Robust Iterative Algorithm Research Articles

Robust nonlinear power iteration algorithm for adaptive blind separation of independent signals

Abstract In this paper, we elaborate an extension of classical power iteration method to nonlinear power iteration for blind separation of multiple independent sources from observed array output signals. The present algorithm, referred to as NPI, considers the estimating of the separating matrix as a nonlinear power iteration problem. By naturally choosing the positive definite normalizer for nonlinear power term, the resulting algorithm not only yields robust convergence behavior but also guarantees the orthonormality of the separating matrix at each iteration. To circumvent the difficulty of solving the inverse square root for the normalizer, an efficient adaptive singular value decomposition (SVD) technique is also adopted to obtain a fast implementation of NPI. The estimation accuracy and convergence speed of the present algorithm are illustrated through simulation results and compared with the existing adaptive algorithms.

Digital Baseband Predistortion Based Linearized Broadband Inverse Class-E Power Amplifier

A newly introduced inverse class-E power amplifier (PA) was designed, simulated, fabricated, and characterized. The PA operated at 2.26 GHz and delivered 20.4-dBm output power with peak drain efficiency (DE) of 65% and power gain of 12 dB. Broadband performance was achieved across a 300-MHz bandwidth with DE of better than 50% and 1-dB output-power flatness. The concept of enhanced injection predistortion with a capability to selectively suppress unwanted sub-frequency components and hence suitable for memory effects minimization is described coupled with a new technique that facilitates an accurate measurement of the phase of the third-order intermodulation (IM3) products. A robust iterative computational algorithm proposed in this paper dispenses with the need for manual tuning of amplitude and phase of the IM3 injected signals as commonly employed in the previous publications. The constructed inverse class-E PA was subjected to a nonconstant envelope 16 quadrature amplitude modulation signal and was linearized using combined lookup table (LUT) and enhanced injection technique from which superior properties from each technique can be simultaneously adopted. The proposed method resulted in 0.7% measured error vector magnitude (in rms) and 34-dB adjacent channel leakage power ratio improvement, which was 10 dB better than that achieved using the LUT predistortion alone.

Experimental and Numerical Investigation of Structural Damage Detection Using Changes in Natural Frequencies

A robust iterative algorithm is used to identify the locations and extent of damage in beams using only the changes in their first several natural frequencies. The algorithm, which combines a first-order, multiple-parameter perturbation method and the generalized inverse method, is tested extensively through experimental and numerical means on cantilever beams with different damage scenarios. If the damage is located at a position within 0–35% or 50–95% of the length of the beam from the cantilevered end, while the resulting system equations are severely underdetermined, the minimum norm solution from the generalized inverse method can lead to a solution that closely represents the desired solution at the end of iterations when the stiffness parameters of the undamaged structure are used as the initial stiffness parameters. If the damage is located at a position within 35–50% of the length of the beam from the cantilevered end, the resulting solution by using the stiffness parameters of the undamaged structure as the initial stiffness parameters deviates significantly from the desired solution. In this case, a new method is developed to enrich the measurement information by modifying the structure in a controlled manner and using the first several measured natural frequencies of the modified structure. A new method using singular value decomposition is also developed to handle the ill-conditioned system equations that occur in the experimental investigation by using the measured natural frequencies of the modified structure.

Sparseness-constrained data continuation with frames: Applications to missing traces and aliased signals in 2/3-D

We present a robust iterative sparseness-constrained interpolation algorithm using 2-/3-D curvelet frames and Fourier-like transforms that exploits continuity along reflectors in seismic data. By choosing generic transforms, we circumvent the necessity to make parametric assumptions (e.g. through linear/parabolic Radon or demigration) regarding the shape of events in seismic data. Simulation and real data examples for data with moderately sized gaps demonstrate that our algorithm provides interpolated traces that accurately reproduce the wavelet shape as well as the AVO behavior. Our method also shows good results for de-aliasing judged by the behavior of the (f − k)-spectrum before and after regularization.

An algorithm for computing the mean response time of a single server queue with generalized on/off traffic arrivals

In this paper, an exact solution for the response time distribution of a single server, infinite capacity, discrete-time queue is presented. This queue is fed by a flexible discrete-time arrival process, which follows an on/off evolution. A workload variable is associated with each arrival instant, which may correspond to the service demand generated by a single arrival, or represent the number of simultaneous arrivals (bulk arrivals). Accordingly, the analysis focuses on two types of queues: (On/Off)/G/1 and (Batch-On/Off)/D/1. For both cases, a decomposition approach is carried out, which divides the problem into two contributions: the response time experienced by single bursts in isolation, and the increase on the response time caused by the unfinished work that propagates from burst to burst. Particularly, the solution for the unfinished work is derived from a Wiener-Hopf factorization of random walks, which was already used in the analysis of discrete GI/G/1 queues. Compared to other related works, the procedure proposed in this paper is exact, valid for any traffic intensity and has no constraints on the distributions of the input random variables characterizing the process: duration of on and off periods, and workload. From the general solution, an efficient and robust iterative algorithm for computing the expected response time of both queues is developed, which can provide results at any desired precision. This algorithm is numerically evaluated for different types of input distributions and proved against simulation.

