Piecewise Linear Filter Research Articles

Trends and cycles during the COVID-19 pandemic period

We perform several trend-cycle decompositions through the lens of two unobserved components models, herein estimated for Portugal and the euro area. Our procedure copes with the COVID-19’s consequences by explicitly considering potentially larger second moments during that period. This is achieved through a set of pandemic-specific shocks affecting only the 2020–21 period and embedded into estimation through a piecewise linear Kalman filter. Our methodology generates negligible historical revisions in key smoothed variables when the sample period is expanded until 2021:4, since pandemic shocks absorb a great deal of data volatility with minimal impacts on filtered data revisions or estimated parameters. Furthermore, non-pandemic shock volatility remains largely unaffected by the pandemic period. Innovations affecting the cycle in our preferred model are the key propellers of GDP developments during the COVID-19 pandemic period.

Set-membership filtering for piecewise linear systems with censored measurements under Round-Robin protocol

In this paper, the set-membership filtering problem is investigated for a class of piecewise linear systems with state constraintsand censored measurements under the Round-Robin (RR) protocol. First of all, the mode of the piecewise linear system is determined by itsstate. The noises under consideration satisfy two ellipsoid constraints. According the schedule of the RR protocol, a set of piecewise linearfilters is constructed in terms of the censored measurements transmitted through the shared network. The objective of this paper is todesign a set of filter gains such that the augmented dynamics satisfies the desirable ellipsoid constraint in the simultaneous presence of stateconstraints, censored measurements and RR protocol. A sufficient condition for the existence of piecewise linear filters is obtained and aconvex optimisation method is presented to derive the minimized ellipsoid in the sense of matrix trace. Finally, a simulation example is givento verify the effectiveness of the proposed design method.

Fault diagnosis in switched‐linear systems by emulation of behavioral models on FPGA: A case study of current‐mode buck converter

AbstractThis paper presents an Field‐Programmable Gate Array (FPGA)‐based fault emulation and detection framework for switched‐linear systems commonly encountered in power electronics. The proposed framework exploits high‐level behavioral modeling that maps analog functionality into fixed‐point architectures supported by FPGAs. This work is mainly concerned with modeling and validation of effectiveness of a fault diagnoser of a power converter much before its fabrication. The proposed concept of fault diagnosis at presilicon stage overcomes several reliability issues in power electronic systems and enables design and development of test resources, verification of test bed, and interconnecting circuitry at an early stage of the design. To illustrate applicability of this environment, well‐accepted fault events including hard and soft faults are emulated with the help of a nonideal model of a buck converter and a piecewise linear detection filter, which follow an observer‐based residual generation for fault detection. The paper also shows that the proposed method is equally applicable for detection of faults under unstable operation of the converter. The effectiveness of the proposed framework is evaluated through FPGA‐based simulation (or “emulation”) of a peak‐current‐mode–controlled buck‐type switching converter implemented on Xilinx Kintex‐7 FPGA in MATLAB/Simulink environment with Xilinx System Generator support. To the best of our knowledge, fault diagnosis in power converter by emulation of its nonideal model on FPGA is attempted for the first time in the literature. Experimental results show that power converter faults can be easily detected by monitoring detection filter residuals while some of the faults can be precisely identified.

Wavelet and FFT Based Image Denoising Using Non-linear Filters

We propose a stationary and discrete wavelet based image denoising scheme and an FFTbased image denoising scheme to remove Gaussian noise. In the first approach, high subbands are added with each other and then soft thresholding is performed. The sum of low subbands is filtered with either piecewise linear (PWL) or Lagrange or spline interpolated PWL filter. In the second approach, FFT is employed on the noisy image and then low frequency and high frequency coefficients are separated with a specified cutoff frequency.Then the inverse of low frequency components is filtered with one of the PWL filters and the inverse of high frequency components is filtered with soft thresholding. The experimental results are compared with Liu and Liu's tensor-based diffusion model (TDM) approach.

