PARAMETER ESTIMATION FOR EXPONENTIAL SIGNALS BY THE QUADRATIC INTERPOLATION
|
|
- Claude Baker
- 5 years ago
- Views:
Transcription
1 Proceedings of the Fourth IASTD International Conference POWR AD RGY SYSTMS (AsiaPS 8 April -4, 8 Langawi, Malaysia ISB CD: PARAMTR STIMATIO FOR XPOTIAL SIGALS BY TH QUADRATIC ITRPOLATIO Rong-Ching Wu*, Tai-Yi Yang*, Jong-Ian Tsai**, and Ting-Chia Ou*** *Department of lectrical ngineering, I-Shou Uniersity, Kaohsiung, Taiwan, R.O.C **Department of lectronic ngineering, Kao Yuan Uniersity, Kaohsiung, Taiwan, R.O.C. ***Department of lectrical ngineering, ational Sun Yat-Sen Uniersity, Kaohsiung, Taiwan, R.O.C ABSTRACT This paper offers a complete method to find the exact frequency, damping, amplitude, and phase of the exponential molds. A simulated signal is taen to fit the one. When this simulated signal is equal to the one, the parameters of the simulated signal are identical to the alues. This method includes three major steps, initial alue setting, gradient method, and quadratic interpolation. In initial alue setting, this method analyzes the mold parameter with the two highest amplitudes of each mold, and the precise alues will e found. The difference etween simulated and practical signals could e expressed as a least mean square prolem. The gradient method proides the initial condition for the quadratic interpolation. The minimum error search is accomplished y the quadratic interpolation, which could improe the search efficiency and reduce iteration time. After a few iterations, the method will otain the exact harmonic parameters. KY WORDS xponential mold, Parameters, Quadratic interpolation.. Introduction In physical systems, dynamic ehaior can e expressed as differential equations. The results of linear and time-inariant differential equations are mostly composed of exponential forms. Parameters of exponential forms include frequencies, dampings, amplitudes, and phases. There are two types of exponential forms. If the damping is equal to zero, the mode is periodic; conersely, if the damping is not equal to zero, the mode will e aperiodic, and it will decay to zero with time. For the different types of signals, many analysis methods hae een deelop [,]. The Irahim time domain (ITD method uses impulse response function (IRF data to identify modal parameters [3]. The random decrement method aerages the response segments as a free response. The auto-regression- moing-aerage (ARMA method identifies a system and presents future responses from the information of its past inputs and outputs. The least-squares complex exponential (LSC method lins the relationship etween the IRF and its complex poles and residues through a complex exponential [4]. The eolutionary programming algorithm is also applied to the analysis of transient signal [5]. This paper proposes a method to analyze exponent signal, which can improe the accuracy and conergence of parameter estimation. This method taes a simulated signal and fits it to the one. The difference etween the simulated signal and the one is the topic of least mean square. The optimal solution must e found y the iteration of optimization searching. This paper uses quadratic interpolation method to improe searching efficiency. The quadratic interpolation has rapid conergence in optimization and can otain the solutions of non-linear function in a few iterations. The quadratic interpolation regards the function as a quadratic cure. The method infers the minimum of the function according to three nown conditions. Therefore, the calculation of quadratic interpolation must e ased on three nown conditions. This paper proides these three nown conditions y gradient method. That is, the first three iterations are done y the gradient method and the following iterations are taen y the quadratic interpolation. Thus, the searching efficiency will e improed for the quadratic interpolation, and the initial conditions will e otained for the gradient method. The modification of gradient method is ased on the initial alues and their gradients, and the conergence of the iterant is decided y suitale initial alues. A process to find suitale initial alues is also used in this paper. The frequency will e located within two FFT components of each pea. This method taes these two FFT components to find the initial alues of frequency, damping, amplitude, and phase. The following sections completely illustrate theory, procedures, and ealuation. Section illustrates the oject function of optimization. Section 3 deduces the quadratic interpolation method, which is the tool for searching optimal solutions. Section 4 descries the gradient method, which runs the first three iterations. Section 5 proides a procedure to calculate initial alues, which proides the data to the gradient method. Section 6 ealuates accuracy, and compares different methods. Section 7 is the conclusion
2 . Oject Function After sampling, a signal can e expressed as x (. This paper regards a signal consist of seeral molds. Moreoer, a simulated signal will e fitted to the one. The mold can e expressed y frequency, damping, amplitude, and phase, that is K α n/ x( A e cos(π fn/ +, ( n,,..., where A is amplitude, and is phase; oth of α and f are damping and frequency respectiely. The actual alues in Hz are α ' α / T,,,..., K ( f ' f / T,,,..., K (3 where T is the whole measurement sampling time. When the distance of the simulated signal and the one is, the simulated signal and the one are identical, and the simulated signal is the one. For this reason, the oject function can e defined as [6] ase n ( x ( (4 where ase n ( x ( quation (4 is within (,, which standardizes the result of estimation. The oject function is influenced from A,, α, and f, and is the high non-linear function with a minimum alue,. The influence of these three parameters on the oject function is shown in Fig.. The purpose of parameter estimation is to mae the oject function descend to. If there