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This paper proposes a novel probabilistic approach for multidisciplinary design optimization (MDO) under uncertainty, especially for systems with feedback coupled analyses with multiple coupling variables. The proposed approach consists of four components: multidisciplinary analysis, Bayesian network, copula-based sampling, and design optimization. The Bayesian network represents the joint distribution of multiple variables through marginal distributions and conditional probabilities, and updates the distributions based on new data. In this methodology, the Bayesian network is pursued in two directions: (1) probabilistic surrogate modeling to estimate the output uncertainty given values of the design variables, and (2) probabilistic multidisciplinary analysis (MDA) to infer the distributions of the coupling and output variables that satisfy interdisciplinary compatibility conditions.

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.

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.

Increasingly Automotive OEMs and their suppliers find themselves spread across different continents. This in turn gives rise to knowledge, physical assets and key decision makers also being spread across the globe. This poses significant challenges for the companies to effectively manage and keep track of their resources. It is also challenging to work with teams spread across globe and for the team to arrive at intelligent decisions quickly and efficiently. In last few years we have spent significant amount of person hours trying to create systems and Software to help manage Workflow and Assets spread across diverse Geographic and Political areas.

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.

This paper discusses the treatment of uncertainties corresponding to relatively few samples of random-variable quantities. The importance of this topic extends beyond experimental data uncertainty to situations involving uncertainty in model calibration, validation, and prediction. With very sparse samples it is not practical to have a goal of accurately estimating the underlying variability distribution (probability density function, PDF). Rather, a pragmatic goal is that the uncertainty representation should be conservative so as to bound a desired percentage of the actual PDF, say 95% included probability, with reasonable reliability. A second, opposing objective is that the representation not be overly conservative; that it minimally over-estimate the random-variable range corresponding to the desired percentage of the actual PDF. The presence of the two opposing objectives makes the sparse-data uncertainty representation problem an interesting and difficult one.

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.

This research assesses the integration of different levels of electric vehicles (EVs) in the distribution system and observes its impacts on environmental emissions and power system operational costs. EVs can contribute to reducing the environmental emission from two different aspects. First, by replacing the traditional combustion engine cars with EVs for providing clean and environment friendly transportation and second, by integrating EVs in the distribution system through the V2G program, by providing power to the utility during peak hours and reducing the emission created by hydrocarbon dependent generators. The PG&E 69-bus distribution system (DS) is used to simulate the integration of EVs and to perform energy management to assess the operational costs and emissions. The uncertainty of driving patterns of EVs are considered in this research to get more accurate results.

Tribological performance of tungsten sulfide (WS2) nanoparticles, microparticles and mixtures of the two were investigated. Previous research showed that friction and wear reduction can be achieved with nanoparticles. Often these improvements were mutually exclusive, or achieved under special conditions (high temperature, high vacuum) or with hard-to-synthesize inorganic-fullerene WS2 nanoparticles. This study aimed at investigating the friction and wear reduction of WS2 of nanoparticles and microparticles that can be synthesized in bulk and/or purchased off the shelf. Mixtures of WS2 nanoparticles and microparticles were also tested to see if a combination of reduced friction and wear would be achieved. The effect of the mixing process on the morphology of the particles was also reported. The microparticles showed the largest reduction in coefficient of friction while the nanoparticles showed the largest wear scar area reduction.

One-dimensional (1D) engine simulation packages are limited in modeling flows through an adverse pressure gradient where boundary layer separation is more likely to occur, as in the case of the diffuser part of the restrictor. The restrictor modeling difficulty usually manifests itself as an engine model that consumes a lot of effort (both computational and from the user) in the modeling of the restrictor. The approach sought in this work was to provide a flow vs pressure drop dependency to the code such that it does not consume too much effort in the analysis of the restrictor. This approach is similar to that used for the valve flow, where a look up table is typically provided for determining the flow. Experimentally determined flow measurements on a thin-plate orifice, a short restrictor and a long restrictor are presented and discussed. The developed model gave excellent results in an acyclic steady-state simulation and is being integrated in the full engine model.

