Orthogonal Projection Approach Research Articles

Efficient Distortion Mitigation and Partition Reduction in Mapping Global Geodata: Dual Orthogonal Equidistant Cylindrical Projection Approach

Efficient Distortion Mitigation and Partition Reduction in Mapping Global Geodata: Dual Orthogonal Equidistant Cylindrical Projection Approach

A hybrid projection/data-driven reduced order model for the Navier-Stokes equations with nonlinear filtering stabilization

We develop a Reduced Order Model (ROM) for the Navier-Stokes equations with nonlinear filtering stabilization. Our approach, that can be interpreted as a Large Eddy Simulation model, combines a three-step algorithm called Evolve-Filter-Relax (EFR) with a computationally efficient finite volume method. The main novelty of our ROM lies in the use within the EFR algorithm of a nonlinear, deconvolution-based indicator function that identifies the regions of the domain where the flow needs regularization. The ROM we propose is a hybrid projection/data-driven strategy: a classical Proper Orthogonal Decomposition Galerkin projection approach for the reconstruction of the velocity and the pressure fields and a data-driven reduction method to approximate the indicator function used by the nonlinear differential filter. This data-driven technique is based on interpolation with Radial Basis Functions. We test the performance of our ROM approach on two benchmark problems: 2D and 3D unsteady flow past a cylinder at Reynolds number 0≤Re≤100. The accuracy of the ROM is assessed against results obtained with the full order model for velocity, pressure, indicator function and time evolution of the aerodynamics coefficients.

Benefits of Chemometric and Raman Spectroscopy Applied to the Kinetics of Setting and Early Age Hydration of Cement Paste.

The addition of water is used to past by internal post-curing of hardening cement. Hydration and curing of cementitious are widely identified by non-destructive 1H nuclear magnetic resonance (NMR) measurements of transverse relaxation time and self-diffusion. However, those non-destructive analytical methodologies do not give a truly chemical characterization of the cement matrix during the hydration and curing process. Indeed, the NMR studies only the water dynamics of hydrating cement with internal post-curing. Recent research indicated chemometrics coupled with Raman spectroscopy allows for a better understanding of chemical processes. Recent advances in computing gave industries and research centers the opportunity to generate cost effective data. In this work, an original method is presented, which uses both a data analysis and a non-invasive, non-destructive Raman monitoring of the hydration reaction of a Portland cement. Data was then analyzed by means of chemometrics methods (principal components analysis (PCA), independent components analysis (ICA), and multivariate curve resolution-alternated least-squares (MCR-ALS) with SIMPLe-to-use Interactive Self-modelling Mixture Analysi (SIMPLISMA) and Orthogonal Projection Approach (OP initialization). Results were compared to the ones obtained with thermogravimetric analysis of this cement paste. Besides the consistency of results from both analytical measurements, chemometrics coupled to Raman spectroscopy accurately revealed the details of the setting without any samples collection. The acquisition frequency allowed a proper identification of the occurrence of each of the various phases involved in the hydration and setting process.

A subspace projection approach to quantify respiratory variations in the f-wave frequency trend.

