OSE801 Engineering System Identification. Lecture 09: Computing Impulse and Frequency Response Functions
|
|
- Camron Gilmore
- 5 years ago
- Views:
Transcription
1 OSE801 Engineering System Identification Lecture 09: Computing Impulse and Frequency Response Functions
2 1 Extracting Impulse and Frequency Response Functions In the preceding sections, signal processing using the Fourier transforms have been presented. In the remainder of this chapter, we will employ a set of sample problems to gain insight into both time and frequency domain methods to obtain the impulse and frequency response functions (IRFs and FRFs In so doing, both the fast Fourier transform(fft) and discrete wavelet transform (DWT) will be introduced, which will be studied in more detail in the subsequent lectures. The following materials are taken mostly from a thesis by Dr. A. Robertson who has graciously allowed the materials for class purposes. 1.1 Single Degree of Freedom Problem This first example is a simple one degree-of-freedom (DOF) spring-mass system that is modeled in the form: ẍ + ω 2 x = f(t), ω = 10π (1) and is subjected to a time-varying harmonic excitation, f(t). The input (forcing function ) and response of this system are shown in Figure 1. Two discontinuities, or spikes, were added to the harmonic input to accentuate the differences between the FFT and DWT algorithms. Theoretically, the Markov parameters (impulse response) of this example problem should be h(t) = A sin ωt (2) regardless of the input variations. Figure 2 shows the Markov parameters (impulse response functions) of the system as determined by both wavelet and FFT-based algorithms. Two FFTbased extractions have been presented: one with windowing and the other without. The DWT method picks up the Markov parameters almost exactly with only a small error at the end. The FFT-based Markov parameters without any filtering are off in magnitude and though they seem to determine the dominant frequency, leakage problems are imposing added frequencies to the representation (see Figure 3). A Hanning window was applied to this case to demonstrate the improvements and weaknesses of windowing procedures in the FFT method. The Hanning window improves the magnitude and representation of the Markov parameters, but also induces artificial damping to the system as seen in Figure 3. It is observed in Figure 3 that the frequency response functions (FRFs) constructed by the two FFT-based algorithms are also inferior to that of the 2
3 Fig. 1. Input and Response of One DOF System Fig. 2. Markov Parameters of One DOF System 3
4 Fig. 3. Frequency Response Functions of One DOF System wavelet algorithm for this system. While the frequency magnitude for the windowed FFT-based algorithm is accurate, induced artificial damping has greatly affected the shape of the curve. The poor results via FFTs are expected and can be attributed to two problems. First is the lack of a rich frequency spectrum for the input to the system. In spectral methods, one must divide by the FFT of the input, which in this case will be mainly zeroes due to lack of frequencies in the signal. This will result in numerical ill-conditioning of the problem making it difficult to find an accurate solution. The second problem is leakage, in this case caused by the abrupt change in frequency mid-way through the input and the two spikes. These problems are typical in spectral methods which generally use broad-band frequency excitation such as random noise instead. Wavelet methods, however, are not prone to these problems and can handle a variety of input functions as seen by the accuracy of the determined Markov parameters in this problem. Note that only the magnitudes of the FRF curves are shown. The phase diagrams, though not shown here, have discrepancies similar to those of the magnitudes. 4
5 Fig. 4. Four DOF Spring-Mass System 1.2 Four DOF Spring-Mass System A four DOF spring-mass system will now be examined to show a slightly more complicated application of the impulse response extraction. The system as shown in Fig. 4 has four inputs and four outputs, one at each of the masses. The masses and stiffnesses are 1 and 10000, respectively Harmonic Excitation For the first example, this system was excited by a combination of harmonic forces at each of the nodes as shown in Figure 5 One set of the corresponding Markov parameters and FRF curves for this problem is shown in Figs. 6 and 7. The Markov parameters obtained by the FFT-based algorithm have more error in magnitude than those obtained by the wavelet algorithm, i.e., 10 4 for the exact and wavelet methods versus 10 5 for the FFT. An examination of the FRF curves for the system corresponding to the fourth DOF input and fourth output reveals that the wavelet method is picking up the correct frequencies with the correct magnitudes. The FFT method can find the correct frequencies, but with a large error in the shape of the frequency curves, affecting the damping of the system. Similar results are obtained for the remaining FRF curves that are not shown here. Once again, harmonic inputs were used to excite the system to show the inability of spectral methods to handle limited frequency band excitation adequately. More general inputs will therefore be utilized in the next section to analyze the same system. 5
