Application of Extreme Value Statistics for Structural Health Monitoring. Hoon Sohn
|
|
- Barbra Gregory
- 6 years ago
- Views:
Transcription
1 Application of Etreme Value Statistics for Structural Health Monitoring Hoon Sohn Weapon Response Group Engineering Sciences and Applications Division Los Alamos National Laboratory Los Alamos, New Meico, USA. Presented at Uncertainty Quantification Working Group May 1st, 2003
2 Four Goals for Structural Health Monitoring Step 1: Damage Identification Step 2: Damage Localization Step 3: Damage Quantification Step 4: Damage Prognosis 2
3 Structural Health Monitoring Is this bridge damaged? Perform pattern comparison. 3
4 Five Steps for Structural Health Monitoring Step 1: Operational Evaluation Step 2: Data Acquisition Step 3: Data Normalization Step 4: Feature Etraction Step 5: Statistical Inference 4
5 Environmental Variation E-1 E-2 E-3 E-4 Freq. Hz Dam0 Dam1 Dam2 Change of the first mode frequency w.r.t. damage cases Dam3 2.3 Dam0 Dam1 Dam2 Dam3 Dam4 5
6 Eample of Debris in Epansion Joint of the Alamosa Canyon Bridge This debris can effect the boundary conditions of the structure and its response to environmental changes 6
7 Statistical Pattern Recognition Paradigm for SHM After Sep. 11, 2001 Before Sep. 11,
8 Data Normalization Eample [Sohn et al. 2002] m8 m1 Shaker Bumper List of time series employed in this study Case Description Input level Data # per input Total data # 0 No bumper 3, 4, 5, 6, 7 Volts 15 sets 75 sets 1 Bumper between m1-m2 3, 4, 5, 6, 7 Volts 5 sets 25 sets 2 Bumper between m5-m6 3, 4, 5, 6, 7 Volts 5 sets 25 sets 3 Bumper between m7-m8 4, 5, 6, 7 Volts 5 sets 20 sets 8
9 9 Outline of Damage Diagnosis using AR-ARX, Auto-Associative Network and Hypothesis Test 1. COLLECT BASELINE DATA Time series from various operation & environmental conditions t 2. FEATURE EXTRACTION = = = b j i a i i j t e i t t t 1 1 β α ε 4. FEATURE EXTRACTION = = = b j i a i i y j t e i t t t 1 1 ˆ ˆ β α ε 3. DATA NORMALIZATION 6. DECISION MAKING Bumper between m1 and m2 DOF σε y /σε 5. STATISTICAL INFERENCE : : 1 y y o H H ε σ ε σ ε σ ε σ
10 Auto-Associative Neural Network for Data Normalization Mapping function G De-mapping function H Put α and β N N Predict and Predict α and β α i β i N Put ecitation level Predict ecitation level N N V L Vˆ N N N L L L αˆi βˆi N N L N N Mapping layer Bottleneck layer De-mapping layer Output layer 10
11 Damage Localization 1.5 No No bumper Bumper 3.5 Bumper between m1 m1 and and m2 m σε y /σε σ ε / σ ε y σε y /σε DOF DOF 3.03 Bumper between m5 and and m6 m6 2.5 Bumper between m7 m7 and and m8 m σε y /σε σ ε / σ ε y σε y /σε DOF DOF 11
12 Real World Application [Sohn et al. 2001] a Surface-Effect Fast Patrol Boat A,B Courtesy of Naval Research Laboratory H,I K J C,D G E,F I B D F b Fiber optic strain gauges K J A G E H C 12
13 Raw Dynamic Strain Time Series Data Low Speed High Speed Strain Strain Strain Strain Strain Strain Data Point # = Time Period = sec t = sec Signal Signal Signal Time Sec Time sec Structural Condition I undamaged Structural Condition II damaged 13
14 Damage Classification using σ ε σ ε. y Signal 1 Signal 2 Signal 3 From from first half half Signal 3 From from second half half 2.5 σ y σε y /σε ε / σ ε H=1.85 h= Test Number 14
15 A Moment Resisting Frame Structure Model Damage 2 Damage 1 15
16 Establishment of Decision Boundaries Unsupervised Learning: Use only the baseline data for training Undamaged Training Undamaged Testing Damaged Testing # of Epected outliers = 1% of 1000 points = 10 outliers From Normal # of outliers: 48 16
17 Normality Assumption of Data Let s look at the baseline prediction errors to see whether they have a normal distribution or not. A normal probability plot graphically assesses whether the data come from a normal distribution. If the data are normal, the plot will be linear. Otherwise, there would be curvature in the plot. The central population of data seems to fit to the normal distribution well, but the tails do not. Probability CDF Normal Probability Plot Prediction Errors 17
