Redundant Basis Research Articles

Wheel-rail force identification for high-speed railway based on a modified weighted l1-norm regularization with optimal strain sensors

Wheel-rail force identification is an important inverse problem for structural health monitoring of high-speed railway train-track-bridge system. It is widely used for dynamic response reconstruction of bridges and early safety warning of dynamic reduction rate of wheel weight for the train. It can also serve as a reference for the calibration of wheel-rail force model. This paper proposes a wheel-rail force identification method for high-speed railway based on a modified weighted l1-norm regularization. Based on numerical simulations, it is found that variations of dynamic component of wheel-rail forces are very small. Therefore, the problem is transformed into the identification of three categories of static wheel weights and two categories of average dynamic components, which greatly simplifies the degree of freedom of the solution compared to traditional methods, thereby improving the solution accuracy and saving the number of sensors needed. The wheel-rail forces are decomposed into the product of a series of redundant basis functions and corresponding coefficients. The fast iterative shrinkage threshold algorithm (FISTA) and the Bayesian information criterion (BIC) are used to seek the solution of l1-norm regularization and to select the optimal regularization coefficients, respectively. Since the number of sensors and their locations have a significant impact on the accuracy of reconstructed wheel-rail forces, they are optimized using a genetic algorithm (GA), aiming to accurately reconstruct the wheel-rail forces with the minimum number of sensors at corresponding optimal positions. Numerical simulation of a 32 m box girder standard beam for high-speed railway shows that the reconstructed wheel-rail forces are in good agreement with the simulated results, which verifies the accuracy of the proposed method. In addition, the results of dynamic load test indirectly demonstrate the effectiveness of the proposed method.

Trend filtering for functional data

Despite increasing accessibility to function data, effective methods for flexibly estimating underlying functional trend are still scarce. We thereby develop a functional version of trend filtering for estimating trend of functional data indexed by time or on general graph by extending the conventional trend filtering, a powerful nonparametric trend estimation technique for scalar data. We formulate the new trend filtering by introducing penalty terms based on ‐norm of the differences of adjacent trend functions. We develop an efficient iteration algorithm for optimizing the objective function obtained by orthonormal basis expansion. Furthermore, we introduce additional penalty terms to eliminate redundant basis functions, which leads to automatic adaptation of the number of basis functions. The tuning parameter in the proposed method is selected via cross validation. We demonstrate the proposed method is locally adaptive and can identify change points through simulation studies and applications to real‐world datasets.

The Role of Redundant Bases and Shrinkage Functions in Image Denoising.

Wavelet denoising is a classical and effective approach for reducing noise in images and signals. Suggested in 1994, this approach is carried out by rectifying the coefficients of a noisy image, in the transform domain, using a set of shrinkage functions (SFs). A plethora of papers deals with the optimal shape of the SFs and the transform used. For example, it is widely known that applying SFs in a redundant basis improves the results. However, it is barely known that the shape of the SFs should be changed when the transform used is redundant. In this paper, we introduce a complete picture of the interrelations between the transform used, the optimal shrinkage functions, and the domains in which they are optimized. We suggest three schemes for optimizing the SFs and provide bounds of the remaining noise, in each scheme, with respect to the other alternatives. In particular, we show that for subband optimization, where each SF is optimized independently for a particular band, optimizing the SFs in the spatial domain is always better than or equal to optimizing the SFs in the transform domain. Furthermore, for redundant bases, we provide the expected denoising gain that can be achieved, relative to the unitary basis, as a function of the redundancy rate.

Efficient uncertainty quantification for permeability of three-dimensional porous media through image analysis and pore-scale simulations.

