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Performance assessment of complex systems is ideally done through full system-level testing which is seldom available for high consequence systems. Further, a reality of engineering practice is that some features of system behavior are not known from experimental data, but from expert assessment, only. On the other hand, individual component data, which are part of the full system are more readily available. The lack of system level data and the complexity of the system lead to a need to build computational models of a system in a hierarchical or building block approach (from simple components to the full system). The models are then used for performance prediction in lieu of experiments, to estimate the confidence in the performance of these systems. Central to this are the need to quantify the uncertainties present in the system and to compare the system response to an expected performance measure. This is the basic idea behind Quantification of Margins and Uncertainties (QMU). QMU is applied in decision making—there are many uncertainties caused by inherent variability (aleatoric) in materials, configurations, environments, etc., and lack of information (epistemic) in models for deterministic and random variables that influence system behavior and performance. This paper proposes a methodology to quantify margins and uncertainty in the presence of both aleatoric and epistemic uncertainty. It presents a framework based on Bayes networks to use available data at multiple levels of complexity (i.e. components, subsystem, etc.) and demonstrates a method to incorporate epistemic uncertainty given in terms of intervals on a model parameter.

This article specifies a virtual structural dynamic subsystem and some systems, as well as mathematical models that approximately simulate them. The purpose is to define a setting for model validations conceived by participants in the Sandia National Laboratories Validation Workshop. Some broad guidelines for the model validations are set, as well as a regulatory requirement to be satisfied by the target system. Participants are directed to present techniques for subsystem model validation, to analytically predict whether or not the regulatory requirement will be met, and to estimate the likelihood of accuracy of the prediction.

The six papers in this special issue that develop solutions to the Structural Dynamics Challenge Problem are summarized herein. The goal is to emphasize different tools and approaches applied to various parts of the structural dynamics problem. Specifically the following issues are considered: (1) Development of a mathematical framework for uncertainty quantification of a substructure. (2) Calibration of a mathematical model for the substructure. (3) Validation of the substructure mathematical model. (4) Use of the mathematical model of the substructure, in conjunction with another structure, to make a prediction of the probability that a regulatory limit is surpassed, and discussion of the uncertainty of the prediction. Different methodologies are presented and specific results vary, however, conclusions regarding satisfaction of the regulatory requirement match.

This special issue presents the results of the Sandia organized Model Validation Challenge Workshop, held May 2006. The workshop brought together researchers from different fields to present various approaches to model validation, and focused on the methodological elements of model validation rather than on model building. Three problems were defined in the disciplines of structural statics, structural dynamics, and heat transfer, all with a uniform structure. The workshop was specifically designed to investigate the relative merits of different approaches to hierarchal model validation through application to these problems. This paper describes a hierarchal approach in the challenge problems, presents the uniform conceptual framework that was used for the challenge problem definitions, and provides an overview of the organization of this special issue.

Interest in the analysis of random vibrations of mechanical systems started to grow about a half century ago in response to the need for a theory that could accurately predict structural response to jet engine noise and missile launch-induced environments. However, the work that enabled development of the theory of random vibrations started about a half century earlier. This paper discusses contributions to the theory of random vibrations from the time of Einstein to the time of an MIT workshop that was organized by Crandall in 1958.

Sandia National Laboratories has been studying calendar and pulse discharge life of prototype high-power lithium-ion cells as part of the Advanced Technology Development (ATD) Program. One of the goals of ATD is to establish validated accelerated life test protocols for lithium-ion cells in the hybrid electric vehicle application. In order to accomplish this, aging experiments have been conducted on 18650-size cells containing a chemistry representative of these high-power designs. Loss of power and capacity are accompanied by increasing interfacial impedance at the cathode. These relationships are consistent within a given state-of-charge (SOC) over the range of storage temperatures and times. Inductive models have been used to construct detailed descriptions of the relationships between power fade and aging time and to relate power fade, capacity loss and impedance rise. These models can interpolate among the different experimental conditions and can also describe the error surface when fitting life prediction models to the data.

Sandia National Laboratories has conducted a sequence of studies on the performance of lithium ion and other types of electrochemical cells using inductive models. The objectives of some of these investigations are: (1) to develop procedures to rapidly determine performance degradation rates while these cells undergo life tests; (2) to model cell voltage and capacity in order to simulate cell output under variable load and temperature conditions; (3) to model rechargeable battery degradation under conditions of cyclic charge/discharge, and many others. Among the uses for the models are: (1) to enable efficient predictions of battery life; (2) to characterize system behavior. Inductive models seek to characterize system behavior using experimentally or analytically obtained data in an efficient and robust framework that does not require phenomenological development. There are certain advantages to this. Among these advantages is the ability to avoid making measurements of hard to determine physical parameters or having to understand cell processes sufficiently to write mathematical functions describing their behavior. We have used artificial neural networks (ANNs) for inductive modeling, along with ancillary mathematical tools to improve their accuracy. This paper summarizes efforts to use inductive tools for cell and battery modeling. Examples of numerical results are presented.

Probabilistic neural nets have been applied in the detection of structural damage. These networks, which rely upon approximating the multivariate density of the training data, have been shown to be effective in some applications. However, quantification of decision errors, which must ultimately be used to rank their effectiveness, has received little attention. In this paper, a two-dimensional probabilistic pattern classifier (PPC) based on an L 2 detector is studied. Each dimension is modelled as a Gaussian random variable in order to directly study the effects introduced by a commonly used density estimator. The region of acceptance is examined for different parameters of the kernel density estimator. The detector behaviour of the original PPC is compared to theory. It is demonstrated that performance is affected by errors introduced by a kernel constructed using a finite set of data, and also from theoretical limitations inherent in the test statistic. A modification of the test statistic is suggested to improve the sensitivity for structural damage detection.

We investigated the reliability of a rechargeable battery acting as the energy storage component in a photovoltaic power supply system. A model system was constructed for this that includes the solar resource, the photovoltaic power supply system, the rechargeable battery and a load. The solar resource and the system load are modelled as stochastic processes. The photovoltaic system and the rechargeable battery are modelled deterministically, and an artificial neural network is incorporated into the model of the rechargeable battery to simulate damage that occurs during deep discharge cycles. The equations governing system behaviour are solved simultaneously in the Monte Carlo framework, and a first passage problem is solved to assess system reliability.