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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, we have previously proposed an approach where design optimization and model validation, are concurrently performed using a sequential approach with variable-size local domains. We used test data and statistical bootstrap methods to size each local domain where the prediction model is considered validated and where design optimization is performed. The method proceeds iteratively until the optimum design is obtained. This method however, requires test data to be available in each local domain along the optimization path. In this paper, we refine our methodology by using polynomial regression to predict the size and shape of a local domain at some steps along the optimization process without using test data.

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.

Fatigue life estimation, reliability and durability are important in acquisition, maintenance and operation of vehicle systems. Fatigue life is random because of the stochastic load, the inherent variability of material properties, and the uncertainty in the definition of the S-N curve. The commonly used fatigue life estimation methods calculate the mean (not the distribution) of fatigue life under Gaussian loads using the potentially restrictive narrow-band assumption. In this paper, a general methodology is presented to calculate the statistics of fatigue life for a linear vibratory system under stationary, non-Gaussian loads considering the effects of skewness and kurtosis. The input loads are first characterized using their first four moments (mean, standard deviation, skewness and kurtosis) and a correlation structure equivalent to a given Power Spectral Density (PSD).

We present an Accelerated Life Testing (ALT) methodology along with a design for fatigue approach, using Gaussian or non-Gaussian excitations. The accuracy of fatigue life prediction at nominal loading conditions is affected by model and material uncertainty. This uncertainty is reduced by performing tests at a higher loading level, resulting in a reduction in test duration. Based on the data obtained from experiments, we formulate an optimization problem to calculate the Maximum Likelihood Estimator (MLE) values of the uncertain model parameters. In our proposed ALT method, we lift all the assumptions on the type of life distribution or the stress-life relationship and we use Saddlepoint Approximation (SPA) method to calculate the fatigue life Probability Density Functions (PDFs).

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.

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.

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.

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.

An experimental investigation of non-intrusive combustion sensing was performed using a tri-axial accelerometer mounted to the engine block of a small-bore high-speed 4-cylinder compression-ignition direct-injection (CIDI) engine. This study investigates potential techniques to extract combustion features from accelerometer signals to be used for cycle-to-cycle engine control. Selection of accelerometer location and vibration axis were performed by analyzing vibration signals for three different locations along the block for all three of the accelerometer axes. A magnitude squared coherence (MSC) statistical analysis was used to select the best location and axis. Based on previous work from the literature, the vibration signal filtering was optimized, and the filtered vibration signals were analyzed. It was found that the vibration signals correlate well with the second derivative of pressure during the initial stages of combustion.

Finite element analysis is a standard tool for deterministic or probabilistic design optimization of dynamic systems. The optimization process requires repeated eigenvalue analyses which can be computationally expensive. Several reanalysis techniques have been proposed to reduce the computational cost including Parametric Reduced Order Modeling (PROM), Combined Approximations (CA), and the Modified Combined Approximations (MCA) method. Although the cost of reanalysis is substantially reduced, it can still be high for models with a large number of degrees of freedom and a large number of design variables. Reanalysis methods use a basis composed of eigenvectors from both the baseline and the modified designs which are in general linearly dependent. To eliminate the linear dependency and improve accuracy, Gram Schmidt orthonormalization is employed which is costly itself.

This study uses full drive cycle simulation to compare the fuel consumption of a vehicle with a turbocharged (TC) engine to the same vehicle with an alternative boosting technology, namely, a hybrid supercharger, in which a planetary gear mechanism governs the power split to the supercharger between the crankshaft and a 48 V 5 kW electric motor. Conventional mechanically driven superchargers or electric superchargers have been proposed to improve the dynamic response of boosted engines, but their projected fuel efficiency benefit depends heavily on the engine transient response and driver/cycle aggressiveness. The fuel consumption benefits depend on the closed-loop engine responsiveness, the control tuning, and the torque reserve needed for each technology. To perform drive cycle analyses, a control strategy is designed that minimizes the boost reserve and employs high rates of combustion dilution via exhaust gas recirculation (EGR).

This paper numerically investigates the performance implications of the use of an electric supercharger in a heavy-duty DD13 diesel engine. Two electric supercharger configurations are examined. The first is a high-pressure (HP) configuration where the supercharger is placed after the turbocharger compressor, while the second is a low-pressure (LP) one, where the supercharger is placed before the turbocharger compressor. At steady state, high engine speed operation, the airflows of the HP and LP implementations can vary by as much as 20%. For transient operation under the Federal Test Procedure (FTP) heavy duty diesel (HDD) engine transient drive cycle, supercharging is required only at very low engine speeds to improve airflow and torque. Under the low speed transient conditions, both the LP and HP configurations show similar increases in torque response so that there are 44 fewer engine cycles at the smoke-limit relative to the baseline turbocharged engine.

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.

Medium trucks constitute a large market segment of the commercial transportation sector, and are also used widely for military tactical operations. Recent technological advances in hybrid powertrains and fuel cell auxiliary power units have enabled design alternatives that can improve fuel economy and reduce emissions dramatically. However, deterministic design optimization of these configurations may yield designs that are optimal with respect to performance but raise concerns regarding the reliability of achieving that performance over lifetime. In this article we identify and quantify uncertainties due to modeling approximations or incomplete information. We then model their propagation using Monte Carlo simulation and perform sensitivity analysis to isolate statistically significant uncertainties. Finally, we formulate and solve a series of reliability-based optimization problems and quantify tradeoffs between optimality and reliability.

Low Pressure (LP) Exhaust Gas Recirculation (EGR) promises fuel economy benefits at high loads in turbocharged SI engines as it allows better combustion phasing and reduces the need for fuel enrichment. Precise estimation and control of in-cylinder EGR concentration is crucial to avoiding misfire. Unfortunately, EGR flow rate estimation using an orifice model based on the EGR valve ΔP measurement can be challenging given pressure pulsations, flow reversal and the inherently low pressure differentials across the EGR valve. Using a GT-Power model of a 1.6 L GDI turbocharged engine with LP-EGR, this study investigates the effects of the ΔP sensor gauge-line lengths and measurement noise on LP-EGR estimation accuracy. Gauge-lines can be necessary to protect the ΔP sensor from high exhaust temperatures, but unfortunately can produce acoustic resonance and distort the ΔP signal measured by the sensor.

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.

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.

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.

Low voltage hybridization (<60 V) supports engine start/stop, regenerative braking, and constrained torque assist/regeneration at a low cost. This work studies the potential benefits of a novel hybrid system, called a power split supercharger (PSS). A 9 kW motor is shared between boosting the engine or providing hybrid functionalities, allowing it to couple with a small engine and still support good acceleration. However, the PSS operation is limited to only one of the parallel hybrid or boosting modes at each time instance. In this work an equivalent consumption minimization strategy (ECMS) is developed to select the PSS mode and the motor torque during hybrid mode. The PSS operation is simulated over standard EPA drive cycles with an engine mean value model that captures detailed air path and PSS dynamics.

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.