18 Why Etreme Value Statistics? In general, the distribution type of the parent data is unknown, and there are infinite numbers of candidate distributions. There are only three types of distributions for etreme the etreme maimum or minimum values regardless the distribution type of the parent data [Fisher and Tippett, 1928]. That means, the model selection for the etreme values becomes much easier, because there are only three models to choose.gumbel, Weibull, Frechet distributions 18
19 19 Feasible Cumulative Density Functions for Maima From Castillo [1988]: = otherwise ep if 1 β δ λ λ F Weibull: = otherwise 0 if ep λ λ δ β F Frechet: Gumbel 0, ep ep > < < = δ δ λ F
20 Fitting to Gumbel Distribution Normal Probability Plot 1.0 Gumbel s CDF Probability Probability 0.5 Points used Fitted CDF Empirical CDF Points used Fitted CDF Data Order statistic maima Divide the original times series with 8192 data points into 128 time series with 64 points. Compute the maimum value from each block and fit the 128 maima to a Gumbel distribution. 20
21 Establishment of Decision Boundaries Undamaged Training Undamaged Testing Damaged Testing From EVS # of outliers: 9 # of Epected outliers = 1% of 1000 points = 10 outliers From Normal # of outliers: 48 21
22 Detection of Rattling Container Frictionless Roller In-Ais Accelerometer Spring Internal component Off-Ais Accelerometer Bumper Base Ecitation at 18 Hz 22
23 Acceleration Response Rattling Rattling 23
24 Discontinuity Detection via Holder Eponent Definition: The Holder Eponent is a measure of the regularity of the signal. The regularity of the signal is the number of continuous derivatives that the signal possesses. Objective: Identify discontinuity in signals that can be caused by certain types of damage. Application: Eamples of damage that might induce discontinuity into the dynamic response signal include: Opening and closing of cracks A loose joint that is allowing contact rattle to occur 24
25 Holder Eponent Analysis Time Signal Wavelet Transform 1 t u Wf u s = *, f t ψ dt s s Translation Scalogram Dilation 25
26 Holder Eponent Analysis Scalogram Slop = Holder Eponent 26
27 Scalogram from Wavelet Transform 27
28 Holder Eponent Analysis 1 Find the ma drop 2 Threshold = C ma drop 3 Discontinuity > Threshold 28
29 Summary Cast structural health monitoring problems in the framework of statistical pattern recognition. Developed various signal-based damage detection algorithms. Embed damage detection algorithms into on-board microprocessors. Address data normalization issue eplicitly. Decision making is based on rigorous statistical modeling. Provide a suite of data interrogation algorithms for structural health monitoring in the format of GUI software called DIAMOND II patent pending. 29
EMBEDDING ALGORITHMS IN A WIRELESS STRUCTURAL MONITORING SYSTEM
Source: Proceedings of International Conference on Advances and New Challenges in Earthquae Engineering Research (ICANCEER02), Hong Kong, China, August 9-20, 2002. EMBEDDING ALGORITHMS IN A WIRELESS STRUCTURAL
More informationStatistical Damage Detection Using Time Series Analysis on a Structural Health Monitoring Benchmark Problem
Source: Proceedings of the 9th International Conference on Applications of Statistics and Probability in Civil Engineering, San Francisco, CA, USA, July 6-9, 2003. Statistical Damage Detection Using Time
More informationBasic Statistical Tools
Structural Health Monitoring Using Statistical Pattern Recognition Basic Statistical Tools Presented by Charles R. Farrar, Ph.D., P.E. Los Alamos Dynamics Structural Dynamics and Mechanical Vibration Consultants
More informationWILEY STRUCTURAL HEALTH MONITORING A MACHINE LEARNING PERSPECTIVE. Charles R. Farrar. University of Sheffield, UK. Keith Worden
STRUCTURAL HEALTH MONITORING A MACHINE LEARNING PERSPECTIVE Charles R. Farrar Los Alamos National Laboratory, USA Keith Worden University of Sheffield, UK WILEY A John Wiley & Sons, Ltd., Publication Preface
More informationMinimizing Misclassification of Damage using Extreme Value Statistics
