Singular Value Method Research Articles

Research on parameter optimization method of thrust vector/aerodynamic rudder composite control law based on singular value method

Advanced aircraft with thrust vectoring/aerodynamic rudder layout have significant control coupling problems. The traditional single-loop control parameter design method cannot take into account the performance of multiple control loops in this scenario. Therefore, a control law parameter optimization method based on the singular value of the hysteresis matrix is proposed. First, the control parameter optimization interval is determined using the time domain control performance index. Then, the singular value method is used to measure the stability margin of the multiple-input multiple-output (MIMO) system on this basis, and the corresponding optimal objective function is established to optimize the controller parameters. The feasibility of this method is verified by numerical simulation. The results show that the designed control parameter optimization algorithm has better time domain control performance and larger system stability margin than the traditional single-loop control parameter design method.

Improved SE-ResNet Acoustic–Vibration Fusion for Rolling Bearing Composite Fault Diagnosis

An enhanced fault diagnosis approach for rolling bearings with composite faults using an optimized Squeeze and Excitation ResNet (SE-ResNet) model is proposed. This method integrates grid search (GS), support vector regression (SVR), ensemble empirical mode decomposition (EEMD), and low-rank multimodal fusion (LMF) to effectively handle the signals of acoustic–vibration fusion. By combining these techniques, the aim is to improve the accuracy and reliability of rolling bearing fault diagnosis. Firstly, improved EEMD combined with GS-SVR and a window function is used for rolling bearing vibration signal decomposition. Singular value methods are used to filter and reconstruct the results. Secondly, Markov transition fields (MTFs) are used to encode vibration signals into 2D images. LMF is used for the fusion of vibration and sound signals. An improved Squeeze and Excitation ResNet50 network is proposed for feature identification and classification of rolling bearing composite fault data. Finally, the method undergoes rigorous testing and evaluation using rolling bearing data. The experimental outcomes demonstrate that, in comparison to traditional neural networks, the enhanced SE-ResNet, integrated with GS-SVR-EEMD and LMF, attains superior diagnostic accuracy. Additionally, the proposed approach can be effectively utilized for diagnosing rolling bearing composite faults.

Multi-station Magnetotelluric Data Processing Based on Singular Value Decompositionl

Singular value decomposition is an efficient matrix analysis method. This paper intends to use SVD to process magnetotelluric data from multiple stations. The data of multiple magnetotellus observation stations can make the main reactance of magnetotellus obtained by data processing more robust, suppress the interference signal, improve the data quality, and effectively increase the signal strength. The obtained results are more in line with the actual situation, and the decomposition by singular value method can greatly improve the efficiency of electromagnetic signal processing. Better access to underground information, geological resource exploration and deep earth research.

A Robust Design Method for Ultra-Low-Frequency Oscillation Suppression Control in Hydro–Photovoltaic Complementary Systems

Aiming at the problem of ultra-low-frequency oscillation (ULFO) in power systems, with an oscillation frequency lower than 0.1 Hz, an oscillation suppression control method is proposed. Firstly, the mathematical modeling of the system is carried out, and a cascade correction control method of the governor of hydropower generators is proposed. Secondly, using the ability of photovoltaic (PV) active power to adjust the system frequency, an additional controller for PV active power is proposed. Then, a unified frequency model considering the two controllers is established for multi-hydro and multi-PV systems, and the structural singular value method is used to coordinate the design of the parameters of the hydropower and PV generator controllers to achieve robust performance. Finally, based on a time-domain simulation of single-hydro and single-PV systems and an actual demonstration system located in Sichuan Province, China, the results show that the control method proposed in this paper has a good suppression effect on ultra-low-frequency oscillation under different working conditions, and meets the requirements of robust performance.