PAPR Reduction in SC-IFDMA Using a Piece-Wise Linear Nyquist Filter

A novel Nyquist filter was proposed to reduce the peak-to-average power ratio (PAPR) in the interleaved single carrier orthogonal frequency division multiple access (SC-IFDMA) system based on pulse shaping. The proposed filter has a piece-wise rectangular frequency characteristic composed of six nonzero linear segments with variable-length projections onto the frequency axis, which are used as a set of independent design parameters from roll-off factor α. Simulation results show that the novel filter has a better PAPR reduction performance and lower symbol error rate compared to some recently proposed filters, and it has lower computational complexity.

Adaptive Sliding Mode Output Synchronization Tracking for Hyper-Chaotic Lü System Based on Adaptive PWL Filters

In this work, an adaptive sliding mode control method is presented to achieve output synchronization tracking for the uncertain hyper-chaotic Lü system. An adaptive piecewise linear (PWL) filter is used to identify the uncertain hyper-chaotic system. Base on the identification results, an adaptive sliding mode controller is designed to obtain output synchronization tracking for the hyper-chaotic Lü system. The convergence condition of the adaptive PWL filter is derived based on the Lyapunov theorem. Simulation is done to verify the effectiveness and correction of the proposed identification and synchronization tracking control method.

Reliable H∞ filtering for discrete piecewise linear systems with infinite distributed delays

This paper is concerned with the reliable filtering problem for discrete-time piecewise linear systems subject to sensor failures and time delays. The considered sensor failures are depicted by bounded variables taking value on a certain interval. The time delays are assumed to be infinitely distributed in the discrete-time domain. The purpose of the addressed reliable filtering problem is to design a piecewise linear filter such that, for the admissible sensor failures and possible infinite distributed delays, the augmented dynamics is exponentially stable and the performance is guaranteed with a prescribed attenuation level . With the aid of the convex optimal method, the filter parameters are obtained in terms of the solution to a set of LMIs which can be solved by the Matlab Toolbox. At last, an illustrative simulation is presented to demonstrate the effectiveness and applicability of the proposed algorithms.

Adaptive identification for hyperchaotic l system based on Weiner model

In order to be able to identify the hyper-chaotic l system with uncertain parameters effectively in real time, so that hyper-chaotic system control and synchronization tracking can be applied, this paper presents a system identification method for the hyper-chaotic system based on Wiener model. The linear part of the Wiener model consists of linear transversal filters, while the nonlinear part is represented approximately by piecewise linear filters. According to the minimum mean square error criterion, the filter parameter updated algorithm is derived, and the convergence condition is also obtained. Simulation results confirm the effectiveness of the adaptive filter for the identification of hyper-chaotic systems. The presented method not only overcomes the difficulty to identify a strongly nonlinear system only by adaptive linear filters, but also have a lower computational complexity compared with other non-linear adaptive filters.

Filter-based multiscale entropy analysis of complex physiological time series

Multiscale entropy (MSE) has been widely and successfully used in analyzing the complexity of physiological time series. We reinterpret the averaging process in MSE as filtering a time series by a filter of a piecewise constant type. From this viewpoint, we introduce filter-based multiscale entropy (FME), which filters a time series to generate multiple frequency components, and then we compute the blockwise entropy of the resulting components. By choosing filters adapted to the feature of a given time series, FME is able to better capture its multiscale information and to provide more flexibility for studying its complexity. Motivated by the heart rate turbulence theory, which suggests that the human heartbeat interval time series can be described in piecewise linear patterns, we propose piecewise linear filter multiscale entropy (PLFME) for the complexity analysis of the time series. Numerical results from PLFME are more robust to data of various lengths than those from MSE. The numerical performance of the adaptive piecewise constant filter multiscale entropy without prior information is comparable to that of PLFME, whose design takes prior information into account.