Minimizing Misclassification of Damage using Extreme Value Statistics Hoon Sohn, Hyun Woo Park, Kincho H. Law 3, and Charles R. Farrar 4 Department of Civil and Environmental Engineering Carnegie Mellon
More informationThe application of statistical pattern recognition methods for damage detection to field data
IOP PUBLISHING Smart Mater. Struct. 17 (2008) 065023 (12pp) SMART MATERIALS AND STRUCTURES doi:10.1088/0964-1726/17/6/065023 The application of statistical pattern recognition methods for damage detection
More informationPh.D student in Structural Engineering, Department of Civil Engineering, Ferdowsi University of Mashhad, Azadi Square, , Mashhad, Iran
Alireza Entezami a, Hashem Shariatmadar b* a Ph.D student in Structural Engineering, Department of Civil Engineering, Ferdowsi University of Mashhad, Azadi Square, 9177948974, Mashhad, Iran b Associate
More informationStructural Health Monitoring Using Statistical Pattern Recognition Techniques
Hoon Sohn Engineering Sciences & Applications Division, Engineering Analysis Group, M/S C926 e-mail: sohn@lanl.gov Charles R. Farrar Engineering Sciences & Applications Division, Engineering Analysis Group,
More informationIntroduction to Statistical Inference
Structural Health Monitoring Using Statistical Pattern Recognition Introduction to Statistical Inference Presented by Charles R. Farrar, Ph.D., P.E. Outline Introduce statistical decision making for Structural
More informationLos Alamos NATIONAL LABORATORY
Validation of Engineering Applications at LANL (*) Thomas A. Butler Scott W. Doebling François M. Hemez John F. Schultze Hoon Sohn Group National Laboratory, New Mexico, U.S.A. National Laboratory Uncertainty
More informationProbability Distribution
Probability Distribution Prof. (Dr.) Rajib Kumar Bhattacharjya Indian Institute of Technology Guwahati Guwahati, Assam Email: rkbc@iitg.ernet.in Web: www.iitg.ernet.in/rkbc Visiting Faculty NIT Meghalaya
More informationUnsupervised Learning Methods
Structural Health Monitoring Using Statistical Pattern Recognition Unsupervised Learning Methods Keith Worden and Graeme Manson Presented by Keith Worden The Structural Health Monitoring Process 1. Operational
More informationStructural health monitoring of offshore jacket platforms by inverse vibration problem. M. T. Nikoukalam On behalf of Kiarash M.
Structural health monitoring of offshore jacket platforms by inverse vibration problem M. T. Nikoukalam On behalf of Kiarash M. Dolatshahi 1 Outline 1- Introduction 2- Motivation 3- Description of inverse
More informationReliable Condition Assessment of Structures Using Uncertain or Limited Field Modal Data
Reliable Condition Assessment of Structures Using Uncertain or Limited Field Modal Data Mojtaba Dirbaz Mehdi Modares Jamshid Mohammadi 6 th International Workshop on Reliable Engineering Computing 1 Motivation
More informationHoon Sohn, Amy N. Robertson, and Charles R. Farrar
Approved for public release; distribution is unlimited. WJ 0-2 Title, SINGULARITY DETECTION USING HQLDER EXPONENT Author(s). Hoon Sohn, Amy N. Robertson, and Charles R. Farrar Submitted to: Proceedings
More informationSkills Practice Skills Practice for Lesson 1.1
Skills Practice Skills Practice for Lesson. Name Date Lots and Projectiles Introduction to Quadratic Functions Vocabular Give an eample of each term.. quadratic function 9 0. vertical motion equation s
More informationThe effect of environmental and operational variabilities on damage detection in wind turbine blades
The effect of environmental and operational variabilities on damage detection in wind turbine blades More info about this article: http://www.ndt.net/?id=23273 Thomas Bull 1, Martin D. Ulriksen 1 and Dmitri
More informationOn the use of wavelet coefficient energy for structural damage diagnosis
Safety, Reliability and Risk of Structures, Infrastructures and Engineering Systems Furuta, Frangopol & Shinozuka (eds) 010 Taylor & Francis Group, London, ISBN 978-0-415-47557-0 On the use of wavelet
More informationComplexity: A New Axiom for Structural Health Monitoring?
