Norm Optimization Research Articles

Classification of EEG Signals Based on Filter Bank and Sparse Representation in Motor Imagery Brain-Computer Interfaces

To improve the classification performance of motor imagery (MI) based brain-computer interfaces (BCIs), a new signal processing algorithm for classifying electroencephalogram (EEG) signals by combining filter bank and sparse representation is proposed. The broadband EEG signals of 8–30[Formula: see text]Hz are segmented into 10 sub-band signals using a filter bank. EEG signals in each sub-band are spatially filtered by common spatial pattern (CSP). Fisher score combined with grid search is used for selecting the optimal sub-band, the band power of which is employed for designing a dictionary matrix. A testing signal can be sparsely represented as a linear combination of some columns of the dictionary. The sparse coefficients are estimated by [Formula: see text] norm optimization, and the residuals of sparse coefficients are exploited for classification. The proposed classification algorithm was applied to two BCI datasets and compared with two traditional broadband CSP-based algorithms. The results showed that the proposed algorithm provided superior classification accuracies, which were better than those yielded by traditional algorithms, verifying the efficacy of the present algorithm.

Gridless Sparse Direction Finding Method for Correlated Signals with Gain-Phase Errors

In practical array systems, the gain-phase errors among antennas degrade the performance of direction finding significantly. In this paper, a novel sparse system model for direction of arrival (DOA) estimation in the scenario with gain-phase errors is proposed by exploiting the signal sparsity in the spatial domain. In contrast to the existing sparse-based methods using the grids to construct the dictionary matrix, a novel gridless method based on atomic norm and convex optimization is proposed, where the gain-phase errors are described by a diagonal matrix. With the Schur complement, a semidefinite programming is formulated from the optimization problem, and can be solved efficiently. With the gain-phase errors, the corresponding Cram’er-Rao lower bound (CRLB) of direction finding is derived as an estimation benchmark. Simulation results show that the proposed method performs better than the state-of-the-art methods in the scenario with correlated signals and gain-phase errors.

Non-negative constrained inverse eigenvalue problems – Application to damage identification

Abstract Damage identification using eigenvalue shifts is ill-posed because the number of identifiable eigenvalues is typically far less than the number of potential damage locations. This paper shows that if damage is defined by sparse and non-negative vectors, such as the case for local stiffness reductions, then the non-negative solution to the linearized inverse eigenvalue problem can be made unique with respect to a subset of eigenvalues significantly smaller than the number of potential damage locations. Theoretical evidence, numerical simulations, and performance comparisons to sparse vector recovery methods based on l 1 -norm optimization are used to validate the findings. These results are then extrapolated to the ill-posed nonlinear inverse eigenvalue problem in cases where damage is large, and linearization induces non-negligible truncation errors. In order to approximate the solution to the non-negative nonlinear least squares, a constrained finite element model updating approach is presented. The proposed method is verified using three simulated structures of increasing complexity: a one-dimensional shear beam, a planar truss, and a three-dimensional space structure. For multiple structures, this paper demonstrates that the proposed method finds sparse solutions in the presence of measurement noise.

Using Dictionary Pair Learning for Seizure Detection.

Automatic seizure detection is extremely important in the monitoring and diagnosis of epilepsy. The paper presents a novel method based on dictionary pair learning (DPL) for seizure detection in the long-term intracranial electroencephalogram (EEG) recordings. First, for the EEG data, wavelet filtering and differential filtering are applied, and the kernel function is performed to make the signal linearly separable. In DPL, the synthesis dictionary and analysis dictionary are learned jointly from original training samples with alternating minimization method, and sparse coefficients are obtained by using of linear projection instead of costly -norm or -norm optimization. At last, the reconstructed residuals associated with seizure and nonseizure sub-dictionary pairs are calculated as the decision values, and the postprocessing is performed for improving the recognition rate and reducing the false detection rate of the system. A total of 530 h from 20 patients with 81 seizures were used to evaluate the system. Our proposed method has achieved an average segment-based sensitivity of 93.39%, specificity of 98.51%, and event-based sensitivity of 96.36% with false detection rate of 0.236/h.

