Pseudo-inverse Technique Research Articles

Accurate measurement of micromachining forces through dynamic compensation of dynamometers

In this paper, we present a comprehensive approach for accurate measurement of high-bandwidth three-dimensional (3D) micromachining forces through dynamic compensation of dynamometers. Accurate measurement of micromachining forces is paramount to gaining fundamental understanding on process mechanics and dynamics of micromachining. Multi-axis dynamometers are used to measure 3D machining forces. However, specified bandwidth of these devices is below the frequencies arising during micromachining while using ultra-high-speed (UHS) spindles. This limitation arises from the effects of the dynamometer's structural dynamics on the measured forces. Therefore, accurate measurement of micromachining forces entails high frequency correction of the signals acquired by the dynamometer by removing the influence of those effects. The presented approach involves: (1) accurate identification of 3D force measurement characteristics of the dynamometer within a 25kHz bandwidth to capture the effects of the dynamometer dynamics; (2) design of a pseudo-inverse filter-based compensation technique to remove the influence of the dynamic response in 3D; and (3) validation of the compensation technique through custom-devised experiments. Subsequently, the compensation method is applied to the micromilling process to obtain accurate broadband 3D micromachining forces using a miniature multi-axis dynamometer. It is concluded that the presented approach enables accurate determination of 3D micromachining forces. The presented compensation technique is also readily applicable for expanding the bandwidth of large dynamometers.

Erratum : Spectral Reflectivity Recovery from Tristimulus Values using 3D Extrapolation with 3D Interpolation

Journal of the Optical Society of Korea Vol. 18, No. 5, October 2014, pp. 507-516 ISSN: 1226-4776(Print) / ISSN: 2093-6885(Online) DOI: http://dx.doi.org/10.3807/JOSK.2014.18.5.507 Spectral Reflectivity Recovery from Tristimulus Values Using 3D Extrapolation with 3D Interpolation Bog G. Kim 1 , John S. Werner 2 , Michael Siminovitch 3 , Kostantinos Papamichael 3 , Jeongwon Han , and Soobeen Park * Department of Physics, Pusan National University, Busan 609-735, Korea Department of Ophthalmology and Vision Science, University of California, Davis, CA 95817, USA Design Department, California Lighting Technology Center, University of California, Davis, CA 95618, USA Department of Housing and Interior design, Pusan National University, Busan 609-735, Korea (Received June 5, 2014 : revised August 22, 2014 : accepted September 5, 2014) We present a hybrid method for spectral reflectivity recovery, using 3D extrapolation as a supplemental method for 3D interpolation. The proposed 3D extrapolation is an extended version of 3D interpolation based on the barycentric algorithm. It is faster and more accurate than the conventional spectral-recovery techniques of principal-component analysis and nonnegative matrix transformation. Four different extrapolation techniques (based on nearest neighbors, circumcenters, in-centers, and centroids) are formulated and applied to recover spectral reflectivity. Under the standard conditions of a D65 illuminant and 1964 10° observer, all reflectivity data from 1269 Munsell color chips are successfully reconstructed. The superiority of the proposed method is demonstrated using statistical data to compare coefficients of correlation and determination. The proposed hybrid method can be applied for fast and accurate spectral reflectivity recovery in image processing. Keywords : Color measurement, Extrapolation, Inverse problem, Spectral reflectivity OCIS codes : (100.3190) Inverse Problems; (300.6550) Spectroscopy, visible; (330.1690) Color; (330.1710) Color, measurement (330.1715) Color, rendering and metamerism I. INTRODUCTION Recently there has been considerable interest in spectral reflectivity recovery methods in the field of color science [1-7] because of their fundamental importance, as well as their technological significance. In general, the color of an object is determined by the illumination conditions and the reflectivity of the surface material [8-10]. The light spectrum reflected by the material is passed through the eye and quantified by tristimulus values [8-10]. The spectral behavior of a colored object is known to be the fingerprint of the color, which is independent of the applied light source and the observer (for nonfluorescent materials). Spectral reflectivity recovery is also important for multispectral image processing, color consistency, color reconstruction, and color image pro- cessing [1-3]. Recovering the spectral reflectivity from known tristimulus values is an inverse problem for a given illumination condition [1, 7, 8]. In general, the solution to such an inverse problem is ill-posed, meaning that an exact and accurate solution is not easy to find. The solution also depends on the noise and initial conditions [11-13]. Two major methods for spectral reflectivity recovery are the pseudo-inverse technique [2-6, 14-17] and the interpolation technique [7, 18-20]. In the pseudo-inverse technique, principal-component analysis [2-6, 14-16] and nonnegative matrix transformation [7, 17, 21-23] are developed with various adaptation techniques. These are partially successful at reflectivity recovery, but finding an appropriate adaptation set requires extensive computation time, and the adaptation algorithm itself suffers from a locali- zation problem. A three-dimensional (3D) interpolation technique is often applied to minimize calculations when approximating mathemati- cally defined complex functions, or to produce intermediate results from sparse data points [11, 24]. Both situations can be directly employed when we convert images from *Corresponding author: sobpark@pusan.ac.kr Color versions of one or more of the figures in this paper are available online.