is noise existing in the measured signal, this error will not descend to, ut to a minimum alue. Oject function 3. Quadratic Interpolation The quadratic interpolation is that the nown data are estalished in a quadratic function. The minimum of this function will e found. A quadratic function could e expressed as ay + y + c (5 If the independent ariales [ y, y, y ] and their corresponding dependent ariales [,, ] which is near the optimal solution, are nown. This method regards that the relation of these data is a quadratic function. That is ( y y a ( y y (6 ( y y c then the coefficients of this function are a ( y y ( y y (7 c ( y y According to (5, its extreme alue will happen when its first-order differentiation is equal to zero. amely d + ay + + (8 dy Therefore, the following condition must e formed if the alue of the quadratic function is a minimum y + (9 a where y can e sustituted y A,, α,or.when all new independent ariales are otained, the f + new oject function will e calculated y (4. In addition, the exact parameters can e otained in this process. This method searches the optimal solution y three nown conditions which do not require a complex formula howeer, the quadratic interpolation must e started at three nown conditions. Shown in Fig.. The first three conditions could e found y the gradient method. Thus, the searching efficiency will e improed for the gradient method, and the initial conditions will e otained for the quadratic interpolation. Phase Frequency Figure. The influence of different parameters on the oject function 94
3 xtreme alue Oject function Quadratic function f + η f η f f + α α η α α where η are accelerating factors. (8 (9 ( y 5. Initial Value Setting Figure. Searching for extreme alue y quadratic interpolation 4. Gradient Method The gradient method is a minimization searching method which can deal with multiariales. quation (4 has 4 K unnown ariales, A,, α, and f. To find the minimum of this function is to satisfy the following equation [7]: ( u ( where is the gradient of, that is, is the first order differential for all ariales. ( u [ / u( / u(4k ] T ( The first order partial differential equations of to each parameter are α n/ ( x( e cos( n/ + A ( ase n ase n α n/ ( x ( e sin( n/ + A πa α n/ ( n( x ( e sin( n/ + 4 f ase n A α ase n α n/ ( n( x ( e cos( n/ + (3 (4 (5 The solution of non-linear equation,, can e expressed as + x ( x ( η ( (6 x ( The ariales are in sustitution for x, and the next states of frequency, amplitude, and phase can e found as + A A η A (7 A This section proides a simple and accurate algorithm to ensure iteration is conerged and efficiency improed. The process is illustrated elow [8]. For a clear description, firstly, symols used are shown in Fig. 3. Fig. 3 is the spectrum of a signal, and the two highest amplitudes are X p and X p+ ε, which are located at the FFT components p and p + ε. Where ε is equal to or, respectiely if X p+ X p or not. These 4 data are the references to set initial alues. To find the initial alues, the two auxiliary equations are estalished firstly. Amplitude 振幅 X p X / ( ρ p+ε X p X p + X p p p + p p Frequency 頻率 Amplitude spectrum Figure 3. Reference data for initial alue ρ z ( ρ exp( jπε / then the frequency and the damping can e found: δ arg( z (3 π f p + δ (4 α ln z (5 Once δ and α are determined, the third auxiliary equation can e estalished. X p 95
4 exp( α jπδ D (6 exp( ( α jπδ / The complex coefficient A is easily determined from (6 A X p / D (7 arg( X p / D (8 6. Procedure This section rearranges the aoe theory as a complete procedure [9]. Step, signal sampling: The sample period T and sample data are decided. In this step, for distinguishing eery and clearly, the sample period must e suitale; for conforming to sampling theorem and calculating aility, the sample data must e suitale. Step, time-frequency transformation: The signal is transformed into spectrum y FFT. Step 3, selection of reference data: Molds will cause their peas on spectrum. From these ands, the method will get the reference data of scales, p, p', X, and. p X p + ε Step 4, initial alue setting: The alues of frequencies and dampings can e found y (4 and (5. Then, referring to the found frequencies, the alues of amplitudes and phases can e calculated y (7 and (8 indiidually. Because the results of parameters approach the ones, it ensures the following iteration is conerging. Step 5, gradient method: Find the next states of frequency, damping, amplitude, and phase y (7 to (. Then the oject function can e found y (4. Step 6, additionally repeat Step 5 twice. Step 7, quadratic interpolation: Coefficients can e otained y (7, and next states can e deried from (9. The next states of frequency, damping, amplitude, and phase are found in turn in this step. Then the oject function can e found y (4. Step 8, conergence examining: If the results haen t conerged to the accepted range, the procedure goes to step 7. The step could also assign the times of iterations, which preents the alues from conerging. Step 9, calculation accomplished. 7. Aility aluation This section ealuates the aility of the method in two parts. The first discusses accuracy; the last compares the results of the different methods. 9. t x( t 4. 65e cos(π 59. 9t cos (π t cos(π.4t e 7. 8t cos (π 4 t. 6 (9 The sample period is sat T(, sec, and the numer of data is sat48. The analysis results are recorded in Tale.The comparison of the simulated signal and one is shown in Fig.4. Satisfactory results will e calculated y the quadratic interpolation, which is shown in the fifth to eighth columns. The fourth column shows results of initial alue setting. Approximate results can e found in this stage. In this example, the conergence is reached after 5 iterations. Real alues can e otained only after a few iterations. Then satisfactory results will e calculated. 7. Comparison Of Different Methods This section compares the quadratic interpolation with gradient method in conergence degree. When analyzing (9, Fig. 5 is the conergence degrees of quadratic interpolation and gradient method. In Fig. 5, the quadratic interpolation can reduce the oject function to * -6 in 5 iterations. With the same initial alues and accuracy required, the gradient method needs more iteration. In all iterations, the conergence degrees of quadratic interpolation are oiously more excellent than the gradient method. Because this method can conerge rapidly, the iterations needed are quite less. Tale Signal analysis Real This method Component Parameter alue Initial st iteration 5th iteration f A Hz α f... A Hz α.7..4 f A Hz α.9.6. f A Hz α Accuracy For proing the accuracy of this method for parameter estimation, this section taes a signal with 4 molds as an example. 96
