Digital Signal Design for Fault Detection in Linear Continuous Dynamical Systems
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Date
2007-04-11
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Abstract
A systematic approach to detect underlying undesirable states of a physical system is to compare its observed behaviors to several competing models and to identify the model that best describes the observation. This model selection process can be enhanced by applying a specially designed auxiliary input signal to the system.
This dissertation applies the auxiliary-signal-based model selection approach for recognizing faulty behaviors of systems whose dynamic behaviors can be described by linear differential equations.
Using an existing analog--signal--based algorithm, the effect of the modeling error on this particular type of detection approach is examined and a geometrical explanation is provided. We also present a variation of the analog--signal--based algorithm which produces signals that are more practical for certain types of applications. In addition, an alternative auxiliary signal design algorithm is developed, producing digital signals that minimally disturb regular system operation and guarantee fault detection for a given amount of the gap between physical system and the corresponding model. The algorithm implements the analytical solution steps derived mostly by the optimal control problem solution technique while converting a nested optimization problem into an equivalent eigenvalue problem. The algorithm provides an option to optimize the duration of each digital piece to yield even more Steel material is widely used in fabricating automotive seat frames. Unfortunately, these materials are not renewable and take a somewhat longer time to degrade in a landfill than natural based biodegradable materials. Unprecedented growth of bio-based textile composites has drawn interest from various industries, such as automotive and transportation. Bio-based composite materials offer products that are biodegradable, easily recycled and can exceed the physical performance of metallic materials that are commercially available. Additional performance characteristics that composite materials can offer include weight reduction and strength improvement.
The purpose of this research is to investigate the physical and mechanical properties of bio-based composite materials incorporating different linear densities of the flax sliver and blend ratios of Epoxy-soybean oil resin. Sliver is defined as a "continuous bundle of loosely untwisted fibers" [46]. The proposed fabrication concept is the impregnation of soybean-Epoxy resin into flax sliver. After resin impregnation of the flax sliver and curing it with the curing agent, the flax sliver — resin mixtures become rigid and support an increase in fiber loading. The resin consolidation method with sliver form is also called Sliver Polymer Matrix Composite (SPMC). One of the potential applications for the particular bio-based composite is automotive seat frames. The properties provided by SPMC, strength, weight reduction and biodegradability, are important to this final product.
Three different bundle sizes of flax sliver were used, namely 8, 9 and 10 ply flax sliver. Each of the flax slivers has individual linear density of 253.41 grains⁄yard. Thus plied sliver bundles had linear densities of 2027.3, 2280.7 and 2534 grains⁄yard respectively. Moreover, three blend ratios of Epoxy and Acrylated Epoxidized Soybean Oil (AESO) are also taken into consideration as another variable, namely 100% Epoxy resin, 30% AESO ⁄ 70% Epoxy resin, and 50% AESO ⁄ 50% Epoxy resin. This research analyzes the mechanical and physical properties of the rigid bio-based composite materials employing flax fibers. Physical testing was performed to determine the flexural rigidity (three-point bend), impact strength and biodegradability at varying sliver linear densities and Epoxy-soybean resin blend ratios. Flexural rigidity test utilized 9" x 1" (Length x diameter) samples, impact strength test utilized 3" x 1" (Length x diameter).
The highest impact test value was achieved with samples of 10 ply flax sliver and 50% Epoxy ⁄ 50% AESO resin mixture. The impact test value for this particular sample was 57 ft-lb. The highest flexural rigidity test value was also achieved with samples of 10 ply of flax sliver with 50% ⁄ 50% Epoxy-AESO resin mixtures. The average flexural rigidity of this sample was 612.74 lbs. (278.5 kg). The algorithm provides an option to optimize the duration of each digital piece to yield even more "plant-friendly" auxiliary detection signals at the cost of a moderate increase in computational time.
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Keywords
multimodel identification, test signal, active, fault detection
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Degree
PhD
Discipline
Operations Research