Constructing an Efficient Self-Tuning Aircraft Engine Model for Control and Health Management Applications


 
 
 Self-tuning aircraft engine models can be applied for control and health management applications. The self-tuning feature of these models minimizes the mismatch between any given engine and the underlying engineering model describing an engine family. This paper provides details of the construction of a self-tuning engine model centered on a piecewise linear Kalman filter design. Starting from a nonlinear transient aerothermal model, a piecewise linear representation is first extracted. The linearization procedure creates a database of trim vectors and state-space matrices that are subsequently scheduled for interpolation based on engine operating point. A series of steady-state Kalman gains can next be constructed from a reduced-order form of the piecewise linear model. Reduction of the piecewise linear model to an observable dimension with respect to available sensed engine measurements can be achieved using either a subset or an optimal linear combination of “health” parameters, which describe engine performance. The resulting piecewise linear Kalman filter is then implemented for faster-than-real-time processing of sensed engine measurements, generating outputs appropriate for trending engine performance, estimating both measured and unmeasured parameters for control purposes, and performing on-board gas-path fault diagnostics. Computational efficiency is achieved by designing multidimensional interpolation algorithms that exploit the shared scheduling of multiple trim vectors and system matrices. An example application illustrates the accuracy of a self-tuning piecewise linear Kalman filter model when applied to a nonlinear turbofan engine simulation. Additional discussions focus on the issue of transient response accuracy and the advantages of a piecewise linear Kalman filter in the context of validation and verification. The techniques described provide a framework for constructing efficient self-tuning aircraft engine models from complex nonlinear simulations.
 
 

Improved Hybrid Kalman Filter for In-Flight Aircraft Engine Performance Estimation

This paper proposes an improved hybrid Kalman filter(IHKF) for in-flight aircraft engine performance estimation. It’s a special hybrid structure of nonlinear on-board engine model(NOBEM) and piecewise linear Kalman filter(PWKF). The outputs of NOBEM are regarded as the baseline of PWKF, while its performance deterioration factors(PDF) regarded as the augmented state vector of PWKF are on-line estimated by the deviation of measured outputs, and fed back to NOBEM which can be on-line updated next time. In addition, the finite state machine logic of work mode has been established, and makes the IHKF work better. By this approach applied to a turbofan engine, a series of simulation results show that the model can estimate the real engine performance effectively within the whole flight envelope, different engine states and severe performance deterioration condition, which lays the foundation for intelligent engine control(IEC), performance seeking control(PSC) and in-flight fault detection, isolation and accommodation (FDIA).

The GMRT Epoch of Reionization experiment: a new upper limit on the neutral hydrogen power spectrum at z≈ 8.6

We present a new upper limit to the 21cm power spectrum during the Epoch of Reionization (EoR) which constrains reionization models with an unheated IGM. The GMRT-EoR experiment is an ongoing effort to make a statistical detection of the power spectrum of 21cm neutral hydrogen emission at redshift z~9. Data from this redshift constrain models of the EoR, the end of the Dark Ages arising from the formation of the first bright UV sources, probably stars or mini-quasars. We present results from approximately 50 hours of observations at the Giant Metrewave Radio Telescope in India from December 2007. We describe radio frequency interference (RFI) localisation schemes which allow bright sources on the ground to be identified and physically removed in addition to automated flagging. Singular-value decomposition is used to remove remaining broadband RFI by identifying ground sources with large eigenvalues. Foregrounds are modelled using a piecewise linear filter and the power spectrum is measured using cross-correlations of foreground subtracted images.

Multi-user Detection of Nonlinearly Distorted MC-CDMA Symbols by Microstatistic Filtering

Multi-carrier code division multiple access is a powerful modulation technique that is being considered in many emerging broadband communication systems. In a downlink scenario orthogonal spreading sequences are used since they reduce multiple access interference compared to non-orthogonal. However, the nonlinear amplification of the transmitted signal destroys the orthogonality and, thus, reduces the system performance. In order to avoid performance degradation without requiring large back-offs in the transmitter amplifier, it becomes necessary to use multi-user detection techniques at the receiver side. Conventional multi-user detectors (MUD) are designed for linear environments and, as a result, might not exhibit enough performance improvement. In this paper a new MUD based on microstatistic filtering is proposed. The presented MUD uses piece-wise linear filtering in conjunction with threshold decomposition of the input signal, which introduces a nonlinear effect, to improve performance when a nonlinearity is present. Maximum performance improvement compared to conventional MUD is achieved for low spreading factors and user loads no greater than 50%.