Research on Power Load Forecasting Based on Random Forest Regression

In recent years, with the development of artificial intelligence, power forecasting based on big data analysis has gradually become intelligent. In order to improve the prediction accuracy and efficiency of the model in dealing with large volume data, this paper combines the compressed sensing algorithm and the random forest regression algorithm. The discrete cosine transform base is used to sparsely represent the data. The original data is restored by solving the norm optimization problem to achieve the purpose of denoising. And the processed data is used for regression prediction, it achieves great results. The results indicate that the compressed sensing algorithm can retain more details and get better effect compared with the traditional denoising method. Combined with the random forest regression algorithm, the prediction accuracy of the model is improved. This method can be implemented in the trend prediction of time series data such as power load, which has very important practical significance.

Practical supplementary controller design for the bi‐layer WAC architecture through structurally constrained H 2 norm optimisation

The objective of this paper is to suggest a suitable design procedure that may be useful for the practical realisation of the bi-layer wide area control (WAC) architecture. The bi-layer WAC architecture indicates the deployment a communication-free supplementary WAC loop in parallel to the conventional WAC loop. The bi-layer WAC system was found to have the potential to counterbalance the communication-related problems that arise in the conventional WAC loop. However, until now, no specific work has been reported in literature for the practical design of the supplementary wide area damping controller (WADC). It is essential to design the supplementary WADC in a way so that it can be practically implemented without the support of any communication network. The particular problem is resolved here by defining a suitable structure of the feedback gain matrix in the supplementary WAC loop. A novel structurally constrained norm optimisation technique is developed to design the particular feedback gain matrix with the proper structure. Here, the structurally constrained norm optimisation is performed for an output feedback loop instead of a state feedback loop. The usefulness of the supplementary WADC design produced is thoroughly verified through real-time (RT) experimentations.

Covariance Matrix Reconstruction for Direction Finding with Nested Arrays Using Iterative Reweighted Nuclear Norm Minimization

In this paper, we address the direction finding problem in the background of unknown nonuniform noise with nested array. A novel gridless direction finding method is proposed via the low-rank covariance matrix approximation, which is based on a reweighted nuclear norm optimization. In the proposed method, we first eliminate the noise variance variable by linear transform and utilize the covariance fitting criteria to determine the regularization parameter for insuring robustness. And then we reconstruct the low-rank covariance matrix by iteratively reweighted nuclear norm optimization that imposes the nonconvex penalty. Finally, we exploit the search-free DoA estimation method to perform the parameter estimation. Numerical simulations are carried out to verify the effectiveness of the proposed method. Moreover, results indicate that the proposed method has more accurate DoA estimation in the nonuniform noise and off-grid cases compared with the state-of-the-art DoA estimation algorithm.

Pilot decontamination in massive multiuser MIMO systems based on low‐rank matrix approximation

In multi-cell massive multiuser multi-input multi-output (MU-MIMO) systems, the channel estimation performance is degraded by the pilot contamination problem. This effect occurs when non-orthogonal pilot sequences are reused by other users in the adjacent cells. In this study, two channel estimation methods based on low-rank matrix approximation technique are proposed to mitigate pilot contamination problem in time division duplex multi-cell massive MU-MIMO systems. In the first method, the massive MU-MIMO channel estimation is formulated as the nuclear norm (NN) optimisation problem and solved by using a novel estimation algorithm proposed in this study. In the second method, the iterative weighted NN (IWNN) is proposed to improve the NN estimation performance. Consequently, the regularisation parameter of both optimisation methods is selected based on the cross-validation curve method. The simulation results show that both proposed methods outperform the traditional least square method in terms of the normalised mean square error. Moreover, the IWNN estimation method demonstrates substantial improvement over the NN estimation method in the presence of strong pilot contamination problem.

Collaborative Compressive Radar Imaging With Saliency Priors

Although several works have been done on high-resolution inverse synthetic aperture radar (ISAR) imaging via compressive sampling technology, they only explore sparse priors of targets in the scene and the image is recovered cell by cell separately. In order to potentially enhance targets and suppress clutters for fast and higher quality imaging, in this paper, we advance a collaborative compressive ISAR (CC-ISAR) imaging approach, by exploring both sparse priors and saliency priors of targets. First, a geometric saliency map is derived by performing pulse contourlet transform on a preliminary image. Then, a graph Laplacian is constructed to regularize a multiple measurement vector problem for collaborative compressive radar imaging. Third, targets are approximately separated from the background in the saliency map, and salient weights are defined for the target and background, respectively, to derive a saliency weighted $l_{1}$ -norm optimization algorithm. Some experiments are taken on real ISAR data to evaluate the performance of the proposed method, and both visual results and numerical guidelines prove that CC-ISAR imaging method can obtain more accurate targets and outperform its counterparts.