Design and analysis of a tendon-based MRI-compatible surgery robot for transperineal prostate needle placement

Tendon-based transmission has significant advantages in the development of a surgical robot, which is fully magnetic resonance imaging compatible and can work dexterously in the very limited space inside magnetic resonance imaging core. According to the requirements of magnetic resonance imaging compatibility, a novel 6 degrees of freedom tendon-based surgical robot composed of three independent modules is developed in this paper. After a brief introduction to the robot, the direct and inverse kinematic equations are deduced by applying the concept of screw displacements, and the reachable workspace of the robot is calculated. As to the static force analysis, we apply the principle of virtual work to derive a transmission between the equivalent joint torques and the tendon forces. By the use of the pseudoinverse technique, a systematic method is developed for the resolution of redundant tendon forces.

Eigen Value and It′s Comparison with Gaussian RBF, Multi-Quadratic RBF and Inverse Multi-Quadratic RBF Methods

For any system Eigen value is the characteristic value and It is the characte ristic roots for an equation which modeled that system. In this paper we have introduce Radial Basis Function (RBF) to evaluate Eigen value approximation for any given system. We have made some approximation to get best possible output with the help of pseudo inverse technique in Radial Basis Functions. We have experimented and compared the Eigen values of matrices with respect to Gaussian RBF, Multi-Quadratic RBF and Inverse Multi-Quadratic RBF methods. In this paper we worked on several matrices and calculated their Eigen value by using different RBF methods.

Fault-tolerant Sliding Mode Control for Uncertain Over-actuated Systems

This paper presents the sliding mode control design based on nonlinear sliding surface that ensures high performance step response of uncertain over-actuated system. High performance sliding mode control is designed for the system with predefined virtual control inputs having order less than the order of the system. Total control effort is then distributed among the actuators using pseudo-inverse control allocation technique. To make the system fault-tolerant (actuator saturation tolerant), the control allocation is updated online in a predefined way.

Signal Space Separation method with block matrix inversion for extraction of signals in magnetoencephalography

Signal Space Separation (SSS) method is a technique utilized to eliminate the contribution of unwanted signals due to external magnetic noise that inevitably get recorded along with the actual magnetic signal due to neuronal currents in the brain. In this paper, the SSS method has been implemented using block matrix inversion. By implementing block matrix inversion along with regrouping of radial terms, it has been possible to extract the true brain signal from the measured magnetic signal which includes the contribution from an external magnetic dipole artifact for measurements from as few as 64 channels. We observe that the minimum root mean square deviation (RMSD) of the signal inferred from block matrix inversion with regrouped terms is around 6 fT when the truncation order is set at L1 = 11 for signals of interest and L2 = 2 for external noise sources and saturates to similar values for higher L1. The RMSD of extracted signal is 50% smaller than the minimum RMSD when the magnetoencephalography signal is extracted by direct pseudoinverse technique and does not have a deep minimum in the truncation order L1 as observed when direct pseudoinverse technique is used.

