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Deep charge and discharge cycling of 24 Volt battery strings composed of two 12 Volt VRLA batteries wired in series affects reliability and life expectancy. This is a matter of interest in vehicle power source applications. These cycles include those specific operational cases requiring the delivery of the full storage capacity during discharge. The concern here is related to applications where batteries serve as a primary power source and the energy content is an issue. It is a common practice for deep cycling a 24 volt battery string to simply add the specified limit voltages during charge and discharge for the individual 12 Volt batteries. In reality, the 12 Volt batteries have an inherent capacity variability and are not identical in their performance characteristics. The actual voltages of the individual 12 Volt batteries are not identical.

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.

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.

An objective evaluation of ground vehicle performance is a challenging task. This is further exacerbated by the increasing level of autonomy, dynamically changing the roles and capabilities of these vehicles. In the context of decision making involving these vehicles, as the capabilities of the vehicles improve, there is a concurrent change in the preferences of the decision makers operating the vehicles that must be accounted for. Decision based methods are a natural choice when multiple conflicting attributes are present, however, most of the literature focuses on static preferences. In this paper, we provide a sequential Bayesian framework to accommodate time varying preferences. The utility function is considered a stochastic function with the shape parameters themselves being random variables. In the proposed approach, initially the shape parameters model either uncertain preferences or variation in the preferences because of the presence of multiple decision makers.

It is challenging to perform probabilistic analysis and design of large-scale structures because probabilistic analysis 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 large numbers of design variables that vary in a wide range. The probabilistic re-analysis method calculates very efficiently the system reliability for many probability distributions of the design variables by performing a single Monte Carlo simulation.

A Reliability-Based Design Optimization (RBDO) method for multiple failure regions is presented. The method uses a Probabilistic Re-Analysis (PRRA) approach in conjunction with an approximate global metamodel with local refinements. The latter serves as an indicator to determine the failure and safe regions. PRRA calculates very efficiently the system reliability of a design by performing a single Monte Carlo (MC) simulation. Although PRRA is based on MC simulation, it calculates “smooth” sensitivity derivatives, allowing therefore, the use of a gradient-based optimizer. An “accurate-on-demand” metamodel is used in the PRRA that allows us to handle problems with multiple disjoint failure regions and potentially multiple most-probable points (MPP). The multiple failure regions are identified by using a clustering technique. A maximin “space-filling” sampling technique is used to construct the metamodel. A vibration absorber example highlights the potential of the proposed method.

Early in the engineering design cycle, it is difficult to quantify product reliability due to insufficient data or information to model uncertainties. Probability theory can not be therefore, used. Design decisions are usually based on fuzzy information which is imprecise and incomplete. Various design methods such as Possibility-Based Design Optimization (PBDO) and Evidence-Based Design Optimization (EBDO) have been developed to systematically treat design with non-probabilistic uncertainties. In practical engineering applications, information regarding the uncertain variables and parameters may exist in the form of sample points, and uncertainties with sufficient and insufficient information may exist simultaneously. Most of the existing optimal design methods under uncertainty can not handle this form of incomplete information. They have to either discard some valuable information or postulate the existence of additional information.

An approach for Probabilistic Reanalysis (PRA) of a system is presented. PRA calculates very efficiently the system reliability or the average value of an attribute of a design for many probability distributions of the input variables, by performing a single Monte Carlo simulation. In addition, PRA calculates the sensitivity derivatives of the reliability to the parameters of the probability distributions. The approach is useful for analysis problems where reliability bounds need to be calculated because the probability distribution of the input variables is uncertain or for design problems where the design variables are random. The accuracy and efficiency of PRA is demonstrated on vibration analysis of a car and on system reliability-based optimization (RBDO) of an internal combustion engine.

An efficient reliability estimation method is presented for engineering systems with multiple failure regions and potentially multiple most probable points. The method can handle implicit, nonlinear limit-state functions, with correlated or non-correlated random variables, which can be described by any probabilistic distribution. It uses a combination of approximate or “accurate-on-demand,” global and local metamodels which serve as indicators to determine the failure and safe regions. Samples close to limit states define transition regions between safe and failure domains. A clustering technique identifies all transition regions which can be in general disjoint, and local metamodels of the actual limit states are generated for each transition region.

In today's light-weight vehicles, the strength of spot welds plays an important role in overall product integrity, reliability and customer satisfaction. Naturally, there is a need for a quick and reliable technique to inspect the quality of the welds. In the past, the primary quality control tests for detecting weld defects are the destructive chisel test and peel test [1]. The non-destructive evaluation (NDE) method currently used in industry is based on ultrasonic inspection [2, 3, 4]. The technique is not always successful in evaluating the nugget size, nor is it effective in detecting the so-called “cold” or “stick” welds. Therefore, it is necessary to develop a precise and reliable noncontact NDE method for spot welds. There have been numerous studies in predicting the weld nugget size by considering the spot-weld process [5, 6].

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.

Our recent work has shown that representation of systems using a reliability block diagram can be used as a decision making tool. In decision making, we called these block diagrams decision topologies. In this paper, we generalize the results and show that decision topologies can be used to make many engineering decisions and can in fact replace decision analysis for most decisions. We also provide a meta-proof that the proposed method using decision topologies is entirely consistent with decision analysis at the limit. The main advantages of the method are that (1) it provides a visual representation of a decision situation, (2) it can easily model tradeoffs, (3) it can incorporate binary attributes, (4) it can model preferences with limited information, and (5) it can be used in a low-fidelity sense to quickly make a decision.

