Publications

Dynamic thermography is a promising technology for inspecting metallic and composite structures used in high-consequence industries. However, the reliability and inspection sensitivity of this technology has historically been limited by the need for extensive operator experience and the use of human judgment and visual acuity to detect flaws in the large volume of infrared image data collected. To overcome these limitations new automated data analysis algorithms and software is needed. The primary objectives of this research effort were to develop a data processing methodology that is tied to the underlying physics, which reduces or removes the data interpretation requirements, and which eliminates the need to look at significant numbers of data frames to determine if a flaw is present. Considering the strengths and weakness of previous research efforts, this research elected to couple both the temporal and spatial attributes of the surface temperature. Of the possible algorithms investigated, the best performing was a radiance weighted root mean square Laplacian metric that included a multiplicative surface effect correction factor and a novel spatio-temporal parametric model for data smoothing. This metric demonstrated the potential for detecting flaws smaller than 0.075 inch in inspection areas on the order of one square foot. Included in this report is the development of a thermal imaging model, a weighted least squares thermal data smoothing algorithm, simulation and experimental flaw detection results, and an overview of the ATAC (Automated Thermal Analysis Code) software that was developed to analyze thermal inspection data.

This report describes the underlying principles and goals of the Sandia ASCI Verification and Validation Program Validation Metrics Project. It also gives a technical description of two case studies, one in structural dynamics and the other in thermomechanics, that serve to focus the technical work of the project in Fiscal Year 2001.

Shock excitations are normally random process realizations, and most of our efforts to represent them either directly or indirectly reflect this fact. The most common indirect representation of shock sources is the shock response spectrum. It seeks to establish the damage-causing potential of random shocks in terms of responses excited in linear, single-degree-of-freedom systems. This paper shows that shock sources can be represented directly by developing the probabilistic and statistical structure that underlies the random shock source. Confidence bounds on process statistics and probabilities of specific excitation levels can be established from the model. Some numerical examples are presented.

One of the key elements of the Stochastic Finite Element Method, namely the polynomial chaos expansion, has been utilized in a nonlinear shock and vibration application. As a result, the computed response was expressed as a random process, which is an approximation to the true solution process, and can be thought of as a generalization to solutions given as statistics only. This approximation to the response process was then used to derive an analytically-based design specification for component shock response that guarantees a balanced level of marginal reliability. Hence, this analytically-based reference SRS might lead to an improvement over the somewhat ad hoc test-based reference in the sense that it will not exhibit regions of conservativeness. nor lead to overtesting of the design.

Most mechanical and structural failures can be formulated as first passage problems. The traditional approach to first passage analysis models barrier crossings as Poisson events. The crossing rate is established and used in the Poisson framework to approximate the no-crossing probability. While this approach is accurate in a number of situations, it is desirable to develop analysis alternatives for those situations where traditional analysis is less accurate and situations where it is difficult to estimate parameters of the traditional approach. This paper develops an efficient simulation approach to first passage failure analysis. It is based on simulation of segments of complex random processes with the Karhunen-Loeve expansion, use of these simulations to estimate the parameters of a Markov chain, and use of the Markov chain to estimate the probability of first passage failure. Some numerical examples are presented.

Abstract not provided.

In the current study, the generality of the key underpinnings of the Stochastic Finite Element (SFEM) method is exploited in a nonlinear shock and vibration application where parametric uncertainty enters through random variables with probabilistic descriptions assumed to be known. The system output is represented as a vector containing Shock Response Spectrum (SRS) data at a predetermined number of frequency points. In contrast to many reliability-based methods, the goal of the current approach is to provide a means to address more general (vector) output entities, to provide this output as a random process, and to assess characteristics of the response which allow one to avoid issues of statistical dependence among its vector components.

The canonical variate analysis technique is used in this investigation, along with a data transformation algorithm, to identify a system in a transform space. The transformation algorithm involves the preprocessing of measured excitation/response data with a zero-memory-nonlinear transform, specifically, the Rosenblatt transform. This transform approximately maps the measured excitation and response data from its own space into the space of uncorrelated, standard normal random variates. Following this transform, it is appropriate to model the excitation/response relation as linear since Gaussian inputs excite Gaussian responses in linear structures. The linear model is identified in the transform space using the canonical variate analysis approach, and system responses in the original space are predicted using inverse Rosenblatt transformation. An example is presented.

