E. Nikolaidis

Reliability based optimization: A safety index approach

Abstract An alternative approach to the classical chance constraint optimization technique is presented. The proposed method employs an advanced second-moment method in evaluating the probabilities of violating the constraints. The approach is applied to the optimal design of a simple structure. The results are compared to those obtained using the classical chance constraint optimization technique. Using the proposed optimization approach the basic drawbacks of the classical chance constraint optimization technique are shown to be overcome. The improved accuracy of the new optimazation method is verified using Monte-Carlo simulation.

NEURAL NETWORKS AND RESPONSE SURFACE POLYNOMIALS FOR DESIGN OF VEHICLE JOINTS

Abstract Typically, design of a complex system starts by setting targets for its performance characteristics. Then, design engineers cascade these targets to the components and design the components to meet these targets. It is important to have efficient tools that check if a set of performance targets for a component corresponds to a feasible design and determine the dimensions and mass of this design. This paper describes a method to develop tools that relate response parameters that describe the performance of a component to the physical design variables that specify its geometry. Neural networks and response surface polynomials are used to rapidly predict the performance characteristics of the components given the component dimensions. The method is demonstrated on design of an automotive joint. The paper compares neural networks and response surface polynomials and shows that they are almost equally accurate for the problem considered.

A two-dimensional model for joints in vehicle structures

Abstract A simple, design-oriented model for joints in vehicle structures is presented. This model accounts for the flexibility of a joint, the offsets for the rotation centers of its branches, and the coupling between movements of the branches. The model consists of springs and rigid sections. The parameters of the joint model are spring rates and lengths of rigid sections and are estimated by using measurements of the static response of the structure. The sensitivity of the static response of a vehicle structure with respect to the parameters of the joint model is studied, and the most important parameters are identified.

Design of Aircraft Wings Subjected to Gust Loads: A System Reliability Approach

A method for system reliability-based design of aircraft wing structures is presented. A wing of a light commuter aircraft designed for gust loads according to the FAA regulations is compared with one designed by system reliability optimization. It is shown that system reliability optimization has the potential of improving dramatically the safety and efficiency of new designs. The reasons for the differences between the deterministic and reliability-based designs are explained.

Comparison of probabilistic and deterministic optimizations using genetic algorithms

This paper describes an application of genetic algorithms to deterministic and probabilistic (reliability-based) optimization of damping augmentation for a truss structure. The probabilistic formulation minimizes the probability of exceeding upper limits on the magnitude of the dynamic response of the structure due to uncertainties in the properties of the damping devices. The corresponding deterministic formulation maximizes a safety margin with respect to these limits. Because this work was done in the context of an experimental comparison of the reliabilities of the resulting designs, antioptimization was used to maximize the contrast between the probabilities of failure of the two designs. This contrast maximization was also performed with a genetic algorithm. The paper describes the genetic algorithm used for the optimization and antioptimization, and a number of modifications to the antioptimization formulation intended to reduce the computational expense to an acceptable level. Optimal designs are obtained for both formulations. The probabilistic design shows a very significant improvement in reliability.

Integrated analysis and design in stochastic optimization

An integrated analysis and design approach for stochastic optimization of structures is presented. The proposed procedure employs a first order second moment (FOSM) method for evaluating the constraints associated with structural safety.Two variants of the new approach are presented. The idea is to integrate the nested iterative procedures for constraint evaluation and optimum search into one. The new approach is applied to simple design examples. The results are compared to those obtained by classical stochastic optimization using the FOSM method to evaluate the constraints. Both methods are robust to a satisfactory degree and substantially reduce the computational effort.

EFFECT OF MEMBER LENGTH ON THE PARAMETER ESTIMATES OF JOINTS

Abstract Concept models of joints are used in the early stages of structural design because they are more economical and practical than detailed models. The concept joint models usually use torsional springs. The magnitudes of torsional spring constants and the positions and orientations of torsional springs can be used as parameters in order to account for the flexibility, location of rotation centers, and coupling effect of joints, respectively. These parameters are usually identified using the results of experiments performed on a substructure that contains a joint itself and the attached members. However, the estimates of parameters may change with the length of the attached members. This is due to the fact that the magnitude of the shear deformation of the cross sections of the joint members changes with the length of members. The effect of member length on the parameters of the concept joint models is studied using system identification as well as decomposition of the total deformation of the substructure into contributions from a joint itself and the attached members. The study is applied to a T-shaped joint made of simple box beams and to a joint in a real automotive body structure.

Design of automotive joints: Using neural networks and optimization to translate performance requirements to physical design parameters

Abstract In the preliminary design stage of a car, targets are first set for the performance characteristics of the overall body and its components using optimization and engineering judgment. Then designers try to design components that meet these targets using empirical, trial-and-error procedures. This process usually yields poor results because it is difficult to find a feasible design that satisfies the targets by trial-and-error (a feasible design is one that satisfies packaging and manufacturing constraints). To improve this process, we need tools to link the performance targets with the physical design parameters that define the geometry of the components of a car body. A methodology is presented for developing two tools for design guidance of joints in car bodies. These tools translate the design parameters that define the geometry of a joint into performance characteristics of that joint and vice versa. The first tool, called translator A, rapidly predicts the performance characteristics of a given joint (at a fraction of a second). The second tool, called translator B, finds a joint design that meets or exceeds given performance targets and satisfies packaging and manufacturing constraints. The methodology is demonstrated on a joint of an actual car.

Closed‐form approximations and series representations for partially saturated ocean acoustic processes

An approximate, closed‐form expression for the value of the integral encountered in the calculation of the probability density function (PDF) of the envelope of a partially saturated ocean acoustic process is obtained. Furthermore, an expression of this PDF as a series of modified Bessel functions is presented. The results may also be directly applied to the evaluation of the PDF encountered in the structural reliability analysis of rotating machinery components. Numerical applications show that the closed‐form expression is always within 1%2% of the exact result. The required computational effort is substantially lower than that required by direct numerical integration.

Review of the book: Y. Ben-Haim, Robust Reliability in the Mechanical Sciences, Springer-Verlag, Berlin, 1996

It is widely accepted that probabilistic methods for reliability assessment can lead to large errors if little information is available about uncertainties. The reason is that constructing a probabilistic model of an uncertain variable usually requires too much data. If little data is available, we usually have to do sweeping assumptions to construct a probabilistic model, which may lead to erroneous results. Ben Haims book presents an alternative method to probabilistie methods for reliability assessment of mechanical systems whose properties and their loads are uncertain. This method constructs a set that is usually centered at the nominal values of the uncertain variables, and envelops their values. The size of this set is controlled by a parameter, called uncertainty parameter. The larger the uncertainty parameter, the larger can be the deviation of the uncertain variables from their nominal values. It is logical to expect that a robust system can operate satisfactorily even when the variables deviate considerably from their nominal values. Thus, robust reliability of a system is the largest value of the uncertainty parameter for which the system survives. The theory presented in this book considers that all uncertain variables vary in a convex set. In many problems, this allows finding closed form solutions for the combination of values of the uncertain variables that correspond to the worst case scenario. This in turn allows us to calculate the robust reliability of a system efficiently. The book is very clearly written and easy to understand. Most theorems that form the foundation of robust reliability theory are not proven. Yet, they are rigorously stated and their physical meaning is presented very well. The book can be used in a senior or a graduate course on structural