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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.

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.

Global surrogate modeling aims to build surrogate model with high accuracy in the whole design domain. A major challenge to achieve this objective is how to reduce the number of function evaluations to the original computer simulation model. To date, the most widely used approach for global surrogate modeling is the adaptive surrogate modeling method. It starts with an initial surrogate model, which is then refined adaptively using the mean square error (MSE) or maximizing the minimum distance criteria. It is observed that current methods may not be able to effectively construct a global surrogate model when the underlying black box function is highly nonlinear in only certain regions. A new surrogate modeling method which can allocate more training points in regions with high nonlinearity is needed to overcome this challenge. This article proposes an efficient global surrogate modeling method based on a multi-layer sampling scheme.

Optimizing the trade-off between reliability and cost of operating a microgrid, including vehicles as both loads and sources, can be a challenge. Optimal energy management is crucial to develop strategies to improve the efficiency and reliability of microgrids, as well as new communication networks to support optimal and reliable operation. Prior approaches modeled the grid using MATLAB, but did not include the detailed physics of loads and sources, and therefore missed the transient effects that are present in real-time operation of a microgrid. This article discusses the implementation of a physics-based detailed microgrid model including a diesel generator, wind turbine, photovoltaic array, and utility. All elements are modeled as sources in Simulink. Various loads are also implemented including an asynchronous motor. We show how a central control algorithm optimizes the microgrid by trying to maximize reliability while reducing operational cost.

Computer-aided engineering (CAE) is an important tool routinely used to simulate complex engineering systems. Virtual simulations enhance engineering insight into prospective designs and potential design issues and can limit the need for expensive engineering prototypes. For complex engineering systems, however, the effectiveness of virtual simulations is often hindered by excessive computational cost. To minimize the cost of running expensive computer simulations, approximate models of the original model (often called surrogate models or metamodels) can provide sufficient accuracy at a lower computing overhead compared to repeated runs of a full simulation. Metamodel accuracy improves if constructed using space-filling designs of experiments (DOEs). The latter provide a collection of sample points in the design space preferably covering the entire space.

Weight reduction is very important in automotive design because of stringent demand on fuel economy. Structural optimization of dynamic systems using finite element (FE) analysis plays an important role in reducing weight while simultaneously delivering a product that meets all functional requirements for durability, crash and NVH. With advancing computer technology, the demand for solving large FE models has grown. Optimization is however costly due to repeated full-order analyses. Reanalysis methods can be used in structural vibrations to reduce the analysis cost from repeated eigenvalue analyses for both deterministic and probabilistic problems. Several reanalysis techniques have been introduced over the years including Parametric Reduced Order Modeling (PROM), Combined Approximations (CA) and the Epsilon algorithm, among others.

To improve fuel economy, there is a trend in automotive industry to use light weight, high strength materials. Automotive body structures are composed of several panels which must be downsized to reduce weight. Because this affects NVH (Noise, Vibration and Harshness) performance, engineers are challenged to recover the lost panel stiffness from down-gaging in order to improve the structure borne noise transmitted through the lightweight panels in the frequency range of 100-300 Hz where most of the booming and low medium frequency noise occurs. The loss in performance can be recovered by optimized panel geometry using beading or damping treatment. Topography optimization is a special class of shape optimization for changing sheet metal shapes by introducing beads. A large number of design variables can be handled and the process is easy to setup in commercial codes. However, optimization methods are computationally intensive because of repeated full-order analyses.

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.

Importance Sampling is a popular method for reliability assessment. Although it is significantly more efficient than standard Monte Carlo simulation if a suitable sampling distribution is used, in many design problems it is too expensive. The authors have previously proposed a method to manage the computational cost in standard Monte Carlo simulation that views design as a choice among alternatives with uncertain reliabilities. Information from simulation has value only if it helps the designer make a better choice among the alternatives. This paper extends their method to Importance Sampling. First, the designer estimates the prior probability density functions of the reliabilities of the alternative designs and calculates the expected utility of the choice of the best design. Subsequently, the designer estimates the likelihood function of the probability of failure by performing an initial simulation with Importance Sampling.

Warranty forecasting of repairable systems is very important for manufacturers of mass produced systems. It is desired to predict the Expected Number of Failures (ENF) after a censoring time using collected failure data before the censoring time. Moreover, systems may be produced with a defective component resulting in extensive warranty costs even after the defective component is detected and replaced with a new design. In this paper, we present a forecasting method to predict the ENF of a repairable system using observed data which is used to calibrate a Generalized Renewal Processes (GRP) model. Manufacturing of products may exhibit different production patterns with different failure statistics through time. For example, vehicles produced in different months may have different failure intensities because of supply chain differences or different skills of production workers, for example.

This paper presents a methodology to evaluate and optimize discrete event systems, such as an assembly line or a call center. First, the methodology estimates the performance of a system for a single probability distribution of the inputs. Probabilistic Reanalysis (PRRA) uses this information to evaluate the effect of changes in the system configuration on its performance. PRRA is integrated with a program to optimize the system. The proposed methodology is dramatically more efficient than one requiring a new Monte Carlo simulation each time we change the system. We demonstrate the approach on a drilling center and an electronic parts factory.

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.

The availability of computational resources has enabled an increased utilization of Design of Experiments (DoE) and metamodeling (response surface generation) for large-scale optimization problems. Despite algorithmic advances however, the analysis of systems such as water jackets of an automotive engine, can be computationally demanding in part due to the required accuracy of metamodels. Because the metamodels may have many inputs, their accuracy depends on the number of training points and how well they cover the entire design (input) space. For this reason, the space-filling properties of the DoE are very important. This paper utilizes a new group-based DoE algorithm with space-filling groups of points to construct a metamodel. Points are added sequentially so that the space-filling properties of the entire group of points is preserved. The addition of points is continuous until a specified metamodel accuracy is met.