6 Fig. 5. Input and Response of Harmonically Excited Four DOF System Random Excitation Next consider the same four DOF system, except now excited by a random input at all four nodes (see Fig. 8). Figure 9 shows that the Markov parameters determined via the WT method are slightly better than the FFT-based ones, though not significantly. As compared to the Markov parameters obtained from the sinusoidal input, the superiority of the random input for spectral methods is not apparent. When using random inputs, ensemble-averaging is a necessity to alleviate the noise found in the resultant Markov parameters. Figure 10 shows how when just five ensembles are averaged together, the results improve significantly. More ensemble-averaging of the random data will improve results further as will be shown more thoroughly in the next section. On the other hand, when harmonic excitations are used to determine Markov parameters (as in the previous section), ensemble-averaging does not improve accuracy. The foregoing three examples are indicative of typical challenges facing structural system identification, including input spectra, filtering of noises, sampling techniques, computational algorithms, and the accuracy of the impulse response or frequency response functions. These and additional aspects will now be studied in this course. 6
7 Fig. 6. Markov Parameters of a Harmonically Excited Four DOF System 7
8 Fig. 7. FRFs of a Harmonically Excited Four DOF System 8
9 Fig. 8. Input and Response of Randomly Excited Four DOF System 9
10 Fig. 9. Markov Parameters of a Four DOF System with 1 ensemble 10
11 Fig. 10. Markov Parameters of a Four DOF System with 5 ensemble 11
Notes for System Identification: Impulse Response Functions via Wavelet
Notes for System Identification: Impulse Response Functions via Wavelet 1 Basic Wavelet Algorithm for IRF Extraction In contrast to the FFT-based extraction procedure which must process the data both in
More informationModeling of Resonators
. 23 Modeling of Resonators 23 1 Chapter 23: MODELING OF RESONATORS 23 2 23.1 A GENERIC RESONATOR A second example where simplified discrete modeling has been found valuable is in the assessment of the
More informationStructural System Identification (KAIST, Summer 2017) Lecture Coverage:
Structural System Identification (KAIST, Summer 2017) Lecture Coverage: Lecture 1: System Theory-Based Structural Identification Lecture 2: System Elements and Identification Process Lecture 3: Time and
More informationVibration Testing. an excitation source a device to measure the response a digital signal processor to analyze the system response
Vibration Testing For vibration testing, you need an excitation source a device to measure the response a digital signal processor to analyze the system response i) Excitation sources Typically either
More informationVibration Testing. Typically either instrumented hammers or shakers are used.
Vibration Testing Vibration Testing Equipment For vibration testing, you need an excitation source a device to measure the response a digital signal processor to analyze the system response Excitation
More informationOSE801 Engineering System Identification. Lecture 05: Fourier Analysis
OSE81 Engineering System Identification Lecture 5: Fourier Analysis What we will study in this lecture: A short introduction of Fourier analysis Sampling the data Applications Example 1 Fourier Analysis
More informationInput-Output Peak Picking Modal Identification & Output only Modal Identification and Damage Detection of Structures using
Input-Output Peak Picking Modal Identification & Output only Modal Identification and Damage Detection of Structures using Time Frequency and Wavelet Techniquesc Satish Nagarajaiah Professor of Civil and
More informationEE 435. Lecture 30. Data Converters. Spectral Performance
EE 435 Lecture 30 Data Converters Spectral Performance . Review from last lecture. INL Often Not a Good Measure of Linearity Four identical INL with dramatically different linearity X OUT X OUT X REF X
More informationSEISMIC WAVE PROPAGATION. Lecture 2: Fourier Analysis
SEISMIC WAVE PROPAGATION Lecture 2: Fourier Analysis Fourier Series & Fourier Transforms Fourier Series Review of trigonometric identities Analysing the square wave Fourier Transform Transforms of some
More informationEstimating the Degree of Nonlinearity in Transient Responses with Zeroed Early Time Fast Fourier Transforms
Estimating the Degree of Nonlinearity in Transient Responses with Zeroed Early Time Fast Fourier Transforms Matthew S. Allen Department of Engineering Physics University of Wisconsin-Madison Randall L.