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.

In this paper, we develop a methodology to enable the isolation of the heat release contribution of knocking combustion from flame-propagation combustion. We first address the empirical modeling of individual non-autoigniting combustion history using the Wiebe function, and subsequently apply this methodology to investigate the effect of autoignition on the heat release history of knocking cycles in a spark ignition (SI) engine. We start by re-visiting the Wiebe function, which is widely used to model empirically mass burned histories in SI engines. We propose a method to tune the parameters of the Wiebe function on a cycle-by-cycle basis, i.e., generating a different Wiebe to suitably fit the heat release history of each cycle. Using non-autoigniting cycles, we show that the Wiebe function can reliably simulate the heat release history of an entire cycle, if only data from the first portion of the cycle is used in the tuning process.

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.

The paper studies the distributions of residual stresses in auto components after induction hardening. Three prototype parts are analyzed in this paper. Firstly, the temperature fields of the analyzed parts are quantitatively simulated during quenching by simulating surface heating to the austenitization temperature of the material. Secondly, the formation and states of the residual stresses are predicted. Therefore the distribution of residual stress is simulated and shows compressive stresses on the surface of components so that the strength can be improved. The simulated results by computer are compared with experimental results. The good comparison indicates that the results obtained by the FEA analysis are reliable. Thus, it can be concluded that the FEA (Finite element analysis) program is effectively developed to simulate heating and quenching processes and residual stresses distribution.

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.

This paper develops a reliability-based methodology for the evaluation of stiffness degradation of spot-welded joints under high mileage. A global-local finite element analysis is used, with the loads on the detailed three-dimensional joint model coming from finite element analysis of the entire car model with proving ground loads. Probabilistic fatigue crack propagation analysis is developed for multi-axial variable amplitude loading history on the joint. Multiple spot welds contribute to the stiffness of the joint. Hence the problem is addressed through system reliability techniques. The effect of spot-weld separation on joint stiffness, and on global vehicle stiffness, is incorporated. This results in the computation of the statistics of vehicle stiffness degradation with mileage.

Reliability and resiliency (R&R) definitions differ depending on the system under consideration. Generally, each engineering sector defines relevant R&R metrics pertinent to their system. While this can impede cross-disciplinary engineering projects as well as research, it is a necessary strategy to capture all the relevant system characteristics. This paper highlights the difficulties associated with defining performance of such systems while using smart microgrids as an example. Further, it develops metrics and definitions that are useful in assessing their performance, based on utility theory. A microgrid must not only anticipate load conditions but also tolerate partial failures and remain optimally operating. Many of these failures happen infrequently but unexpectedly and therefore are hard to plan for. We discuss real life failure scenarios and show how the proposed definitions and metrics are beneficial.

Frames are important structures found in many transportation applications such as automotive bodies and train cars. They are also widely employed in buildings, bridges, and other load bearing designs. When a frame is carrying multiple loads, it can potentially risk a catastrophic buckling failure. The loads on the frame may be non-proportional in that one force stays constant while the other is increased until buckling occurs. In this study the buckling problem is formulated as a constrained eigenvalue problem (CEVP). As opposed to other CEVP in which the eigenvectors are forced to comply with a number of the constraints, the eigenvalues in the current CEVP are subject to some equality constraints. A numerical algorithm for solving the constrained eigenvalue problem is presented. The algorithm is a simple trapping scheme in which the computation starts with an initial guess and a window containing the potential target for the eigenvalue is identified.

Existing methods for design optimization under uncertainty assume that a high level of information is available, typically in the form of data. In reality, however, insufficient data prevents correct inference of probability distributions, membership functions, or interval ranges. In this article we use an engine design example to show that optimal design decisions and reliability estimations depend strongly on uncertainty characterization. We contrast the reliability-based optimal designs to the ones obtained using worst-case optimization, and ask the question of how to obtain non-conservative designs with incomplete uncertainty information. We propose an answer to this question through the use of Bayesian statistics. We estimate the truck's engine reliability based only on available samples, and demonstrate that the accuracy of our estimates increases as more samples become available.