Orthogonal Algorithm Research Articles

Algorithms for Evaluation of Biooptical Characteristics in the Gulf of Finland Using Empirical Orthogonal Functions

The paper presents the results of testing the possibility of using empirical orthogonal functions to develop algorithms for estimating the concentration of chlorophyll a and suspended matter, the biomass of cyanobacteria in the eastern part of the Gulf of Finland. To develop the algorithms, we used an array of data from field measurements of the subsurface radiance reflectance in 2012–2014, carried out simultaneously with the determination of bio-optical characteristics. It turned out that in the case of the concentration of chlorophyll a and suspended matter, such algorithms can be created not only using the hyperspectral radiance reflectance, but also for the spectral channels of satellite color scanners MODIS and OLCI. An estimation of the cyanobacteria biomass with the empirical orthogonal functions method is not applicable in the case of using satellite channels. A study of the possibility of the most prone to atmospheric correction errors shortwave MODIS channels exclusion was also made. It turned out that the concentration of chlorophyll a is more sensitive to such exclusion than the concentration of suspended matter. Validation on a MODIS data showed that empirical orthogonal functions algorithms give results no worse than regression ones.

Equivalent-Input-Disturbance-Based Dynamic Tracking Control for Soft Robots via Reduced-Order Finite-Element Models

This article develops a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">systematic</i> framework for dynamic tracking control of soft robots. To this end, we propose a new projector for the proper orthogonal decomposition algorithm to significantly reduce the large-scale robot models, obtained from finite-element methods (FEM), while preserving their structure and stability properties. Such a property preservation enables an effective equivalent-input-disturbance-based scheme for dynamic tracking control of elastic soft robots with various geometries and materials. The proposed control scheme is composed of three key components, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> , feedforward control, disturbance-estimator control, and feedback control. To account for the trajectory reference, the feedforward action is designed from the dynamic FEM reduced-order robot model. The disturbance-estimator control action is obtained from an unknown input observer, which also provides the estimates of the reduced states for the feedback control design. The feedback gains of the observer-based controller are computed from an optimization problem under linear matrix inequality constraints. The closed-loop tracking properties are guaranteed using the Lyapunov stability theory. The effectiveness of the proposed dynamic control framework has been demonstrated via both high-fidelity SOFA simulations and experimental validations, performed on two soft robots with different natures. In particular, comparative studies with state-of-the-art control methods have been also carried out to highlight the interests of the new soft robot control results. This article is complemented with a video: <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://bit.ly/2VVwtLn</uri> .

Transient characteristics of a typical vacuum ejector—An experimental study

Using simultaneous measurements of unsteady pressures in conjunction with time-resolved Schlieren images and oil flow visualization, we investigate the characteristics of a typical vacuum ejector's starting transient, steady-state, and shut-down transient. With varying primary jet chamber pressure, the pressure evolution in the secondary chamber shows smooth, perturbed, rapid, and steady evacuation stages, as well as hysteresis and rapid filling stages. It is noticed that the evacuation in the secondary chamber is improved during stopping transient just before the unstart event. By using oil flow images, we illustrate the separation bubble characteristics during each stage of the vacuum ejector operation and their influence on the pressure evolution. Through cross correlation, it has been determined that the primary jet flapping during the starting transient causes the jet to attach to one of the diffuser walls. We also demonstrate that the primary jet undergoes both longitudinal and lateral oscillations in the starting transient, the former having a major effect on unsteadiness in the secondary chamber using proper orthogonal decomposition and spectral proper orthogonal decomposition algorithms and power spectral density (PSD). Simultaneous acquisition of unsteady pressures and high-speed Schlieren images allow us to correlate the frequency peaks (PSD spectra) in the flow. Using magnitude-squared coherence and cross correlation analyses, we confirm communication of unsteadiness and its direction of propagation between the secondary chamber and the diffuser. In this study, we demonstrate that a high ramping rate of primary jet chamber pressure reduces the unsteadiness in the secondary chamber during the transient starting phase.

Modal analysis of subway tunnel in soft soil during operation

Modal parameters are of great significance in civil engineering because they can characterize the properties of structures and be used for vibration control and structural health monitoring. Subway tunnels are long linear truss structures combined with the mutual coupling of the surrounding soil. Therefore, the operational modal analysis of a mutual coupling tunnel is complicate, as is the modal identification of shield tunnels in a time–frequency domain, and these are hot civil engineering topics. Using the shield tunnel of Shanghai metro line No.12 project as a case study, we carried out the vibration response monitoring of a subway tunnel during operation and presented methods to identify structural modal parameters. The modal parameters of lower vibration modes were estimated using response measurements. Modal frequencies and shapes were identified with high precision and accuracy using the orthogonal polynomial clustering algorithm under hammer excitation conditions and the autoregressive-moving-average model under ambient excitation conditions. The dynamic behavior of a mutual coupling tunnel presented obvious low frequency characteristics, and the first 9th order mode frequencies were less than 100 Hz. The diagonal values of the modal assurance criteria were all greater than 0.85. The modal parameters can be used for the health monitoring of operational subway tunnels.

