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Technical Paper

Axial Fatigue Strength Metamodels for Ferrous Powder Metals

2018-04-03
2018-01-1395
Two metamodels are presented to describe 107 cycles axial fatigue strength of four ferrous powder metal material series: sintered and heat-treated iron-carbon steel, iron-copper and copper steel, iron-nickel and nickel steel and prealloyed steel. The materials are defined at ranges of carbon content and densities using the broad data available in MPIF Standard 35 for powder metal structural parts. The first metamodel evaluates 107 cycles axial fatigue strength as a function of density and ultimate strength and the second metamodel as a function of density and hardness. For all studied materials, both metamodels are found to have a good correlation between the distributions of the calculated and measured 107 cycles axial fatigue strength with a Pearson’s correlation coefficient of 0.97.
Technical Paper

Optimal Water Jacket Flow Distribution using a New Group-Based Space-Filling Design of Experiments

2018-04-03
2018-01-1017
The advancement of computational resources has enabled the increased utilization of Design of Experiments (DOE) in large scale optimization problems. Despite algorithmic advances however, analysis of systems such as water jackets of an automotive engine, can be computationally demanding in part due to the required accuracy of metamodels (response surfaces). The metamodels may have many design and response variables, in which case their accuracy depends on the space-filling properties of the DOE. This paper utilizes a unique group-based DOE algorithm with space-filling groups of points to construct a metamodel. Points are added sequentially such that the space-filling properties of the entire group of points is preserved. The addition of points continuous until a specified metamodel accuracy is met.
Technical Paper

Reliability and Cost Trade-off Analysis of a Microgrid

2018-04-03
2018-01-0619
The optimal trade-off between reliability and cost of a microgrid, including vehicles as both loads and sources, can be a challenge. Prior approaches have modeled the microgrid using MATLAB, but did not include the detailed physics of loads and sources, and therefore missed the transient effects which are important in representing the real time behavior of a microgrid. This paper discusses the physics implementation of a detailed microgrid model including a diesel generator, wind turbine, photovoltaic array and utility as sources, in Simulink. Various loads are also implemented including an asynchronous motor. A vehicle is connected to the grid and is represented as a battery. A central control algorithm optimizes the microgrid by trying to maximize reliability while reducing operational cost.
Technical Paper

Efficient Global Surrogate Modeling Based on Multi-Layer Sampling

2018-04-03
2018-01-0616
Global surrogate modeling aims to build a surrogate model with high accuracy covering the entire design domain. A major challenge to achieve this objective is how to reduce the number of function evaluations of 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 or by 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 locally highly nonlinear. A new surrogate modeling method which can allocate more training points in regions with high nonlinearity is needed to overcome this challenge. This paper proposes an efficient global surrogate modeling method based on a multi-layer sampling scheme.
Technical Paper

A Group-Based Space-Filling Design of Experiments Algorithm

2018-04-03
2018-01-1102
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, surrogate interpolating approximation models (often called metamodels – approximate models of the original model) can provide sufficient accuracy at a lower computing overhead as compared to repeated runs of a full simulation. Metamodel accuracy improves if constructed using space-filling designs of experiments (DOEs). The latter provides a collection of sample points in the design space preferably covering the entire space.
Journal Article

Warranty Forecasting of Repairable Systems for Different Production Patterns

2017-03-28
2017-01-0209
Abstract 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.
Journal Article

Mean-Value Second-Order Saddlepoint Approximation for Reliability Analysis

2017-03-28
2017-01-0207
Abstract A new second-order Saddlepoint Approximation (SA) method for structural reliability analysis is introduced. The Mean-value Second-order Saddlepoint Approximation (MVSOSA) is presented as an extension to the Mean-value First-order Saddlepoint Approximation (MVFOSA). The proposed method is based on a second-order Taylor expansion of the limit state function around the mean value of the input random variables. It requires not only the first but also the second-order sensitivity derivatives of the limit state function. If sensitivity analysis must be avoided because of computational cost, a quadrature integration approach, based on sparse grids, is also presented and linked to the saddlepoint approximation (SGSA - Sparse Grid Saddlepoint Approximation). The SGSA method is compared with the first and second-order SA methods in terms of accuracy and efficiency. The proposed MVSOSA and SGSA methods are used in the reliability analysis of two examples.
Journal Article

Time-Dependent Reliability Analysis Using a Modified Composite Limit State Approach