5 Amplitude Time (ms Real Initial alue Figure 4. Comparison of the simulated signal and one Oject function (*^ Iteration times Gradient method Quadratic interpolation Figure 5. Conergence of different methods References [].D. yman, Modeling, Simulation, and Control, St. Paul, West Pulication Company, 988. [] T. Soderstorm, P. Stoica, System Identification, ew-jersey: Prentice Hall, 989. [3] J. He, Z.F. Fu, Modal Analysis, Boston: Butterworth- Heinemann, 3. [4] T. Soderstrom, H. Fan, B. Carlsson, and S. Bigi, Least Squares Parameter stimation of Continuous-Time ARX Models from Discrete-Time Data, I Trans. Automatic Control, ol. 4, no. 5, pp , May 997. [5] L.L. Lai and J.T. Ma, Application of olutionary Programming to Transient and Sutransient Parameter stimation, I Trans. nergy Conersion, ol., no. 3, pp , Sept [6] R.C. Wu, S.L. Yan, and C.W. Yang, Parameter stimation of the xponential Signals Using the Conjugate Gradient Method, 3 International Conference ICICS, pp , 3. [7] B. Li, A Generalized Conjugate Gradient Model for the Mild Slope quation, Coastal ngineering, ol. 3, 994, pp [8] M. Bertocco, C. Offelli, and D. Petri, Analysis of Damped Sinusoidal Signals ia a Frequency-Domain Interpolation Algorithm, I Transactions on Instrumentation and Measurement, ol. 43, no., pp. 45-5, April 994. [9] R.C. Wu, S.L. Yan, and C.W. Yang, Parameter stimation for the Complex xponential Signals y the Second Order Differentiation, The 4 rd Symposiumon lectrical Power ngineering, 3, pp Conclusion This paper offers a complete method to find the exact frequency, damping, amplitude, and phase of molds. This method includes three major processes, initial alue setting, gradient method, and quadratic interpolation. In initial alue setting, the process has otained the approximate alues. The gradient method proides the initial condition to the quadratic interpolation. The quadratic interpolation can find the optimal solution in a few iterations. This method possesses the adantages of accuracy and excellent conergence. These features are:. ( Accuracy: The mold parameters are found y least mean square, which maes oject function decrease to minimum. ( xcellent conergence: Since the approximate alues hae een otained in initial alue setting, results are conerged quicly. 97
Vibro-Acoustical Diagnostics of Turbine Cavitation Examples of Application*
Viro-Acoustical Diagnostics of Turine Caitation Examples of Application* By Branko Bajic, Korto Caitation Serices, Luxemourg 12, rue Ste Zithe, L-2763 Luxemourg phone +49 89 4445144 fax +49 89 44451325
More informationParameters Identification of Equivalent Circuit Diagrams for Li-Ion Batteries
Parameters Identification of Equialent Circuit Diagrams for Li-Ion eries Ahmad ahmoun, Helmuth Biechl Uniersity of Applied ciences Kempten Ahmad.ahmoun@stud.fh-empten.de, biechl@fh-empten.de Abstract-eries
More informationPlanning the most suitable travel speed for high frequency railway lines
Planning the most suitale trael speed for high frequency railway lines Alex Landex Technical Uniersity of Denmark, Centre for Traffic and Transport, Bygningstoret 1, 800 Kgs. Lyngy, Denmark, e-mail: al@ctt.dtu.dk
More informationG022 Multi-azimuth Seismic Data Imaging in the Presence of Orthorhombic Anisotropy
G0 Multi-azimuth Seismic Data Imaging in the Presence of Orthorhomic Anisotropy Y. Xie* (CGGVeritas), S. Birdus (CGGVeritas), J. Sun (CGGVeritas) & C. Notfors (CGGVeritas) SUMMARY The presence of orthorhomic
More informationIN this paper, we consider the estimation of the frequency
Iterative Frequency Estimation y Interpolation on Fourier Coefficients Elias Aoutanios, MIEEE, Bernard Mulgrew, MIEEE Astract The estimation of the frequency of a complex exponential is a prolem that is
More informationERASMUS UNIVERSITY ROTTERDAM Information concerning the Entrance examination Mathematics level 2 for International Business Administration (IBA)
ERASMUS UNIVERSITY ROTTERDAM Information concerning the Entrance examination Mathematics level 2 for International Business Administration (IBA) General information Availale time: 2.5 hours (150 minutes).
More informationMathematical Ideas Modelling data, power variation, straightening data with logarithms, residual plots
Kepler s Law Level Upper secondary Mathematical Ideas Modelling data, power variation, straightening data with logarithms, residual plots Description and Rationale Many traditional mathematics prolems
More informationA matrix Method for Interval Hermite Curve Segmentation O. Ismail, Senior Member, IEEE
International Journal of Video&Image Processing Network Security IJVIPNS-IJENS Vol:15 No:03 7 A matrix Method for Interal Hermite Cure Segmentation O. Ismail, Senior Member, IEEE Abstract Since the use
More informationTHEORY OF THE LEMPOR EJECTOR AS APPLIED TO PRODUCE DRAUGHT IN STEAM LOCOMOTIVES
Introductory Note Note added eruary 999. This theory refers to the fundamentals defining the main dimensions of the ejector. It requires the calculation (or the otention y experimental procedures) of the
More informationEssential Maths 1. Macquarie University MAFC_Essential_Maths Page 1 of These notes were prepared by Anne Cooper and Catriona March.