(FIRST PAGE OF ARTICLE) Complexity: A New Axiom for Structural Health Monitoring? C. FARRAR, K. WORDEN AND G. PARK ABSTRACT The basic purpose of the paper is simple; having proposed a set of axioms or
More informationDamage Detection and Identification in Structures by Spatial Wavelet Based Approach
International Journal of Applied Science and Engineering 2012. 10, 1: 69-87 Damage Detection and Identification in Structures by Spatial Wavelet Based Approach D. Mallikarjuna Reddy a, * and S. Swarnamani
More informationDamage Characterization of the IASC-ASCE Structural Health Monitoring Benchmark Structure by Transfer Function Pole Migration. J. P.
SOURCE: Jerome P. Lynch, " Damage Characterization of the IASC-ASCE Structural Health Monitoring Benchmark Structure by Transfer Function Pole Migration, " Proceedings of the 2005 ASCE Structures Congress,
More informationProblem d d d B C E D. 0.8d. Additional lecturebook examples 29 ME 323
Problem 9.1 Two beam segments, AC and CD, are connected together at C by a frictionless pin. Segment CD is cantilevered from a rigid support at D, and segment AC has a roller support at A. a) Determine
More informationA Wavelet based Damage Diagnosis Algorithm Using Principal Component Analysis
A Wavelet based Damage Diagnosis Algorithm Using Principal Component Analysis K. Krishnan Nair and Anne S. Kiremidian K. Krishnan Nair, Post Doctoral Student, Departments of Civil and Environmental Engineering
More informationMath 180A. Lecture 16 Friday May 7 th. Expectation. Recall the three main probability density functions so far (1) Uniform (2) Exponential.
Math 8A Lecture 6 Friday May 7 th Epectation Recall the three main probability density functions so far () Uniform () Eponential (3) Power Law e, ( ), Math 8A Lecture 6 Friday May 7 th Epectation Eample
More information: Probabilistic Engineering Analysis and Design Professor Youn, Byeng Dong
CHAPTER 9. HEALTH DIAGNOSTICS AND PROGNOSTICS 9.1 Introduction Last several decades, tremendous advance has been made on the physics-based analysis and design under uncertainties. However, it is still
More informationBenchmark Data for Structural Health Monitoring
Benchmark Data for Structural Health Monitoring Jyrki Kullaa To cite this version: Jyrki Kullaa. Benchmark Data for Structural Health Monitoring. Le Cam, Vincent and Mevel, Laurent and Schoefs, Franck.
More informationDonnées, SHM et analyse statistique
Données, SHM et analyse statistique Laurent Mevel Inria, I4S / Ifsttar, COSYS, SII Rennes 1ère Journée nationale SHM-France 15 mars 2018 1 Outline 1 Context of vibration-based SHM 2 Modal analysis 3 Damage
More informationVibration Based Health Monitoring for a Thin Aluminum Plate: Experimental Assessment of Several Statistical Time Series Methods
Vibration Based Health Monitoring for a Thin Aluminum Plate: Experimental Assessment of Several Statistical Time Series Methods Fotis P. Kopsaftopoulos and Spilios D. Fassois Stochastic Mechanical Systems
More informationA Statistical Input Pruning Method for Artificial Neural Networks Used in Environmental Modelling
A Statistical Input Pruning Method for Artificial Neural Networks Used in Environmental Modelling G. B. Kingston, H. R. Maier and M. F. Lambert Centre for Applied Modelling in Water Engineering, School
More informationAdvanced Methods for Fault Detection
Advanced Methods for Fault Detection Piero Baraldi Agip KCO Introduction Piping and long to eploration distance pipelines activities Piero Baraldi Maintenance Intervention Approaches & PHM Maintenance
More information6. Vector Random Variables
6. Vector Random Variables In the previous chapter we presented methods for dealing with two random variables. In this chapter we etend these methods to the case of n random variables in the following
More informationLecture 3: Pattern Classification. Pattern classification
EE E68: Speech & Audio Processing & Recognition Lecture 3: Pattern Classification 3 4 5 The problem of classification Linear and nonlinear classifiers Probabilistic classification Gaussians, mitures and
More informationDamage detection of shear connectors in composite bridges under operational conditions
Southern Cross University epublications@scu 23rd Australasian Conference on the Mechanics of Structures and Materials 214 Damage detection of shear connectors in composite bridges under operational conditions