Background: The autonomic nervous system (ANS) is known as a potent modulator of the initiation and perpetuation of atrial fibrillation (AF), hence information about ANS activity during AF may improve treatment strategy. Respiratory induced ANS variation in the f-waves of the ECG may provide such information. Objective: This paper proposes a novel approach for improved estimation of such respiratory induced variations and investigates the impact of deep breathing on the f-wave frequency in AF patients. Methods: A harmonic model is fitted to the f-wave signal to estimate a high-resolution f-wave frequency trend, and an orthogonal subspace projection approach is employed to quantify variations in the frequency trend that are linearly related to respiration using an ECG-derived respiration signal. The performance of the proposed approach is evaluated and compared to that of a previously proposed bandpass filtering approach using simulated f-wave signals. Further, the proposed approach is applied to analyze ECG data recorded for 5 min during baseline and 1 min deep breathing from 28 AF patients from the Swedish cardiopulmonary bioimage study (SCAPIS). Results: The simulation results show that the estimates of respiratory variations obtained using the proposed approach are more accurate than estimates obtained using the previous approach. Results from the analysis of SCAPIS data show no significant differences between baseline and deep breathing in heart rate (75.5 ± 22.9 vs. 74 ± 22.3) bpm, atrial fibrillation rate (6.93 ± 1.18 vs. 6.94 ± 0.66) Hz and respiratory f-wave frequency variations (0.130 ± 0.042 vs. 0.130 ± 0.034) Hz. However, individual variations are large with changes in heart rate and atrial fibrillatory rate in response to deep breathing ranging from −9% to +5% and −8% to +6%, respectively and there is a weak correlation between changes in heart rate and changes in atrial fibrillatory rate (r = 0.38, p < 0.03). Conclusion: Respiratory induced f-wave frequency variations were observed at baseline and during deep breathing. No significant changes in the magnitude of these variations in response to deep breathing was observed in the present study population.

On convergence of a structure preserving difference scheme for two-dimensional space-fractional nonlinear Schrödinger equation and its fast implementation

In this paper we intend to construct a structure preserving difference scheme for two-dimensional space-fractional nonlinear Schrödinger (2D SFNS) equation with the integral fractional Laplacian. The temporal direction is discretized by the modified Crank-Nicolson method, and the spatial variable is approximated by a novel fractional central difference method. The mass and energy conservations and the convergence are rigorously proved for the proposed scheme. For 1D SFNS equation, the convergence relies heavily on the L∞-norm boundness of the numerical solution of the proposed scheme. However, we cannot obtain the L∞-norm boundness of the numerical solution by using the similar process for the 2D SFNS equation. One of the major significance of this paper is that we first obtain the L∞-norm boundness of the numerical solution and L2-norm error estimate via the popular “cut-off” function for the 2D SFNS equation. Further, we reveal that the spatial discretization generates a block-Toeplitz coefficient matrix, and it will be ill-conditioned as the spatial grid mesh number M and the fractional order α increase. Thus, we exploit an linearized iteration algorithm for the nonlinear system, so that it can be efficiently solved by the Krylov subspace solver with a suitable preconditioner, where the 2D fast Fourier transform (2D FFT) is applied in the solver to accelerate the matrix-vector product, and the standard orthogonal projection approach is used to eliminate the drift of mass and energy. Extensive numerical results are reported to confirm the theoretical analysis and high efficiency of the proposed algorithm.

Factor dimension determination for panel interactive effects models: an orthogonal projection approach

We consider a computationally simple orthogonal projection method to implement the (Bai and Ng in Econometrica 70:191–221, 2002) information criterion to select the factor dimension for panel interactive effects models that bypasses issues arising from the joint estimation of the slope coefficients and factor structure. Our simulations show that it performs well in cases the method can be implemented.

Improved OP approach utilising correlated projection and eigenspace processing for robust adaptive beamforming

The capability of orthogonal projection (OP) approach degrades severely in the presence of array model mismatch, especially when the training samples are mixed with the strong desired signal. Therefore, an improved OP robust adaptive beamforming is proposed based on correlated projection and eigenspace processing in wide input signal-to-noise ratio to remove the desired signal self-null effect and improve robustness. In the proposed approach, the interference subspace is constructed combining the correlated projection and eigenspace processing first. Then, the interference-plus-noise covariance matrix is accurately reconstructed via super-resolution spatial spectrum estimator to eliminate desired signal from sample covariance matrix. Subsequently, the desired signal steering vector is corrected applying correlated projection and then the adaptive weighted vector is modified by OP approach. Simulation results demonstrate that the capability of the proposed approach is almost consistently same as the optimal beamformer in many scenarios.

Regression credibility estimator with two-level common effects

In this paper, we extend the regression credibility model to account for a type of dependence structures over individual risks and portfolio risks induced by common effects. By using orthogonal projection approach, the corresponding credibility estimators are derived, which extend those for the existing models to slightly more general versions. Finally, a numerical example is presented to show the effectiveness of the regression credibility estimator.

