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Process Monitoring
Published in Jose A. Romagnoli, Ahmet Palazoglu, Introduction to Process Control, 2020
Jose A. Romagnoli, Ahmet Palazoglu
Independent component analysis (ICA)9,10 is used in multivariate signal separation for extracting hidden and statistically independent components (ICs) from the observed data and can be adopted for process monitoring tasks similar to PCA.11,12 In this technique, signal source separation recovers the independent signals after linear mixing. On the other hand, Kernel Principal Component Analysis (KPCA)13 extends the traditional PCA to capture features of nonlinear data spaces. Instead of directly taking eigenvalue decomposition of the covariance matrix like PCA, KPCA takes a data set with nonlinear features that that PCA fails to preserve and projects them to a higher dimensional space where they vary linearly.
Dynamic System Models and Basic Concepts
Published in Jitendra R. Raol, Girija Gopalratnam, Bhekisipho Twala, Nonlinear Filtering, 2017
Jitendra R. Raol, Girija Gopalratnam, Bhekisipho Twala
Filtering, in general, is used for either separating two signals that have been combined or to restore signals that are distorted in some way. Signal separation is required when interference by other signals or noise contaminates the desired/true signal as in signal transmission through a noisy channel/medium. Signal restoration is required when distortion of signals occurs as in de-blurring of an image acquired by a shaky camera. In analogue filtering applications, we encounter low pass, high pass and band pass filters which are used in signal processing applications to remove unwanted frequencies above, below or in a band of frequency of interest. Analogue filters are designed using electronic circuits. In DSP, the equivalent digital filters are designed by choosing appropriate impulse response functions which are also called filter kernels. The choice of a filter for a particular application is dictated by the specification of the requirements. Important characteristics for selection of a filter include cutoff frequency sharpness or roll off, pass band ripple and step response. It is found that while roll off is optimized by the Chebyshev filter, pass band flatness is ensured by Butterworth and step response is optimized by the Bessel filter [15]. Although analogue filters are cheap, fast and have a large dynamic range, digital filters have far superior levels of performance in terms of accuracy, range and any criterion that one can specify.
Unsupervised Learning and Blind Source Separation
Published in Francis F. Li, Trevor J. Cox, Digital Signal Processing in Audio and Acoustical Engineering, 2019
Unsupervised learning finds many applications in feature extraction and signal separation. This chapter discussed unsupervised learning and Hebbian learning, and outlined a method to perform PCA through unsupervised learning. ICA, an algorithm closely related to the machine-learning-based PCA, was then presented and discussed in the context of blind source separation and blind de-convolution. It can be demonstrated that blind source separation, or the cocktail party problem as it is known in audio acoustics, may be solved with the ICA algorithm, with some necessary assumptions.
Fractal component analysis: an integrated approach for autocorrelated signal separation and health monitoring of feedback control system
Published in Journal of Industrial and Production Engineering, 2021
Chih-Min Fan, Shao-Jen Weng, Yao-Te Tsai, Wei-Hsuan Wu, Chih-Hao Chen
In this paper, we address the gap in prior research by developing and presenting a method to identify autocorrelation over time. Our proposed method will improve the process of feedback control because autocorrelation will no longer hide problem signals. In doing so, the health of the system will be much improved. To specifically identify the gap in research, we note that past work on signal separation focus mainly on cross-correlation between observed signals but there is a dearth of signal processing research focusing on autocorrelation. For instance, when a process appears with an observed signal (or a control signal such as temperature) at a certain time point, signal separation is utilized for separating observed signals that are mixed over time. Algorithms for monitoring processes that have been established in the literature and that are commonly used signal separation methods include principal component analysis (PCA) [7–9] and independent component analysis (ICA) [10,11].
Results on approximate controllability for a second-order semilinear nonlocal control system with monotonic nonlinearity
Published in Journal of Control and Decision, 2022
Urvashi Arora, V. Vijayakumar, Arun Kumar Singh, Harish Kumar Sahu, Anurag Shukla
Digital filters perform incredibly significant aspect in Digital Signal Processing (DSP). Indeed, the execution of digital filters is outstanding; each of the vital considerations that DSP has growing very famous. Generally, we classify filters with two main applications: Signal separation and Signal restoration. Signal separation is essential when a signal has infected with disturbance, noise, or other signals.