On the numerical integration of rate independent single crystal behavior at large strain

This paper presents a new numerical algorithm for the integration of the constitutive equations of a single crystal for finite rate-independent elastoplastic strains. The algorithm addressed in this paper is dedicated to face-centered-cubic (FCC) crystal structures. Its first feature is a much more efficient and more accurate integration scheme of the constitutive equations compared to previous attempts. This scheme is based on a fully implicit integration procedure, yet it may be transformed easily into an explicit scheme. Determining the set of active slip systems is performed by the use of a combinatorial search procedure, and the determination of the slip rates of the different active slip systems is based on the fixed point method. The second feature of this algorithm stems from the original method used to solve the ambiguity of the possible non-uniqueness of the set of active slip systems. A robust method, based on a small positive perturbation of the critical shear stresses, is proposed to overcome this difficulty. It is worth mentioning that the algorithm developed in this paper is not limited to one particular hardening law or to FCC crystal structures. Rather, it can be used and extended to various hardening laws and crystal structures (e.g. BCC or HCP…) in a straightforward manner. The authors demonstrate the performance of the proposed algorithm and illustrate its accuracy and efficiency through various numerical simulations at the single crystal and polycrystal scales. The predicted results obtained from those simulations were compared with those obtained using other numerical techniques and algorithms (i.e., a pseudo-inversion technique and an explicit algorithm). Our numerical predictions are also compared with some numerical and experimental results from other papers. The response of the polycrystal was computed by using the proposed algorithm combined with Taylor’s homogenization scheme, which is used to compute the overall polycrystalline behavior. The paper ends with a statistical study of the influence of the perturbation technique on the response prediction for a single crystal and a polycrystal.

Image noise reduction using Wiener filtering with pseudo-inverse

We present a preliminary design and experimental results of a Gaussian noise reduction method for ultrasound images. Our method utilizes a Wiener filtering algorithm with pseudo-inverse technique. The method is capable of solving the Gaussian noise problem in ultrasound image by setup a constant dB of noise function. The key idea of the Wiener filtering algorithm is to process the given ultrasound signal by making the filtering less sensitive to slight changes in input conditions. In this paper, we investigate the possibility of employing this approach for pre-processing ultrasound image application. The application of the proposed method for reducing Gaussian noise is demonstrated by four examples. Meanwhile, we also made the comparisons with median filter, mean filter and adaptive filter; the results reveal that the proposed method has the best noise filtering capability than other three methods. The results also show that the proposed method produces recovery images with quiet high peak-signal-to-noise ratio.

Multistage inversion algorithm for biological tissue imaging

A new inversion method for diffuse optical tomography is proposed. This is a multistage algorithm, that uses a signal subspace-based method to simplify the inverse problem and proposes a guided iterative inversion process to improve the imaging. First, subspace-based analysis is used to determine the voxels that definitely belong to the background and exclude them from further consideration. Then, the pseudo-inverse technique is applied for reconstruction. In the final stage, the reconstruction is improved iteratively by finding and excluding more voxels belonging to background. The method reduces the ill-posedness of the image reconstruction problem iteratively such that good imaging results are obtained for multiple heterogeneities having complicated geometries even in the presence of 3% additive white noise.

Radial Basis Function Neural Network Models for Peak Stress and Strain in Plain Concrete under Triaxial Stress

In the analysis or design process of reinforced concrete structures, the peak stress and strain in plain concrete under triaxial stress are critical. However, the nonlinear behavior of concrete under triaxial stresses is very complicated; modeling its behavior is therefore a complicated task. In the present study, several radial basis function neural network (RBFN) models have been developed for predicting peak stress and strain in plain concrete under triaxial stress. For the purpose of constructing the RBFN models, 56 records including normal- and high-strength concretes under triaxial loads were retrieved from literature for analysis. The K-means clustering algorithm and the pseudoinverse technique were employed to train the network for extracting knowledge from training examples. Besides, the performance of the developed RBFN models was estimated by the method of three-way data splits and K-fold cross-validation. On the other hand, a comparative study between the RBFN models and existing regression models was made. The results demonstrate the versatility of RBFN in constructing relationships among multiple variables of nonlinear behavior of concrete under triaxial stresses. Moreover, the results also show that the RBFN models provided better accuracy than the existing parametric models, both in terms of root-mean-square error and correlation coefficient.

Distributed localization for anisotropic sensor networks

In this article, we address the issue of localization in anisotropic sensor networks. Anisotropic networks differ from isotropic networks in that they possess properties that vary according to the direction of measurement. Anisotropic characteristics result from various factors such as the geographic shape of the region (nonconvex region), different node densities, irregular radio patterns, and anisotropic terrain conditions. In order to characterize anisotropic features, we devise a linear mapping method that projects one embedding space built upon proximity measures into geographic distance space by using the truncated singular value decomposition (SVD) pseudo-inverse technique. This transformation retains as much topological information as possible and reduces the effect of measurement noise on the estimates of geographic distances. We show via simulation that the proposed localization method outperforms DV-hop, DV-distance, and MDS-MAP, and makes robust and accurate estimates of sensor locations in both isotropic and anisotropic sensor networks.