Research and application of forward three-dimensional design method of substation

During the operation of digital substations, they are vulnerable to the influence of different fault feature extraction, resulting in weak anti-interference in the detection process. To solve this problem, the singular value decomposition method is combined detection method to establish a prediction model. Firstly, the three-dimensional control mode model is established based on mathematical method to process the current signal with anti-interference; Secondly, the singular value method is used to optimize the current transmission process and denoise the fault signal feature extraction; Finally, the method of singular value decomposition is used to realize fault detection in substation operation.

Robust Stability Assessment of Single-Phase Inverter With Multiparameter Distributions

Grid-connected inverters inevitably operate under uncertain system parameters. These uncertain parameters such as inductance and capacitance are caused by device aging or uncertain grid conditions. And they will affect the stability margin of the inverter and bring an unstable operation risk even with a well initial design. The existing research articles mainly focus on robust stability analysis and control strategies while ignoring the influence of parameter distributions on operational risk. How to evaluate the instability risk of the inverter under multiparameter distribution is still an open question. In this article, the structured singular value (SSV) method is proposed to evaluate the robust stability of the inverter with multiparameter distributions. The distribution characteristics of uncertain parameters are briefly reviewed. The system model of a single-phase grid-connected inverter is established with the parameter distributions of the system key components. The probability of stable system operation can be quantified by the SSV method. Experiment and case study results verify the correctness and effectiveness of the proposed method.

The contribution of temporal analysis of pupillometry measurements to cognitive research.

Reaction time (RT) is one of the most frequently used measures to detect cognitive processes. When tasks require more cognitive processes/resources, reaction is slower. However, RTs may provide only restricted information regarding the temporal characteristics of cognitive processes. Pupils respond reflexively to light but also to cognitive activation. The more cognitive resources a task requires, the more the pupil dilates. However, despite being able to use temporal changes in pupil size (advanced devices measure changes in pupil diameter with sampling rates of above 1000 samples per second), most past studies using pupil dilation have not investigated temporal changes in pupil response. In the current paper, we discuss the advantage of the temporal approach to analyze pupil changes compared to a more traditional perspective, specifically, singular value methods such as mean value and peak amplitude value. Using data from two recent studies conducted in our laboratory, we demonstrate the differences in findings arising from the various analyses. In particular, we focus on the advantage of temporal analysis in detecting hidden effects, investigating temporal characterizations of the effects, and validating the experimental manipulation.

Damping of Low-Frequency Oscillations via Active Disturbance Rejection Control

Linear active disturbance rejection control (LADRC) is applied as power system stabilizer (PSS) in power systems to damp the low-frequency oscillations. A tuning method for second-order LADRC is proposed specifically for damping the low-frequency oscillations. The tuning method is based on its own structure (zeros and poles) and the oscillation frequencies that need to be damped, thus it is independent of system models and not restricted to single-machine-infinite-bus (SMIB) systems. Moreover, a method to analyze the robustness is proposed for SMIB systems using the structured singular value method. Simulation studies on a SMIB system and two multi-machine power systems show that LADRC is easy to tune and can achieve good performance in damping both the local modes and the inter-area modes, thus it has great potential in power system stability control.

Building Recommendation Systems Using the Algorithms KNN and SVD

<p>Recommendation systems are used successfully to provide items (example:<br />movies, music, books, news, images) tailored to user preferences.<br />Among the approaches proposed, we use the collaborative filtering approach<br />of finding the information that satisfies the user by using the<br />reviews of other users. These ratings are stored in matrices that their<br />sizes increase exponentially to predict whether an item is interesting<br />or not. The problem is that these systems overlook that an assessment<br />may have been influenced by other factors which we call the cold start<br />factor. Our objective is to apply a hybrid approach of recommendation<br />systems to improve the quality of the recommendation. The advantage<br />of this approach is the fact that it does not require a new algorithm<br />for calculating the predictions. We we are going to apply the two Kclosest<br />neighbor algorithms and the matrix factorization algorithm of<br />collaborative filtering which are based on the method of (singular value<br />decomposition).</p>

Data Reconstruction in Heterogeneous Environmental Wireless Sensor Networks Using Robust Tensor Principal Component Analysis