In this paper, we propose an efficient coupled approach for uncertainty quantification of permeability for randomly reconstructed three-dimensional (3D) pore images, where the porosity and two-point correlations of a realistic sandstone sample are honored. The Joshi-Quiblier-Adler approach and Karhunen-Loève expansion are utilized for quick reconstruction of 3D pore images with reduced random dimensionality. The eigenvalue problem for the covariance matrix of 3D intermediate Gaussian random fields is solved equivalently by a kernel method. Then, the lattice Boltzmann method is adopted to simulate fluid flow in reconstructed pore space and evaluate permeability. Lastly, the sparse polynomial chaos expansion (sparse PCE) integrated with a feature selection method is employed to predict permeability distributions incurred by the randomness in microscopic pore structures. The feature selection process, which is intended to discard redundant basis functions, is carried out by the least absolute shrinkage and selection operator-modified least angle regression along with cross validation. The competence of our proposed approach is validated by the results from Monte Carlo simulation. It reveals that a small number of samples is sufficient for sparse PCE with feature selection to produce convincing results. Then, we utilize our method to quantify the uncertainty of permeability under different porosities and correlation parameters. It is found that the predicted permeability distributions for reconstructed 3D pore images are close to experimental measurements of Berea sandstones in the literature. In addition, the results show that porosity and correlation length are the critical influence factors for the uncertainty of permeability.

Extended integrated force method for the analysis of prestress-stable statically and kinematically indeterminate structures

This paper presents a new force method to predict the structural response of statically and kinematically indeterminate systems that can be stabilized through prestress, i.e. prestress-stable structures. This new force method, here named Extended Integrated Force Method (IFME), extends the existing Integrated Force Method (IFM) which is only applicable to the analysis of kinematically determinate systems. The product force concept is adopted and incorporated into the IFME to model the effect of infinitesimal mechanisms. This makes the IFME capable of dealing with cases in which the external loads contain components that cannot be taken by the system in its initial configuration. As the original IFM, the IFME bypasses the well-known concept of redundant forces and basis determinant structure of the Standard Force Method (SFM) by taking the internal forces as the independent variables which are obtained simultaneously. A proof is provided to show that, when the product force is not included in the formulation, the IFME reduces to the IFM for kinematically determinate systems and it also reduces to another force method based on singular value decomposition of the equilibrium matrix which is here named SVD-FM. Compared to the better known Displacement Method (DM), the IFME is a suitable alternative and it offers a deeper insight into the structure response which is decoupled into an extensional and an inextensional part for prestress-stable kinematically indeterminate systems. Numerical examples are carried out to test accuracy and effectiveness of the IFME on kinematically indeterminate structures with multiple self-stress states and mechanism modes. Application of the IFME to active structural control of kinematically indeterminate systems is also discussed through a numerical example.

Tensorial generalization of characters

In rainbow tensor models, which generalize rectangular complex matrix model (RCM) and possess a huge gauge symmetry U(N1) × … × U(Nr), we introduce a new sub-basis in the linear space of gauge invariant operators, which is a redundant basis in the space of operators with non-zero Gaussian averages. Its elements are labeled by r-tuples of Young diagrams of a given size equal to the power of tensor field. Their tensor model averages are just products of dimensions: leftlangle chi {R}_1,dots, {R}_rrightrangle sim {C}_{R_1},dots {,}_{R_r}left({N}_1right)dots {D}_{R_r}left({N}_rright) of representations Ri of the linear group SL(Ni), with {C}_{R_1},dots {,}_{R_r} , made of the Clebsch­Gordan coefficients of representations Ri of the symmetric group. Moreover, not only the averages, but the operators {chi}_{overrightarrow{R}} themselves exist only when these {C}_{overrightarrow{R}} are non-vanishing. This sub-basis is much similar to the basis of characters (Schur functions) in matrix models, which is distinguished by the property \\character) ~ character, which opens a way to lift the notion and the theory of characters (Schur functions) from matrices to tensors. In particular, operators {chi}_{overrightarrow{R}} are eigenfunctions of operators which generalize the usual cut-and­join operators hat{W} ; they satisfy orthogonality conditions similar to the standard characters, but they do not form a full linear basis for all gauge-invariant operators, only for those which have non-vanishing Gaussian averages.

