Maximum Singular Value Research Articles

H<inline-formula> <tex-math notation="LaTeX">$\infty$ </tex-math> </inline-formula> Optimal Control-Based Robust Pose Estimation in Light Field Three-Dimensional Display

Naked eye augmented reality technology has the capability of satisfying the immersion feeling. Therefore, light field three-dimensional (3-D) display technology has received considerable attention. In this paper, a novel pose estimation method in light field 3D display based on H∞ optimal control is proposed. Compared with the current pure hardware platform method, the proposed method releases hardware resources such as the graphic processing unit and avoids numerous parameter adjustments. The proposed method comprises three key parts. First, we calculate the normal of the rigid objects and apply it to obtain the normal estimation. Second, we calculate H∞ of the normal estimation result on the Hardy space, which is the maximum singular value of the rational function matrix parsed in the right half plane of the complex plane. Finally, we use the optimal result of H∞ for pose estimation and transformation. The experiments are carried out on the virtual and real classical datasets acquired by Kinect, Mian, and Clutter. The experiments show that the proposed method can be used to obtain high-quality display effects with low cost and high efficiency.

<inline-formula> <tex-math notation="LaTeX">$\mathcal{H}_\infty$ </tex-math> </inline-formula>-Optimal Parallel Feedforward Control Using Minimum Gain

This letter presents static and dynamic parallel feedforward controller synthesis methods that render a linear time-invariant system minimum phase by augmenting its output. The system output is perturbed the least amount possible by minimizing the gain of the parallel feedforward controller while ensuring the augmented system is minimum phase. This is done by minimizing the maximum singular value of a static parallel feedforward controller or the weighted H ∞ norm of a dynamic parallel feedforward controller. Static and dynamic parallel feedforward controllers are synthesized using direct and indirect methods that involve bilinear matrix inequality constraints and are solved iteratively using linear matrix inequalities. The direct method enforces a minimum gain constraint directly on the augmented system, while the indirect method solves for an asymptotically stabilizing negative feedback controller that is inverted to obtain the parallel feedforward controller. Numerical examples are provided to demonstrate the effectiveness of the proposed controller synthesis methods.

Separate estimation schemes for time-frequency overlapped micro-doppler signal in single channel infrared laser detection

The micro-Doppler (MD) effect of weak vibration target is obvious in infrared laser detection. This provides the foundation for precise estimation of micro-motion parameters, and makes the target classification and recognition possible. The multi-targets or multi-scattering points existing in the detecting field will generate the single-channel multi-component (SCMC) signal in laser detection. Further, the similar micro-motion parameters will lead to the feature overlapping in time-frequency domain, which will increase the difficulty of parameter estimation. In this paper, a separate parameter estimator based on the maximum likelihood framework and singular value decomposition is proposed to deal with this mixed signal. First, an improved singular value ratio (SVR) spectrum with detailed period scanning is presented to locate the vibration frequency. The amplitude ratio information of each component is also extracted from the SVR spectrum. Then, the analytic expression of the maximum likelihood estimation (MLE) of micro-motion parameters is derived. To solve the high nonlinear problem in laser MD signal, a new likelihood function (LF) is designed in the derivation process. The Robustness and efficiency are both increased with this new LF. The Markov chain Monte Carlo (MCMC) sampling is employed to implement the MLE. Finally, the simulation results verifies the validity of the proposed method. The comparison with the Cramer-Rao bound shows the ability of accurate estimation of the proposed method.