The major challenges during the data acquisition process in an environmental wireless sensor network (EWSN) architecture are the presence of outliers and missing data. Outliers and missing data are ubiquitous in EWSN due to sensor failures, external noise, power dwindling, communication failures etc. Robust tensor principal component analysis (RTPCA) decomposes a noisy data tensor into a low-rank tensor and a sparse tensor, which can be exploited for the data recovery in EWSNs, where the low-rank component represents the intrinsic data tensor and the sparse component represents the gross outlier tensor. In this paper, a novel probabilistic outlier modelling scheme using multivariate Chebyshev's inequality hypothesis is proposed, which maps the sample population and the associated magnitudes of outliers with the spatio-temporal correlations in the acquired data. The inherent spatio-temporal and multi-attribute correlations in the EWSN data are established using singular value methods. A tensor nuclear norm (TNN) which extracts more temporal and multi-attribute correlations in the sensory data through block circulant matricization is used as the minimization function in RTPCA. In the forest surveillance scenario, usage of RTPCA results in a reconstruction accuracy of approximately 90% for a dataset with a high missing ratio of 0.95 and the outliers having largest possible magnitudes considered. For oceanographic data, in which the variance is lower, the simulations show similar performance for different outlier contaminations, although RPTCA performs better than other matrix and tensor data completion methods in terms of reconstruction accuracy.

一类反应扩散方程的孤立周期波和局部临界周期分支

The small-amplitude solitary periodic wave solutions and the local critical periodic bifurcations of the traveling wave equations for a class of reaction-diffusion equations with quintic nonlinear reaction terms and constant diffusion terms were studied. First, the reaction-diffusion equation was transformed into the corresponding traveling wave system through traveling wave transformation. The first 8 singular point quantities of the system were calculated with the singular point value method and the computer algebra software MATHEMATICA. Then, 2 center conditions for the singular point of the system were obtained, 8 limit cycles were proved to bifurcate at the origin of the traveling wave system, and 8 small-amplitude solitary periodic wave solutions were found to exist in the corresponding nonlinear reaction-diffusion equation. Furthermore, through computation of the period constants, the weak center order for the origin of the traveling wave system was derived. Then, the system was proved to have at most 3 local critical periodic bifurcations and be able to reach the 3 bifurcations. Moreover, the analysis of the critical periodic bifurcations of the traveling wave system reveals that the reaction-diffusion equation has 3 critical periodic wavelengths.

Research on sparsity of frequency modulated signal in fractional Fourier transform domain

Frequency modulated (FM) signal is extensively applied in sonar, radar, laser and emerging optical cross-research, its sparsity is a common basic issue for the sampling, denoising and compression of FM signal. This paper mainly studies the sparsity of FM signal in the fractional Fourier transform (FRFT) domain, and a maximum singular value method (MSVM) is proposed to estimate the compact FRFT domain of FM signal. This method uses the maximum singular value of amplitude spectrum of FM signal to measure the compact domain, and WOA is used to search the compact domain, which effectively improves the shortcomings of the existing methods. Compared with MNM and MACF, this method gives a sparser representation of FM signal in the FRFT domain, which has less number of significant amplitudes. Finally, the primary application of this method in the FM signal filtering is given.

Influence of characteristic parameters of signal on fault feature extraction of singular value method

The detection of mechanical fault signals by singular value decomposition is a commonly used method in fault diagnosis. The delay time of the fault signal time series and the rationality of the value of the phase space embedding dimension, as well as the fluctuation of the characteristic parameters of the fault signal, will cause the singular value decomposition method to have a greater impact on the accuracy of fault feature identification and diagnosis. In this article, the simulation model of the similarity signal is established by the combination of the autocorrelation function method and the Cao’s algorithm. Then, the delay time of the signal sequence and the optimal value of the embedded dimension are obtained through simulation. Next, using this method to study the fluctuation of the characteristic parameters such as the frequency, amplitude and initial phase of the signal, the relationship between the characteristic parameters of the signal and the singular value of the signal is obtained. Finally, through the experimental study of the pitting corrosion of the gear tooth surface, the vibration of the fault feature is obtained. The research shows that the combination of autocorrelation function method and Cao's algorithm can calculate the optimal characteristic parameters for the singular value decomposition method and improve the ability of the method to identify fault features.

