Abstract:The aim of this study was to compare algorithms for solving inverse problems generally encountered in spatial audio signal processing. Tikhonov regularization is typically utilized to solve overdetermined linear systems in which the regularization parameter is selected by the golden section search (GSS) algorithm. For underdetermined problems with sparse solutions, several iterative compressive sampling (CS) methods are suggested as alternatives to traditional convex optimization (CVX) methods that are computationally expensive. The focal underdetermined system solver (FOCUSS), the steepest descent (SD) method, Newton's (NT) method, and the conjugate gradient (CG) method were developed to solve CS problems more efficiently in this study. These algorithms were compared in terms of problems, including source localization and separation, noise source identification, and analysis and synthesis of sound fields, by using a uniform linear array (ULA), a uniform circular array (UCA), and a random array. The derived results are discussed herein and guidelines for the application of these algorithms are summarized.
In this paper, an iterative Compressive Sensing (CS) algorithm is proposed for acoustical source characterization problems with block sparsity constraints. Source localization and signal separation are accomplished in a unified CS framework. The inverse problem is formulated with the Equivalent Source Method as a linear underdetermined system of equations. As conventional approaches based on convex optimization can be computationally expensive and fail to deal with continuously distributed sources, the proposed approach that is adapted from the Newton's method and is augmented with a special pruning procedure is capable of solving the inverse problem far more efficiently with comparable accuracy. The pruning procedure employs a binary mask that admits sparsity constraints of two-dimensional block sources. The binary mask is heuristic in that it tends to promote nonzero positive source magnitudes. In each iteration, the source amplitude vector is on one hand updated by the Newton's method and on the other hand pruned with the binary mask. With the pruning procedure, the source magnitudes become increasingly sparse and clustered such that the block characteristics are enhanced. In the post-processing phase, particle velocity is calculated on the basis of the equivalent source amplitudes. Numerical and experimental investigations are conducted to validate the proposed technique. The results have demonstrated the efficacy of the proposed Compressive Newton's method in imaging block sources and extracting signal waveforms with little computational cost, as compared to a convex optimization package.
Chatter identification is necessary in order to achieve stable machining conditions. However, the linear approximation in regenerative chatter vibration is problematic because of the rich nonlinear characteristics in machining. In this study, a novel method to detect chatter is proposed. Firstly, measured cutting force signals are decomposed into a set of intrinsic mode functions by using ensemble empirical mode decomposition. Hilbert transform is following to extract the instantaneous frequency. Fast Fourier transform is also utilized for each intrinsic mode function to determine the intrinsic mode function that contains rich chatter. Finally, the standard deviation and energy ratio in frequency domain of intrinsic mode functions are found as simply dimensionless chatter indicators. The effectively proposed approach is validated by analyzing the machined surface topography and also compared to the stability lobe diagram.
Fixed diamond wire saw has the advantages such as higher cutting rate and clearer operating environment over the slurry wire saw in wafering. However, the higher cost and poor sliced wafer surface are still the obstacles for the diamond wire saw to totally replace slurry wire saw. In this study, the distribution of diamond grits on the wire was investigated by numerical simulation. The results show that there is a critical value of the abrasive interval to transfer the machining mechanism from plastic plowing to brittle indentation cracking for the material removal. The value depends on both the wire tension and bow angle during the operation.
Polymer materials have been utilized in microfluidic devices because of their properties and competitive cost for single-use devices. However, most microfabrication processes can not produce true three dimensional features in polymers. In this study, a new method with lost-wax casting was proposed to fabricate three dimensional microstructures in polymer-based microchannels. A feasibility study was conducted with epoxy and paraffin wax sacrifice. The microchannel with both-end fixed horizontal rods was produced with precise dimension. This structure is not possible to be fabricated by other replicating methods such as hot embossing or casting. The proposed lost-wax casting process is expected to advance the development of three dimensional polymer-based microchips for both the experimental research in laboratory and the mass production in industry.
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