Optimization of Fixture Layout Based on Error Amplification Factors

Fixture locators are used to precisely locate and stably support a workpiece so that the desired position and orientation (pose) of the workpiece relative to the cutting tool can be maintained during machining or inspection process. It is believed that manufacturing errors of locators and locating datum surfaces are key factors for the pose error between the workpiece and the cutting tool. Optimizing the layout of locators is helpful to reduce the pose error so as to improve machining accuracy of the workpiece. In order to minimize the pose error, we introduced, for the first time, a singular value decomposition (SVD) technique for the location matrix to derive error amplification factors (EAF) in six degrees-of-freedom of the workpiece. The EAF principle defines the maximal singular value, the condition number, the product of all singular values and the manipulability as the maximal error amplification factor, the relative error amplification factor, the error ellipsoid volume and the location stability, respectively. The four defined indices taken as objective functions are optimized, by a nondominated sort genetic algorithm (NSGA-II), so that an optimal layout of locators is obtained due to the minimization of the pose error. Also, the feasibility of the proposed method was comprehensively validated by simulation and machining experiments.

Effective leg stiffness of animal running and the co-optimization of energetic cost and stability

The relative leg stiffness of most running animals falls in a small range between 7 and 27. Here we present a theoretical study of an established running model, an actuated Spring Loaded Inverted Pendulum model, to determine if the energetic cost and stability of running might be co-optimized over this range of leg stiffness values. The energetic cost of the model is quantified as the energy spent to move a unit mass a unit distance. The stability of the model is based on the system response to perturbations with respect to periodic locomotion solutions, and uses the linearized dynamics of Poincaré return maps and the resulting maximum eigenvalue and singular value decomposition in order to analyze asymptotic stability and the overall system response to perturbations, respectively. We find that there exists a tradeoff between stability and energetic cost in the model with respect to variation in forcing (actuation) level: For a given leg stiffness, the energetic cost tends to be more optimal with smaller forcing, and the opposite for stability. We find that intermediate levels of forcing can achieve near asymptotic stability or complete asymptotic stability while remaining small enough to yield a relatively low energetic cost consistent with human-like values. We demonstrate that this outcome can be achieved in the model with a simple optimization function that balances stability and energetic cost. We then investigate the stability and energetic cost when both leg stiffness and forcing are varied. Overall, the analysis shows that leg stiffness values in or near the biological range offers a good chance of simultaneously achieving both reasonable energetic cost and stability in the model. The results of this study suggest that stability and energetic cost may be interacting factors that have a combined influence on the effective leg stiffness and actuation (forcing) used by running animals.

A robust indicator based on singular value decomposition for flaw feature detection from noisy ultrasonic signals

Singular value decomposition (SVD) has been proven to be an effective de-noising tool for flaw echo signal feature detection in ultrasonic non-destructive evaluation (NDE). However, the uncertainty in the arbitrary manner of the selection of an effective singular value weakens the robustness of this technique. Improper selection of effective singular values will lead to bad performance of SVD de-noising. What is more, the computational complexity of SVD is too large for it to be applied in real-time applications. In this paper, to eliminate the uncertainty in SVD de-noising, a novel flaw indicator, named the maximum singular value indicator (MSI), based on short-time SVD (STSVD), is proposed for flaw feature detection from a measured signal in ultrasonic NDE. In this technique, the measured signal is first truncated into overlapping short-time data segments to put feature information of a transient flaw echo signal in local field, and then the MSI can be obtained from the SVD of each short-time data segment. Research shows that this indicator can clearly indicate the location of ultrasonic flaw signals, and the computational complexity of this STSVD-based indicator is significantly reduced with the algorithm proposed in this paper. Both simulation and experiments show that this technique is very efficient for real-time application in flaw detection from noisy data.

Scattering-based stabilization of non-planar conic systems

Methods for scattering-based stabilization of interconnections of nonlinear systems are developed for the case where the subsystems are non-planar conic. The notion of non-planar conicity is a generalization of the conicity notion to the case where the cone’s center is a subspace with dimension greater than one. For a feedback interconnection of non-planar conic systems, a graph separation condition for finite-gain L2-stability is derived in terms of relationship between the maximal singular value of the product of projection operators onto the subsystems’ central subspaces and the radii of the corresponding cones. Furthermore, a new generalized scattering transformation is developed that allows for rendering the dynamic characteristics of a non-planar conic system into an arbitrary prescribed cone with compatible dimensions. The new scattering transformation is subsequently applied to the problem of stabilization of interconnections of non-planar conic systems, with and without communication delays. Applications of the developed scattering-based stabilization methods to the problems of stable robot–environment interaction and bilateral teleoperation with multiple heterogeneous communication delays are discussed.

