To assure that the functional requirements of a manufactured component are satisfied, the field of manufacturing and design needs more accurate and reliable methods to analyze and predict the quality of produced parts, as well as to monitor the part and machine condition. Traditional methods, based on monitoring average variables, often fail to provide sufficient information about the fault status of a manufacturing process or part. To obtain a more advanced understanding of manufacturing variations, there is a growing interest in analyzing "signals" from manufacturing processes. These signals contain a fingerprint or signature of the manufacturing condition over time. To handle the complexity of such signals, advanced mathematical tools from signal processing are needed. Specifically, a great emphasis has been placed on "transforming" the signals collected from manufacturing processes into a different domain where the information is easier to interpret. The Fourier transform is such an example, but has many shortcomings, especially when there are nonstationarities that typically obscure the true information. Alternatives to the standard Fourier-based techniques (e.g., Short-time Fourier transform, Wigner-Ville transform, wavelet transform) have been proposed in the literature. However, they still lack the ability to provide a clear and physically meaningful interpretation of the various possible signal components, hence making their use in manufacturing practice difficult. Unless an accurate means of interpreting and predicting manufacturing data is developed, the difficulty in establishing a reliable channel of communication between design and manufacturing remains a serious problem.; In this work, an alternative transform is introduced to overcome the problems facing the fields of manufacturing and design. In particular, the Karhunen-Loeve transform is introduced and extended for condition monitoring of manufacturing signals (e.g., tool vibrations, part surface deviations). The extension is formulated using mathematical functions, numerically-generated signals, and experimentally-obtained signals. The detection and monitoring method developed in this dissertation offers an equal capability of handling deterministic, stochastic, stationary, and nonstationary components. Furthermore, the method also allows for the detection of faults of unknown nature, which becomes crucial when analyzing newly-developed manufacturing processes.; The effectiveness of the detection and monitoring method enables the systematic "fingerprinting" of a manufacturing machine or process. A methodology is presented to help designers and manufacturers in making informed decisions about a machine and/or part condition. A formal means of understanding and redesigning the manufacturing machine components and process parameters is essential in improving the accuracy and precision of parts produced from manufacturing machines. By providing a systematic means of understanding the individual mechanisms which affect part production, this work opens the way to a future of more advanced automation in manufacturing and design.
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