More informationSystem Theory- Based Iden2fica2on of Dynamical Models and Applica2ons
System Theory- Based Iden2fica2on of Dynamical Models and Applica2ons K. C. Park Center for Aerospace Structures Department of Aerospace Engineering Sciences University of Colorado at Boulder, CO, USA
More informationC.-H. Lamarque. University of Lyon/ENTPE/LGCB & LTDS UMR CNRS 5513
Nonlinear Dynamics of Smooth and Non-Smooth Systems with Application to Passive Controls 3rd Sperlonga Summer School on Mechanics and Engineering Sciences on Dynamics, Stability and Control of Flexible
More informationSimple Identification of Nonlinear Modal Parameters Using Wavelet Transform
Proceedings of the 9 th ISSM achen, 7 th -9 th October 4 1 Simple Identification of Nonlinear Modal Parameters Using Wavelet Transform Tegoeh Tjahjowidodo, Farid l-bender, Hendrik Van Brussel Mechanical
More informationME 563 HOMEWORK # 7 SOLUTIONS Fall 2010
ME 563 HOMEWORK # 7 SOLUTIONS Fall 2010 PROBLEM 1: Given the mass matrix and two undamped natural frequencies for a general two degree-of-freedom system with a symmetric stiffness matrix, find the stiffness
More informationAn Estimation of Error-Free Frequency Response Function from Impact Hammer Testing
85 An Estimation of Error-Free Frequency Response Function from Impact Hammer Testing Se Jin AHN, Weui Bong JEONG and Wan Suk YOO The spectrum of impulse response signal from the impact hammer testing
More informationPrecision Machine Design
Precision Machine Design Topic 10 Vibration control step 1: Modal analysis 1 Purpose: The manner in which a machine behaves dynamically has a direct effect on the quality of the process. It is vital to
More informationInvestigation of Operational Modal Analysis Damping Estimates MASTER OF SCIENCE
Investigation of Operational Modal Analysis Damping Estimates A thesis submitted to the Division of Research and Advanced Studies of the University of Cincinnati in partial fulfillment of the requirements
More informationNew Developments in Tail-Equivalent Linearization method for Nonlinear Stochastic Dynamics
New Developments in Tail-Equivalent Linearization method for Nonlinear Stochastic Dynamics Armen Der Kiureghian President, American University of Armenia Taisei Professor of Civil Engineering Emeritus
More informationTime and Spatial Series and Transforms
Time and Spatial Series and Transforms Z- and Fourier transforms Gibbs' phenomenon Transforms and linear algebra Wavelet transforms Reading: Sheriff and Geldart, Chapter 15 Z-Transform Consider a digitized
More informationABSTRACT Modal parameters obtained from modal testing (such as modal vectors, natural frequencies, and damping ratios) have been used extensively in s
ABSTRACT Modal parameters obtained from modal testing (such as modal vectors, natural frequencies, and damping ratios) have been used extensively in system identification, finite element model updating,
More informationME scope Application Note 28
App Note 8 www.vibetech.com 3/7/17 ME scope Application Note 8 Mathematics of a Mass-Spring-Damper System INTRODUCTION In this note, the capabilities of ME scope will be used to build a model of the mass-spring-damper
More information13. Power Spectrum. For a deterministic signal x(t), the spectrum is well defined: If represents its Fourier transform, i.e., if.
For a deterministic signal x(t), the spectrum is well defined: If represents its Fourier transform, i.e., if jt X ( ) = xte ( ) dt, (3-) then X ( ) represents its energy spectrum. his follows from Parseval
More informationFrequency Resolution Effects on FRF Estimation: Cyclic Averaging vs. Large Block Size
Frequency Resolution Effects on FRF Estimation: Cyclic Averaging vs. Large Block Size Allyn W. Phillips, PhD Andrew. Zucker Randall J. Allemang, PhD Research Assistant Professor Research Assistant Professor
More informationCentral to this is two linear transformations: the Fourier Transform and the Laplace Transform. Both will be considered in later lectures.