More informationApplication of Classical and Output-Only Modal Analysis to a Laser Cutting Machine
Proc. of ISMA2002; Leuven, Belgium; 2002 Application of Classical and Output-Only Modal Analysis to a Laser Cutting Machine Carsten Schedlinski 1), Marcel Lüscher 2) 1) ICS Dr.-Ing. Carsten Schedlinski
More informationUsing SDM to Train Neural Networks for Solving Modal Sensitivity Problems
Using SDM to Train Neural Networks for Solving Modal Sensitivity Problems Brian J. Schwarz, Patrick L. McHargue, & Mark H. Richardson Vibrant Technology, Inc. 18141 Main Street Jamestown, California 95327
More informationApplication of load-dependent Ritz vectors to Bayesian probabilistic damage detection
Probabilistic Engineering Mechanics 15 (2000) 139 153 www.elsevier.com/locate/probengmech Application of load-dependent Ritz vectors to Bayesian probabilistic damage detection Hoon Sohn, Kincho H. Law*
More informationVIBRATION-BASED DAMAGE DETECTION USING STATISTICAL PROCESS CONTROL
MSSP=20001323 Susan Giri BG Mechanical Systems and Signal Processing (2001) 15(4), 707}721 doi:10.1006/mssp.2000.1323, available online at http://www.idealibrary.com on VIBRATION-BASED DAMAGE DETECTION
More informationStatistical Pattern Recognition Based Structural Damage Detection Strategies
Statistical Pattern Recognition Based Structural Damage Detection Strategies Luciana Balsamo Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Graduate
More information4.3 How derivatives affect the shape of a graph. The first derivative test and the second derivative test.
Chapter 4: Applications of Differentiation In this chapter we will cover: 41 Maimum and minimum values The critical points method for finding etrema 43 How derivatives affect the shape of a graph The first
More informationChapter 2. Discrete Distributions
Chapter. Discrete Distributions Objectives ˆ Basic Concepts & Epectations ˆ Binomial, Poisson, Geometric, Negative Binomial, and Hypergeometric Distributions ˆ Introduction to the Maimum Likelihood Estimation
More informationDamage detection and identification in beam structure using modal data and wavelets
ISSN 1 746-7233, England, UK World Journal of Modelling and Simulation Vol. 13 (2017) No. 1, pp. 52-65 Damage detection and identification in beam structure using modal data and wavelets Shivasharanayya
More informationDiscovery Through Situational Awareness
Discovery Through Situational Awareness BRETT AMIDAN JIM FOLLUM NICK BETZSOLD TIM YIN (UNIVERSITY OF WYOMING) SHIKHAR PANDEY (WASHINGTON STATE UNIVERSITY) Pacific Northwest National Laboratory February
More informationDamage detection in a reinforced concrete slab using outlier analysis
Damage detection in a reinforced concrete slab using outlier analysis More info about this article: http://www.ndt.net/?id=23283 Abstract Bilal A. Qadri 1, Dmitri Tcherniak 2, Martin D. Ulriksen 1 and
More informationPHYSICS PART II SECTION- I. Straight objective Type
PHYSICS PAT II SECTION- I Straight objective Tpe This section contains 9 multiple choice questions numbered to 1. Each question has choices,, (C) and, out of which ONLY ONE is correct.. A parallel plate
More informationMachine Learning Lecture 2
Announcements Machine Learning Lecture 2 Eceptional number of lecture participants this year Current count: 449 participants This is very nice, but it stretches our resources to their limits Probability
More informationA3. Statistical Inference
Appendi / A3. Statistical Inference / Mean, One Sample-1 A3. Statistical Inference Population Mean μ of a Random Variable with known standard deviation σ, and random sample of size n 1 Before selecting
More informationUnit 11 - Solving Quadratic Functions PART ONE
Unit 11 - Solving Quadratic Functions PART ONE PREREQUISITE SKILLS: students should be able to add, subtract and multiply polynomials students should be able to factor polynomials students should be able
More informationIntelligent Systems Statistical Machine Learning
Intelligent Systems Statistical Machine Learning Carsten Rother, Dmitrij Schlesinger WS2014/2015, Our tasks (recap) The model: two variables are usually present: - the first one is typically discrete k