An Orthogonal Matching Pursuit Variable Screening Algorithm for High-Dimensional Linear Regression Models

Variable selection plays an important role in data mining. It is crucial to filter useful variables and extract useful information in a high-dimensional setup when the number of predictor variables d tends to be much larger than the sample size n . Statistical inferences can be more precise after irrelevant variables are moved out by the screening method. This article proposes an orthogonal matching pursuit algorithm for variable screening under the high-dimensional setup. The proposed orthogonal matching pursuit method demonstrates good performance in variable screening. In particular, if the dimension of the true model is finite, OMP might discover all relevant predictors within a finite number of steps. Throughout theoretical analysis and simulations, it is confirmed that the orthogonal matching pursuit algorithm can identify relevant predictors to ensure screening consistency in variable selection. Given the sure screening property, the BIC criterion can be used to practically select the best candidate from the models generated by the OMP algorithm. Compared with the traditional orthogonal matching pursuit method, the resulting model can improve prediction accuracy and reduce computational cost by screening out the relevant variables.

Parallel solution of optimal control problems using the graphics processing unit

AbstractThis paper presents an indirect method for solving optimal control problems (OCPs) using graphics processing unit (GPU). The OCPs considered here include control variable inequality constraints (CVICs), state variable inequality constraints (SVICs), and parameters. The necessary conditions of the minimum for the OCPs are written as a boundary value problem with index‐1 differential algebraic equations (BVP‐DAEs). The complementarity conditions associated with those inequality constraints are approximated using Kanzow's smoothed Fisher‐Burmeister formula. The numerical solution for solving the BVP‐DAEs is based on the multiple shooting technique and the DAEs are solved using a single step linearly implicit Runge–Kutta (Rosenbrock–Wanner, ROW) method. A Newton's continuation method is performed to solve the BVP‐DAEs system and the descent direction is found by solving a sparse bordered almost block diagonal (BABD) linear system with a structured orthogonal factorization algorithm. Parallel computing techniques are used to accelerate the code which is implemented using Python and CUDA on GPU. Numerical examples are presented to illustrate the efficiency of the code. The GPU based parallel implementation is shown to be significantly faster than the implementation using central processing unit (CPU) alone.

Data-driven reduced order modeling for parametrized time-dependent flow problems

This paper proposes a nonintrusive reduced basis (RB) method based on dynamic mode decomposition (DMD) for parameterized time-dependent flows. In the offline stage, the reduced basis functions are extracted by a two-step proper orthogonal decomposition algorithm. Then, a novel hybrid DMD regression model that combines windowed DMD and optimized DMD is introduced for the temporal evolution of the RB coefficients. To improve the stability of this method for complex nonlinear problems, we introduce a threshold value to modify the DMD eigenvalues and eigenvectors. Moreover, the interpolation of the coefficients in parameter space is conducted by a feedforward neural network or random forest algorithm. The prediction of the RB solution at a new time/parameter value can be recovered at a low computational cost in the online stage, which is completely decoupled from the high-fidelity dimension. We demonstrate the performance of the proposed model with two cases: (i) laminar flow past a two-dimensional cylinder and (ii) turbulent flow around a three-dimensional SD7003 airfoil. The results show reasonable efficiency and robustness of this novel reduced-order model.

An Improved Fault Diagnosis Approach Using LSSVM for Complex Industrial Systems

Fault diagnosis is a challenging topic for complex industrial systems due to the varying environments such systems find themselves in. In order to improve the performance of fault diagnosis, this study designs a novel approach by using particle swarm optimization (PSO) with wavelet mutation and least square support (LSSVM). The implementation entails the following three steps. Firstly, the original signals are decomposed through an orthogonal wavelet packet decomposition algorithm. Secondly, the decomposed signals are reconstructed to obtain the fault features. Finally, the extracted features are used as the inputs of the fault diagnosis model established in this research to improve classification accuracy. This joint optimization method not only solves the problem of PSO falling easily into the local extremum, but also improves the classification performance of fault diagnosis effectively. Through experimental verification, the wavelet mutation particle swarm optimazation and least sqaure support vector machine ( WMPSO-LSSVM) fault diagnosis model has a maximum fault recognition efficiency that is 12% higher than LSSVM and 9% higher than extreme learning machine (ELM). The error of the corresponding regression model under the WMPSO-LSSVM algorithm is 0.365 less than that of the traditional linear regression model. Therefore, the proposed fault scheme can effectively identify faults that occur in complex industrial systems.