Essential Maths 1 The information in this document is the minimum assumed knowledge for students undertaking the Macquarie University Masters of Applied Finance, Graduate Diploma of Applied Finance, and
More informationSolving Homogeneous Trees of Sturm-Liouville Equations using an Infinite Order Determinant Method
Paper Civil-Comp Press, Proceedings of the Eleventh International Conference on Computational Structures Technology,.H.V. Topping, Editor), Civil-Comp Press, Stirlingshire, Scotland Solving Homogeneous
More informationModule 9: Further Numbers and Equations. Numbers and Indices. The aim of this lesson is to enable you to: work with rational and irrational numbers
Module 9: Further Numers and Equations Lesson Aims The aim of this lesson is to enale you to: wor with rational and irrational numers wor with surds to rationalise the denominator when calculating interest,
More informationA possible mechanism to explain wave-particle duality L D HOWE No current affiliation PACS Numbers: r, w, k
A possible mechanism to explain wae-particle duality L D HOWE No current affiliation PACS Numbers: 0.50.-r, 03.65.-w, 05.60.-k Abstract The relationship between light speed energy and the kinetic energy
More informationSample Average Approximation for Stochastic Empty Container Repositioning
Sample Aerage Approimation for Stochastic Empty Container Repositioning E Peng CHEW a, Loo Hay LEE b, Yin LOG c Department of Industrial & Systems Engineering ational Uniersity of Singapore Singapore 9260
More informationNotes on Linear Minimum Mean Square Error Estimators
Notes on Linear Minimum Mean Square Error Estimators Ça gatay Candan January, 0 Abstract Some connections between linear minimum mean square error estimators, maximum output SNR filters and the least square
More informationHORIZONTAL MOTION WITH RESISTANCE
DOING PHYSICS WITH MATLAB MECHANICS HORIZONTAL MOTION WITH RESISTANCE Ian Cooper School of Physics, Uniersity of Sydney ian.cooper@sydney.edu.au DOWNLOAD DIRECTORY FOR MATLAB SCRIPTS ec_fr_b. This script
More informationIn-Orbit Magnetometer Calibration for a Spinning Satellite
In-Orit Magnetometer Caliration for a Spinning Satellite Halil Ersin Söen and Shin-ichiro Saai Japan Aerospace Exploration Agenc (JAXA), Sagamihara, 5-50 Japan Magnetometers are commonl used attitude sensors
More informationFinQuiz Notes
Reading 9 A time series is any series of data that varies over time e.g. the quarterly sales for a company during the past five years or daily returns of a security. When assumptions of the regression
More informationON THE COMPARISON OF BOUNDARY AND INTERIOR SUPPORT POINTS OF A RESPONSE SURFACE UNDER OPTIMALITY CRITERIA. Cross River State, Nigeria
ON THE COMPARISON OF BOUNDARY AND INTERIOR SUPPORT POINTS OF A RESPONSE SURFACE UNDER OPTIMALITY CRITERIA Thomas Adidaume Uge and Stephen Seastian Akpan, Department Of Mathematics/Statistics And Computer
More informationInternational Journal of Solids and Structures
International Journal of Solids and Structures 46 (9) 95 4 Contents lists aailale at ScienceDirect International Journal of Solids and Structures journal homepage: www.elseier.com/locate/ijsolstr Comparison
More informationLecture 12! Center of mass! Uniform circular motion!
Lecture 1 Center of mass Uniform circular motion Today s Topics: Center of mass Uniform circular motion Centripetal acceleration and force Banked cures Define the center of mass The center of mass is a
More informationLongitudinal Dispersion Coefficient in Estuaries
Journal of Coastal Research SI 9 57-5 ICS (Proceedings) Brazil ISSN 79-8 Longitudinal ispersion Coefficient in Estuaries E. Jaari ; R. Bozorgi anda. Etemad-Shahidi College of Ciil Engineering Iran Uniersity
More informationMATHEMATICAL MODELLING AND IDENTIFICATION OF THE FLOW DYNAMICS IN
MATHEMATICAL MOELLING AN IENTIFICATION OF THE FLOW YNAMICS IN MOLTEN GLASS FURNACES Jan Studzinski Systems Research Institute of Polish Academy of Sciences Newelska 6-447 Warsaw, Poland E-mail: studzins@ibspan.waw.pl
More informationERASMUS UNIVERSITY ROTTERDAM
Information concerning Colloquium doctum Mathematics level 2 for International Business Administration (IBA) and International Bachelor Economics & Business Economics (IBEB) General information ERASMUS
More informationSIMULATIONS OF CHARACTERISTICS OF TUNED LIQUID COLUMN DAMPER USING AN ELLIPTICAL FLOW PATH ESTIMATION METHOD
October -7, 008, Beijing, China SIMULATIONS OF CHARACTERISTICS OF TUNED LIQUID COLUMN DAMPER USING AN ELLIPTICAL FLOW PATH ESTIMATION METHOD P. Chaiiriyawong, S. Limkatanyu and T. Pinkaew 3 Lecturer, Dept.
More informationDifferential Geometry of Surfaces
Differential Geometry of urfaces Jordan mith and Carlo équin C Diision, UC Berkeley Introduction These are notes on differential geometry of surfaces ased on reading Greiner et al. n. d.. Differential
More information1. Define the following terms (1 point each): alternative hypothesis
1 1. Define the following terms (1 point each): alternative hypothesis One of three hypotheses indicating that the parameter is not zero; one states the parameter is not equal to zero, one states the parameter
More informationMODAL IDENTIFICATION OF STRUCTURES USING ARMAV MODEL FOR AMBIENT VIBRATION MEASUREMENT
MODAL IDENTIFICATION OF STRUCTURES USING MODEL FOR AMBIENT VIBRATION MEASUREMENT 72 C S HUANG SUMMARY A procedure is presented for evaluating the dynamic characteristics of structures from ambient vibration
More informationTwo-sided bounds for L p -norms of combinations of products of independent random variables
Two-sided bounds for L p -norms of combinations of products of independent random ariables Ewa Damek (based on the joint work with Rafał Latała, Piotr Nayar and Tomasz Tkocz) Wrocław Uniersity, Uniersity
More informationOnline Companion to Pricing Services Subject to Congestion: Charge Per-Use Fees or Sell Subscriptions?