More informationAutoregressive Gaussian processes for structural damage detection
Autoregressive Gaussian processes for structural damage detection R. Fuentes 1,2, E. J. Cross 1, A. Halfpenny 2, R. J. Barthorpe 1, K. Worden 1 1 University of Sheffield, Dynamics Research Group, Department
More informationIntroduction to Support Vector Machines
Introduction to Support Vector Machines Hsuan-Tien Lin Learning Systems Group, California Institute of Technology Talk in NTU EE/CS Speech Lab, November 16, 2005 H.-T. Lin (Learning Systems Group) Introduction
More informationLocalization of vibration-based damage detection method in structural applications
University of Iowa Iowa Research Online Theses and Dissertations Fall 2012 Localization of vibration-based damage detection method in structural applications Charles Joseph Schallhorn University of Iowa
More informationUSING WAVELET NEURAL NETWORK FOR THE IDENTIFICATION OF A BUILDING STRUCTURE FROM EXPERIMENTAL DATA
13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 24 Paper No. 241 USING WAVELET NEURAL NETWORK FOR THE IDENTIFICATION OF A BUILDING STRUCTURE FROM EXPERIMENTAL DATA
More informationTime series-based damage detection and localization algorithm with application to the ASCE benchmark structure
Journal of Sound and Vibration 291 (2006) 349 368 JOURNAL OF SOUND AND VIBRATION www.elsevier.com/locate/jsvi Time series-based damage detection and localization algorithm with application to the ASCE
More informationChapter 1. Statistics of Waves
Chapter 1 Statistics of Waves 1.1 Introduction The theory of linear ship motion in the Gaussian seaway has been applied for the design of offshore structures in the past half century (St. Denis and Pierson,
More informationLesson Goals. Unit 2 Functions Analyzing Graphs of Functions (Unit 2.2) Graph of a Function. Lesson Goals
Unit Functions Analzing Graphs of Functions (Unit.) William (Bill) Finch Mathematics Department Denton High School Lesson Goals When ou have completed this lesson ou will: Find the domain and range of
More informationA Structural Health Monitoring System for the Big Thunder Mountain Roller Coaster. Presented by: Sandra Ward and Scot Hart
A Structural Health Monitoring System for the Big Thunder Mountain Roller Coaster Presented by: Sandra Ward and Scot Hart 1 On Sept. 5, 2003, an accident on Big Thunder Mountain lead to one death and 10
More informationResearch Article Structural Damage Identification Based on Rough Sets and Artificial Neural Network
e Scientific World Journal, Article ID 193284, 9 pages http://dx.doi.org/10.1155/2014/193284 Research Article Structural Damage Identification Based on Rough Sets and Artificial Neural Network Chengyin
More informationModal Based Fatigue Monitoring of Steel Structures
Modal Based Fatigue Monitoring of Steel Structures Jesper Graugaard-Jensen Structural Vibration Solutions A/S, Denmark Rune Brincker Department of Building Technology and Structural Engineering Aalborg
More informationReview of elements of Calculus (functions in one variable)
Review of elements of Calculus (functions in one variable) Mainly adapted from the lectures of prof Greg Kelly Hanford High School, Richland Washington http://online.math.uh.edu/houstonact/ https://sites.google.com/site/gkellymath/home/calculuspowerpoints
More informationSTRUCTURAL HEALTH MONITORING FOR BRIDGES USING ADVANCED DATA ANALYSIS FOR PROCESS NON-LINEARITY AND NON- STATIONARITY ERMIAS BIRU
STRUCTURAL HEALTH MONITORING FOR BRIDGES USING ADVANCED DATA ANALYSIS FOR PROCESS NON-LINEARITY AND NON- STATIONARITY By ERMIAS BIRU Bachelor of Science in Industrial Engineering Bahir Dar University Bahir
More informationDamage detection of truss bridge via vibration data using TPC technique
Damage detection of truss bridge via vibration data using TPC technique Ahmed Noor AL-QAYYIM 1,2, Barlas Özden ÇAĞLAYAN 1 1 Faculty of Civil Engineering, Istanbul Technical University, Istanbul, Turkey
More informationthe Functional Model Based Method
Multi-Site Damage Localization via the Functional Model Based Method Christos S. Sakaris, John S. Sakellariou and Spilios D. Fassois Stochastic Mechanical Systems & Automation (SMSA) Laboratory Department
More informationChapter 9 Regression. 9.1 Simple linear regression Linear models Least squares Predictions and residuals.