Pseudoinverse in clustering problems

The clustering of vector observations of hyperplanes is studied. Different cases of correspondence distances are proposed and investigated, including the algebraic Jack Knife one. The efficiency, constructivity, and explicit form of formulas are provided by using the pseudoinverse technique including the pseudoinverse-perturbation theory. Results important for the application of pseudoinverse and related operators are presented.

Imaging defects with reduced space inversion of magnetic flux leakage fields

Magnetic flux leakage technique is being used for detection of defects inside a magnetically permeable bar by measuring the leakage fields outside the bar. Defects in magnetically permeable bar have been modeled as localized anti-dipoles whose moments and locations have to be determined. Generalized inverse or pseudo-inverse technique has been used to image the defects using least-square minimum-norm solution. An initial estimate of the defects is obtained by utilizing the generalized inverse of the lead matrix over the entire region of the sample space using the measured magnetic field data including random noise. By defining a suitable threshold, and ignoring the defect locations where the moment inferred in the initial estimate was below the chosen threshold, the image of the defect is again obtained by repeating the calculation in this reduced space for the lead matrix. The leakage fields from both a line defect and a deeply buried defect were simulated and utilized for inversion using this approach. It has been possible to image the defects and quantify the strengths of the moments with the correlation coefficient approaching unity for low-noise case and attain significant improvement in the correlation coefficient for data with reasonable levels of noise.

Nondestructive damage evaluation of a curved thin beam

A vibration-based nondestructive damage evaluation technique for a curved thin beam is introduced. The proposed method is capable of detecting, locating, and sizing structural damage simultaneously by using a few of the lower natural frequencies and their corresponding mode shapes before and after a small damage event. The proposed approach utilizes modal flexibilities reconstructed from measured modal parameters. A rigorous system of equations governing damage and curvature of modal flexibility is derived in the context of elasticity. To solve the resulting system of governing equations, an efficient pseudo-inverse technique is introduced. The direct inspection of the resulting solutions provides the location and severity of damage in a curved thin beam. This study confirms that there is a strong linear relationship between the curvature of modal flexibility and flexural damage in the selected class of structures. Several numerical case studies are provided to justify the performance of the proposed approach. The proposed method introduces a way to avoid the singularity and mode selection problems from earlier attempts.

Imaging buried defects in a three dimensional magnetically permeable medium using pseudoinverse technique

Pseudoinverse technique has been used to identify the location and distribution of buried defects inside a magnetically permeable medium by measuring the leakage fields outside the medium. Defects have been modeled as localized antidipoles whose moments and locations have to be determined. Use of pseudoinverse technique has enabled us to separate the moment variables and space variables and factor out the moment variables in the least square minimum norm solution. The leakage fields from two different flaws with an additive noise were simulated and utilized for inversion using this approach. It has been possible to identify the locations of defects and quantify the strength of the moments in the three dimensional medium even in the presence of reasonably large noise. This imaging technique has also been utilized to identify a single defect located 20mm below the top surface in the presence of noise.

Optimal dimensionality reduction of sensor data in multisensor estimation fusion

When there exists the limitation of communication bandwidth between sensors and a fusion center, one needs to optimally precompress sensor outputs-sensor observations or estimates before the sensors' transmission in order to obtain a constrained optimal estimation at the fusion center in terms of the linear minimum error variance criterion, or when an allowed performance loss constraint exists, one needs to design the minimum dimension of sensor data. This paper will answer the above questions by using the matrix decomposition, pseudo-inverse, and eigenvalue techniques.

Matrix pseudo-inversion technique for diagnostics of planar arrays

It is shown, by means of numerical simulation, that the Moore-Penrose pseudoinverse of a matrix taken from an overdetermined system can be applied to retrieve the excitation distribution of a planar array of parallel dipoles with faulty elements, by measuring the complex radiated field in its near zone. Failures on voltage (considering mutual coupling) and current of several elements, and systematic or random measurement errors, are considered in the simulation.