In this second lecture, I will be considering signals from the frequency perspective. This is a complementary view of signals, that in the frequency domain, and is fundamental to the subject of signal
More informationLectures on. Engineering System Identification ( Lund University, Spring 2015)
Lectures on Engineering System Identification ( Lund University, Spring 2015) Lecture 2: Elements of System Identification, Identification Process and Examples!!! Instructor: K. C. Park, University of
More informationDynamics of structures
Dynamics of structures 2.Vibrations: single degree of freedom system Arnaud Deraemaeker (aderaema@ulb.ac.be) 1 One degree of freedom systems in real life 2 1 Reduction of a system to a one dof system Example
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 informationIdentification of crack parameters in a cantilever beam using experimental and wavelet analysis
Identification of crack parameters in a cantilever beam using experimental and wavelet analysis Aniket S. Kamble 1, D. S. Chavan 2 1 PG Student, Mechanical Engineering Department, R.I.T, Islampur, India-415414
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 informationElec4621 Advanced Digital Signal Processing Chapter 11: Time-Frequency Analysis
Elec461 Advanced Digital Signal Processing Chapter 11: Time-Frequency Analysis Dr. D. S. Taubman May 3, 011 In this last chapter of your notes, we are interested in the problem of nding the instantaneous
More informationSNR Calculation and Spectral Estimation [S&T Appendix A]
SR Calculation and Spectral Estimation [S&T Appendix A] or, How not to make a mess of an FFT Make sure the input is located in an FFT bin 1 Window the data! A Hann window works well. Compute the FFT 3
More informationANNEX A: ANALYSIS METHODOLOGIES
ANNEX A: ANALYSIS METHODOLOGIES A.1 Introduction Before discussing supplemental damping devices, this annex provides a brief review of the seismic analysis methods used in the optimization algorithms considered
More informationModal Parameter Estimation from Operating Data
Modal Parameter Estimation from Operating Data Mark Richardson & Brian Schwarz Vibrant Technology, Inc. Jamestown, California Modal testing, also referred to as Experimental Modal Analysis (EMA), underwent
More informationCHAPTER 2. Frequency Domain Analysis
FREQUENCY DOMAIN ANALYSIS 16 CHAPTER 2 Frequency Domain Analysis ASSESSMENTOF FREQUENCY DOMAIN FORCE IDENTIFICATION PROCEDURES CHAPTE,R 2. FREQUENCY DOMAINANALYSIS 17 2. FREQUENCY DOMAIN ANALYSIS The force
More informationExperimental Fourier Transforms
Chapter 5 Experimental Fourier Transforms 5.1 Sampling and Aliasing Given x(t), we observe only sampled data x s (t) = x(t)s(t; T s ) (Fig. 5.1), where s is called sampling or comb function and can be
More information221B Lecture Notes on Resonances in Classical Mechanics
1B Lecture Notes on Resonances in Classical Mechanics 1 Harmonic Oscillators Harmonic oscillators appear in many different contexts in classical mechanics. Examples include: spring, pendulum (with a small
More informationAcoustic holography. LMS Test.Lab. Rev 12A
Acoustic holography LMS Test.Lab Rev 12A Copyright LMS International 2012 Table of Contents Chapter 1 Introduction... 5 Chapter 2... 7 Section 2.1 Temporal and spatial frequency... 7 Section 2.2 Time
More informationStructural changes detection with use of operational spatial filter
Structural changes detection with use of operational spatial filter Jeremi Wojcicki 1, Krzysztof Mendrok 1 1 AGH University of Science and Technology Al. Mickiewicza 30, 30-059 Krakow, Poland Abstract
More informationIn-Structure Response Spectra Development Using Complex Frequency Analysis Method
Transactions, SMiRT-22 In-Structure Response Spectra Development Using Complex Frequency Analysis Method Hadi Razavi 1,2, Ram Srinivasan 1 1 AREVA, Inc., Civil and Layout Department, Mountain View, CA
More informationEE 435. Lecture 28. Data Converters Linearity INL/DNL Spectral Performance
EE 435 Lecture 8 Data Converters Linearity INL/DNL Spectral Performance Performance Characterization of Data Converters Static characteristics Resolution Least Significant Bit (LSB) Offset and Gain Errors
More informationEE 505 Lecture 10. Spectral Characterization. Part 2 of 2
EE 505 Lecture 10 Spectral Characterization Part 2 of 2 Review from last lecture Spectral Analysis If f(t) is periodic f(t) alternately f(t) = = A A ( kω t + ) 0 + Aksin θk k= 1 0 + a ksin t k= 1 k= 1
More informationStructural Damage Detection Using Time Windowing Technique from Measured Acceleration during Earthquake
Structural Damage Detection Using Time Windowing Technique from Measured Acceleration during Earthquake Seung Keun Park and Hae Sung Lee ABSTRACT This paper presents a system identification (SI) scheme
More informationExperimental Aerodynamics. Experimental Aerodynamics
Lecture 3: Vortex shedding and buffeting G. Dimitriadis Buffeting! All structures exposed to a wind have the tendency to vibrate.! These vibrations are normally of small amplitude and have stochastic character!
