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Marcin Kaminski - One of the best experts on this subject based on the ideXlab platform.
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generalized stochastic Perturbation Technique in engineering computations
International Conference of Computational Methods in Sciences and Engineering (ICCMSE 2005), 2010Co-Authors: Marcin KaminskiAbstract:The main aim of the paper is to provide the generalized stochastic Perturbation Technique based on the classical Taylor expansion with a single random variable. The main problem discussed below is an application of this expansion to the solution of various partial differential equations with random coefficients by the fundamental numerical methods, i.e. Boundary Element Method, Finite Element Method as well as the Finite Difference Method. Since nth order expansion is employed for this purpose, the probabilistic moments of the solution can be determined with a priori given accuracy. Contrary to the second order Techniques used before, a Perturbation parameter e is also included in the relevant approximations, so that the overall solution convergence can be sped up by some modification of its value. Application of computational methodologies presented in transient problems (dynamics or heat transfer) are also commented on in the paper, together with stochastic processes modelling by the double Taylor expansion.
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random eigenvibrations of elastic structures by the response function method and the generalized stochastic Perturbation Technique
Archives of Civil and Mechanical Engineering, 2009Co-Authors: Marcin Kaminski, Jacek SzafranAbstract:This paper addresses the important question in structural analysis how to efficiently model the eigenvibrations of the spatial structures with random physical and/or geometrical parameters. The entire computational methodology is based on the traditional Finite Element Method enriched with the stochastic Perturbation Technique in its generalized nth order approach, while the computational implementation is performed by the use of the academic FEM software in conjunction with the symbolic algebra computer system MAPLE. Contrary to the previous straightforward solution Techniques, now the response function method is applied to compute any order probabilistic moments and coefficients of the structural eigenvalues. The response function is assumed in the polynomial form, the coefficients of which are computed from the several solutions of the deterministic problem around the mean value of the given input random parameter. This method is illustrated with the stochastic eigenvibrations of the simple single degree of freedom system and small steel tower modelled as the 3D truss structure with random mass density and Young modulus. This Technique may find its wide application in reliability analysis of the real existing engineering structures using the commercial Finite Element Method packages as well as the other discrete computational Techniques like the Finite Difference Method at least.
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generalized Perturbation based stochastic finite element method in elastostatics
Computers & Structures, 2007Co-Authors: Marcin KaminskiAbstract:Generalised nth order stochastic Perturbation Technique that can be applied to solve some boundary value or boundary initial problems in computational physics and/or engineering with random coefficients is presented here. This Technique is implemented in conjunction with the finite element method (FEM) to model 1D linear elastostatics problem with a single random variable. Main motivation of this work is to improve essentially the accuracy of the stochastic Perturbation Technique, which in its second order realization was ineffective for large variations of the input random fields. The nth order approach makes it possible to specify the accuracy of the computations a priori for the expected values and variances separately. The symbolic computer program is employed to perform computational studies on convergence of the first two probabilistic moments for simple unidirectional tension of the bar. These numerical studies verify the influence of coefficient of variation of the random input and, in the same time, of the Perturbation parameter on the first four probabilistic moments of the final solution vector.
D De Zutter - One of the best experts on this subject based on the ideXlab platform.
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analysis of coupled exponential microstrip lines by means of a multi step Perturbation Technique
IEEE Workshop on Signal and Power Integrity, 2016Co-Authors: Paolo Manfredi, D De Zutter, Dries Vande GinsteAbstract:In this contribution, an iterative and adaptive multi-step Perturbation Technique for nonuniform transmission lines is presented and applied to the analysis of coupled exponential lines. The Telegrapher's equations for nonuniform lines, which do not have a closed-form solution, are recast as the equations for uniform lines with equivalent distributed sources, for which a well-known numerical solution procedure exists. The line voltages and currents are computed in multiple steps by iteratively updating the distributed sources. The method turns out to be faster than classical solutions based on the discretization of the line into uniform subsections. Two validation examples are proposed that deal with coupled exponential lines, which have relevant applicability in microwave components.