Towards an Algebraic Theory of Orthogonal Polynomials in Several Variables

In this paper, we review on a general theory of orthogonal polynomials in several variables (O.P.S.V) in which we present two different approaches for the three-term recurrence relation. We draw attention to the fact that it is possible to take advantage of the orthogonal projection approach of the three-term recurrence relation towards the development of the algebraic theory of O.P.S.V.

Band-Specified Virtual Dimensionality for Band Selection: An Orthogonal Subspace Projection Approach

This paper develops a new Neyman–Pearson detection approach, to be called band-specified virtual dimensionality (BSVD), to estimating the number of bands required by band selection (BS), $n_{\mathrm {BS}}$ , as well as finding desired bands at the same time. Its idea is derived from target-specified virtual dimensionality (TSVD) where targets under hypotheses as signal sources in TSVD are replaced with bands as signal sources and the test statistics derived for a Neyman–Pearson detector (NPD) is signal-to-noise ratio (SNR) that is used to derive orthogonal subspace projection (OSP) approach for hyperspectral image classification and dimensionality reduction. Accordingly, the resulting virtual dimensionality is referred to as OSP-based BSVD. Several benefits resulting from BSVD cannot be offered by the traditional BS methods. One is its direct approach to dealing with $n_{\mathrm {BS}}$ . Another is no-search strategy needed for finding optimal bands. Instead, it uses NPD to determine and rank desired bands for band prioritization. Most importantly, it determines $n_{\mathrm {BS}}$ and finds desired bands simultaneously and progressively.

Krein space-based H∞ adaptive smoother design for a class of Lipschitz nonlinear discrete-time systems

In this paper, the problem of H∞ adaptive smoother design is addressed for a class of Lipschitz nonlinear discrete-time systems with l2 bounded disturbance input. By comprehensively analyzing the H∞ performance, Lipschitz conditions and unknown parameter’s bounded condition, a positive minimum problem for an indefinite quadratic form is introduced such that the H∞ adaptive smoothing problem is achieved. A Krein space stochastic system with multiple fictitious outputs is constructed by associating with the minimum problem of the introduced indefinite quadratic form. The minimum of indefinite quadratic form is derived in the form of innovations through utilizing Krein space orthogonal projection and innovation analysis approach. Via choosing the suitable fictitious outputs to guarantee the minimum of indefinite quadratic form is positive, the existence condition of the adaptive smoother and its analytical solutions are obtained in virtue of nonstandard Riccati difference equations. The quality of the estimator is checked on an example.

Determining the number of principal factors by eigenvector comparison of the original bi-linear data matrix and the one reconstructed from key variables

It is an essential step in analyzing hyphenated chromatographic data of complex chemical systems to determine the number of principal factors of the bi-linear matrix. The determination is difficult due to the co-existence of non-chemical factors, such as background, noise, etc. A new method was proposed for the determination based on comparing eigenvectors of the original data matrix and the one reconstructed from key spectral variables that are selected with orthogonal projection approach (OPA). The proposed method is mathematically rigorous and the determination is clear. In comparison with other four indices, i.e., NPFPCA (noise perturbation in functional principal component analysis), RESO (the ratio of eigenvalues calculated by smoothed principal component analysis and those calculated by ordinary principal component analysis), DRAUG (determination of rank by augmentation) and DRMAD (determination of rank by median absolute deviation), this proposed method was proven to have good performance in both simulated GC-IR and experimental HPLC-DAD data.