Online Companion to Pricing Serices Subject to Congestion: Charge Per-Use Fees or Sell Subscriptions? Gérard P. Cachon Pnina Feldman Operations and Information Management, The Wharton School, Uniersity
More informationUNIVERSITY OF TRENTO ITERATIVE MULTI SCALING-ENHANCED INEXACT NEWTON- METHOD FOR MICROWAVE IMAGING. G. Oliveri, G. Bozza, A. Massa, and M.
UNIVERSITY OF TRENTO DIPARTIMENTO DI INGEGNERIA E SCIENZA DELL INFORMAZIONE 3823 Poo Trento (Italy), Via Sommarie 4 http://www.disi.unitn.it ITERATIVE MULTI SCALING-ENHANCED INEXACT NEWTON- METHOD FOR
More informationFu Yuhua 1. Beijing, China
85 An Example of Guiding Scientific Research with hilosophical rinciples Based on Uniqueness of Truth and Neutrosophy eriing Newton's Second Law and the like Fu Yuhua 1 1 CNOOC Research Institute Beijing,
More informationNoise constrained least mean absolute third algorithm
Noise constrained least mean absolute third algorithm Sihai GUAN 1 Zhi LI 1 Abstract: he learning speed of an adaptie algorithm can be improed by properly constraining the cost function of the adaptie
More informationHolomorphy of the 9th Symmetric Power L-Functions for Re(s) >1. Henry H. Kim and Freydoon Shahidi
IMRN International Mathematics Research Notices Volume 2006, Article ID 59326, Pages 1 7 Holomorphy of the 9th Symmetric Power L-Functions for Res >1 Henry H. Kim and Freydoon Shahidi We proe the holomorphy
More informationSemi-implicit Treatment of the Hall Effect in NIMROD Simulations
Semi-implicit Treatment of the Hall Effect in NIMROD Simulations H. Tian and C. R. Soinec Department of Engineering Physics, Uniersity of Wisconsin-Madison Madison, WI 5376 Presented at the 45th Annual
More informationA New Extended Uniform Distribution
International Journal of Statistical Distriutions and Applications 206; 2(3): 3-4 http://wwwsciencepulishinggroupcom/j/ijsda doi: 0648/jijsd20602032 ISS: 2472-3487 (Print); ISS: 2472-309 (Online) A ew
More informationOptimal Joint Detection and Estimation in Linear Models
Optimal Joint Detection and Estimation in Linear Models Jianshu Chen, Yue Zhao, Andrea Goldsmith, and H. Vincent Poor Abstract The problem of optimal joint detection and estimation in linear models with
More informationMean-variance receding horizon control for discrete time linear stochastic systems
Proceedings o the 17th World Congress The International Federation o Automatic Control Seoul, Korea, July 6 11, 008 Mean-ariance receding horizon control or discrete time linear stochastic systems Mar
More information+ h4. + h5. 6! f (5) i. (C.3) Since., it yields
Appendix C. Derivation of the Numerical Integration Formulae C.1. Derivation of the Numerical Integration of dy(x) / dx = f (x) For a given analytical or taulated function f (x), the left column in Tale
More informationModal Identification from Field Test and FEM Updating of a Long Span Cable-Stayed Bridge
International Journal of Applied Science and Engineering 9. 6, 3: 5-6 Modal Identification from Field est and FEM Updating of a Long Span Cable-Stayed Bridge Chern-Hwa Chen a * and Chia-I Ou b a Department
More informationDynamic Vehicle Routing with Heterogeneous Demands
Dynamic Vehicle Routing with Heterogeneous Demands Stephen L. Smith Marco Paone Francesco Bullo Emilio Frazzoli Abstract In this paper we study a ariation of the Dynamic Traeling Repairperson Problem DTRP
More informationTowards Green Distributed Storage Systems
Towards Green Distributed Storage Systems Abdelrahman M. Ibrahim, Ahmed A. Zewail, and Aylin Yener Wireless Communications and Networking Laboratory (WCAN) Electrical Engineering Department The Pennsylania
More informationRandom Error Analysis of Inertial Sensors output Based on Allan Variance Shaochen Li1, a, Xiaojing Du2,b and Junyi Zhai3,c
International Conerence on Civil, Transportation and Environment (ICCTE 06) Random Error Analysis o Inertial Sensors output Based on Allan Variance Shaochen Li, a, Xiaojing Du, and Junyi Zhai3,c School
More informationA METHOD FOR NONLINEAR SYSTEM CLASSIFICATION IN THE TIME-FREQUENCY PLANE IN PRESENCE OF FRACTAL NOISE. Lorenzo Galleani, Letizia Lo Presti
A METHOD FOR NONLINEAR SYSTEM CLASSIFICATION IN THE TIME-FREQUENCY PLANE IN PRESENCE OF FRACTAL NOISE Lorenzo Galleani, Letizia Lo Presti Dipartimento di Elettronica, Politecnico di Torino, Corso Duca
More informationGRATING-LOBE PATTERN RETRIEVAL FROM NOISY IRREGULAR BEAM DATA FOR THE PLANCK SPACE TELESCOPE
GRATING-LOBE PATTERN RETRIEVAL FROM NOISY IRREGULAR BEAM DATA FOR THE PLANCK SPACE TELESCOPE Per Heighwood Nielsen (1), Oscar Borries (1), Frank Jensen (1), Jan Tauber (2), Arturo Martín-Polegre (2) (1)
More informationAsymptotic Normality of an Entropy Estimator with Exponentially Decaying Bias
Asymptotic Normality of an Entropy Estimator with Exponentially Decaying Bias Zhiyi Zhang Department of Mathematics and Statistics Uniersity of North Carolina at Charlotte Charlotte, NC 28223 Abstract
More informationLR-KFNN: Logistic Regression-Kernel Function Neural Networks and the GFR-NN Model for Renal Function Evaluation
LR-KF: Logistic Regression-Kernel Function eural etworks and the GFR- Model for Renal Function Evaluation Qun Song, Tianmin Ma and ikola Kasaov Knowledge Engineering & Discovery Research Institute Auckland
More informationTransient Response of a Second-Order System
Transient Response of a Second-Order System ECEN 830 Spring 01 1. Introduction In connection with this experiment, you are selecting the gains in your feedback loop to obtain a well-behaved closed-loop
More informationFUZZY FINITE ELEMENT METHOD AND ITS APPLICATION
TRENDS IN COMPUTATIONAL STRUCTURAL MECHANICS W.A. Wall, K.U. Bletzinger and K. Schweizerhof (Eds.) CIMNE, Barcelona, Spain 2001 FUZZY FINITE ELEMENT METHOD AND ITS APPLICATION B. Möller*, M. Beer, W. Graf