In this paper, the development of random vibration testing schedules for durability design verification of engine mounted products is presented, based on the equivalent fatigue damage concept and the 95th-percentile customer engine usage data for 150,000 miles. Development of the 95th-percentile customer usage profile is first discussed. Following that, the field engine excitation and engine duty cycle definition is introduced. By using a simplified transfer function of a single degree-of-freedom (SDOF) system subjected to a base excitation, the response acceleration and stress PSDs are related to the input excitation in PSD, which is the equivalent fatigue damage concept. Also, the narrow-band fatigue damage spectrum (FDS) is calculated in terms of the input excitation PSD based on the Miner linear damage rule, the Rayleigh statistical distribution for stress amplitude, a material's S-N curve, and the Miles approximate solution.

A reliability analysis method is presented for time-dependent systems under uncertainty. A level-crossing problem is considered where the system fails if its maximum response exceeds a specified threshold. The proposed method uses a double-loop optimization algorithm. The inner loop calculates the maximum response in time for a given set of random variables, and transforms a time-dependent problem into a time-independent one. A time integration method is used to calculate the response at discrete times. For each sample function of the response random process, the maximum response is found using a global-local search method consisting of a genetic algorithm (GA), and a gradient-based optimizer. This dynamic response usually exhibits multiple peaks and crosses the allowable response level to form a set of complex limit states, which lead to multiple most probable points (MPPs).

Reliability-based design optimization accounts for variation. However, it assumes that statistical information is available in the form of fully defined probabilistic distributions. This is not true for a variety of engineering problems where uncertainty is usually given in terms of interval ranges. In this case, interval analysis or possibility theory can be used instead of probability theory. This paper shows how possibility theory can be used in design and presents a computationally efficient sequential optimization algorithm. The algorithm handles problems with only uncertain or a combination of random and uncertain design variables and parameters. It consists of a sequence of cycles composed of a deterministic design optimization followed by a set of worst-case reliability evaluation loops. A crank-slider mechanism example demonstrates the accuracy and efficiency of the proposed sequential algorithm.

High-fidelity finite element (FE) tire-snow interaction models have the advantage of better understanding the physics of the tire-snow system. They can be used to develop semi-analytical models for vehicle design as well as to design and interpret field test results. For off-terrain conditions, there is a high level of uncertainties inherent in the system. The FE models are computationally intensive even when uncertainties of the system are not taken into account. On the other hand, field tests of tire-snow interaction are very costly. In this paper, dynamic metamodels are established to interpret interaction forces from FE simulation and to predict those forces by using part of the FE data as training data and part as validation data. Two metamodels are built based upon the Krieging principle: one has principal component analysis (PCA) taken into account and the other does not.

In reliability design, often, there is scarce data for constructing probabilistic models. It is particularly challenging to model uncertainty in variables when the type of their probability distribution is unknown. Moreover, it is expensive to estimate the upper and lower bounds of the reliability of a system involving such variables. A method for modeling uncertainty by using Polynomial Chaos Expansion is presented. The method requires specifying bounds for statistical summaries such as the first four moments and credible intervals. A constrained optimization problem, in which decision variables are the coefficients of the Polynomial Chaos Expansion approximation, is formulated and solved in order to estimate the minimum and maximum values of a system’s reliability. This problem is solved efficiently by employing a probabilistic re-analysis approach to approximate the system reliability as a function of the moments of the random variables.

An accurate and efficient Monte Carlo simulation (MCS) method is developed in this paper for limit state-based reliability analysis, especially at system levels, by using a response surface approximation of the failure indicator function. The Moving Least Squares (MLS) method is used to construct the response surface of the indicator function, along with an Optimum Symmetric Latin Hypercube (OSLH) as the sampling technique. Similar to MCS, the proposed method can easily handle implicit, highly nonlinear limit-state functions, with variables of any statistical distributions and correlations. However, the efficiency of MCS can be greatly improved. The method appears to be particularly efficient for multiple limit state and multiple design point problem. A mathematical example and a practical example are used to highlight the superior accuracy and efficiency of the proposed method over traditional reliability methods.

An efficient simulation-based method is proposed for the reliability analysis of a vehicle body-door subsystem with respect to an important quality issue -- wind noise. A nonlinear seal model is constructed for the automotive wind noise problem and the limit state function is evaluated using finite element analysis. Existing analytical as well as simulation-based methods are used to solve this problem. A multi-modal adaptive importance sampling method is then developed for reliability analysis at system level. It is demonstrated through this industrial application problem that the multi-modal adaptive importance sampling method is superior to existing methods in terms of efficiency and accuracy. The method can easily handle implicit limit-state functions, with variables of any statistical distributions.

This paper proposes an approach for optimal design of multilevel systems under uncertainty. The approach utilizes the stochastic extension of the analytical target cascading formulation. The reliability of satisfying the probabilistic constraints is computed by means of the most probable point method using the hybrid mean value algorithm. A linearization technique is employed for estimating the propagation of uncertainties throughout the problem hierarchy. The proposed methodology is applied to a piston-ring/cylinder-liner engine subassembly design problem. Specifically, we assess the impact of variations in manufacturing-related properties such as surface roughness on engine attributes such as brake-specific fuel consumption. Results are compared to the ones obtained using Monte Carlo simulation.