More informationA priori verification of local FE model based force identification.
A priori verification of local FE model based force identification. M. Corus, E. Balmès École Centrale Paris,MSSMat Grande voie des Vignes, 92295 Châtenay Malabry, France e-mail: corus@mssmat.ecp.fr balmes@ecp.fr
More informationVibrations Qualifying Exam Study Material
Vibrations Qualifying Exam Study Material The candidate is expected to have a thorough understanding of engineering vibrations topics. These topics are listed below for clarification. Not all instructors
More informationMODAL SPACE. (in our own little world)
MODAL SPACE (in our own little world) Could you explain modal analysis and how is it used for solving dynamic problems? Illustration by Mike Avitabile Illustration by Mike Avitabile Illustration by Mike
More informationNonparametric identification of added masses in frequency domain: a numerical study
IPPT Reports 4f/2013 1 Nonparametric identification of added masses in frequency domain: a numerical study Grzegorz Suwała 1, Jan Biczyk 2, Łukasz Jankowski 1,* 1 Institute of Fundamental Technological
More informationOrder Tracking Analysis
1. Introduction Order Tracking Analysis Jaafar Alsalaet College of Engineering-University of Basrah Mostly, dynamic forces excited in a machine are related to the rotation speed; hence, it is often preferred
More informationReview of modal testing
Review of modal testing A. Sestieri Dipartimento di Meccanica e Aeronautica University La Sapienza, Rome Presentation layout - Modelling vibration problems - Aim of modal testing - Types of modal testing:
More informationThe (Fast) Fourier Transform
The (Fast) Fourier Transform The Fourier transform (FT) is the analog, for non-periodic functions, of the Fourier series for periodic functions can be considered as a Fourier series in the limit that the
More informationDigital Baseband Systems. Reference: Digital Communications John G. Proakis
Digital Baseband Systems Reference: Digital Communications John G. Proais Baseband Pulse Transmission Baseband digital signals - signals whose spectrum extend down to or near zero frequency. Model of the
More informationLecture 27 Frequency Response 2
Lecture 27 Frequency Response 2 Fundamentals of Digital Signal Processing Spring, 2012 Wei-Ta Chu 2012/6/12 1 Application of Ideal Filters Suppose we can generate a square wave with a fundamental period
More informationUsing Simulink to analyze 2 degrees of freedom system
Using Simulink to analyze 2 degrees of freedom system Nasser M. Abbasi Spring 29 page compiled on June 29, 25 at 4:2pm Abstract A two degrees of freedom system consisting of two masses connected by springs
More informationKLT for transient signal analysis
The Labyrinth of the Unepected: unforeseen treasures in impossible regions of phase space Nicolò Antonietti 4/1/17 Kerastari, Greece May 9 th June 3 rd Qualitatively definition of transient signals Signals
More informationAnalysis of the Temperature Influence on a Shift of Natural Frequencies of Washing Machine Pulley
American Journal of Mechanical Engineering, 2015, Vol. 3, No. 6, 215-219 Available online at http://pubs.sciepub.com/ajme/3/6/12 Science and Education Publishing DOI:10.12691/ajme-3-6-12 Analysis of the
More informationDynamics of structures
Dynamics of structures 2.Vibrations: single degree of freedom system Arnaud Deraemaeker (aderaema@ulb.ac.be) 1 Outline of the chapter *One degree of freedom systems in real life Hypothesis Examples *Response
More informationEvaluation of a Simple Method of Identification of Dynamic Parameters of a Single-Degree-of-Freedom System
Journal of Vibrations in Physical Systems, 8, 017005, 017 1 of 8 Evaluation of a Simple Method of Identification of Dynamic Parameters of a Single-Degree-of-Freedom System Maciej TABASZEWSKI Institute
More informationSystem Identification & Parameter Estimation
