Publications

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It is vital that avionic packages used for testing and certifying the reliability and safety of U.S. nuclear weapons with platform aircraft survive exposure to shock environments during transportation and delivery. The objective of this research was to characterize the response to these transportation shock environments delivering accurate shock test specifications in order to set laboratory programming material and device certification rigor. Responses to shock events were analyzed in the frequency domain via the Shock Response Spectrum (SRS). Shocks were then grouped based on respective behavior of maximum response accelerations which were pseudorandomly resampled and compared to test data to form test specifications based on the MinerPalmgren hypothesis. In addition to discovering significant over testing in current shock specifications, a new systematic, data-driven approach to designing shock specifications was formulated.

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The information impulse function (IIF), running Variance, and local Hölder Exponent are three conceptually different time-series evaluation techniques. These techniques examine time-series for local changes in information content, statistical variation, and point-wise smoothness, respectively. Using simulated data emulating a randomly excited nonlinear dynamical system, this study interrogates the utility of each method to correctly differentiate a transient event from the background while simultaneously locating it in time. Computational experiments are designed and conducted to evaluate the efficacy of each technique by varying pulse size, time location, and noise level in time-series. Our findings reveal that, in most cases, the first instance of a transient event is more easily observed with the information-based approach of IIF than with the Variance and local Hölder Exponent methods. While our study highlights the unique strengths of each technique, the results suggest that very robust and reliable event detection for nonlinear systems producing noisy time-series data can be obtained by incorporating the IIF into the analysis.

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A system’s response to disturbances in an internal or external driving signal can be characterized as performing an implicit computation, where the dynamics of the system are a manifestation of its new state holding some memory about those disturbances. Identifying small disturbances in the response signal requires detailed information about the dynamics of the inputs, which can be challenging. This paper presents a new method called the Information Impulse Function (IIF) for detecting and time-localizing small disturbances in system response data. The novelty of IIF is its ability to measure relative information content without using Boltzmann’s equation by modeling signal transmission as a series of dissipative steps. Since a detailed expression of the informational structure in the signal is achieved with IIF, it is ideal for detecting disturbances in the response signal, i.e., the system dynamics. Those findings are based on numerical studies of the topological structure of the dynamics of a nonlinear system due to perturbated driving signals. The IIF is compared to both the Permutation entropy and Shannon entropy to demonstrate its entropy-like relationship with system state and its degree of sensitivity to perturbations in a driving signal.

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The purpose of this research is to describe and illustrate practical methods that can be used to construct tolerance bounds for a multivariate measurement associated with a covariate. These methods rely on principal components analysis and the parametric bootstap. The methods are illustrated with an example in which the vibration environment experienced by a test object being carried by an aircraft (known as captive carry) is characterized.