A Novel Wheelset Bearing Fault Diagnosis Method Integrated CEEMDAN, Periodic Segment Matrix, and SVD

A novel fault diagnosis method, named CPS, is proposed based on the combination of CEEMDAN (complete ensemble empirical mode decomposition with adaptive noise), PSM (periodic segment matrix), and SVD (singular value decomposition). Firstly, the collected vibration signals are decomposed into a set of IMFs using CEEMDAN. Secondly, the PSM of the selected IMFs is constructed. Thirdly, singular values are obtained by SVD conducted on the space of PSM. Fourthly, the impulse components are enhanced by the singular value reconstruction with the first maximal singular value. Finally, the squared envelope spectra of the reconstructed signals are used to diagnose the wheelset bearing faults. The effectiveness of the proposed CPS has been verified by simulations and experiments. Compared to the well‐known Hankel‐based SVD, the proposed CPS performs better at extracting the weak periodic impulse responses from the measured signals with strong noise and interferences.

Techniques for Computation of Frequency Limited H∞ Norm

Traditional H∞ norm depicts peak system gain over infinite frequency range, but many applications like filter design, model order reduction and controller design etc. require computation of peak system gain over specific frequency interval rather than infinite range. In present work, new computationally efficient techniques for computation of H∞ norm over frequency limited interval are proposed. Proposed techniques link norm computation with maximum singular value of the system in limited frequency interval. Numerical examples are incorporated to validate the proposed concept.

Long‐Time Predictive Modeling of Nonlinear Dynamical Systems Using Neural Networks

We study the use of feedforward neural networks (FNN) to develop models of nonlinear dynamical systems from data. Emphasis is placed on predictions at long times, with limited data availability. Inspired by global stability analysis, and the observation of strong correlation between the local error and the maximal singular value of the Jacobian of the ANN, we introduce Jacobian regularization in the loss function. This regularization suppresses the sensitivity of the prediction to the local error and is shown to improve accuracy and robustness. Comparison between the proposed approach and sparse polynomial regression is presented in numerical examples ranging from simple ODE systems to nonlinear PDE systems including vortex shedding behind a cylinder and instability‐driven buoyant mixing flow. Furthermore, limitations of feedforward neural networks are highlighted, especially when the training data does not include a low dimensional attractor. Strategies of data augmentation are presented as remedies to address these issues to a certain extent.

Calculating the H∞ norm of a fractional system given in state-space form

We present an efficient algorithm to compute the H ∞ norm of a fractional system. The algorithm is based on the computation of level sets of the maximum singular value of the transfer function, as a function of frequency. Numerical examples are given to illustrate the new method.

Performance of nonlinear detectors in spatial multiplexing for spatially correlated channels

Spatial multiplexing is used in multiple input multiple output (MIMO) wireless systems to increase the data rate. Some nonlinear detectors, such as minimum mean square error (MMSE) Vertical Bell laboratories layered space-time (VBLAST), Maximum A-Posteriori (MMSE VBLAST MAP), and MMSE Improved VBLAST detectors are used in place of a over more complex detector, such as maximum likelihood detector or singular value decomposition based detector. We have presented simulation results of MIMO symbol error rate versus average SNR for MMSE VBLAST MAP and MMSE Improved VBLAST schemes assuming spatially correlated channels for M-ary QAM. We have observed that the performance of MMSE VBLAST MAP and MMSE Improved VBLAST detectors is almost identical in spatially uncorrelated channels. However, in the case of spatially correlated channels, MMSE Improved VBLAST outperforms MMSE VBLAST MAP. We have also seen that complexity of the Improved VBLAST algorithm is higher than the complexity of VBLAST MAP algorithm.