System Identification & Parameter Estimation Wb3: SIPE lecture Correlation functions in time & frequency domain Alfred C. Schouten, Dept. of Biomechanical Engineering (BMechE), Fac. 3mE // Delft University
More informationFourier Analysis of Signals Using the DFT
Fourier Analysis of Signals Using the DFT ECE 535 Lecture April 29, 23 Overview: Motivation Many applications require analyzing the frequency content of signals Speech processing study resonances of vocal
More informationANALOG AND DIGITAL SIGNAL PROCESSING ADSP - Chapter 8
ANALOG AND DIGITAL SIGNAL PROCESSING ADSP - Chapter 8 Fm n N fnt ( ) e j2mn N X() X() 2 X() X() 3 W Chap. 8 Discrete Fourier Transform (DFT), FFT Prof. J.-P. Sandoz, 2-2 W W 3 W W x () x () x () 2 x ()
More informationNonlinear system identification with the use of describing functions a case study
Nonlinear system identification with the use of describing functions a case study Zhongge Zhao 1, Chuanri Li 2, Kjell Ahlin 3, Huan Du 4 1, 2, 4 School of Reliability and System Engineering, Beihang University,
More informationDr.Vinod Hosur, Professor, Civil Engg.Dept., Gogte Institute of Technology, Belgaum
STRUCTURAL DYNAMICS Dr.Vinod Hosur, Professor, Civil Engg.Dept., Gogte Institute of Technology, Belgaum Overview of Structural Dynamics Structure Members, joints, strength, stiffness, ductility Structure
More informationSignal Modeling, Statistical Inference and Data Mining in Astrophysics
ASTRONOMY 6523 Spring 2013 Signal Modeling, Statistical Inference and Data Mining in Astrophysics Course Approach The philosophy of the course reflects that of the instructor, who takes a dualistic view
More informationIdentification Methods for Structural Systems. Prof. Dr. Eleni Chatzi Lecture 9-23 April, 2013
Prof. Dr. Eleni Chatzi Lecture 9-23 April, 2013 Identification Methods The work is done either in the frequency domain - Modal ID methods using the Frequency Response Function (FRF) information or in the
More informationEffects of data windows on the methods of surrogate data
Effects of data windows on the methods of surrogate data Tomoya Suzuki, 1 Tohru Ikeguchi, and Masuo Suzuki 1 1 Graduate School of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo
More informationIntroduction to Wavelet. Based on A. Mukherjee s lecture notes
Introduction to Wavelet Based on A. Mukherjee s lecture notes Contents History of Wavelet Problems of Fourier Transform Uncertainty Principle The Short-time Fourier Transform Continuous Wavelet Transform
More informationEXPERIMENTAL MODAL ANALYSIS (EMA) OF A SPINDLE BRACKET OF A MINIATURIZED MACHINE TOOL (MMT)
5 th International & 26 th All India Manufacturing Technology, Design and Research Conference (AIMTDR 2014) December 12 th 14 th, 2014, IIT Guwahati, Assam, India EXPERIMENTAL MODAL ANALYSIS (EMA) OF A
More informationAnnouncements. Filtering. Image Filtering. Linear Filters. Example: Smoothing by Averaging. Homework 2 is due Apr 26, 11:59 PM Reading:
Announcements Filtering Homework 2 is due Apr 26, :59 PM eading: Chapter 4: Linear Filters CSE 52 Lecture 6 mage Filtering nput Output Filter (From Bill Freeman) Example: Smoothing by Averaging Linear
More informationEE 435. Lecture 29. Data Converters. Linearity Measures Spectral Performance
EE 435 Lecture 9 Data Converters Linearity Measures Spectral Performance Linearity Measurements (testing) Consider ADC V IN (t) DUT X IOUT V REF Linearity testing often based upon code density testing
More informationContinuous Time Signal Analysis: the Fourier Transform. Lathi Chapter 4
Continuous Time Signal Analysis: the Fourier Transform Lathi Chapter 4 Topics Aperiodic signal representation by the Fourier integral (CTFT) Continuous-time Fourier transform Transforms of some useful
More informationChapter 2: Rigid Bar Supported by Two Buckled Struts under Axial, Harmonic, Displacement Excitation..14
Table of Contents Chapter 1: Research Objectives and Literature Review..1 1.1 Introduction...1 1.2 Literature Review......3 1.2.1 Describing Vibration......3 1.2.2 Vibration Isolation.....6 1.2.2.1 Overview.