Orthogonal projection approach and continuous wavelet transform-feed forward neural networks for simultaneous spectrophotometric determination of some heavy metals in diet samples

Simultaneous spectrophotometric determination of a mixture of overlapped complexes of Fe3+, Mn2+, Cu2+, and Zn2+ ions with 2-(3-hydroxy-1-phenyl-but-2-enylideneamino) pyridine-3-ol(HPEP) by orthogonal projection approach-feed forward neural network (OPA-FFNN) and continuous wavelet transform-feed forward neural network (CWT-FFNN) is discussed. Ionic complexes HPEP were formulated with varying reagent concentration, pH and time of color formation for completion of complexation reactions. It was found that, at 5.0×10−4molL−1 of HPEP, pH 9.5 and 10min after mixing the complexation reactions were completed. The spectral data were analyzed using partial response plots, and identified non-linearity modeled using FFNN. Reducing the number of OPA-FFNN and CWT-FFNN inputs were simplified using dissimilarity pure spectra of OPA and selected wavelet coefficients. Once the pure dissimilarity plots ad optimal wavelet coefficients are selected, different ANN models were employed for the calculation of the final calibration models. The performance of these two approaches were tested with regard to root mean square errors of prediction (RMSE %) values, using synthetic solutions. Under the working conditions, the proposed methods were successfully applied to the simultaneous determination of metal ions in different vegetable and foodstuff samples. The results show that, OPA-FFNN and CWT-FFNN were effective in simultaneously determining Fe3+, Mn2+, Cu2+, and Zn2+ concentration. Also, concentrations of metal ions in the samples were determined by flame atomic absorption spectrometry (FAAS). The amounts of metal ions obtained by the proposed methods were in good agreement with those obtained by FAAS.

Optimisation of chromatographic resolution using objective functions including both time and spectral information

The optimisation of the resolution in high-performance liquid chromatography is traditionally performed attending only to the time information. However, even in the optimal conditions, some peak pairs may remain unresolved. Such incomplete resolution can be still accomplished by deconvolution, which can be carried out with more guarantees of success by including spectral information. In this work, two-way chromatographic objective functions (COFs) that incorporate both time and spectral information were tested, based on the peak purity (analyte peak fraction free of overlapping) and the multivariate selectivity (figure of merit derived from the net analyte signal) concepts. These COFs are sensitive to situations where the components that coelute in a mixture show some spectral differences. Therefore, they are useful to find out experimental conditions where the spectrochromatograms can be recovered by deconvolution. Two-way multivariate selectivity yielded the best performance and was applied to the separation using diode-array detection of a mixture of 25 phenolic compounds, which remained unresolved in the chromatographic order using linear and multi-linear gradients of acetonitrile–water. Peak deconvolution was carried out using the combination of orthogonal projection approach and alternating least squares.

Optimal linear estimators for multi-sensor stochastic uncertain systems with packet losses of both sides

Optimal linear estimators (OLEs) are designed for networked control systems (NCSs) with stochastic uncertainties, multiple sensors and multiple packet loss rates. Packet losses of both sides from sensors to an estimator (S–E) and from a controller to an actuator (C–A) are taken into account. A group of mutually uncorrelated stochastic variables obeying Bernoulli distributions are employed to depict the phenomenon of multiple packet losses from different S–E channels. The stochastic uncertainties in state and output matrices are depicted by white multiplicative noises. The OLEs dependent on the packet loss rates are presented in the least mean square (LMS) sense via the orthogonal projection approach (OPA) which is a universal and useful tool to obtain the optimal linear estimators in LMS sense. They are solved by three recursive equations including one Riccati equation, one Lyapunov equation and one simple difference equation. The stability of the OLEs is studied. A sufficient condition is provided to guarantee the steady-state property for time-invariant systems. Finally, a mass–spring–damper system is applied to confirm the performance of the derived algorithms.

Bias-eliminated subspace model identification under time-varying deterministic type load disturbance

Unexpected or time-varying deterministic type load disturbances are often encountered when performing identification tests in practical applications. A bias-eliminated subspace identification method is proposed in this paper by developing an orthogonal projection approach to guarantee consistent estimation on the deterministic part of the plant, in combination with a Maclaurin time series approximation on the output response arising from deterministic type load disturbance. The rank condition for such an orthogonal projection is disclosed in terms of the state-space model structure adopted for identification. Using principal component analysis (PCA), the extended observability matrix and the lower triangular Toeplitz matrix of the state-space model are explicitly derived. Accordingly, the plant state-space matrices can be retrieved from the above matrices through a shift-invariant algorithm. A benchmark example from the literature and an illustrative example of industrial injection molding are used to demonstrate the effectiveness and merit of the proposed identification method.