Accuracy and sensitivity of a hole drilling and digital speckle pattern interferometry combined technique to measure residual stresses

This paper reports on the accuracy and sensitivity of digital speckle pattern interferometry (DSPI) when it is combined with the hole drilling technique for measuring residual stresses. The in-plane displacement field generated by the introduction of a small hole is determined using an automated data analysis approach. This method is based on the calculation of the optical phase distribution through a phase-shifting method and the application of a robust iterative phase unwrapping algorithm. It is experimentally demonstrated that residual stresses can be measured with a relative uncertainty of 7.5%. It is also shown that the minimum value of residual stress that can be determined with the DSPI and hole drilling combined technique is about 10% of the yield stress of the material.

Complete location of poles for thick lossy grounded dielectric slab

In order to obtain accurate closed-form representations of the microstrip Green's functions, it is often necessary to find the locations of the proper and improper surface-wave poles. In this paper, we present an efficient and robust iterative algorithm based on contraction mapping, which can locate all the proper and improper solutions of the characteristic equations of the grounded dielectric slab. The dielectric may also be lossy.

A Symmetrical Streamline Stabilization scheme for high advective transport

An overview of numerical techniques and previous investigations related to the solution of advection-dominated transport processes is presented. In addition a new Symmetrical Streamline Stabilization (S3) scheme is introduced. The basis of the technique is to treat the transport equation in two steps. In the first step the dispersion part is approximated by a standard Galerkin approach, while in the second step the advection is approximated by a least-squares method. The two parts are reassembled, resulting in one system of equations. The resulting coefficients' matrix is symmetric. Only half of a sparse matrix needs to be stored. Robust iterative algorithms for symmetrical systems of equations such as the preconditioned conjugate gradient method (PCG) can be successfully used. The new method leads to an implicit introduction of an ‘artificial diffusion’ term. Solute transport with high Peclet and Courant numbers does not lead to oscillations due to an inherent upwind damping. The upwind effect acts only in flow direction. The efficiency of the new formulation in terms of accuracy and computation time is shown in comparison with the Galerkin approach for mesh parallel and mesh oblique high advective solute transport. Copyright © 2000 John Wiley & Sons, Ltd.

A Symmetrical Streamline Stabilization scheme for high advective transport

An overview of numerical techniques and previous investigations related to the solution of advection-dominated transport processes is presented. In addition a new Symmetrical Streamline Stabilization (S3) scheme is introduced. The basis of the technique is to treat the transport equation in two steps. In the first step the dispersion part is approximated by a standard Galerkin approach, while in the second step the advection is approximated by a least-squares method. The two parts are reassembled, resulting in one system of equations. The resulting coefficients' matrix is symmetric. Only half of a sparse matrix needs to be stored. Robust iterative algorithms for symmetrical systems of equations such as the preconditioned conjugate gradient method (PCG) can be successfully used. The new method leads to an implicit introduction of an ‘artificial diffusion’ term. Solute transport with high Peclet and Courant numbers does not lead to oscillations due to an inherent upwind damping. The upwind effect acts only in flow direction. The efficiency of the new formulation in terms of accuracy and computation time is shown in comparison with the Galerkin approach for mesh parallel and mesh oblique high advective solute transport. Copyright © 2000 John Wiley & Sons, Ltd.

Stability of large excavations in laminated hard rock masses: the voussoir analogue revisited

The voussoir beam analogue has provided a useful stability assessment tool for more than 55 years and has seen numerous improvements and revisions over the years. In this paper, a simplified and robust iterative algorithm is presented for this model. This approach includes an improved assumption for internal compression arch geometry, simplified displacement determination, support pressure and surcharge analysis and a corrected stabilizing moment in the two dimensional case. A discrete element simulation is used to verify these enhancements and to confirm traditional assumptions inherent in the model. In the case of beam snap-through failure, dominant in hard rock excavations of moderately large span, design criteria are traditionally based on a stability limit which represents an upper bound for stable span estimates. A deflection threshold has been identified and verified through field evidence, which corresponds to the onset of non-linear deformation behaviour and therefore, of initial instability. This threshold is proposed as a more reasonable stability limit for this failure mode in rockmasses and particularly for data limited cases. Design charts, based on this linearity limit for unsupported stability of jointed rock beams, are presented here summarizing critical span–thickness–modulus relationships.

A new image motion estimation algorithm based on the EM technique

This paper focuses on the presentation and implementation of a new iterative algorithm for image motion coefficient estimation from noisy measurements based on the expectation-maximization (EM) technique. We also compare this algorithm with two other robust iterative algorithms. We represent the motion field by a (unitary) series expansion to obtain the motion coefficients, and show this characterization to have several virtues. First, an inherent property of motion, referred to as smoothness, is imposed. Second, the nonuniform motion estimation is reduced to the estimation of a few coefficients using the low-pass property of the motion. Finally, the motion estimation can be accomplished without the need for a motion model; in the events for which the motion model is completely unknown, the DCT representation is shown to be very effective in describing the true motion.

A class of robust entropic functionals for image restoration

This paper considers the concept of robust estimation in regularized image restoration. Robust functionals are employed for the representation of both the noise and the signal statistics. Such functionals allow the efficient suppression of a wide variety of noise processes and permit the reconstruction of sharper edges than their quadratic counterparts. A new class of robust entropic functionals is introduced, which operates only on the high-frequency content of the signal and reflects sharp deviations in the signal distribution. This class of functionals can also incorporate prior structural information regarding the original image, in a way similar to the maximum information principle. The convergence properties of robust iterative algorithms are studied for continuously and noncontinuously differentiable functionals. The definition of the robust approach is completed by introducing a method for the optimal selection of the regularization parameter. This method utilizes the structure of robust estimators that lack analytic specification. The properties of robust algorithms are demonstrated through restoration examples in different noise environments.