Resonance Interference Research of MEMS Inertial Sensors and Algorithm Elimination

The mechanical structure of MEMS inertial sensors is a spring-mass-damper system, which is susceptible to interference near the resonant frequency. This work compared the resonance interference effects of mechanical vibrations and high frequency sound waves on inertial sensors. Three MEMS gyroscopes ADXRS620 were interfered by vibrations and sound waves near the resonant frequency. The error outputs increased linearly with the increase of interference intensity. In amplitude sweep experiment, the max error could reach 126.00 °/s, which seriously affect the normal operation of the gyroscope. The waveforms of gyroscope outputs under acoustic and vibration interference were almost coincident, which showed the similarity of acoustic and vibration interference. However, the MEMS accelerometer ADXL103 has a very different performance under acoustic and vibration interference, not only the resonant frequency and max error change, but also the error output and interference intensity are nonlinearly related. In amplitude sweep experiment, the max error could reach 9.78 m/s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . In addition, to produce the same effect on MEMS inertial sensors, the power required of vibration interference was much less than that of acoustic interference. The effectiveness against vibration interference of the filtering algorithm based on orthogonal demodulation was verified by testing the self-developed gyroscope. To the best of our knowledge, it is the first time that use the IQ two-channel orthogonal demodulation filtering algorithm to eliminate vibration interference. The elimination effect was over 97%.

SLA-Based Orthogonal Parallel Detection of Global Rotationally Coherent Lagrangian Vortices

Abstract In this paper, we present a highly effective orthogonal parallel algorithm for identifying global rotationally coherent Lagrangian vortices (RCLVs) in heterogeneous systems and a long-time-scale global sea level anomaly (SLA)-based RCLVs product. First, a many-core parallel computing method is used to accelerate the Lagrangian-averaged vorticity deviation (LAVD) computing process. The computation is approximately 8000 times faster than that of a previous method. Second, the global LAVD field is divided into several regions. These regions are searched with a multiprocess CPU parallel pool to identify simultaneously RCLVs. All the identified RCLVs in these regions are merged seamlessly into a global eddy map. The algorithm improves the global RCLV identification efficiency, making the proposed method approximately 20 times faster than a single-threaded method. The LAVD many-core computing method and the RCLV multiprocess parallel method are orthogonally combined. The resulting algorithm is at least 500 times faster than previous nonparallel methods, making the computing of global RCLVs feasible. Third, the advection of Lagrangian particles in RCLVs and Eulerian eddies is analyzed to demonstrate the material coherence of RCLVs and the reliability of our algorithm. Finally, a global RCLVs product from 1993 to 2019 containing 52 567 eddies is produced with a 90-day time interval. This is the first time that a long-time-scale global Lagrangian eddy product has been presented.

Orthogonal projection constant false alarm rate algorithm in fractional domain for small surface targets

In this article, a constant false alarm rate (CFAR) detection algorithm based on the fractional Fourier transform (FRFT) and orthogonal projection (OP) is proposed. With a low signal-to-clutter ratio (SCR), the radar returns of sea-surface small targets are often submerged by sea clutter. The FRFT can accumulate target energy in the optimal order. Meanwhile, the OP suppresses the sea clutter in a projection space in the FRFT domain, thus enhancing the output SCR. The FRFT and the OP are in conjunction with the CFAR to realise target detection, which is referred to as the FRFT-OP-CFAR. For the FRFT-OP-CFAR detector, the most important is the selection of the optimal order p and the calculation of the OP operator ψ x ⊥ . The experimental results show that the proposed FRFT-OP-CFAR has a better clutter suppression and detection performance than some detectors in the authors’ comparison.

Estimation Method for Mixed Near-Field and Far-Field Sources Based on Four-Order Cumulant and Polarization Sensitive Array

A new multidimensional parameters joint estimation method of mixed near-field and far-field sources based on polarization sensitive array, fourth-order cumulant, joint diagonalization technology, and propagator method is presented, which can realize the joint estimation of DOA (Direction of Arrival), range, frequency, polarization auxiliary angle, and polarization phase difference without multidimensional spectral peak searching and parameter pairing, and it is suitable for any additive Gaussian noise environment and effective for reducing the loss of array aperture. The algorithm skillfully constructs the fourth-order cumulant matrix by using the output on the label of specific dipole pairs of the received array, which effectively avoids the matrix rank reduction caused by the far-field sources coexistence situation. In addition, the presented algorithm utilizes the orthogonal propagation algorithm for subspace decomposition and uses the total least square solution to replace the orthogonal solution of singular value decomposition, which effectively reduces the computational complexity. The experiment proved the effectiveness of the proposed algorithm.