2017-03-28
2017-01-0206
Abstract Recent developments in time-dependent reliability have introduced the concept of a composite limit state. The composite limit state method can be used to calculate the time-dependent probability of failure for dynamic systems with limit-state functions of input random variables, input random processes and explicit in time. The probability of failure can be calculated exactly using the composite limit state if the instantaneous limit states are linear, forming an open or close polytope, and are functions of only two random variables. In this work, the restriction on the number of random variables is lifted. The proposed algorithm is accurate and efficient for linear instantaneous limit state functions of any number of random variables. An example on the design of a hydrokinetic turbine blade under time-dependent river flow load demonstrates the accuracy of the proposed general composite limit state approach.
Journal Article

Time-Dependent Reliability-Based Design Optimization of Vibratory Systems

2017-03-28
2017-01-0194
Abstract A methodology for time-dependent reliability-based design optimization of vibratory systems with random parameters under stationary excitation is presented. The time-dependent probability of failure is computed using an integral equation which involves up-crossing and joint up-crossing rates. The total probability theorem addresses the presence of the system random parameters and a sparse grid quadrature method calculates the integral of the total probability theorem efficiently. The sensitivity derivatives of the time-dependent probability of failure with respect to the design variables are computed using finite differences. The Modified Combined Approximations (MCA) reanalysis method is used to reduce the overall computational cost from repeated evaluations of the system frequency response or equivalently impulse response function. The method is applied to the shape optimization of a vehicle frame under stochastic loading.
Technical Paper

Reliability and Resiliency Definitions for Smart Microgrids Based on Utility Theory

2017-03-28
2017-01-0205
Abstract 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.
Journal Article

A Methodology for Fatigue Life Estimation of Linear Vibratory Systems under Non-Gaussian Loads

2017-03-28
2017-01-0197
Abstract 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).
Journal Article

Computational Efficiency Improvements in Topography Optimization Using Reanalysis

2016-04-05
2016-01-1395
Abstract 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.
Journal Article

An Improved Reanalysis Method Using Parametric Reduced Order Modeling for Linear Dynamic Systems

2016-04-05
2016-01-1318
Abstract 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.
Journal Article

Reanalysis of Linear Dynamic Systems using Modified Combined Approximations with Frequency Shifts

2016-04-05
2016-01-1338
Abstract 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.
Journal Article

Uncertainty Assessment in Restraint System Optimization for Occupants of Tactical Vehicles

2016-04-05
2016-01-0316
Abstract 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.
Journal Article

An Efficient Method to Calculate the Failure Rate of Dynamic Systems with Random Parameters Using the Total Probability Theorem

2015-04-14
2015-01-0425
Abstract Using the total probability theorem, we propose a method to calculate the failure rate of a linear vibratory system with random parameters excited by stationary Gaussian processes. The response of such a system is non-stationary because of the randomness of the input parameters. A space-filling design, such as optimal symmetric Latin hypercube sampling or maximin, is first used to sample the input parameter space. For each design point, the output process is stationary and Gaussian. We present two approaches to calculate the corresponding conditional probability of failure. A Kriging metamodel is then created between the input parameters and the output conditional probabilities allowing us to estimate the conditional probabilities for any set of input parameters. The total probability theorem is finally applied to calculate the time-dependent probability of failure and the failure rate of the dynamic system. The proposed method is demonstrated using a vibratory system.
Journal Article

Enhancing Decision Topology Assessment in Engineering Design

2014-04-01
2014-01-0719
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.
Journal Article

Flexible Design and Operation of a Smart Charging Microgrid

2014-04-01
2014-01-0716
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.
Journal Article

A New Metamodeling Approach for Time-Dependent Reliability of Dynamic Systems with Random Parameters Excited by Input Random Processes

2014-04-01
2014-01-0717
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.
Journal Article

New Metrics to Assess Reliability and Functionality of Repairable Systems

2013-04-08
2013-01-0606
The classical definition of reliability may not be readily applicable for repairable systems. Commonly used concepts such as the Mean Time Between Failures (MTBF) and availability can be misleading because they only report limited information about the system functionality. In this paper, we discuss a set of metrics that can help with the design of repairable systems. Based on a set of desirable properties for these metrics, we select a minimal set of metrics (MSOM) which provides the most information about a system, with the smallest number of metrics. The metric of Minimum Failure Free Period (MFFP) with a given probability generalizes MTBF because the latter is simply the MFFP with a 0.5 probability. It also generalizes availability because coupled with repair times it provides a clearer picture of the length of the expected uninterrupted service. Two forms of MFFP are used: transient and steady state.
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