for many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of ‘Fourier intrinsic band functions’ (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of band-limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a time–frequency–energy (TFE) distribution that reveals the intrinsic structure of a data. Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms.
in Wiley Online Library (wileyonlinelibrary.com).The current work aims to develop a reliable theoretical model capable of simulating the depletion process of urea-water-solution (UWS) droplets injected in a hot exhaust stream as experienced in an automotive urea-based selective catalytic reduction system. A modified multicomponent vaporization model is presented and implemented in the current study to simulate the behavior of UWS droplet in heated environment. Although water depletion is modeled as a vaporization process, urea depletion is modeled using two different approaches: (i) vaporization and (ii) direct thermal decomposition. The suitability of both depletion approaches is assessed in the current study by comparison with experimental data of the decay of a single UWS droplet in a quiescent heated environment. The decay rate of UWS droplet is accurately predicted with the multicomponent vaporization model. The possibility of internal gasification is demonstrated. Based on the complex decomposition behavior of urea, the current study proposes a decomposition mechanism for UWS droplet. The suitability of implementing the rapid mixing approach is assessed through comparison with the diffusion limit approach at various operating conditions and initial UWS droplet sizes. V V C 2011 American Institute of Chemical Engineers AIChE J, 57: 3210-3225, 2011
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