Transform Learning Based Sparse Coding for LiDAR Data Denoising

In recent years, sparse coding (SC) has been exploited for light detection and ranging (LiDAR) data restoration, and promising results have been reported. However, such methods are usually time consuming, because much computational resource has been devoted to solving batches of $\ell _0$ or $\ell _1$ -norm optimization problems iteratively. More recently, fast SC method has been proposed to achieve nearly real-time performance at the expense of applicability. In this letter, we propose a transform learning based SC method for LiDAR data denoising. Moreover, we present a detailed evaluation for our series of SC methods with different models, and together with concluding remarks. Such remarks can be applied as a guide to apply appropriate SC model for specific application.

State estimation for multiple clocks under anomalies using -norm optimization

We investigate an estimation strategy for multiple clock systems, which is in particular resilient against clock anomalies. The clock anomalies, including frequency or phase jumps, can potentially degrade the estimation performance for multiple clock systems. While the conventional Kalman filter is known as one of the powerful methods for the estimation problem of multiple clock systems, we will show that it is vulnerable to the effects of clock anomalies. In this paper, we overcome this issue by employing an alternative approach to the Kalman filter, which is based on solving the -norm optimization problem. The estimation method employs a multiple clock model that includes only phase states. Nevertheless, the approach is shown to have more resilience against clock anomalies than the Kalman filter, because the deviation of the state from the apriori estimate is evaluated based on the -norm instead of the -norm. Moreover, the approach is shown to be competitive with many reset algorithms, since it does neighter require special stability assumptions about the reference clock, nor require any threshold for detecting the anomalies. The usefulness of the proposed method is validated through several numerical examples using actual clock data.

Енергетична ефективність технологій вирощування пшениці озимої у сівозмінах південного степу України

The results of the researches got in the protracted and temporal field researches during 2007–2017 are represented in the article. The aim of researches was determination of power efficiency of technologies of growing of wheat winter-annual for different predecessors, systems of till of soil, terms of sowing, bringing of mineral fertilizers, microfertilizers and biologics in short term crop rotations. Researches executed on the experienced field of the Odesa state agricultural experimental station of the National academy of agrarian sciences of Ukraine. It is set that a decision of problem of increase of production of high-quality grain-growing goods with diminishing of charges on condition of maintenance of the ecological state of environment and increase of level of fertility of soil was and remains a key task for agriculture of Ukraine. The important condition of increase of power efficiency of production of high-quality grain-growing goods are determination and introduction of effective technologies of growing of wheat winter-annual in the crop rotations of different ground-climatic terms of country. Certainly, that one of basic measures in relation to stopping and prevention of development of negative processes and crisis phenomena in agriculture there is the scientifically reasonable placing of wheat winter-annual after the best predecessors in crop rotations with application of rational till of soil, optimization of norms of bringing of mineral fertilizers and biologics. In particular, lands are more productively used, potential possibilities of sorts of plants will be realized better, an impurit goes down, influence of wreckers and illnesses diminishes in sowing of agricultural cultures. All of it positively influences on the state of environment, opens additional possibilities of increase of grain-growing products with diminishing of charges on her production. It is found out, that the tendency of increase of power charges in an agricultural production can result in negative consequences, that is why in the entire countries of the world large attention is spared the problem of energy-savings. One of important tasks that appear before modern agriculture is realization of control after the use of all types of power resources and translation of his industries on an energy keeping level. During realization of efficiency of technologies of growing of wheat winter-annual, a power analysis that considerably complements possibilities economic is applied Tom. Besides, the indexes of power analysis do not require the prices given about a change at comparison in time and does not depend on inflationary factors. Certainly, that corresponding methodologies of power and biopower analysis are worked out for today. Methodologies of power analysis principle of expression of all charges through a power index and corresponding correlation of all power charges is the basis of on the production of goods to energy, that in her is contained. On the basis of modern researches power indexes after that estimated efficiency of technologies of growing of wheat winter-annual are certain. For the calculation of the combined energy, gross products expended in a production on every technology, used power equivalents. Power equivalents are an amount of primary energy in Joules, that is needed for implementation of certain type of work. On this index compared power-hungryness of different technologies, determined the power structure of charges, different elements related to application. Account of the combined energy, grain-growing products expended in a production, carried out on the basis of flowsheets growing of cultures and charges of energy on implementation of works, and also power equivalents of the used capital goods. For the basic criterion of power efficiency of technologies took the coefficient of power efficiency, that was determined by the relation of mass of energy that is contained in the grown products, to the energy expended in her receipt. On results comparative power efficiency of technologies the rational growing of wheat winter-annual is set in the short term crop rotations of South Steppe of Ukraine. The favourable action of the system of shallow without shelves till of soil is certain in crop rotations, where as a predecessor of wheat winter-annual peas and mustard came forward white, on the receipt of the greatest indexes of power efficiency. It is found out, that at growing of wheat winter-annual after peas and mustard white the most coefficient of power efficiency was got at bringing of mineral fertilizers in combination with the variants of additional for a root signup by nitrogen and biologics of Gumatal nano and Azotofit. Certainly, that in a control variant without bringing of mineral fertilizers and biologics and additional for a root signup the coefficient of power efficiency headily went down nitric fertilizers, that unsatisfactorily had influenced on power efficiency of production of grain-growing goods.