An Image-Enhancement System Based on Noise Estimation

A novel multiparameter system for accurate enhancement of noisy images is presented. The proposed system includes cascaded blocks performing directional smoothing and sharpening whose behavior is finely controlled by a set of parameters. Since the most important parameter settings depend on the noise, the standard deviation of the Gaussian noise is estimated by an algorithm that is based on piecewise linear filtering. Thus, simple functions (or lookup tables) are adopted to choose satisfactory parameter values for the overall enhancement system. Computer simulations and experiments with images that are acquired by digital cameras show that the proposed approach yields effective results.

Efficient Nonlinear Wiener Model Identification Using a Complex-Valued Simplicial Canonical Piecewise Linear Filter

This paper proposes an efficient adaptive realization of the Wiener model for the identification of complex-valued nonlinear systems. Using a two-dimensional simplicial canonical piecewise linear filter for the complex-valued nonlinear mapping, we derive a realization of the Wiener model requiring fewer parameters than previous approaches. An adaptive implementation of the proposed Wiener model is derived, and local convergence analysis for the updating algorithm is presented. The tradeoff between computational complexity and modeling performance is discussed. Simulations of a system identification example show that the proposed algorithm can provide similar or better performance than other approaches in terms of computational complexity, convergence speed, and final mean-squared error (MSE)

Technique for Image Denoising Based on Adaptive Piecewise Linear Filters and Automatic Parameter Tuning

A novel technique for image denoising is presented. The proposed approach adopts multipass processing based on a simple piecewise linear filter whose behavior is locally adapted by means of an edge detection algorithm. A method for an automatic parameter tuning when the noise variance is unknown is also presented. Computer simulations and experiments with pictures acquired by digital cameras show that the proposed approach yields very satisfactory results for images corrupted by Gaussian noise

H2 Filtering for Discrete-Time Piecewise Linear Systems

This paper addresses the problem of H2 filtering for piecewise linear discrete-time systems. Both the system and filter have structures that change according to switching rules. Two types of switching rules are considered: (i) the system and filter switching rules are the same and based on an auxiliary signal which is supposed to be available on-line; (ii) the filter and system switching rules are different and based on the filter and system states, respectively. Based on piecewise quadratic Lyapunov functions, LMI conditions are derived for designing piecewise linear filters that ensure an optimized average estimation error variance.

Schlieren systems with coherent illumination for quantitative measurements.

Schlieren systems with a coherent light source were investigated by the Fourier optics technique. The imaging properties of the systems with various cutoff filters were studied. Systems with a graded piecewise linear filter and a Gaussian step function convolution (graded) filter are considered, demonstrating that the image can be approximated by the geometrical-optics theory of conventional schlieren systems. A nonlinear phase contribution was estimated, allowing for the measurement of strong phase objects. Within the framework of linear approximation the results are described by the phase derivative point-spread function, introduced in this paper as the schlieren point-spread function. In addition, modification of the Lopez cutoff filter is proposed, demonstrating its superiority over the piecewise linear and the Gaussian step convolution filters. Simulations of coherent schlieren imaging as well as phase derivative measurements were performed. Finally, the imaging properties of the schlieren systems with the different filters are compared.

Unification of order-statistics based filters to piecewise-linear filters

Order-statistics based filters that were originally provided by the robust estimation theory have proved to be efficient in image/signal filtering in the presence of additive white noise or impulsive noise. Their algorithms are simple and easy to implement. Their analysis, however, is not straightforward. In this paper, we show that filters based on order statistics can be explained by using the theory of piecewise-linear (PWL) functions which was established originally for circuit analysis and has recently been applied to nonlinear filtering. We also prove that an L-filter is a PWL filter defined on IR/sup n/ and a median filter by threshold decomposition is a piecewise-constant (PWC) filter on [0,M-1]/sup n/. The main results lead to the unification of order-statistics based filters with the PWL filter class. Based on the fact that PWL functions are a general class of approximation functions which are uniformly dense in the domain concerned, it is expected that the results obtained can provide a new way to the extension, as well as further study of, order-statistics based filters.

PWL nonlinear adaptive filter via RLS and NLMS algorithms

The recursive least square (RLS) and the normalized least mean square (NLMS) algorithms are proposed for canonical piecewise linear (PWL) adaptive filters. The parameters are updated recursively in a manner similar to back-propagation. The simulation results indicate PWL adaptive filters can suitably model nonlinear systems.