Slip Hankel matrix series‐based singular value decomposition and its application for fault feature extraction

The failure of rolling bearings is one of the most important factors for rotating machinery breakdown. The detection of initial fault in rolling bearings is crucial for the further prevention of equipment malfunction and failure. In this study, a new rolling bearing fault diagnosis method based on the singular value decomposition, slip Hankel matrix series construction and maximum singular value energy analysis is proposed. It has been validated that the proposed method has an excellent impulse recognition capacity, which can be further applied to design the optimal band-pass filter for rolling bearing fault diagnosis. Then, the minimum entropy deconvolution (MED) technique is introduced to improve the fault extraction ability of the proposed method. Simulated signals and artificial fault tests are used to prove the capacity of the new method for rolling bearing fault detection. Furthermore, the result of accelerated life test indicates the initial bearing fault can be recognised by the proposed method, while the envelope spectrum cannot directly distinguish the failure type because of the redundant frequency interference. It can be concluded that the proposed method has the effectiveness of initial fault identification and redundant frequency elimination for rolling bearing fault diagnosis.

Alignment Distances on Systems of Bags

Recent research in image and video recognition indicates that many visual processes can be thought of as being generated by a time-varying generative model. A nearby descriptive model for visual processes is thus a statistical distribution that varies over time. Specifically, modeling visual processes as streams of histograms generated by a kernelized linear dynamic system turns out to be efficient. We refer to such a model as a System of Bags. In this work, we investigate Systems of Bags with special emphasis on dynamic scenes and dynamic textures. Parameters of linear dynamic systems suffer from ambiguities. In order to cope with these ambiguities in the kernelized setting, we develop a kernelized version of the alignment distance. For its computation, we use a Jacobi-type method and prove its convergence to a set of critical points. We employ it as a dissimilarity measure on Systems of Bags. As such, it outperforms other known dissimilarity measures for kernelized linear dynamic systems, in particular the Martin Distance and the Maximum Singular Value Distance, in every tested classification setting. A considerable margin can be observed in settings, where classification is performed with respect to an abstract mean of video sets. For this scenario, the presented approach can outperform state-of-the-art techniques, such as Dynamic Fractal Spectrum or Orthogonal Tensor Dictionary Learning.

Upper Bounds for the Spectral Radii of Nonnegative Tensors

In this paper, we present several sharper upper bounds for the M-spectral radius and Z-spectral radius based on the eigenvalues of some unfolding matrices of nonnegative tensors. Meanwhile, we show that these bounds could be tight for some special tensors. For a general nonnegative tensor which can be transformed into a matrix, we prove the maximal singular value of this matrix is an upper bound of its Z-eigenvalues. Some examples are provided to show these proposed bounds greatly improve some existing ones.

Improved Decentralized Controllers for Stable Systems by IMC Method

In the present work, the matrix notation is used to derive the Internal Model Control (IMC) decentralized Proportional Integral (PI) controllers. MacLaurin series is applied to the resulting equation to get the controller parameters. For design of the controllers, the diagonal elements of the process are used, whereas for evaluating the performance of the controllers, the full transfer function matrix of the process is used. For a two input–two output (2 × 2) system example, the recently available methods for designing decentralized PI controllers (Equivalent Transfer Function methods, Effective Relative Gain Array method, Direct multi-loop method) are compared with the present method. For a 4 × 4 system, the corresponding recent reported methods are compared. The performance of the present method is better than the above methods. The performances of the control systems are compared in terms of the Integral absolute error and the controller output behaviour is compared in terms of total variation. The robustness of the control system is evaluated by the maximum sensitivity and by the inverse maximum singular value of the input and the output multiplicative uncertainties.

Transceivers Based on Ping-Pong Beam Training for Large Multiuser MIMO Systems

Ping-pong beam training (PPBT) is a procedure for estimating the singular vectors of a channel matrix. It relies on alternate transmissions between two devices and is applicable to reciprocal channels. In a large multi-user MIMO system with massive antenna arrays at both base station and user devices, PPBT is used to obtain an estimate of the left and right singular vectors associated to the maximal singular value. Based on those singular vectors, multi-user MIMO transceivers are built and their performance is analyzed. A zero-forcing structure is shown to lead to an inter-user interference-free performance under asymptotic conditions.