We have developed a stochastic model for the power generated by a photovoltaic (PV) power supply system that includes a rechargeable energy storage device. The ultimate objective of this work is to integrate this photovoltaic generator along with other generation sources to perform power flow calculations to estimate the reliability of different electricity grid configurations. For this reason, the photovoltaic power supply model must provide robust, efficient realizations of the photovoltaic electricity output under a variety of conditions and at different geographical locations. This has been achieved by use of a Karhunen-Loeve framework to model the solar insolation data. The capacity of the energy storage device, in this case a lead-acid battery, is represented by a deterministic model that uses an artificial neural network to estimate the reduction in capacity that occurs over time. When combined with an appropriate stochastic load model, all three elements yield a stochastic model for the photovoltaic power system. This model has been operated on the Monte Carlo principle in stand-alone mode to infer the probabilistic behavior of the system. In particular, numerical examples are shown to illustrate the use of the model to estimate battery life. By the end of one year of operation, there is a 50% probability for the test case shown that the battery will be at or below 95% of initial capacity. © 2000 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Device penetration into media such as metal and soil is an application of some engineering interest. Often, these devices contain internal components and it is of paramount importance that all significant components survive the severe environment that accompanies the penetration event. In addition, the system must be robust to perturbations in its operating environment, some of which exhibit behavior which can only be quantified to within some level of uncertainty. In the analysis discussed herein, methods to address the reliability of internal components for a specific application system are discussed. The shock response spectrum (SRS) is utilized in conjunction with the Advanced Mean Value (AMV) and Response Surface methods to make probabilistic statements regarding the predicted reliability of internal components. Monte Carlo simulation methods are also explored.

Random vibration is the phenomenon wherein random excitation applied to a mechanical system induces random response. We summarize the state of the art in random vibration analysis and testing, commenting on history, linear and nonlinear analysis, the analysis of large-scale systems, and probabilistic structural testing.

We investigate the reliability If 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 supp Iy system, the rechargeable battery and a load. The solar resource and the system load are modeled as SI ochastic processes. The photovoltaic system and the rechargeable battery are modeled deterministically, imd an artificial neural network is incorporated into the model of the rechargeable battery to simulate dartage that occurs during deep discharge cycles. The equations governing system behavior are solved simultaneously in the Monte Carlo framework and a fwst passage problem is solved to assess system reliability.

We developed a model for the probabilistic behavior of a rechargeable battery acting as the energy storage component in a photovoltaic power supply system. Stochastic and deterministic models are created to simulate the behavior of the system component;. The components are the solar resource, the photovoltaic power supply system, the rechargeable battery, and a load. Artificial neural networks are incorporated into the model of the rechargeable battery to simulate damage that occurs during deep discharge cycles. The equations governing system behavior are combined into one set and solved simultaneously in the Monte Carlo framework to evaluate the probabilistic character of measures of battery behavior.

Efforts to optimize the design of mechanical systems for preestablished use environments and to extend the durations of use cycles establish a need for in-service health monitoring. Numerous studies have proposed measures of structural response for the identification of structural damage, but few have suggested systematic techniques to guide the decision as to whether or not damage has occurred based on real data. Such techniques are necessary because in field applications the environments in which systems operate and the measurements that characterize system behavior are random. This paper investigates the use of artificial neural networks (ANNs) to identify damage in mechanical systems. Two probabilistic neural networks (PNNs) are developed and used to judge whether or not damage has occurred in a specific mechanical system, based on experimental measurements. The first PNN is a classical type that casts Bayesian decision analysis into an ANN framework; it uses exemplars measured from the undamaged and damaged system to establish whether system response measurements of unknown origin come from the former class (undamaged) or the latter class (damaged). The second PNN establishes the character of the undamaged system in terms of a kernel density estimator of measures of system response; when presented with system response measures of unknown origin, it makes a probabilistic judgment whether or not the data come from the undamaged population. The physical system used to carry out the experiments is an aerospace system component, and the environment used to excite the system is a stationary random vibration. The results of damage identification experiments are presented along with conclusions rating the effectiveness of the approaches.