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analysis of nonuniform transmission lines with an iterative and adaptive Perturbation Technique
IEEE Transactions on Electromagnetic Compatibility, 2016Co-Authors: Paolo Manfredi, D De Zutter, Dries Vande GinsteAbstract:This paper presents an iterative and adaptive Perturbation Technique for the analysis of nonuniform transmission lines. Place-dependent variations of the per-unit-length parameters are interpreted as Perturbations with respect to their average values along the line. This allows casting the governing equations for the corresponding Perturbations of the voltages and currents as those of a uniform transmission line with distributed sources. Therefore, standard transmission line theory is used to calculate these Perturbation terms. Specifically, Perturbations of increasing order are computed iteratively starting from the solution of the unperturbed line. The accuracy is adaptively adjusted by setting a threshold on the convergence of the solution. The algorithm turns out to be simple to implement and very accurate, yet faster than traditional approaches based on the discretization of the line into uniform sections. The Technique is validated through the analysis of several nonuniform transmission line structures of relevance in EMC applications, namely uniformly and nonuniformly twisted wire pairs as well as a cable bundle with lacing cords.
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nonuniform multiconductor transmission line analysis by a two step Perturbation Technique
IEEE Transactions on Components Packaging and Manufacturing Technology, 2014Co-Authors: Mykola Chernobryvko, D De Zutter, Dries Vande GinsteAbstract:A two-step Perturbation Technique to model nonuni- form multiconductor transmission lines in the frequency domain is presented. In this method, nonuniformities are treated as per- turbations with respect to the nominal uniform multiconductor line. Starting from the Telegrapher's equations and applying two consecutive Perturbations steps, at each step, we obtain second- order ordinary differential equations with distributed source terms. Solving these equations together with the appropriate boundary conditions provides the sought-for voltages and cur- rents along the interconnect structure. The method is validated by means of a frequency domain analysis of a ten-conductor microstrip line with random uniformities, confirming its accu- racy and efficiency. Additionally, the time-domain accuracy and efficiency is demonstrated by means of a high-speed packaging nonuniform interconnect with six signal conductors.
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a two step Perturbation Technique for nonuniform single and differential lines
IEEE Transactions on Microwave Theory and Techniques, 2013Co-Authors: Mykola Chernobryvko, Dries Vande Ginste, D De ZutterAbstract:A novel two-step Perturbation Technique to analyze nonuniform single and differential transmission lines in the frequency domain is presented. Here, nonuniformities are considered as Perturbations with respect to a nominal uniform line, allowing an interconnect designer to easily see what the effect of (unwanted) Perturbations might be. Based on the Telegrapher's equations, the proposed approach yields second-order ordinary distributed differential equations with source terms. Solving these equations in conjunction with the pertinent boundary conditions leads to the sought-for currents and voltages along the lines. The accuracy and efficiency of the Perturbation Technique is demonstrated for a linearly tapered microstrip line and for a pair of coupled lines with random nonuniformities. Moreover, the necessity of adopting a two-step Perturbation in order to get a good accuracy is also illustrated.
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A Perturbation Technique to analyze the influence of fiber weave effects on differential signaling
2013 IEEE 22nd Conference on Electrical Performance of Electronic Packaging and Systems, 2013Co-Authors: Mykola Chernobryvko, Dries Vande Ginste, D De ZutterAbstract:We study differential signaling via a pair of striplines in a substrate that is comprised of an epoxy/fiberglass woven composite structure. The transmission characteristics, which are deteriorated due to the presence of the fiber weave, are analyzed via an efficient modeling Technique for nonuniform transmission lines. This Technique is based on the solution of the pertinent differential equations using a Perturbation approach. For a challenging application example, it is shown that the unavoidable phase errors can be controlled by subdividing electrically long lines into smaller pieces, as such increasing accuracy whilst maintaining efficiency.
Dries Vande Ginste - One of the best experts on this subject based on the ideXlab platform.