More informationChapter 7. 1 a The length is a function of time, so we are looking for the value of the function when t = 2:
Practice questions Solution Paper type a The length is a function of time, so we are looking for the value of the function when t = : L( ) = 0 + cos ( ) = 0 + cos ( ) = 0 + = cm We are looking for the
More informationJournal of Computational and Applied Mathematics. New matrix iterative methods for constraint solutions of the matrix
Journal of Computational and Applied Mathematics 35 (010 76 735 Contents lists aailable at ScienceDirect Journal of Computational and Applied Mathematics journal homepage: www.elseier.com/locate/cam New
More informationSHOCK AND VIBRATION RESPONSE SPECTRA COURSE Unit 1B. Damping
SHOCK AND VIBRATION RESPONSE SPECTRA COURSE Unit 1B. Damping By Tom Irvine Introduction Recall the homework assignment from Unit 1A. The data.txt time history represented a rocket vehicle dropped from
More informationComposite Plates Under Concentrated Load on One Edge and Uniform Load on the Opposite Edge
Mechanics of Advanced Materials and Structures, 7:96, Copyright Taylor & Francis Group, LLC ISSN: 57-69 print / 57-65 online DOI:.8/5769955658 Composite Plates Under Concentrated Load on One Edge and Uniform
More informationInteger Parameter Synthesis for Real-time Systems
1 Integer Parameter Synthesis for Real-time Systems Aleksandra Joanoić, Didier Lime and Oliier H. Roux École Centrale de Nantes - IRCCyN UMR CNRS 6597 Nantes, France Abstract We proide a subclass of parametric
More informationSolving Systems of Linear Equations Symbolically
" Solving Systems of Linear Equations Symolically Every day of the year, thousands of airline flights crisscross the United States to connect large and small cities. Each flight follows a plan filed with
More informationA. Idesman. Keywords: time integration, spurious oscillations, numerical dispersion
COMPDYN 0 rd ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering M. Papadrakakis, M. Fragiadakis, V. Pleris (eds.) Corfu, Greece, -8 May 0 ACCURATE NUMERICAL
More informationChapter 12. Feedback Control Characteristics of Feedback Systems
Chapter 1 Feedbac Control Feedbac control allows a system dynamic response to be modified without changing any system components. Below, we show an open-loop system (a system without feedbac) and a closed-loop
More informationChapter 6: The Laplace Transform. Chih-Wei Liu
Chapter 6: The Laplace Transform Chih-Wei Liu Outline Introduction The Laplace Transform The Unilateral Laplace Transform Properties of the Unilateral Laplace Transform Inversion of the Unilateral Laplace
More informationPolynomial Degree and Finite Differences
CONDENSED LESSON 7.1 Polynomial Degree and Finite Differences In this lesson, you Learn the terminology associated with polynomials Use the finite differences method to determine the degree of a polynomial
More informationRANDOM DECREMENT AND REGRESSION ANALYSIS OF TRAFFIC RESPONSES OF BRIDGES
RANDOM DECREMENT AND REGRESSION ANALYSIS OF TRAFFIC RESPONSES OF BRIDGES J.C. Asmussen, S.R. Ibrahid & R. Brincker Department of Building Technology and Structural Engineering Aalborg University, Sohngaardsholmsvej
More informationLesson 10 Steady Electric Currents
Lesson Steady lectric Currents 楊尚達 Shang-Da Yang Institute of Photonics Technologies Department of lectrical ngineering National Tsing Hua Uniersity, Taiwan Outline Current density Current laws Boundary
More informationA Design for the Pitch Curve of Noncircular Gears with Function Generation
Proceedings of the International ulticonference of Engineers and Computer Scientists 008 Vol II IECS 008, 9- arch, 008, Hong Kong A Design for the Pitch Curve of Noncircular Gears with Function Generation
More informationSixth World Conference on Structural Control and Monitoring
Sixth World Conference on Structural Control and Monitoring Proceedings of the 6th edition of the World Conference of the International Association for Structural Control and Monitoring (IACSM), held in
More informationIterative Controller Tuning Using Bode s Integrals
Iterative Controller Tuning Using Bode s Integrals A. Karimi, D. Garcia and R. Longchamp Laboratoire d automatique, École Polytechnique Fédérale de Lausanne (EPFL), 05 Lausanne, Switzerland. email: alireza.karimi@epfl.ch
More informationPosition in the xy plane y position x position
Robust Control of an Underactuated Surface Vessel with Thruster Dynamics K. Y. Pettersen and O. Egeland Department of Engineering Cybernetics Norwegian Uniersity of Science and Technology N- Trondheim,
More informationIMPROVEMENTS IN MODAL PARAMETER EXTRACTION THROUGH POST-PROCESSING FREQUENCY RESPONSE FUNCTION ESTIMATES
IMPROVEMENTS IN MODAL PARAMETER EXTRACTION THROUGH POST-PROCESSING FREQUENCY RESPONSE FUNCTION ESTIMATES Bere M. Gur Prof. Christopher Niezreci Prof. Peter Avitabile Structural Dynamics and Acoustic Systems
More informationPropagation of Electromagnetic Field From a Pulsed Electric Dipole in a Dielectric Medium
CHINESE JOURNAL OF PHYSICS VOL. 39, NO. 2 APRIL 2001 Propagation of Electromagnetic Field From a Pulsed Electric Dipole in a Dielectric Medium Osama M. Abo-Seida 1 and Samira T. Bishay 2 1 Department of
More informationSystem Modeling and Identification CHBE 702 Korea University Prof. Dae Ryook Yang
System Modeling and Identification CHBE 702 Korea University Prof. Dae Ryook Yang 1-1 Course Description Emphases Delivering concepts and Practice Programming Identification Methods using Matlab Class
More informationReferences Ideal Nyquist Channel and Raised Cosine Spectrum Chapter 4.5, 4.11, S. Haykin, Communication Systems, Wiley.