Many dynamical systems tested in the field and the laboratory display significant nonlinear behavior. Accurate characterization of such systems requires modeling in a nonlinear framework. One construct forming a basis for nonlinear modeling is that of the artificial neural network (ANN). However, when system behavior is complex, the amount of data required to perform training can become unreasonable. The authors reduce the complexity of information present in system response measurements using decomposition via canonical variate analysis. They describe a method for decomposing system responses, then modeling the components with ANNs. A numerical example is presented, along with conclusions and recommendations.

We frequently develop mathematical models of system behavior and sometimes use test data to help identify the parameters of the mathematical model. However, no general-purpose technique exists for formally, statistically judging the quality of a model. This paper suggests a formal statistical procedure for the validation of mathematical models of systems when data taken during operation of the system are available. The statistical validation procedure is based on the bootstrap, and it seeks to build a framework where a statistical test of hypothesis can be run to determine whether or not a mathematical model is an acceptable model of a system with regard to user-specified measures of system behavior. A numerical example is presented to demonstrate the application of the technique.

Mathematical models of physical systems are used, among other purposes, to improve our understanding of the behavior of physical systems, predict physical system response, and control the responses of systems. Phenomenological models are frequently used to simulate system behavior, but an alternative is available - the artificial neural network (ANN). The ANN is an inductive, or data-based model for the simulation of input/output mappings. The ANN can be used in numerous frameworks to simulate physical system behavior. ANNs require training data to learn patterns of input/output behavior, and once trained, they can be used to simulate system behavior within the space where they were trained.They do this by interpolating specified inputs among the training inputs to yield outputs that are interpolations of =Ming outputs. The reason for using ANNs for the simulation of system response is that they provide accurate approximations of system behavior and are typically much more efficient than phenomenological models. This efficiency is very important in situations where multiple response computations are required, as in, for example, Monte Carlo analysis of probabilistic system response. This paper describes two frameworks in which we have used ANNs to good advantage in the approximate simulation of the behavior of physical system response. These frameworks are the non-recurrent and recurrent frameworks. It is assumed in these applications that physical experiments have been performed to obtain data characterizing the behavior of a system, or that an accurate finite element model has been run to establish system response. The paper provides brief discussions on the operation of ANNs, the operation of two different types of mechanical systems, and approaches to the solution of some special problems that occur in connection with ANN simulation of physical system response. Numerical examples are presented to demonstrate system simulation with ANNs.

It is common practice in structural dynamics to develop mathematical models for system behavior, and the authors are now capable of developing stochastic models, i.e., models whose parameters are random variables. Such models have random characteristics that are meant to simulate the randomness in characteristics of experimentally observed systems. This paper suggests a formal statistical procedure for the validation of mathematical models of stochastic systems when data taken during operation of the stochastic system are available. The statistical characteristics of the experimental system are obtained using the bootstrap, a technique for the statistical analysis of non-Gaussian data. The authors propose a procedure to determine whether or not a mathematical model is an acceptable model of a stochastic system with regard to user-specified measures of system behavior. A numerical example is presented to demonstrate the application of the technique.

Structural dynamic testing is concerned with the estimation of system properties, including frequency response functions and modal characteristics. These properties are derived from tests on the structure of interest, during which excitations and responses are measured and Fourier techniques are used to reduce the data. The inputs used in a test are frequently random, and they excite random responses in the structure of interest When these random inputs and responses are analyzed they yield estimates of system properties that are random variable and random process realizations. Of course, such estimates of system properties vary randomly from one test to another, but even when deterministic inputs are used to excite a structure, the estimated properties vary from test to test. When test excitations and responses are normally distributed, classical techniques permit us to statistically analyze inputs, responses, and some system parameters. However, when the input excitations are non-normal, the system is nonlinear, and/or the property of interest is anything but the simplest, the classical analyses break down. The bootstrap is a technique for the statistical analysis of data that are not necessarily normally distributed. It can be used to statistically analyze any measure of input excitation or response, or any system property, when data are available to make an estimate. It is designed to estimate the standard error, bias, and confidence intervals of parameter estimates. This paper shows how the bootstrap can be applied to the statistical analysis of modal parameters.

Structural system simulation is important in analysis, design, testing, control, and other areas, but it is particularly difficult when the system under consideration is nonlinear. Artificial neural networks offer a useful tool for the modeling of nonlinear systems, however, such modeling may be inefficient or insufficiently accurate when the system under consideration is complex. This paper shows that there are several transformations that can be used to uncouple and simplify the components of motion of a complex nonlinear system, thereby making its modeling and simulation a much simpler problem. A numerical example is also presented.