Improved Mathematical Models of Thermal Residual Stresses in Functionally Graded Adhesively Bonded Joints: A Critical Review

Functionally graded material (FGM) concept has been applied successfully in order to improve/design heat transfer, electric and electronic conductivity, static and dynamic strengths of adhesive joints by reliving stress distributions in both adhesive and adherend materials. This new approach relies on tailoring material composition of adhesive and adherends along one or more coordinate directions. Thermal residual stresses in adhesive joints are a vital issue in terms of the joint strength. FGM concept also allows to relieve/control thermal residual stresses encountered in adhesive joints due to mismatches between coefficients of thermal expansion of adhesive and adherend materials. Mathematical models and solutions on the thermal residual stress analysis have been continuously improved. This paper reviews the current status of mathematical models, and offers an improved mathematical model and numerical solution method by considering two-dimensional thermal stress and deformation states of adhesively bonded bi-directional functionally graded clamped plates subjected to an in-plane heat flux along one of the ceramic edges. This mathematical model assumes the material properties of the functionally graded plates to vary with a power law along two in-plane directions and not through the plate thickness direction, in particular, considers the spatial derivatives of thermal and mechanical properties of the material, and enables the investigation of the effects of the bi-directional composition variations and spatial derivative terms on the displacement, strain and stress distributions. The heat conduction and Navier equations describing the twodimensional thermo-elastic problem are discretized using finite-difference method, and the set of linear equations are solved using the pseudo singular value method. The functionally graded plates relieve both stress and strain distributions and levels in the adhesive layer and in the plates even though the adhesive layer is still ungraded. The spatial derivatives of mechanical and thermal properties of the local material become more effective on the strain and stress distributions of the plates and adhesive layer. The model, disregarding these derivative terms, exhibits sensitivity to small changes in the compositional gradients (n, m) by adjusting the variations of ceramic volume fraction along the x - and y-directions, respectively, and instability in the calculation of stress and strain distributions and levels. However, the improved model with material derivatives, which considers the effects of these derivative terms, predicts stress and strain distributions and levels complying with changes in the compositional gradient exponents.

Thermal stress analysis of functionally graded plates with temperature-dependent material properties using theory of elasticity

Abstract Based on the three-dimensional elasticity theory, the transient thermal residual stress analyses of one-dimensional functionally graded rectangular plates (FGPs) have been performed under in-plane constant heat flux for different compositional gradient exponents. The thermo-mechanical properties of FGPs were assumed to be vary with a power law along an in-plane direction, not through the plate thickness direction and temperature-dependent/independent. The Heat Transfer and Navier's Equations in cartesian coordinates which represent the two-dimensional thermoelastic problem were resolved by means of the Finite-Difference Method (FDM), and the set of linear equations were solved using the pseudo singular value method. The effect of the coordinate derivatives of material properties were considered in both Heat Transfer and Navier's Equations. The current study aims at determining the effect of temperature dependence and temperature independence of material properties and the compositional gradient exponents in FGPs on the levels of temperature, strain and stress. The FGPs with temperature-dependent material properties showed higher levels of temperature, strain and stress than those with temperature-independent material properties. In order to verify the results of this study, two-dimensional thermo-elastic problem was resolved using the Finite Element Method (FEM) and the results are compared.

