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A simulation-based, system reliability-based design optimization (RBDO) method is presented that can handle problems with multiple failure regions and correlated random variables. Copulas are used to represent the correlation. The method uses a Probabilistic Re-Analysis (PRRA) approach in conjunction with a trust-region optimization approach and local metamodels covering each trust region. PRRA calculates very efficiently the system reliability of a design by performing a single Monte Carlo (MC) simulation per trust region. Although PRRA is based on MC simulation, it calculates “smooth” sensitivity derivatives, allowing therefore, the use of a gradient-based optimizer. The PRRA method is based on importance sampling. It provides accurate results, if the support of the sampling PDF contains the support of the joint PDF of the input random variables. The sequential, trust-region optimization approach satisfies this requirement.

Piston design is a challenging engineering problem which involves complex physics and requires satisfying multiple performance objectives. Uncertainty in piston operating conditions and variability in piston design variables are inevitable and must be accounted for. The piston assembly can be a major source of engine mechanical friction and cold start noise, if not designed properly. In this paper, an analytical piston model is used in a deterministic and probabilistic (reliability-based) multi-objective design optimization process to obtain an optimal piston design. The model predicts piston performance in terms of scuffing, friction and noise, In order to keep the computational cost low, efficient and accurate metamodels of the piston performance metrics are used. The Pareto set of all optimal solutions is calculated allowing the designer to choose the “best” solution according to trade-offs among the multiple objectives.

Vehicle restraint system design is a difficult optimization problem to solve because (1) the nature of the problem is highly nonlinear, non-convex, noisy, and discontinuous; (2) there are large numbers of discrete and continuous design variables; (3) a design has to meet safety performance requirements for multiple crash modes simultaneously, hence there are a large number of design constraints. Based on the above knowledge of the problem, it is understandable why design of experiment (DOE) does not produce a high-percentage of feasible solutions, and it is difficult for response surface methods (RSM) to capture the true landscape of the problem. Furthermore, in order to keep the restraint system more robust, the complexity of restraint system content needs to be minimized in addition to minimizing the relative risk score to achieve New Car Assessment Program (NCAP) 5-star rating.

We propose a new metamodeling method to characterize the output (response) random process of a dynamic system with random parameters, excited by input random processes. The metamodel can be then used to efficiently estimate the time-dependent reliability of a dynamic system using analytical or simulation-based methods. The metamodel is constructed by decomposing the input random processes using principal components or wavelets and then using a few simulations to estimate the distributions of the decomposition coefficients. A similar decomposition is also performed on the output random process. A kriging model is then established between the input and output decomposition coefficients and subsequently used to quantify the output random process corresponding to a realization of the input random parameters and random processes. What distinguishes our approach from others in metamodeling is that the system input is not deterministic but random.

Implications of decision analysis (DA) on engineering design are important and well-documented. However, widespread adoption has not occurred. To that end, the authors recently proposed decision topologies (DT) as a visual method for representing decision situations and proved that they are entirely consistent with normative decision analysis. This paper addresses the practical issue of assessing the DTs of a designer using their responses. As in classical DA, this step is critical to encoding the DA's preferences so that further analysis and mathematical optimization can be performed on the correct set of preferences. We show how multi-attribute DTs can be directly assessed from DM responses. Furthermore, we show that preferences under uncertainty can be trivially incorporated and that topologies can be constructed using single attribute topologies similarly to multi-linear functions in utility analysis. This incremental construction simplifies the process of topology construction.

We have recently obtained experimental data and used them to develop computational models to quantify occupant impact responses and injury risks for military vehicles during frontal crashes. The number of experimental tests and model runs are however, relatively small due to their high cost. While this is true across the auto industry, it is particularly critical for the Army and other government agencies operating under tight budget constraints. In this study we investigate through statistical simulations how the injury risk varies if a large number of experimental tests were conducted. We show that the injury risk distribution is skewed to the right implying that, although most physical tests result in a small injury risk, there are occasional physical tests for which the injury risk is extremely large. We compute the probabilities of such events and use them to identify optimum design conditions to minimize such probabilities.