Adaptive equalization based on dynamic compressive sensing for single-carrier multiple-input multiple-output underwater acoustic communications.

The sparse property of a direct adaptive equalizer (DAE) for single-carrier underwater acoustic communications is well recognized. It has been used to improve the performance and/or reduce the complexity of a DAE. Extensive investigations have been performed in terms of performance improvement. On the contrary, research on complexity reduction remains preliminary. A fundamental way for reducing the complexity of a DAE is to keep only significant taps while discarding trivial taps, that is, to run a partial-tap DAE. Existing partial-tap DAE designs assume a slowly varying sparse structure and may suffer performance degradation under a severe underwater environment. Motivated by this fact, the dynamic compressed sensing (DCS) technique is resorted to and a partial-tap DAE based on the sparse adaptive orthogonal matching pursuit-affine projection algorithm is proposed. The sparse adaptive orthogonal matching pursuit-affine projection algorithm-direct adaptive equalizer (SpAdOMP-APA-DAE) achieves symbol-wise updating of both positions and values of the significant coefficients. In this paper, a more extensive study on DCS-based DAEs is performed, and an enhanced dynamic compressed sensing-direct adaptive equalizer design enabled by the sparse adaptive subspace pursuit-improved proportionate affine projection algorithm (SpAdOMP-IPAPA) is proposed. The sparse adaptive subspace pursuit-improved proportionate affine projection algorithm-direct adaptive equalizer enjoys lower complexity while better performance than the previous SpAdOMP-APA-DAE. Experimental results corroborated the superiority of the SpAdOMP-IPAPA-DAE.

Almost Optimality of the Orthogonal Super Greedy Algorithm for μ-Coherent Dictionaries

We study the approximation capability of the orthogonal super greedy algorithm (OSGA) with respect to μ-coherent dictionaries in Hilbert spaces. We establish the Lebesgue-type inequalities for OSGA, which show that the OSGA provides an almost optimal approximation on the first [1/(18μs)] steps. Moreover, we improve the asymptotic constant in the Lebesgue-type inequality of OGA obtained by Livshitz E D.

Continuous Rotor Dynamics of Multi-Disc and Multi-Span Rotors: A Theoretical and Numerical Investigation of the Identification of Rotor Unbalance from Unbalance Responses

Rotor unbalance identification plays a critical role in balancing rotors. In this paper, concerned with multi-disc and multi-span rotor-bearing systems, two novel algorithms called the Single Direction Algorithm (SDA) and the Two Orthogonal Direction Algorithm (TODA) are proposed for identifying rotor unbalance from unbalance responses. A matrix method is proposed to solve the problem of the equations being non-linear transcendental, there being too many unknown variables in the equations, and rotor unbalances and bearing coefficients being coupled together. The unbalance responses at all the eccentric discs are necessary for identifying their unbalances. Numerical simulations are conducted to validate the proposed methods. Moreover, an adjustment point is found, and a proper sensor resolution is suggested to achieve high identification accuracy by means of numerical studies. In addition, the identification accuracy of SDA is better than TODA, and SDA is more practical and suitable for medium-speed and high-speed rotors. The proposed algorithms have the flexibility to incorporate any number of bearings and discs and provide a technique for monitoring rotor unbalance without test runs or external exciters.

Research on Aerodynamic Modeling of Axisymmetric Aircraft Based on Orthogonal Least Squares

Abstract Aerodynamic modeling is of great importance for design of axisymmetric aircraft control system. In this paper, an axisymmetric aircraft aerodynamic model selection method is constructed, which involves an orthogonal least squares algorithm using in model structure selection, and the method based on it is selected for determining the aerodynamic coefficients. Then the method is tested in three axis coefficient modeling of a certain axisymmetric aircraft, and the modeling result is consistent with the wind tunnel test data.