Spatially multi-scale dynamic factor modeling via sparse estimation

In many spatio-temporal data, their spatial variations have inherent global and local structures. The spatially continuous dynamic factor model (SCDFM) decomposes the spatio-temporal data into a small number of spatial and temporal variations, where the spatial variations are represented by the factor loading (FL) functions. However, the FL functions estimated by the maximum likelihood or maximum [Formula: see text] penalized likelihood capture global structures but do not capture local structures. We propose a method for estimating the spatially multiscale FL functions using a sparse penalty. To overcome the problems of existing sparse penalties, we propose the adaptive graph lasso (AGL) penalty. The method with the AGL penalty eliminates redundant basis functions contained in the FL functions, and leads to the FL functions having global and localized structures. We derive the EM algorithm with block coordinate descent that enables us to maximize the AGL penalized log-likelihood stably. Applications to synthetic and real data show that the proposed modeling procedure accurately extract not only the spatially global structures but also spatially local structures, which the [Formula: see text] penalized estimation do not extract.

An economical representation of PDE solution by using compressive sensing approach

We introduce a redundant basis for numerical solution to the Poisson equation and find a sparse solution to the PDE by using a compressive sensing approach. That is, we refine a partition of the underlying domain of the PDE several times and use the multi-level nested spline subspaces over these refinements to express the solution of the PDE redundantly. We then use a compressive sensing algorithm to find an economical representation of the spline approximation of the PDE solution. The number of nonzero coefficients of an economical representation is less than the number of the standard spline representation over the last refined partition, i.e. finite element solution while we will show that the error of the spline approximation with an economical representation is the same to the standard FEM solution. This approach will be useful, e.g. in the situation when the PDE solver has a much powerful computer than the users of the solution.

Bridge influence line identification based on adaptive B‐spline basis dictionary and sparse regularization

Bridge influence line (BIL) is a promising tool for the real applications in the fields of bridge weight-in-motion (BWIM), model updating, damage identification, and load carrying capacity evaluation. The key of such applications is how to obtain the accurate results of BIL. To accurately identify BIL based on bridge dynamic responses induced by a moving vehicle, two critical problems, including how to construct a general representation function of BIL and how to deal with the ill-posed inverse problem, should be properly resolved. This paper proposes a novel approach based on the adaptive B-spline basis dictionary and sparse regularization technique for BIL identification. A representation of basis function is first established to construct BIL, and then integrated with a redundant B-spline basis dictionary to ensure the sparsity of solution. A curvature-based adaptive node optimization method is proposed to automatically adjust the spatial arrangement of nodes according to the shape of BILs. Numerical and experimental validations are conducted to verify the accuracy and robustness of the proposed approach. The identified BIL results are accurate, indicating that the proposed node-adaptive optimization and sparse regularization techniques are effective to improve the quality of BIL identification. It is also shown that the proposed approach is not sensitive to the noise interference and configuration of testing vehicle. Through the robustness testing, it is proved that the proposed approach has the merits of high accuracy and strong robustness.

Extension of sound field separation technique based on the equivalent source method in a sparsity framework

The equivalent source method (ESM)-based sound field separation technique has been successfully introduced into near-field acoustic holography as a preprocessing tool to eliminate the influence of disturbing sources or reflections from the opposite side of the array. In this paper, that technique is further extended in a sparsity framework, which makes it possible to take the advantage of the theory of compressive sensing to achieve reasonable separation accuracy with a limited number of spatial sampling points. In this study, three sparse bases are considered, including two existing bases that are suitable for spatially sparse and spatially extended sources, respectively, and a more flexible, redundant sparse basis that is constructed by combining the two sparse bases above, and the ℓ1-norm minimization is used to promote sparse solutions. Numerical simulation and experimental results demonstrate the validity of the proposed technique and show the superiority of the use of the redundant sparse basis. Besides, the effects of the relative strength of the target source to the disturbing source, the number of spatial sampling points and the signal-to-noise ratio on the separation accuracy are analyzed numerically.

