ability to predict static response.

Engineering design reliability applications : for the aerospace, automotive, and ship industries

Preface Applications of Reliability Assessment, D.S. Riha, B.H. Thacker, L.J. Huyse, M.P. Enright, C.J. Waldhart, W.L. Francis, D.P. Nicolella, S.J. Hudak, W. Liang, and S.H.K. Fitch Reliability Assessment of Aircraft Structure Joints under Corrosion-Fatigue Damage, D.M. Ghiocel and E. Tuegel Selected Topics in Probabilistic Gas Turbine Engine Turbomachinery Design, J.A. Griffiths and J.A. Tschopp Applications of Reliability-based Design Optimization, R.H. Sues, Y. Shin, and Y-T Wu Probabilistic Progressive Buckling of Conventional and Adaptive Trusses, S.S. Pai and C.C. Chamis Probabilistic Analysis of HSCT (High Speed Civil Transport) Combustor Liner Components, S.S. Pai and P.L.N. Murthy Probabilistic Analysis and Design in Automotive Industry, Z.P. Mourelatos, J. Tu, and X. Ding Integrated Computer-Aided Engineering Methodology for Various Uncertainties and Multidisciplinary Applications, K.K. Choi, B.D. Youn, J. Tang, J.S. Freeman, T.J. Stadterman, A.L. Peltz, and W. Connon Reliability Assessment of Ships, J.K. Paik and A.K. Thayamballi Reliability Analysis of Composite Structures and Materials, S. Mahadevan Micromechanics Modeling and Reliability Analysis of Carbon Nanofiber Composite Structures, S. Pilla, A. Hammitt, and E. Nikolaidis

Decision-Based Approach for Reliability Design

We propose a decision-based approach for reliability design when there is insufficient information for constructing probabilistic models. The approach enables a designer to perform reliability-cost trade-offs and to assess the importance of variability and epistemic uncertainty. A method for decision under epistemic uncertainty is first presented and justified by presenting axioms on a decision maker’s (DM’s) preferences and by assuming that the DM’s goal is to find the most immune act (in terms of having undesirable consequences) to deviations of the state of the world from an expected state. Thus, the philosophy of the method is similar to that of robust reliability (Ben Haim, Y., 1996, Robust Reliability in the Mechanical Sciences, Springer-Verlag, Berlin). A new formulation of reliability design problems is proposed based on the above decision method and is compared to two reliability-based design optimization formulations that minimize cost given a maximum acceptable failure probability or maximize expected utility. The method is demonstrated on a decision where a designer has to choose between two materials for a structure.

Combined Approximations for Efficient Probalistic Analysis of Structures

Real-life analysis and design problems involve uncertainties. Quantification of the uncertainties in a systems response is important and requires a probabilistic analysis of the system. A main challenge in probabilistic analysis of large structural systems is the high computational effort due to the multiple repeated analyses involved. The combined approximations (CA) method, which combines the strengths of both local and global approximations, can be used for efficient probabilistic analysis of structures. The CA method is a combination of binomial series (local) approximations (also called Neumann expansion approximations) and reduced basis (global) approximations. An efficient method is presented for probabilistic analysis of structural systems using the CA method. The effectiveness of this method is demonstrated on analysis of mistuned bladed disk assemblies and systems with progressive collapse using Monte Carlo simulation. It is shown that the method can predict accurately the probability distribution function of the responses of these systems at a considerably lower cost than a method using finite element analysis in each cycle of Monte Carlo simulation.