Baseand Data Transmission III Reerences Ideal yquist Channel and Raised Cosine Spectrum Chapter 4.5, 4., S. Haykin, Communication Systems, iley. Equalization Chapter 9., F. G. Stremler, Communication Systems,
More informationASEISMIC DESIGN OF TALL STRUCTURES USING VARIABLE FREQUENCY PENDULUM OSCILLATOR
ASEISMIC DESIGN OF TALL STRUCTURES USING VARIABLE FREQUENCY PENDULUM OSCILLATOR M PRANESH And Ravi SINHA SUMMARY Tuned Mass Dampers (TMD) provide an effective technique for viration control of flexile
More informationConservation of Momentum -1
Impulse, Action-Reaction and Change in Momentum: Prolem 1: A pitcher throws a 150g aseall y applying a 50N force for 0.1 second. Assuming that the ase all starts from rest, otain a. the initial velocity
More informationSchool of Business. Blank Page
Equations 5 The aim of this unit is to equip the learners with the concept of equations. The principal foci of this unit are degree of an equation, inequalities, quadratic equations, simultaneous linear
More informationDESIGN METHOD BASED ON THE CONCEPT OF EMERGENCE AND ITS APPLICATION
DESIGN METHOD BASED ON THE CONCEPT OF EMERGENCE AND ITS APPLICATION Koichiro Sato¹ and Yoshiyuki Matsuoka 2 ¹ Graduate School of Science and Technology, Keio Uniersity, Yokohama, Japan Koichiro_Sato@a7.keio.jp,
More informationDYNAMICS OF ESSENTIALLY NONLINEAR VIBRATION ABSORBER COUPLED TO HARMONICALLY EXCITED 2 DOF SYSTEM
ENOC 008, Saint Petersburg, Russia, June, 0-July, 4 008 DYNAMICS OF ESSENTIALLY NONLINEAR VIBRATION ABSORBER COUPLED TO HARMONICALLY EXCITED DOF SYSTEM Yuli Starosetsky Faculty of Mechanical Engineering
More informationDynamical Systems Solutions to Exercises
Dynamical Systems Part 5-6 Dr G Bowtell Dynamical Systems Solutions to Exercises. Figure : Phase diagrams for i, ii and iii respectively. Only fixed point is at the origin since the equations are linear
More informationab is shifted horizontally by h units. ab is shifted vertically by k units.
Algera II Notes Unit Eight: Eponential and Logarithmic Functions Sllaus Ojective: 8. The student will graph logarithmic and eponential functions including ase e. Eponential Function: a, 0, Graph of an
More informationTransmission lines using a distributed equivalent circuit
Cambridge Uniersity Press 978-1-107-02600-1 - Transmission Lines Equialent Circuits, Electromagnetic Theory, and Photons Part 1 Transmission lines using a distributed equialent circuit in this web serice
More informationEvolution Analysis of Iterative LMMSE-APP Detection for Coded Linear System with Cyclic Prefixes
Eolution Analysis of Iteratie LMMSE-APP Detection for Coded Linear System with Cyclic Prefixes Xiaoun Yuan Qinghua Guo and Li Ping Member IEEE Department of Electronic Engineering City Uniersity of Hong
More informationIntroduction DCT
Introduction... NASTRAN model and analytical model.... NASTRAN model.... Analytical model...3.3 Comparison of NASTRAN and analytical model...7 Transformation to time domain...9. Displacement to velocity
More informationarxiv: v1 [physics.comp-ph] 17 Jan 2014
An efficient method for soling a correlated multi-item inentory system Chang-Yong Lee and Dongu Lee The Department of Industrial & Systems Engineering, Kongu National Uniersity, Kongu 34-70 South Korea
More informationMulti Criteria Analysis of the Supporting System of a Reciprocating Compressor
Purdue Uniersity Purdue e-pubs International Compressor Engineering Conference School of Mechanical Engineering 2000 Multi Criteria Analysis of the Supporting System of a Reciprocating Compressor M. Lamantia
More informationTools for Investigation of Dynamics of DC-DC Converters within Matlab/Simulink
Tools for Inestigation of Dynamics of DD onerters within Matlab/Simulink Riga Technical Uniersity, Riga, Latia Email: pikulin03@inbox.l Dmitry Pikulin Abstract: In this paper the study of complex phenomenon
More informationStatistical Multiplexing and Traffic Shaping Games for Network Slicing
Statistical Multiplexing and Traffic Shaping Games for Network Slicing Jiaxiao Zheng, Palo Caallero, Gustao de Veciana, Seung Jun Baek and Alert Banchs The Uniersity of Texas at Austin, TX Korea Uniersity,
More informationAP Physics Multiple Choice Practice Gravitation
AP Physics Multiple Choice Practice Graitation. Each of fie satellites makes a circular orbit about an object that is much more massie than any of the satellites. The mass and orbital radius of each satellite
More informationNONLINEAR COMPLEX MODULUS IN BITUMENS