Mechanical Fault Diagnosis of High Voltage Circuit Breakers Based on Variational Mode Decomposition and Multi-Layer Classifier.

Mechanical fault diagnosis of high-voltage circuit breakers (HVCBs) based on vibration signal analysis is one of the most significant issues in improving the reliability and reducing the outage cost for power systems. The limitation of training samples and types of machine faults in HVCBs causes the existing mechanical fault diagnostic methods to recognize new types of machine faults easily without training samples as either a normal condition or a wrong fault type. A new mechanical fault diagnosis method for HVCBs based on variational mode decomposition (VMD) and multi-layer classifier (MLC) is proposed to improve the accuracy of fault diagnosis. First, HVCB vibration signals during operation are measured using an acceleration sensor. Second, a VMD algorithm is used to decompose the vibration signals into several intrinsic mode functions (IMFs). The IMF matrix is divided into submatrices to compute the local singular values (LSV). The maximum singular values of each submatrix are selected as the feature vectors for fault diagnosis. Finally, a MLC composed of two one-class support vector machines (OCSVMs) and a support vector machine (SVM) is constructed to identify the fault type. Two layers of independent OCSVM are adopted to distinguish normal or fault conditions with known or unknown fault types, respectively. On this basis, SVM recognizes the specific fault type. Real diagnostic experiments are conducted with a real SF6 HVCB with normal and fault states. Three different faults (i.e., jam fault of the iron core, looseness of the base screw, and poor lubrication of the connecting lever) are simulated in a field experiment on a real HVCB to test the feasibility of the proposed method. Results show that the classification accuracy of the new method is superior to other traditional methods.

Numerical Estimation of Stability Region of Self-Clocked Bipedal Robots with Inertial Disk

Bipedal robot control techniques implementing self clocking properties, as presented in Westervelt et al. (Feedback control of dynamic bipedal robot locomotion, Taylor & Francis LLC, Milton Park, 2007) and Novaes et al. (IFAC 19th world congress, 4843–4848, 2014), have desirable properties, like the ability to drive the robot step with respect to its own geometry. In this control technique, one of the possible angular coordinates of the robot is made monotonic during the step execution. The other angular coordinates will track reference functions of the former. One difficulty with this approach is to determine the region around the nominal step for which the stability is assured. In this paper, we propose an algorithm to estimate this stability region by computing numerically an interval matrix related to a Poincare return map. In conjunction with the algorithm proposed in Ahn and Chen (IEEE Trans Autom Control 52(3):510–514, 2007), we are able to determine the maximum singular value of this interval matrix and so determine a guaranteed stability region.

Estimating inter-area dominant oscillation mode in bulk power grid using multi-channel continuous wavelet transform

This paper proposes a novel continuous wavelet transform (CWT) based approach to holistically estimate the dominant oscillation using measurement data from multiple channels. CWT has been demonstrated to be effective in estimating power system oscillation modes. Using singular value decomposition (SVD) technique, the original huge phasor measurement unit (PMU) datasets are compressed to finite useful measurement data which contain critical dominant oscillation information. Further, CWT is performed on the constructed measurement signals to form wavelet coefficient matrix (WCM) at the same dilation. Then, SVD is employed to decompose the WCMs to obtain the maximum singular value and its right eigenvector. A singular value vector with the entire dilation is constructed through the maximum singular values. The right eigenvector corresponding to the maximum singular value in the singular-value vector is adopted as the input of CWT to estimate the dominant modes. Finally, the proposed approach is evaluated using the simulation data from China Southern Power Grid (CSG) as well as the actual field-measurement data retrieved from the PMUs of CSG. The simulation results demonstrate that the proposed approach performs well to holistically estimate the dominant oscillation modes in bulk power systems.