Indirect measurement of main bearing loads in an operating diesel engine

This paper deals with the application of indirect measurement techniques to an operating diesel engine. Internal loads exciting the engine block during operation are not directly measurable with force sensors; they have to be assessed from the dynamic deformation of the structure. The idea is to use the structure itself as a multi-force sensor, which requires the knowledge of the transfer functions between considered excitations and measured responses. The first part is devoted to the description of the methodology. In Section 1, the extraction of uncorrelated deflection shapes from stationary measurements is presented. Then the pseudo-inversion technique, needed to invert the transfer system, is reviewed. Optimization of the inversion, based on a weighing technique, is presented in Section 3. Then a regularization process based on the truncated singular value decomposition and the L-curve principle is suggested. In the second part, a basic model of a drive train is used to directly assess internal excitations from the measured cylinder pressures. Outputs of this model are compared with excitations indirectly measured on the operating engine in a third part. The efficiency of the optimization and regularization processes is illustrated, and encouraging results are presented, allowing information on defects of the drive train model to be obtained. Finally, a ranking operation is realized on internal excitations to illustrate the strong interest of the results of indirect force measurement.

A markov random field approach to spatio-temporal contextual image classification

Markov random fields (MRFs) provide a useful and theoretically well-established tool for integrating temporal contextual information into the classification process. In particular, when dealing with a sequence of temporal images, the usual MRF-based approach consists in adopting a scheme, i.e., in propagating the temporal information from the current image to the next one of the sequence. The simplicity of the cascade scheme makes it attractive; on the other hand, it does not fully exploit the temporal information available in a sequence of temporal images. In this paper, a mutual MRF approach is proposed that aims at improving both the accuracy and the reliability of the classification process by means of a better exploitation of the temporal information. It involves carrying out a bidirectional exchange of the temporal information between the defined single-time MRF models of consecutive images. A difficult issue related to MRFs is the determination of the MRF model parameters that weight the energy terms related to the available information sources. To solve this problem, we propose a simple and fast method based on the concept of minimum perturbation and implemented with the pseudoinverse technique for the minimization of the sum of squared errors. Experimental results on a multitemporal dataset made up of two multisensor (Landsat Thematic Mapper and European Remote Sensing 1 synthetic aperture radar) images are reported. The results obtained by the proposed mutual approach show a clear improvement in terms of classification accuracy over those yielded by a reference MRF-based classifier. The presented method to automatically estimate the MRF parameters yielded significant results that make it an attractive alternative to the usual trial-and-error search procedure.

런지-커타 기법과 유전자 알고리즘을 이용한 제어기 설계 시스템의 구현

유전자 알고리즘은 생물의 유전적 진화과정을 이용한 새로운 문제 해결의 방안으로 결정론적 방법으로 해결하지 못한 난제에 적합한 알고리즘이다. 제어기 설계 기법은 주파수에 의존하는 명세에 의한 설계는 있어 왔으나 Manabe 표준형을 기본으로 사용하는 시간에 의존하는 명세를 만족시키는 제어기 설계 기법은 미미한 단계에 있다. 본 논문에서는 일반화된 Manabe 표준형을 이용하여 플랜트의 성능을 충족시키는 제어기의 설계에 관해 연구한다. 두 변수 구조를 갖는 제어시스템에서 제어기의 계수 설계시 역행렬 방법이나 기존의 의역 행렬 방법으로 해결할 수 없는 경우가 있다. 이 경우에 원하는 폐루프 다항식이 설계된 다항식과 같거나 근사적으로 같도록 새로운 의역 행렬 방법과 경사알고리즘을 이용하여 제어기를 설계하는 두 가지 방법을 제안한다. 다음으로 제안된 제어기 설계 방법들을 자바로 구현한다 Genetic algorithms using a Process of genetic evolution of an organism are appropriate for hard problems that have not been solved by any deterministic method. Up to now, the controller design method has been made with the frequency dependent specification but the design method with the time specification has gotten little progress. In this paper, we study the controller design to satisfy the performance of a plant using the generalized Manabe standard form. When dealing with a controller design in the case of two parameter configurations, there are some situations that neither a known pseudo inverse technique nor the inverse method can be applicable. In this case, we propose two methods of designing a controller by the gradient algorithm and the new pseudo inverse method so that the desired closed polynomials are either equalized to or approximated to the designed polynomial. Design methods of the proposed controller are implemented in Java.