Research on Resolution Enhancement Technology of Orthogonal Multimode Fiber Imaging

This paper presents a new scheme to improve the imaging resolution of optical fiber endoscope. Multimode fiber imaging is combined with correlation imaging experimental architecture, and Schmidt orthogonalization algorithm is used to reduce the correlation of light field. The simulation and experimental results show that this scheme can greatly improve the imaging quality and resolution, especially in the case of under sampling. In addition, the scheme can also resist the low resolution problem caused by the light field divergence of multimode fiber correlation imaging, and when the light field divergence reaches a certain extent, the resolution of the orthogonalized multimode fiber light field will no longer be affected. The feasibility of orthogonal multimode fiber imaging scheme in large depth of field is verified.

Performance Analysis of Orthogonal Gradient Sign Algorithm Using Spline-based Hammerstein Model for Smart Application

This paper presents a spline-based Hammerstein model for adaptive filtering based on a sign algorithm with the normalised orthogonal gradient algorithm. Spline-based Hammerstein architecture consists of an interpolation spline-based adaptive lookup table in the part of nonlinear filter and an adaptive finite impulse response filter used in the part of linear filter. Hammerstein spline adaptive filter (HSAF) is a nonlinear filter for the nonlinear systems among the advantages in the low computational cost and high performance. An adaptive lookup table and spline control points are determined and derived with the orthogonal gradient-based mechanism. Performance analysis in terms of convergence properties and mean square analysis based on the mean square error (MSE) constraint are proven by using the Taylor series expansion of the estimation error in the form of the excess MSE. Experimental results indicate the robust performance of the proposed algorithm can provide the better performance than the other models based on the conventional least mean square Hammerstein spline adaptive filtering algorithm.

A Method for the Design of Bicomplex Orthogonal DSP Algorithms for Applications in Intelligent Radio Access Networks

In this paper, a new method for designing orthogonal bicomplex digital signal processing (DSP) algorithms is developed. In contrast to those previously reported on, the method proposed is universal, since it is not affected by the order or the type of the real digital processing algorithm employed as a prototype. The method is based on a transformation starting with either real or complex orthogonal DSP algorithms represented in the z-domain, and transforming them into orthogonal bicomplex algorithms. The proposed new method is applied in the design of bilinear orthogonal bicomplex DSP systems with a canonical number of elements, the main advantage of which is that the order of the digital system is reduced by a factor of four. As well as being canonical, the orthogonal bicomplex digital systems are also symmetrical structures, as a result of which they offer parallelism and subsequent unification. It is experimentally shown that bicomplex orthogonal DSP algorithms acquire the properties of the initial algorithm prototype, irrespective of whether it is real or complex. Since the new design method is universally applicable, it can be used to develop bicomplex orthogonal digital algorithms of any order and type. Being simple, canonical, and symmetrical—and, thus, leading to lower equipment cost, reduced complexity, and higher energy efficiency—these structures may well be appropriate for the enhancement of the implementation of intelligent algorithms in next-generation radio access networks.

Comparing Two Different Development Methods of External Parameter Orthogonalization for Estimating Organic Carbon from Field-Moist Intact Soils by Reflectance Spectroscopy

Visible and near-infrared (Vis–NIR) spectroscopy can provide a rapid and inexpensive estimation for soil organic carbon (SOC). However, with respect to field in situ spectroscopy, external environmental factors likely degrade the model accuracy. Among these factors, moisture has the greatest effect on soil spectra. The external parameter orthogonalization (EPO) algorithm in combination with the Chinese soil spectroscopic database (Dataset A, 1566 samples) was investigated to eliminate the interference of the external parameters for SOC estimation. Two different methods of EPO development, namely, laboratory-rewetting archive soil samples and field-collecting actual moist samples, were compared to balance model performance and analytical cost. Memory-based learning (MBL), a local modeling technique, was introduced to compare with partial least square (PLS), a global modeling method. A total of 250 soil samples from Central China were collected. Of these samples, 120 dry ground samples (Dataset B) were rewetted to different moisture levels to develop EPO P1 matrix. Seventy samples (Dataset C) containing field-moist intact and laboratory dry ground soils were used to establish EPO P2 matrix. The remaining 60 samples (Dataset D) also containing field-moist intact and laboratory dry ground soils were employed to validate the spectral models developed based on Dataset A. Results showed that EPO could correct the effect of external factors on soil spectra. For PLS, the validation statistics were as follows: no correction, validation R2 = 0.02; P1 correction, validation R2 = 0.56; and P2 correction, validation R2 = 0.57. For MBL, the validation results were as follows: no correction, validation R2 = 0.06; P1 correction, validation R2 = 0.65; and P2 correction, validation R2 = 0.69. The P2 consistently yielded better results than P1 did but simultaneously increased the sampling time and economic cost. The use of the P1 matrix and the MBL algorithm was recommended because it could reduce the cost of establishing in situ models for SOC.