NONLINEAR COMPLEX MODULUS IN BITUMENS J. Stastna, K. Jorshari and L. Zanzotto Bituminous Materials Chair University of Calgary 2500 University Drive NW Calgary, Alberta T2N 1N4 Canada Large Amplitude Oscillations
More informationMinimizing a convex separable exponential function subject to linear equality constraint and bounded variables
Minimizing a convex separale exponential function suect to linear equality constraint and ounded variales Stefan M. Stefanov Department of Mathematics Neofit Rilski South-Western University 2700 Blagoevgrad
More informationExample: Bipolar NRZ (non-return-to-zero) signaling
Baseand Data Transmission Data are sent without using a carrier signal Example: Bipolar NRZ (non-return-to-zero signaling is represented y is represented y T A -A T : it duration is represented y BT. Passand
More informationExpansion formula using properties of dot product (analogous to FOIL in algebra): u v 2 u v u v u u 2u v v v u 2 2u v v 2
Least squares: Mathematical theory Below we provide the "vector space" formulation, and solution, of the least squares prolem. While not strictly necessary until we ring in the machinery of matrix algera,
More informationMOTION OF FALLING OBJECTS WITH RESISTANCE
DOING PHYSICS WIH MALAB MECHANICS MOION OF FALLING OBJECS WIH RESISANCE Ian Cooper School of Physics, Uniersity of Sydney ian.cooper@sydney.edu.au DOWNLOAD DIRECORY FOR MALAB SCRIPS mec_fr_mg_b.m Computation
More informationIntroduction to Thermodynamic Cycles Part 1 1 st Law of Thermodynamics and Gas Power Cycles
Introduction to Thermodynamic Cycles Part 1 1 st Law of Thermodynamics and Gas Power Cycles by James Doane, PhD, PE Contents 1.0 Course Oeriew... 4.0 Basic Concepts of Thermodynamics... 4.1 Temperature
More informationCONTROL SYSTEMS, ROBOTICS, AND AUTOMATION - Vol. V - Prediction Error Methods - Torsten Söderström
PREDICTIO ERROR METHODS Torsten Söderström Department of Systems and Control, Information Technology, Uppsala University, Uppsala, Sweden Keywords: prediction error method, optimal prediction, identifiability,
More informationBlow up of Solutions for a System of Nonlinear Higher-order Kirchhoff-type Equations
Mathematics Statistics 6: 9-9, 04 DOI: 0.389/ms.04.00604 http://www.hrpub.org Blow up of Solutions for a System of Nonlinear Higher-order Kirchhoff-type Equations Erhan Pişkin Dicle Uniersity, Department
More informationNon-Linear Regression Samuel L. Baker
NON-LINEAR REGRESSION 1 Non-Linear Regression 2006-2008 Samuel L. Baker The linear least squares method that you have een using fits a straight line or a flat plane to a unch of data points. Sometimes
More informationSolutions to Exam 2, Math 10560
Solutions to Exam, Math 6. Which of the following expressions gives the partial fraction decomposition of the function x + x + f(x = (x (x (x +? Solution: Notice that (x is not an irreducile factor. If
More informationOptimized Concatenated LDPC Codes for Joint Source-Channel Coding
Optimized Concatenated LDPC Codes for Joint Source-Channel Coding Maria Fresia, Fernando Pérez-Cruz, H. Vincent Poor Department of Electrical Engineering, Princeton Uniersity, Princeton, New Jersey 08544
More informationTHE ANALYSIS OF THE CONVECTIVE-CONDUCTIVE HEAT TRANSFER IN THE BUILDING CONSTRUCTIONS. Zbynek Svoboda
THE NLSIS OF THE CONECTIE-CONDUCTIE HET TRNSFER IN THE BUILDING CONSTRUCTIONS Zbynek Soboda Czech Technical Uniersity in Prague Faculty of Ciil Engineering 166 29 Prague 6 - Czech Republic BSTRCT The numerical
More informationSecond Order and Higher Order Systems
Second Order and Higher Order Systems 1. Second Order System In this section, we shall obtain the response of a typical second-order control system to a step input. In terms of damping ratio and natural
More informationSimulation of Electro-Thermal Effects in Device and Circuit
Simulation of Electro-Thermal Effects in Device and Circuit S. SHARIFIAN ATTAR 1, M.C.E. YAGOUB 2 and F. MOHAMMADI 1 1 Ryerson University, Electrical and Computer Engineering Department 2 University of
More informationThe Importance of Anisotropy for Prestack Imaging
The Importance of Anisotropy for Prestack Imaging Xiaogui Miao*, Daid Wilkinson and Scott Cheadle Veritas DGC Inc., 715-5th Ae. S.W., Calgary, AB, T2P 5A2 Calgary, AB Xiaogui_Miao@eritasdgc.com ABSTRACT
More informationSimulations of bulk phases. Periodic boundaries. Cubic boxes
Simulations of bulk phases ChE210D Today's lecture: considerations for setting up and running simulations of bulk, isotropic phases (e.g., liquids and gases) Periodic boundaries Cubic boxes In simulations
More information