9.1 Simple linear regression 9.1.1 Linear models Response and eplanatory variables Chapter 9 Regression With bivariate data, it is often useful to predict the value of one variable (the response variable,
More information2. A Basic Statistical Toolbox
. A Basic Statistical Toolbo Statistics is a mathematical science pertaining to the collection, analysis, interpretation, and presentation of data. Wikipedia definition Mathematical statistics: concerned
More informationMathematics syllabus for Grade 11 and 12 For Bilingual Schools in the Sultanate of Oman
03 04 Mathematics syllabus for Grade and For Bilingual Schools in the Sultanate of Oman Prepared By: A Stevens (Qurum Private School) M Katira (Qurum Private School) M Hawthorn (Al Sahwa Schools) In Conjunction
More informationSINGULARITY DETECTION FOR STRUCTURAL HEALTH MONITORING USING HOLDER EXPONENTS
Mechanical Systems and Signal Processing (23) 17(6), 1163 1184 doi:1.16/mssp.22.1569 SINGULARITY DETECTION FOR STRUCTURAL ALTH MONITORING USING HOLDER EXPONENTS A. N. Robertson, C.R.Farrar and H. Sohn
More informationSmall Crack Fatigue Growth and Detection Modeling with Uncertainty and Acoustic Emission Application
Small Crack Fatigue Growth and Detection Modeling with Uncertainty and Acoustic Emission Application Presentation at the ITISE 2016 Conference, Granada, Spain June 26 th 29 th, 2016 Outline Overview of
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 informationExperimental Modal Analysis of a Flat Plate Subjected To Vibration
American Journal of Engineering Research (AJER) 2016 American Journal of Engineering Research (AJER) e-issn: 2320-0847 p-issn : 2320-0936 Volume-5, Issue-6, pp-30-37 www.ajer.org Research Paper Open Access
More informationIT S TIME FOR AN UPDATE EXTREME WAVES AND DIRECTIONAL DISTRIBUTIONS ALONG THE NEW SOUTH WALES COASTLINE
IT S TIME FOR AN UPDATE EXTREME WAVES AND DIRECTIONAL DISTRIBUTIONS ALONG THE NEW SOUTH WALES COASTLINE M Glatz 1, M Fitzhenry 2, M Kulmar 1 1 Manly Hydraulics Laboratory, Department of Finance, Services
More informationIntroduction to Probability Theory for Graduate Economics Fall 2008
Introduction to Probability Theory for Graduate Economics Fall 008 Yiğit Sağlam October 10, 008 CHAPTER - RANDOM VARIABLES AND EXPECTATION 1 1 Random Variables A random variable (RV) is a real-valued function
More informationINTERNAL STRAIN MEASUREMENTS IN CFRP PLATES SUBJECTED TO IMPACT LOAD USING FBG SENSORS
INTERNAL STRAIN MEASUREMENTS IN CFRP PLATES SUBJECTED TO IMPACT LOAD USING FBG SENSORS J. Frieden, J. Cugnoni, J. Botsis, Th. Gmür, D. Coric Laboratoire de Mécanique appliquée et d Analyse de Fiabilité
More informationAlgebra Concepts Equation Solving Flow Chart Page 1 of 6. How Do I Solve This Equation?
Algebra Concepts Equation Solving Flow Chart Page of 6 How Do I Solve This Equation? First, simplify both sides of the equation as much as possible by: combining like terms, removing parentheses using
More informationstiffness to the system stiffness matrix. The nondimensional parameter i is introduced to allow the modeling of damage in the ith substructure. A subs
A BAYESIAN PROBABILISTIC DAMAGE DETECTION USING LOAD-DEPENDENT RIT VECTORS HOON SOHN Λ and KINCHO H. LAW y Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 9435-42,U.S.A.