More information6.435, System Identification
System Identification 6.435 SET 3 Nonparametric Identification Munther A. Dahleh 1 Nonparametric Methods for System ID Time domain methods Impulse response Step response Correlation analysis / time Frequency
More informationIdentification Methods for Structural Systems. Prof. Dr. Eleni Chatzi Lecture March, 2016
Prof. Dr. Eleni Chatzi Lecture 4-09. March, 2016 Fundamentals Overview Multiple DOF Systems State-space Formulation Eigenvalue Analysis The Mode Superposition Method The effect of Damping on Structural
More informationLINEAR RESPONSE THEORY
MIT Department of Chemistry 5.74, Spring 5: Introductory Quantum Mechanics II Instructor: Professor Andrei Tokmakoff p. 8 LINEAR RESPONSE THEORY We have statistically described the time-dependent behavior
More informationStochastic Dynamics of SDOF Systems (cont.).
Outline of Stochastic Dynamics of SDOF Systems (cont.). Weakly Stationary Response Processes. Equivalent White Noise Approximations. Gaussian Response Processes as Conditional Normal Distributions. Stochastic
More informationSignals & Systems. Lecture 5 Continuous-Time Fourier Transform. Alp Ertürk
Signals & Systems Lecture 5 Continuous-Time Fourier Transform Alp Ertürk alp.erturk@kocaeli.edu.tr Fourier Series Representation of Continuous-Time Periodic Signals Synthesis equation: x t = a k e jkω
More informationEQUIVALENT SINGLE-DEGREE-OF-FREEDOM SYSTEM AND FREE VIBRATION
1 EQUIVALENT SINGLE-DEGREE-OF-FREEDOM SYSTEM AND FREE VIBRATION The course on Mechanical Vibration is an important part of the Mechanical Engineering undergraduate curriculum. It is necessary for the development
More informatione jωt = cos(ωt) + jsin(ωt),
This chapter introduces you to the most useful mechanical oscillator model, a mass-spring system with a single degree of freedom. Basic understanding of this system is the gateway to the understanding
More informationChapter 23: Principles of Passive Vibration Control: Design of absorber
Chapter 23: Principles of Passive Vibration Control: Design of absorber INTRODUCTION The term 'vibration absorber' is used for passive devices attached to the vibrating structure. Such devices are made
More informationModule 4: Dynamic Vibration Absorbers and Vibration Isolator Lecture 19: Active DVA. The Lecture Contains: Development of an Active DVA
The Lecture Contains: Development of an Active DVA Proof Mass Actutor Application of Active DVA file:///d /chitra/vibration_upload/lecture19/19_1.htm[6/25/2012 12:35:51 PM] In this section, we will consider
More informationDeveloping a Multisemester Interwoven Dynamic Systems Project to Foster Learning and Retention of STEM Material
100 10 1 ζ=0.1% ζ=1% ζ=2% ζ=5% ζ=10% ζ=20% 0-90 -180 ζ=20% ζ=10% ζ=5% ζ=2% ζ=1% ζ=0.1% Proceedings of 2004 IMECE: November 13-19, 2004, Anaheim, CA 2004 ASME International Mechanical Engineering Congress
More informationA523 Signal Modeling, Statistical Inference and Data Mining in Astrophysics Spring 2011
A523 Signal Modeling, Statistical Inference and Data Mining in Astrophysics Spring 2011 Lecture 1 Organization:» Syllabus (text, requirements, topics)» Course approach (goals, themes) Book: Gregory, Bayesian
More informationChapter 4 Discrete Fourier Transform (DFT) And Signal Spectrum
Chapter 4 Discrete Fourier Transform (DFT) And Signal Spectrum CEN352, DR. Nassim Ammour, King Saud University 1 Fourier Transform History Born 21 March 1768 ( Auxerre ). Died 16 May 1830 ( Paris ) French
More informationTHE FOURIER TRANSFORM (Fourier series for a function whose period is very, very long) Reading: Main 11.3
THE FOURIER TRANSFORM (Fourier series for a function whose period is very, very long) Reading: Main 11.3 Any periodic function f(t) can be written as a Fourier Series a 0 2 + a n cos( nωt) + b n sin n
More informationDynamics of Structures
Dynamics of Structures Elements of structural dynamics Roberto Tomasi 11.05.2017 Roberto Tomasi Dynamics of Structures 11.05.2017 1 / 22 Overview 1 SDOF system SDOF system Equation of motion Response spectrum
More informationMAXIMUM LOADS ON A 1-DOF MODEL-SCALE OFFSHORE WIND TURBINE