Recurrent Neural Network-Based Dictionary Learning for Compressive Speech Sensing

We propose a novel dictionary learning technique for compressive sensing of speech signals based on the recurrent neural network. First, we exploit the recurrent neural network to solve an $$\ell _{0}$$ -norm optimization problem based on a sequential linear prediction model for estimating the linear prediction coefficients for voiced and unvoiced speech, respectively. Then, the extracted linear prediction coefficient vectors are clustered through an improved Linde–Buzo–Gray algorithm to generate codebooks for voiced and unvoiced speech, respectively. A dictionary is then constructed for each type of speech by concatenating a union of structured matrices derived from the column vectors in the corresponding codebook. Next, a decision module is designed to determine the appropriate dictionary for the recovery algorithm in the compressive sensing system. Finally, based on the sequential linear prediction model and the proposed dictionary, a sequential recovery algorithm is proposed to further improve the quality of the reconstructed speech. Experimental results show that when compared to the selected state-of-the-art approaches, our proposed method can achieve superior performance in terms of several objective measures including segmental signal-to-noise ratio, perceptual evaluation of speech quality and short-time objective intelligibility under both noise-free and noise-aware conditions.

Subspace-based spectrum estimation in innovation models by mixed norm minimization

In this paper, identification of discrete-time power spectra of multi-input/multi-output (MIMO) systems in innovation models from output-only time-domain measurements is considered.A hybrid identification algorithm unifying mixed norm minimization with subspace estimation method is proposed. The proposed algorithm first estimates a covariance matrix from measurements. A significant dimension reduction is achieved in this step. Next, a regularized nuclear norm optimization problem is solved to enforce sparsity on the selection of most parsimonious model structure. A modification of the covariance estimates in the proposed algorithm generates yet another algorithm capable of handling data records with sequentially and intermittently missing values. The new and the modified identification algorithms are tested on a numerical study and a real-life application example concerned with the estimation of joint power spectral density (PSD) of parallel road tracks.

Active vibration control of motorized spindle based on mixed /Kalman filter robust state feedback control

In its working process, a high-speed motorized spindle bearing-rotor system is affected by a variety of vibration excitations, which severely affect the machining precision and reliability. In view of the problems in the active vibration control of current smart-material-based bearing-rotor systems and based on the structural layout of a piezoelectric device and a controlled bearing-rotor system, a bearing was directly connected to a piezoelectric actuator via a sleeve, which improved the working efficiency of the piezoelectric stack actuator. Furthermore, to improve the robustness of the system’s vibration control performance under different external excitations (e.g., cutting force and mass unbalance), uncertainties in internal parameters (changes in bearing stiffness and stiffness nonlinearity of piezoelectric materials), process and measure noises, a mixed state feedback algorithm based on norm optimization and a Kalman filter observer with state disturbance estimation was established. The dynamic and robust performance of the proposed method was compared with that of the linear quadratic Gaussian optimal control methods and output feedback control method through both simulation and experiment by changing the piezoelectric stacks without changing the control program.