A Fully Serial-In Parallel-Out Digit-Level Finite Field Multiplier in $\mathbb {F}_{2^{m}}$ Using Redundant Representation

Redundant basis (RB) is one of the appealing representation systems for finite field arithmetic due to its specific features in providing cost-free squaring operation in hardware implementation and because it eliminates the need for modular reduction. In this brief, a new architecture for digit-level finite field multiplication in $\mathbb {F}_{2^{m}}$ using redundant representation is proposed. Contrary to previously presented redundant basis multipliers, in the proposed architecture one digit of each operand is concurrently fed into the multiplier at each clock cycle which, in turn, reduces the total number of the clock cycles required in the multiplication process. To draw an accurate comparison, the proposed multiplier together with several existing digit-level RB multipliers were fully implemented in 65-nm CMOS technology.

Multi-Dimensional Sparse Models.

Traditional synthesis/analysis sparse representation models signals in a one dimensional (1D) way, in which a multidimensional (MD) signal is converted into a 1D vector. 1D modeling cannot sufficiently handle MD signals of high dimensionality in limited computational resources and memory usage, as breaking the data structure and inherently ignores the diversity of MD signals (tensors). We utilize the multilinearity of tensors to establish the redundant basis of the space of multi linear maps with the sparsity constraint, and further propose MD synthesis/analysis sparse models to effectively and efficiently represent MD signals in their original form. The dimensional features of MD signals are captured by a series of dictionaries simultaneously and collaboratively. The corresponding dictionary learning algorithms and unified MD signal restoration formulations are proposed. The effectiveness of the proposed models and dictionary learning algorithms is demonstrated through experiments on MD signals denoising, image super-resolution and texture classification. Experiments show that the proposed MD models outperform state-of-the-art 1D models in terms of signal representation quality, computational overhead, and memory storage. Moreover, our proposed MD sparse models generalize the 1D sparse models and are flexible and adaptive to both homogeneous and inhomogeneous properties of MD signals.

Low Complexity Digit Serial Multiplier for Finite Field using Redundant Basis

Cryptography has been increasingly used due to its rapid trends. In recent days, it has been used mostly in communication and in financial transactions through automated machines or internet. The applications of cryptography and coding theory require finite field operations and are realized based on the finite field computations. In this paper efficient digit-serial multiplier over finite field is implemented and is obtained by using Redundant Basis (RB), intend to present highthroughput multiplier. Area and power are the two factors which obtain less when compared to the previous multipliers. The digit-serial multiplier for 32-bit is implemented using Verilog HDL and synthesized to know its better performance in terms of area and power compared to previous multipliers.

Image inpainting using reproducing kernel Hilbert space and Heaviside functions

Image inpainting, a technique of repairing damaged images, is an important topic in image processing. In this paper, we solve the problem from an intensity function estimation perspective. We assume the underlying image is defined on a continuous domain and belongs to a space spanned by a basis of a reproducing kernel Hilbert space and some variations of the Heaviside function. The reproducing kernel Hilbert space is used to model the smooth component of the image while Heaviside function variations are used to model the edges. The coefficients of the redundant basis are computed by the discrete intensity at undamaged domain. We test the proposed model through various images. Numerical experiments show the effectiveness of the proposed method, especially in recovering edges.

Surface approximation via sparse representation and parameterization optimization

Surface approximation with smooth functions suffers the problems of choosing the basis functions and representing non-smooth features. In this work, we introduce a sparse representation for surfaces with a set of redundant basis functions, which efficiently overcomes the overfitting artifacts. Moreover, we propose an approach of parameterization transformation, which makes the possibility to represent non-smooth features by the composition of a smooth function and a non-smooth domain optimization. We couple the sparse representation and the parameterization transformation in a global optimization to respect sharp features with smooth polynomial basis functions. Our approach is capable for approximating a wide range of surfaces with different level of sharp features. Experimental results have shown the feasibility and applicability of our proposed method in various applications.