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analysis of coupled exponential microstrip lines by means of a multi step Perturbation Technique
IEEE Workshop on Signal and Power Integrity, 2016Co-Authors: Paolo Manfredi, D De Zutter, Dries Vande GinsteAbstract:In this contribution, an iterative and adaptive multi-step Perturbation Technique for nonuniform transmission lines is presented and applied to the analysis of coupled exponential lines. The Telegrapher's equations for nonuniform lines, which do not have a closed-form solution, are recast as the equations for uniform lines with equivalent distributed sources, for which a well-known numerical solution procedure exists. The line voltages and currents are computed in multiple steps by iteratively updating the distributed sources. The method turns out to be faster than classical solutions based on the discretization of the line into uniform subsections. Two validation examples are proposed that deal with coupled exponential lines, which have relevant applicability in microwave components.
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analysis of nonuniform transmission lines with an iterative and adaptive Perturbation Technique
IEEE Transactions on Electromagnetic Compatibility, 2016Co-Authors: Paolo Manfredi, D De Zutter, Dries Vande GinsteAbstract:This paper presents an iterative and adaptive Perturbation Technique for the analysis of nonuniform transmission lines. Place-dependent variations of the per-unit-length parameters are interpreted as Perturbations with respect to their average values along the line. This allows casting the governing equations for the corresponding Perturbations of the voltages and currents as those of a uniform transmission line with distributed sources. Therefore, standard transmission line theory is used to calculate these Perturbation terms. Specifically, Perturbations of increasing order are computed iteratively starting from the solution of the unperturbed line. The accuracy is adaptively adjusted by setting a threshold on the convergence of the solution. The algorithm turns out to be simple to implement and very accurate, yet faster than traditional approaches based on the discretization of the line into uniform sections. The Technique is validated through the analysis of several nonuniform transmission line structures of relevance in EMC applications, namely uniformly and nonuniformly twisted wire pairs as well as a cable bundle with lacing cords.
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nonuniform multiconductor transmission line analysis by a two step Perturbation Technique
IEEE Transactions on Components Packaging and Manufacturing Technology, 2014Co-Authors: Mykola Chernobryvko, D De Zutter, Dries Vande GinsteAbstract:A two-step Perturbation Technique to model nonuni- form multiconductor transmission lines in the frequency domain is presented. In this method, nonuniformities are treated as per- turbations with respect to the nominal uniform multiconductor line. Starting from the Telegrapher's equations and applying two consecutive Perturbations steps, at each step, we obtain second- order ordinary differential equations with distributed source terms. Solving these equations together with the appropriate boundary conditions provides the sought-for voltages and cur- rents along the interconnect structure. The method is validated by means of a frequency domain analysis of a ten-conductor microstrip line with random uniformities, confirming its accu- racy and efficiency. Additionally, the time-domain accuracy and efficiency is demonstrated by means of a high-speed packaging nonuniform interconnect with six signal conductors.
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a two step Perturbation Technique for nonuniform single and differential lines
IEEE Transactions on Microwave Theory and Techniques, 2013Co-Authors: Mykola Chernobryvko, Dries Vande Ginste, D De ZutterAbstract:A novel two-step Perturbation Technique to analyze nonuniform single and differential transmission lines in the frequency domain is presented. Here, nonuniformities are considered as Perturbations with respect to a nominal uniform line, allowing an interconnect designer to easily see what the effect of (unwanted) Perturbations might be. Based on the Telegrapher's equations, the proposed approach yields second-order ordinary distributed differential equations with source terms. Solving these equations in conjunction with the pertinent boundary conditions leads to the sought-for currents and voltages along the lines. The accuracy and efficiency of the Perturbation Technique is demonstrated for a linearly tapered microstrip line and for a pair of coupled lines with random nonuniformities. Moreover, the necessity of adopting a two-step Perturbation in order to get a good accuracy is also illustrated.