Modeling and estimation for networked systems with multiple random transmission delays and packet losses

In networked systems, data packets are transmitted through networks from a sensor to a data processing center. Due to the unreliability of communication channels, a packet may be delayed even lost during the transmission. At each moment, the data processing center may receive one or multiple data packets or nothing at all. A novel model is developed to describe the possible multiple random transmission delays and data packet losses by employing a group of Bernoulli distributed random variables. It is transformed to a measurement model with multiple random delayed states and noises. Based on the model, an optimal linear filter in the linear minimum variance sense is proposed by using the orthogonal projection approach which is a universal tool to find the optimal linear estimate. It does not have a steady-state performance since it depends on the values of random variables that depict the phenomena of delays and losses at each moment. So it needs to be computed online. To reduce the online computational cost, a suboptimal linear filter dependent on the probabilities of random variables is also proposed. However, it is worth noting that it is linearly optimal among all the linear filters dependent on the probabilities. It can be computed offline since it has the steady-state performance. A sufficient condition of existence for the steady-state performance is given. A simulation example shows the effectiveness.

Improved orthogonal projection approach utilising interference covariance matrix reconstruction for adaptive beamforming

When the training snapshots are contaminated by the desired signal, the performance of the orthogonal projection (OP) approach degrades significantly. Therefore, an improved OP adaptive beamforming is proposed by reconstructing interference covariance matrix to eliminate the desired signal cancellation effect. In the proposed method, by integrating the Capon spatial spectrum over a region separated from the desired signal direction, the interference-plus-noise covariance matrix is reconstructed first to remove the desired signal component from the sample covariance matrix. Subsequently, the interference subspace is estimated by eigenvalue decomposition, and then the adaptive weight vector is calculated using the OP algorithm to eliminate the noise perturbation. Simulation results show that the performance of the proposed algorithm is almost the same as the optimum beamforming.

Active mass driver control system for suppressing wind-induced vibration of the Canton Tower

In order to suppress the wind-induced vibrations of the Canton Tower, a pair of active mass driver (AMD) systems has been installed on the top of the main structure. The structural principal directions in which the bending modes of the structure are uncoupled are proposed and verified based on the orthogonal projection approach. For the vibration control design in the principal X direction, the simplified model of the structure is developed based on the finite element model and modified according to the field measurements under wind excitations. The AMD system driven by permanent magnet synchronous linear motors are adopted. The dynamical models of the AMD subsystems are determined according to the open-loop test results by using nonlinear least square fitting method. The continuous variable gain feedback (VGF) control strategy is adopted to make the AMD system adaptive to the variation in the intensity of wind excitations. Finally, the field tests of free vibration control are carried out. The field test results of AMD control show that the damping ratio of the first vibration mode increases up to 11 times of the original value without control.

N4SID and MOESP Algorithms to Highlight the Ill-conditioning into Subspace Identification

In this paper, an analysis for ill conditioning problem in subspace identification method is provided. The subspace identification technique presents a satisfactory robustness in the parameter estimation of process model which performs control. As a first step, the main geometric and mathematical tools used in subspace identification are briefly presented. In the second step, the problem of analyzing ill-conditioning matrices in the subspace identification method is considered. To illustrate this situation, a simulation study of an example is introduced to show the ill-conditioning in subspace identification. Algorithms numerical subspace state space system identification (N4SID) and multivariable output error state space model identification (MOESP) are considered to study, the parameters estimation while using the induction motor model, in simulation (Matlab environment). Finally, we show the inadequacy of the oblique projection and validate the effectiveness of the orthogonal projection approach which is needed in ill-conditioning; a real application dealing with induction motor parameters estimation has been experimented. The obtained results proved that the algorithm based on orthogonal projection MOESP, overcomes the situation of ill-conditioning in the Hankel's block, and thereby improving the estimation of parameters.