A common approach to the validation of simulation models focuses on validation throughout the entire design space. A more recent methodology validates designs as they are generated during a simulation-based optimization process. The latter method relies on validating the simulation model in a sequence of local domains. To improve its computational efficiency, this paper proposes an iterative process, where the size and shape of local domains at the current step are determined from a parametric bootstrap methodology involving maximum likelihood estimators of unknown model parameters from the previous step. Validation is carried out in the local domain at each step. The iterative process continues until the local domain does not change from iteration to iteration during the optimization process ensuring that a converged design optimum has been obtained.

Reliability is an important engineering requirement for consistently delivering acceptable product performance through time. As time progresses, the product may fail due to time-dependent operating conditions and material properties, component degradation, etc. The reliability degradation with time may increase the lifecycle cost due to potential warranty costs, repairs and loss of market share. Reliability is the probability that the system will perform its intended function successfully for a specified time interval. In this work, we consider the first-passage reliability which accounts for the first time failure of non-repairable systems. Methods are available in the literature, which provide an upper bound to the true reliability which may overestimate the true value considerably. Monte-Carlo simulations are accurate but computationally expensive.

Understanding reliability is critical in design, maintenance and durability analysis of engineering systems. A reliability simulation methodology is presented in this paper for vehicle fleets using limited data. The method can be used to estimate the reliability of non-repairable as well as repairable systems. It can optimally allocate, based on a target system reliability, individual component reliabilities using a multi-objective optimization algorithm. The algorithm establishes a Pareto front that can be used for optimal tradeoff between reliability and the associated cost. The method uses Monte Carlo simulation to estimate the system failure rate and reliability as a function of time. The probability density functions (PDF) of the time between failures for all components of the system are estimated using either limited data or a user-supplied MTBF (mean time between failures) and its coefficient of variation.

Reliability is an important engineering requirement for consistently delivering acceptable product performance through time. It also affects the scheduling for preventive maintenance. Reliability usually degrades with time increasing therefore, the lifecycle cost due to more frequent failures which result in increased warranty costs, costly repairs and loss of market share. In a lifecycle cost based design, we must account for product quality and preventive maintenance using time-dependent reliability. Quality is a measure of our confidence that the product conforms to specifications as it leaves the factory. For a repairable system, preventive maintenance is scheduled to avoid failures, unnecessary production loss and safety violations. This article proposes a methodology to obtain the optimal scheduling for preventive maintenance using time-dependent reliability principles.

In this article we present an approach to identify the system topology using simulation for reliability calculations. The system topology provides how all components in a system are functionally connected. Most reliability engineering literature assumes that either the system topology is known and therefore all failure modes can be deduced or if the system topology is not known we are only interested in identifying the dominant failure modes. The authors contend that we should try to extract as much information about the system topology from failure or success information of a system as possible. This will not only identify the dominant failure modes but will also provide an understanding of how the components are functionally connected, allowing for more complicated analyses, if needed. We use an evolutionary approach where system topologies are generated at random and then tested against failure or success data. The topologies evolve based on how consistent they are with test data.

Design optimization often relies on computational models, which are subjected to a validation process to ensure their accuracy. Because validation of computer models in the entire design space can be costly, a recent approach was proposed where design optimization and model validation were concurrently performed using a sequential approach with both fixed and variable-size local domains. The variable-size approach used parametric distributions such as Gaussian to quantify the variability in test data and model predictions, and a maximum likelihood estimation to calibrate the prediction model. Also, a parametric bootstrap method was used to size each local domain. In this article, we generalize the variable-size approach, by not assuming any distribution such as Gaussian. A nonparametric bootstrap methodology is instead used to size the local domains. We expect its generality to be useful in applications where distributional assumptions are difficult to verify, or not met at all.

Multi-attribute decision making and multi-objective optimization complement each other. Often, while making design decisions involving multiple attributes, a Pareto front is generated using a multi-objective optimizer. The end user then chooses the optimal design from the Pareto front based on his/her preferences. This seemingly simple methodology requires sufficient modification if uncertainty is present. We explore two kinds of uncertainties in this paper: uncertainty in the decision variables which we call inherent design problem (IDP) uncertainty and that in knowledge of the preferences of the decision maker which we refer to as preference assessment (PA) uncertainty. From a purely utility theory perspective a rational decision maker maximizes his or her expected multi attribute utility.