Structural dynamic testing is concerned with estimation of system properties, including frequency response functions and modal characteristics. These properties are derived from tests on the structure of interest, during which excitations and responses are measured and Fourier techniques are used to reduce the data. The inputs used in a test are frequently radom and excite random responses in the structure of interest. When these random inputs and responses are analyzed they yield estimates of system properties that are random variable and random process realizations. Of course, such estimates of system properties vary randomly from one test to another, but even when deterministic inputs are used to excite a structure, the estimated properties vary from test to test. When test excitations and responses are normally distributed, classical techniques permit us to statistically analyze inputs, responses, and system parameters. However, when the input excitations are non-normal, the system is nonlinear, and/or the property of interest is anything but the simplest, the classical analyses break down. The bootstrap is a technique for the statistical analysis of data that are not necessarily normally distributed. It can be used to statistically analyze any measure of input excitation on response, or any system property, when data are available to make an estimate. It is designed to estimate the standard error, bias, and confidence intervals of parameter estimates. This paper shows how the bootstrap can be applied to the statistical analysis of modal parameters.

Artificial neural networks (ANNs) have been shown capable of simulating the behavior of complex, nonlinear, systems, including structural systems. Under certain circumstances, it is desirable to simulate structures that are analyzed with the finite element method. For example, when we perform a probabilistic analysis with the Monte Carlo method, we usually perform numerous (hundreds or thousands of) repetitions of a response simulation with different input and system parameters to estimate the chance of specific response behaviors. In such applications, efficiency in computation of response is critical, and response simulation with ANNs can be valuable. However, finite element analyses of complex systems involve the use of models with tens or hundreds of thousands of degrees of freedom, and ANNs are practically limited to simulations that involve far fewer variables. This paper develops a technique for reducing the amount of information required to characterize the response of a general structure. We show how the reduced information can be used to train a recurrent ANN. Then the trained ANN can be used to simulate the reduced behavior of the original system, and the reduction transformation can be inverted to provide a simulation of the original system. A numerical example is presented.

System behaviors can be accurately simulated using artificial neural networks (ANNs), and one that performs well in simulation of structural response is the radial basis function network. A specific implementation of this is the connectionist normalized linear spline (CNLS) network, investigated in this study. A useful framework for ANN simulation of structural response is the recurrent network. This framework simulates the response of a structure one step at a time. It requires as inputs some measures of the excitation, and the response at previous times. On output, the recurrent ANN yields the response at some time in the future. This framework is practical to implement because every ANN requires training, and this is executed by showing the ANN examples of correct input/output behavior (exemplars), and requiring the ANN to simulate this behavior. In practical applications, hundreds or, perhaps, thousands, of exemplars are required for ANN training. The usual laboratory and non-neural numerical applications to be simulated by ANNs produce these amounts of information. Once the recurrent ANN is trained, it can be provided with excitation information, and used to propagate structural response, simulating the response it was trained to approximate. The structural characteristics, parameters in the CNLS network, and degree of training influence the accuracy of approximation. This investigation studies the accuracy of structural response simulation for a single-degree-of-freedom (SDF), nonlinear system excited by random vibration loading. The ANN used to simulate structural response is a recurrent CNLS network. We investigate the error in structural system simulation.

This paper proposes a framework for the comprehensive analysis of complex problems in probabilistic structural mechanics. Tools that can be used to accurately estimate the probabilistic behavior of mechanical systems are discussed, and some of the techniques proposed in the paper are developed and used in the solution of a problem in nonlinear structural dynamics.

System dynamicists frequently encounter signals they interpret as realizations of normal random processes. To simulate these analytically and in the laboratory they use methods that yield approximately normal random signals. The traditional digital methods for generating such signals have been developed during the past 25 years. During the same period of time much development has been done in the theory of chaotic processes. The conditions under which chaos occurs have been studied, and several measures of the nature of chaotic processes have been developed. Some of the measures used to characterize the nature of dynamic system motions are common to the study of both random vibrations and chaotic processes. This paper considers chaotic processes and random vibrations. It shows contrasts between the two and situations where they are indistinguishable. The applicability of the Central Limit Theorem to chaotic processes is demonstrated. 12 refs., 8 figs.