18 Years of Redundant Basis Multipliers over Galois Field

Redundant basis multipliers over Galois Field have gained huge popularity in elliptic curve cryptography mainly because of their negligible hardware cost for squaring and modular reduction. Different techniques used so far for the implementation of redundant basis multipliers over Galois Field are explored here. Based on review the Word Level Redundant Basis multiplier is the most efficient among all multipliers in terms of hardware utilization. Digit serial Redundant Basis multiplication in a bit level matrix vector form is most efficient in terms of area-time complexities. General Terms Redundant Basis Multiplication

Single image super-resolution by approximated Heaviside functions

Image super-resolution involves the estimation of a high-resolution image from one or multiple low resolution images. It is widely used in medical imaging, satellite imaging, target recognition, etc. In this paper, we solve the problem of single image super-resolution from an image intensity function estimation perspective. We assume that the unknown image intensity function is defined on a continuous domain and belongs to a space with a redundant basis. The selection of the redundant basis is based on an observation: an image is composed of smooth and non-smooth components, and we use two classes of approximated Heaviside functions (AHFs) to represent them respectively. The coefficients of the redundant basis are computed iteratively from a given low-resolution image. In addition, we apply the proposed iterative scheme to image patches to reduce computation and storage size. Comparisons with some existing competitive methods show the effectiveness of the proposed method.

ON CONVERGENCE OF GENETIC ALGORITHM FOR FPGA RECONFIGURATION

The article discusses the problem of increasing the reliability and fault tolerance of programmable logic integrated circuits of type FPGA. Currently there are several approaches to improve the reliability. One of them is to use elements with redundant basis, an appropriate diagnosis and reconfiguration. The aim of the study is to develop a genetic algorithm for FPGA reconfiguration, with the use of elements with redundant basis. Reconfiguration task is understood as a problem of finding a workable elements that cover a given functional circuit. These elements should be arranged more compactly. In this paper we prove a theorem, which theoretically justifies the convergence of the algorithm to an optimal solution. Practical experiments confirm the theoretical conclusions. The results can be used to develop new genetic algorithms and creating FPGA based on elements with redundant basis.

Efficient Compressed Sensing Method for Moving-Target Imaging by Exploiting the Geometry Information of the Defocused Results

Compressed sensing (CS) has been increasingly used in the synthetic aperture radar ground moving-target indication system, particularly for imaging the moving targets, which satisfy the sparse precondition of the CS method. However, efficient moving-target imaging is a key challenge for current CS methods, since the redundant basis brings heavy computation load. In this letter, by exploiting the geometry information of the defocused results, we present an efficient fractional Fourier transform (FRFT) to estimate the Doppler rate and image the moving targets by only two times FRFT rather than time-consuming searching operation. Then, the concept is extended into an efficient CS (ECS) imaging method by two bases consisting of two discrete FRFT matrices rather than the redundant basis. Simulations and real-data process are provided to demonstrate the effectiveness of the ECS method. The proposed ECS method can achieve accurate parameter estimation and imaging performance with low computational complexity.

High-Throughput Finite Field Multipliers Using Redundant Basis for FPGA and ASIC Implementations

Redundant basis (RB) multipliers over Galois Field ( GF(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> )) have gained huge popularity in elliptic curve cryptography (ECC) mainly because of their negligible hardware cost for squaring and modular reduction. In this paper, we have proposed a novel recursive decomposition algorithm for RB multiplication to obtain high-throughput digit-serial implementation. Through efficient projection of signal-flow graph (SFG) of the proposed algorithm, a highly regular processor-space flow-graph (PSFG) is derived. By identifying suitable cut-sets, we have modified the PSFG suitably and performed efficient feed-forward cut-set retiming to derive three novel multipliers which not only involve significantly less time-complexity than the existing ones but also require less area and less power consumption compared with the others. Both theoretical analysis and synthesis results confirm the efficiency of proposed multipliers over the existing ones. The synthesis results for field programmable gate array (FPGA) and application specific integrated circuit (ASIC) realization of the proposed designs and competing existing designs are compared. It is shown that the proposed high-throughput structures are the best among the corresponding designs, for FPGA and ASIC implementation. It is shown that the proposed designs can achieve up to 94% and 60% savings of area-delay-power product (ADPP) on FPGA and ASIC implementation over the best of the existing designs, respectively.