Styrene-Butadiene Rubber (SBR), a copolymer of butadiene and styrene, is widely used in the automotive industry due to its high durability and resistance to abrasion, oils and oxidation. Some of the common applications include tires, vibration isolators, and gaskets, among others. This paper characterizes the dynamic behavior of SBR and discusses the suitability of a visco-elastic model of elastomers, known as the Kelvin model, from a mathematical and physical point of view. An optimization algorithm is used to estimate the parameters of the Kelvin model. The resulting model was shown to produce reasonable approximations of measured dynamic stiffness. The model was also used to calculate the self heating of the elastomer due to energy dissipation by the viscous damping components in the model. Developing such a predictive capability is essential in understanding the dynamic behavior of elastomers considering that their dynamic stiffness can in general depend on temperature.

Monte Carlo simulation is a popular tool for reliability assessment because of its robustness and ease of implementation. A major concern with this method is its computational cost; standard Monte Carlo simulation requires quadrupling the number of replications for halving the standard deviation of the estimated failure probability. Efforts to increase efficiency focus on intelligent sampling procedures and methods for efficient calculation of the performance function of a system. This paper proposes a new method to manage cost that views design as a decision among alternatives with uncertain reliabilities. Information from a simulation has value only if it enables the designer to make a better choice among the alternative options. Consequently, the value of information from the simulation is equal to the gain from using this information to improve the decision. A designer can determine the number of replications that are worth performing by using the method.

Reaching a system level reliability target is an inverse problem. Component level reliabilities are determined for a required system level reliability. Because this inverse problem does not have a unique solution, one approach is to tradeoff system reliability with cost and to allow the designer to select a design with a target system reliability, using his/her preferences. In this case, the component reliabilities are readily available from the calculation of the reliability-cost tradeoff. To arrive at the set of solutions to be traded off, one encounters two problems. First, the system reliability calculation is based on repeated system simulations where each system state, indicating which components work and which have failed, is tested to determine if it causes system failure, and second, the task of eliciting and encoding the decision maker's preferences is extremely difficult because of uncertainty in modeling the decision maker's preferences.

Response Surface Model (RSM)-based optimization is widely used in engineering design. The major strength of RSM-based optimization is its short computational time. The expensive real simulation models are replaced with fast surrogate models. However, this method may have some difficulties to reach the full potential due to the errors between RSM and the real simulations. RSM's accuracy is limited by the insufficient number of Design of Experiments (DOE) points and the inherent randomness of DOE. With recent developments in advanced optimization algorithms and High Performance Computing (HPC) capability, Direct Multidisciplinary Design Optimization (DMDO) receives more attention as a promising future optimization strategy. Advanced optimization algorithm reduces the number of function evaluations, and HPC cut down the computational turnaround time of function evaluations through fully utilizing parallel computation.

As the use of electronic devices in automobiles increases, the reliability of such devices is becoming increasingly important. One possible failure is due to leakage resulted from imperfect hermetical seal in mircochips and microelectronic packages. This paper presents an optical technique referred to as shearography for rapid evaluation of hermetics seals. The proposed process of leaking testing is very fast and practical.

The reliability theory of repairable systems is vastly different from that of non-repairable systems. The authors have recently proposed a ‘decision-based’ framework to design and maintain repairable systems for optimal performance and reliability using a set of metrics such as minimum failure free period, number of failures in planning horizon (lifecycle), and cost. The optimal solution includes the initial design, the system maintenance throughout the planning horizon, and the protocol to operate the system. In this work, we extend this idea by incorporating flexibility and demonstrate our approach using a smart charging electric microgrid architecture. The flexibility is realized by allowing the architecture to change with time. Our approach “learns” the working characteristics of the microgrid. We use actual load and supply data over a short time to quantify the load and supply random processes and also establish the correlation between them.

Reliability is an important engineering requirement for consistently delivering acceptable product performance through time. As time progresses, the product may fail due to time-dependent operating conditions and material properties, component degradation, etc. The reliability degradation with time may increase the lifecycle cost due to potential warranty costs, repairs and loss of market share. Reliability is the probability that the system will perform its intended function successfully for a specified time interval. In this work, we consider the first-passage reliability which accounts for the first time failure of non-repairable systems. Methods are available in the literature, which provide an upper bound to the true reliability which may overestimate the true value considerably. This paper proposes a methodology to calculate the cumulative probability of failure (probability of first passage or upcrossing) of a dynamic system, driven by an ergodic input random process.