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A Perturbation Technique to analyze the influence of fiber weave effects on differential signaling
2013 IEEE 22nd Conference on Electrical Performance of Electronic Packaging and Systems, 2013Co-Authors: Mykola Chernobryvko, Dries Vande Ginste, D De ZutterAbstract:We study differential signaling via a pair of striplines in a substrate that is comprised of an epoxy/fiberglass woven composite structure. The transmission characteristics, which are deteriorated due to the presence of the fiber weave, are analyzed via an efficient modeling Technique for nonuniform transmission lines. This Technique is based on the solution of the pertinent differential equations using a Perturbation approach. For a challenging application example, it is shown that the unavoidable phase errors can be controlled by subdividing electrically long lines into smaller pieces, as such increasing accuracy whilst maintaining efficiency.
Jyh Sheen - One of the best experts on this subject based on the ideXlab platform.
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modifications of the cavity Perturbation Technique for permittivity measurements of laminated samples
IEEE Transactions on Dielectrics and Electrical Insulation, 2016Co-Authors: Jyh Sheen, Chungming WengAbstract:New equations are derived for the measurement of microwave dielectric properties by the cavity Perturbation Technique. The limitation of very small sample dimension of the traditional Perturbation method is avoided by these new equations. Instead of using very small bar or rod shaped samples, the presented theory can be applied to larger laminated samples for dielectric properties measurements. The accuracy of these new equations is examined by experimental measurements.
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measurements of microwave dielectric properties by an amended cavity Perturbation Technique
Measurement, 2009Co-Authors: Jyh SheenAbstract:The accuracy of an amendment theory on the cavity Perturbation Technique for microwave dielectric properties measurements has been studied. The accuracy was confirmed by comparisons of experimental results with those measured by another well known measurement method – post resonance Technique. Based on the conventional circular aperture coupling structure, a new equation is proposed to determine the quality factor of TE modes for the rectangular cavity resonator. The relation of quality factor with the aperture radius was studied for determining the adequate aperture diameter.
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amendment of cavity Perturbation Technique for loss tangent measurement at microwave frequencies
Journal of Applied Physics, 2007Co-Authors: Jyh SheenAbstract:Theoretically, the quality factor of a metal resonant cavity will be increased after introducing a lossless dielectric sample. However, this increment of quality factor is not put into the consideration of the calculation of loss tangent measurement for the conventional cavity Perturbation method, widely used on the measurements of microwave dielectric properties. Therefore, the conventional resonant Perturbation formulas for dielectric loss measurement should be amended. This amendment is introduced in this study and the amended formulas for loss tangent measurement are given. With the amended formulas, no standard sample is required for measurement which simplifies the measuring procedure suggested by the previous publication. In addition, the measuring error on loss tangent on the conventional formula is discussed. Experiments have shown the improvement of measurement accuracy by this modification.
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amendment of cavity Perturbation Technique for loss tangent measurement at microwave frequencies
International Symposium on Antennas Propagation and EM Theory, 2006Co-Authors: Jyh SheenAbstract:Theoretically, the quality factor of a metal resonant cavity will be increased after introducing a lossless dielectric sample. However, for the conventional cavity Perturbation method, widely used on the measurements of microwave dielectric properties, this increment of quality factor is not put into the consideration of calculation on loss tangent measurement. Therefore, the conventional resonant Perturbation formulae for dielectric loss measurement should be amended. This amendment is introduced in this study and the measuring error on loss tangent on the conventional formula is discussed. Experiments have shown the improvement of measurement accuracy by this modification.
Marcin Marek Kamiński - One of the best experts on this subject based on the ideXlab platform.
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A generalized stochastic Perturbation Technique for plasticity problems
Computational Mechanics, 2009Co-Authors: Marcin Marek KamińskiAbstract:The main aim of this paper is to present an algorithm and the solution to the nonlinear plasticity problems with random parameters. This methodology is based on the finite element method covering physical and geometrical nonlinearities and, on the other hand, on the generalized n th order stochastic Perturbation method. The Perturbation approach resulting from the Taylor series expansion with uncertain parameters is provided in two different ways: (i) via the straightforward differentiation of the initial incremental equation and (ii) using the modified response surface method. This methodology is illustrated with the analysis of the elasto-plastic plane truss with random Young’s modulus leading to the determination of the probabilistic moments by the hybrid stochastic symbolic-finite element method computations.