MAXIMUM LOADS ON A 1-DOF MODEL-SCALE OFFSHORE WIND TURBINE Loup Suja-Thauvin (Industry PhD) Jørgen Krokstad (prof II) Joakim Fürst Frimann-Dahl (DNV-GL) Table of contents 1. Motivation 2. Presentation
More informationIdentification Techniques for Operational Modal Analysis An Overview and Practical Experiences
Identification Techniques for Operational Modal Analysis An Overview and Practical Experiences Henrik Herlufsen, Svend Gade, Nis Møller Brüel & Kjær Sound and Vibration Measurements A/S, Skodsborgvej 307,
More informationLaboratory handout 5 Mode shapes and resonance
laboratory handouts, me 34 82 Laboratory handout 5 Mode shapes and resonance In this handout, material and assignments marked as optional can be skipped when preparing for the lab, but may provide a useful
More informationTopic 3: Fourier Series (FS)
ELEC264: Signals And Systems Topic 3: Fourier Series (FS) o o o o Introduction to frequency analysis of signals CT FS Fourier series of CT periodic signals Signal Symmetry and CT Fourier Series Properties
More informationCHAPTER 4 FOURIER SERIES S A B A R I N A I S M A I L
CHAPTER 4 FOURIER SERIES 1 S A B A R I N A I S M A I L Outline Introduction of the Fourier series. The properties of the Fourier series. Symmetry consideration Application of the Fourier series to circuit
More informationIntroduction to Signal Analysis Parts I and II
41614 Dynamics of Machinery 23/03/2005 IFS Introduction to Signal Analysis Parts I and II Contents 1 Topics of the Lecture 11/03/2005 (Part I) 2 2 Fourier Analysis Fourier Series, Integral and Complex
More information2.0 Theory. 2.1 Ground Vibration Test
2.0 Theory The following section provides a comprehensive overview of the theory behind the concepts and requirements of a GVT (Ground Vibration Test), as well as some of the background knowledge required
More informationDesigning Information Devices and Systems II Fall 2015 Note 5
EE 16B Designing Information Devices and Systems II Fall 01 Note Lecture given by Babak Ayazifar (9/10) Notes by: Ankit Mathur Spectral Leakage Example Compute the length-8 and length-6 DFT for the following
More informationMassachusetts Institute of Technology Department of Electrical Engineering and Computer Science : Discrete-Time Signal Processing
Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.34: Discrete-Time Signal Processing OpenCourseWare 006 ecture 8 Periodogram Reading: Sections 0.6 and 0.7
More informationFrequency- and Time-Domain Spectroscopy
Frequency- and Time-Domain Spectroscopy We just showed that you could characterize a system by taking an absorption spectrum. We select a frequency component using a grating or prism, irradiate the sample,
More informationCurve Fitting Analytical Mode Shapes to Experimental Data
Curve Fitting Analytical Mode Shapes to Experimental Data Brian Schwarz, Shawn Richardson, Mar Richardson Vibrant Technology, Inc. Scotts Valley, CA ABSTRACT In is paper, we employ e fact at all experimental
More informationAn algorithm for detecting oscillatory behavior in discretized data: the damped-oscillator oscillator detector
An algorithm for detecting oscillatory behavior in discretized data: the damped-oscillator oscillator detector David Hsu, Murielle Hsu, He Huang and Erwin B. Montgomery, Jr Department of Neurology University
More informationAnalytic discrete cosine harmonic wavelet transform(adchwt) and its application to signal/image denoising
Analytic discrete cosine harmonic wavelet transform(adchwt) and its application to signal/image denoising M. Shivamurti and S. V. Narasimhan Digital signal processing and Systems Group Aerospace Electronic
More informationTheoretical Seismology. Astrophysics and Cosmology and Earth and Environmental Physics. FTAN Analysis. Fabio ROMANELLI
Theoretical Seismology Astrophysics and Cosmology and Earth and Environmental Physics FTAN Analysis Fabio ROMANELLI Department of Mathematics & Geosciences University of Trieste romanel@units.it 1 FTAN
More informationIntroduction to Biomedical Engineering
Introduction to Biomedical Engineering Biosignal processing Kung-Bin Sung 6/11/2007 1 Outline Chapter 10: Biosignal processing Characteristics of biosignals Frequency domain representation and analysis
More information