Thermal stress analysis of one- and two-dimensional functionally graded plates subjected to in-plane heat fluxes

This study addresses the thermal stress analysis of one- and two-dimensional functionally graded plates subjected to in-plane heat fluxes. The material composition variation is assumed in-plane, not through the plate thickness according to a power-law distribution in terms of the volume fraction of the constituents. The mathematical model considers the spatial derivatives of local mechanical and thermal properties. The heat transfer and Navier equations of the two-dimensional thermo-elastic model were discretized using the finite difference method, and the set of linear equations were solved using the pseudo singular value method. The performance of both one- and two-dimensional functionally gradient material plates was investigated under two types of in-plane fluxes: one-edge and two-edges. For each type of heat fluxes, one- and two-dimensional functionally gradient material plates exhibited different displacement, stress and strain distributions. The temperature levels and distributions were affected with increasing ceramic constituent in the composition variation of the plate. One-dimensional functionally gradient material plate was more suitable for an one-edge heat flux along the direction of material composition variation, whereas two-dimensional functionally gradient material plate was more effective on the relieving the thermal stresses for a two-edges heat flux.

A Class of Three-Dimensional Quadratic Systems with Ten Limit Cycles

Our work is concerned with a class of three-dimensional quadratic systems with two symmetric singular points which can yield ten small limit cycles. The method used is singular value method, we obtain the expressions of the first five focal values of the two singular points that the system has. Both singular symmetric points can be fine foci of fifth order at the same time. Moreover, we obtain that each one bifurcates five small limit cycles under a certain coefficient perturbed condition, consequently, at least ten limit cycles can appear by simultaneous Hopf bifurcation.

Limit Cycle Bifurcation of Infinity and Degenerate Singular Point in Three-Dimensional Vector Field

Our work focuses on investigating limit cycle bifurcation for infinity and a degenerate singular point of a fifth degree system in three-dimensional vector field. By using singular value method to compute focal values carefully, we give the expressions of the focal values (Lyapunov constants) at the origin and at infinity. Moreover, we obtain that four limit cycles at most can bifurcate from the origin and three limit cycles can bifurcate from infinity. At the same time, we show the structure of limit cycles from the origin and the infinity. It is interesting for this kind of nonlinear phenomenon that a string of large limit cycles encircle a string of small limit cycles by simultaneous Hopf bifurcation, which is hardly seen for similar published results in three-dimensional vector field, our result is new.

Thermal stress analysis of in-plane two-directional functionally graded plates subjected to in-plane edge heat fluxes

This study investigates the thermal stress and deformation states of bi-directional functionally graded clamped plates subjected to constant in-plane heat fluxes along two ceramic edges. The material properties of the functionally graded plates were assumed to vary with a power law along two in-plane directions not through the plate thickness direction. The spatial derivatives of thermal and mechanical properties of the material composition were considered, and the effects of the bi-directional composition variations and spatial derivative terms on the displacement, strain and stress distributions were also investigated. The heat conduction and Navier equations describing the two-dimensional thermo-elastic problem were discretized using finite-difference method, and the set of linear equations were solved using the pseudo singular value method. The compositional gradient exponents and the spatial derivatives of thermal and mechanical properties of the material composition were observed to play an important role especially on the heat transfer durations, the displacement and strain distributions, but had a minor effect on the temperature and stress distributions.

The Fault Feature Extraction of Rolling Bearing Based on EMD and Difference Spectrum of Singular Value

Nowadays, the fault diagnosis of rolling bearing in aeroengines is based on the vibration signal measured on casing, instead of bearing block. However, the vibration signal of the bearing is often covered by a series of complex components caused by other structures (rotor, gears). Therefore, when bearings cause failure, it is still not certain that the fault feature can be extracted from the vibration signal on casing. In order to solve this problem, a novel fault feature extraction method for rolling bearing based on empirical mode decomposition (EMD) and the difference spectrum of singular value is proposed in this paper. Firstly, the vibration signal is decomposed by EMD. Next, the difference spectrum of singular value method is applied. The study finds that each peak on the difference spectrum corresponds to each component in the original signal. According to the peaks on the difference spectrum, the component signal of the bearing fault can be reconstructed. To validate the proposed method, the bearing fault data collected on the casing are analyzed. The results indicate that the proposed rolling bearing diagnosis method can accurately extract the fault feature that is submerged in other component signals and noise.