Tight Bounds for Online Vector Scheduling

Modern data centers face a key challenge of effectively serving user requests that arrive online. Such requests are inherently multidimensional and characterized by demand vectors over multiple resources such as processor cycles, storage space, and network bandwidth. Typically, different resources require different objectives to be optimized, and $L_r$ norms of loads are among the most popular objectives considered. Furthermore, the server clusters are also often heterogeneous making the scheduling problem more challenging. To address these problems, we consider the online vector scheduling problem in this paper. Introduced by Chekuri and Khanna in 2006, vector scheduling is a generalization of classical load balancing, where every job has a vector load instead of a scalar load. The scalar problem, introduced by Graham in 1966, and its many variants (identical and unrelated machines, makespan and $L_r$ norm optimization, offline and online jobs, etc.) have been extensively studied over the last 50 years. In this paper, we resolve the online complexity of the vector scheduling problem and its important generalizations---for all $L_r$ norms and in both the identical and unrelated machines settings. For an instance with $m$ machines and $d$ dimensions, our main results are: For identical machines, we show that the optimal competitive ratio is $\Theta(\log d / \log \log d)$ by giving an online lower bound and an algorithm with an asymptotically matching competitive ratio. The lower bound is technically challenging, and is obtained via an online lower bound for the minimum monochromatic clique problem using a novel online coloring game and randomized coding scheme. Our techniques also extend to asymptotically tight upper and lower bounds for general $L_r$ norms. For unrelated machines, we show that the optimal competitive ratio is $\Theta(\log m + \log d)$ by giving an online lower bound that matches a previously known upper bound. Unlike identical machines, however, extending these results, particularly the upper bound, to general $L_r$ norms requires new ideas. In particular, we use a carefully constructed potential function that balances the individual $L_r$ objectives with the overall (convexified) min-max objective to guide the online algorithm and track the changes in potential to bound the competitive ratio.

Some Convergence and Optimality Results of Adaptive Mixed Methods in Finite Element Exterior Calculus

In this paper, we present several new a posteriori error estimators and two adaptive mixed finite element methods \textsf{AMFEM1} and \textsf{AMFEM2} for the Hodge Laplacian problem in finite element exterior calculus. We prove that \textsf{AMFEM1} and \textsf{AMFEM2} are both convergent starting from any initial coarse mesh. A suitably defined quasi error is crucial to the convergence analysis. In addition, we prove the optimality of \textsf{AMFEM2}. The main technical contribution is a localized discrete upper bound. As opposed to existing literature, our results work on Lipschitz domains with nontrivial cohomology and provide the first norm convergence and optimality results.

H∞ controller synthesis for AGV trajectory tracking using a linearized kinematic model

This paper proposes a design procedure for H∞ optimal linear feedback controllers for trajectory tracking of an automated guided vehicle (AGV) based on a linearized kinematic model. The design specifications are expressed as a constrained H∞ norm optimization problem to assess the potential of the H∞ framework for the considered application. This problem is then solved for a linear parameter-varying (LPV), a full-block and a decoupled linear time-invariant (LTI) controller. The performance of all controllers is compared through numerical simulations and experiments on an AGV prototype targeted at agricultural applications.

Alternating direction and Taylor expansion minimization algorithms for unconstrained nuclear norm optimization

In the past decade, robust principal component analysis (RPCA) and low-rank matrix completion (LRMC), as two very important optimization problems with the view of recovering original low-rank matrix from sparsely and highly corrupted observations or a subset of its entries, have already been successfully adopted in image denoising, video processing, web search, biological information, etc. This paper proposes an efficient and effective algorithm, named the alternating direction and step size minimization (ADSM) algorithm, which employs the alternating direction minimization idea to solve the general relaxed model that can describe small noise (e.g., Gaussian noise). The coupling of sparse noise and small noise makes low-rank matrix recovery more challenging than that of RPCA. We make use of Taylor expansion, singular value decomposition and shrinkage operator as the alternating direction minimization method to deduce iterative direction matrices. A continuous technology is incorporated into ADSM to accelerate convergence. Similarly, the Taylor expansion and step size minimization (TESM) algorithm for LRMC is designed by the above way, but the alternating direction minimization idea needs to be ruled out since there is not a sparse matrix in it. Theoretically, it is proved that the two algorithms globally converge to their respective optimal points based on some conditions. The numerical results are reported, illustrating that ADSM and TESM are quite efficient and effective for recovering large-scale low-rank matrix problems at many cases.

Revisiting norm optimization for multi-objective black-box problems: a finite-time analysis

The complexity of Pareto fronts imposes a great challenge on the convergence analysis of multi-objective optimization methods. While most theoretical convergence studies have addressed finite-set and/or discrete problems, others have provided probabilistic guarantees, assumed a total order on the solutions, or studied their asymptotic behaviour. In this paper, we revisit the Tchebycheff weighted method in a hierarchical bandits setting and provide a finite-time bound on the Pareto-compliant additive $$\epsilon $$ -indicator. To the best of our knowledge, this paper is one of few that establish a link between weighted sum methods and quality indicators in finite time.