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 informationRobot Dynamics II: Trajectories & Motion
Robot Dynamics II: Trajectories & Motion Are We There Yet? METR 4202: Advanced Control & Robotics Dr Surya Singh Lecture # 5 August 23, 2013 metr4202@itee.uq.edu.au http://itee.uq.edu.au/~metr4202/ 2013
More informationUn-measurable, but Inferable Attributes. Data Processing
Identification of Civil Engineering Structures and Uncertainty Qin Pan, John Prader, Nathaniel Dubbs, A. Emin Aktan, and Franklin L. Moon Drexel University Kirk Grimmelsman University of Arkansas identification
More informationEarthquake Loads According to IBC IBC Safety Concept
Earthquake Loads According to IBC 2003 The process of determining earthquake loads according to IBC 2003 Spectral Design Method can be broken down into the following basic steps: Determination of the maimum
More informationNew Methods for Structural Health Monitoring and Damage Localization
New Methods for Structural Health Monitoring and Damage Localization By Xueyan Zhao A thesis submitted for the degree of Doctor of Philosophy in the Department of Automatic Control and Systems Engineering,
More informationJournal of Biostatistics and Epidemiology
Journal of Biostatistics and Epidemiology Original Article Robust correlation coefficient goodness-of-fit test for the Gumbel distribution Abbas Mahdavi 1* 1 Department of Statistics, School of Mathematical
More informationHST.582J / 6.555J / J Biomedical Signal and Image Processing Spring 2007
MIT OpenCourseWare http://ocw.mit.edu HST.582J / 6.555J / 16.456J Biomedical Signal and Image Processing Spring 2007 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
More information2330. A study on Gabor frame for estimating instantaneous dynamic characteristics of structures Wei-Chih Su 1, Chiung-Shiann Huang 2 1
2330. A study on Gabor frame for estimating instantaneous dynamic characteristics of structures Wei-Chih Su 1, Chiung-Shiann Huang 2 1 National Center for High-Performance Computing, National Applied Research
More informationROBUST VIRTUAL DYNAMIC STRAIN SENSORS FROM ACCELERATION MEASUREMENTS
7th European Workshop on Structural Health Monitoring July 8-11, 2014. La Cité, Nantes, France More Info at Open Access Database www.ndt.net/?id=17230 ROBUST VIRTUAL DYNAMIC STRAIN SENSORS FROM ACCELERATION
More informationAn example to illustrate frequentist and Bayesian approches
Frequentist_Bayesian_Eample An eample to illustrate frequentist and Bayesian approches This is a trivial eample that illustrates the fundamentally different points of view of the frequentist and Bayesian
More informationInterest Operators. All lectures are from posted research papers. Harris Corner Detector: the first and most basic interest operator
Interest Operators All lectures are from posted research papers. Harris Corner Detector: the first and most basic interest operator SIFT interest point detector and region descriptor Kadir Entrop Detector
More informationDoing Right By Massive Data: How To Bring Probability Modeling To The Analysis Of Huge Datasets Without Taking Over The Datacenter
Doing Right By Massive Data: How To Bring Probability Modeling To The Analysis Of Huge Datasets Without Taking Over The Datacenter Alexander W Blocker Pavlos Protopapas Xiao-Li Meng 9 February, 2010 Outline
More informationRandom variables, distributions and limit theorems
Questions to ask Random variables, distributions and limit theorems What is a random variable? What is a distribution? Where do commonly-used distributions come from? What distribution does my data come
More informationMachine Learning Lecture 2
Machine Perceptual Learning and Sensory Summer Augmented 6 Computing Announcements Machine Learning Lecture 2 Course webpage http://www.vision.rwth-aachen.de/teaching/ Slides will be made available on
More informationComputer Science, Informatik 4 Communication and Distributed Systems. Simulation. Discrete-Event System Simulation. Dr.
Simulation Discrete-Event System Simulation Chapter 4 Statistical Models in Simulation Purpose & Overview The world the model-builder sees is probabilistic rather than deterministic. Some statistical model
More informationPATTERN RECOGNITION AND MACHINE LEARNING
PATTERN RECOGNITION AND MACHINE LEARNING Chapter 1. Introduction Shuai Huang April 21, 2014 Outline 1 What is Machine Learning? 2 Curve Fitting 3 Probability Theory 4 Model Selection 5 The curse of dimensionality
More informationSTATISTICAL DAMAGE IDENTIFICATION TECHNIQUES APPLIED TO THE I-40 BRIDGE OVER THE RIO GRANDE RIVER
STATISTICAL DAMAGE IDENTIFICATION TECHNIQUES APPLIED TO THE I-4 BRIDGE OVER THE RIO GRANDE RIVER Scott W. Doebling 1, Charles R. Farrar 2 Los Alamos National Laboratory Los Alamos, NM, 87545 ABSTRACT The
More informationPENULTIMATE APPROXIMATIONS FOR WEATHER AND CLIMATE EXTREMES. Rick Katz
PENULTIMATE APPROXIMATIONS FOR WEATHER AND CLIMATE EXTREMES Rick Katz Institute for Mathematics Applied to Geosciences National Center for Atmospheric Research Boulder, CO USA Email: rwk@ucar.edu Web site:
More information8-1 Exploring Exponential Models
8- Eploring Eponential Models Eponential Function A function with the general form, where is a real number, a 0, b > 0 and b. Eample: y = 4() Growth Factor When b >, b is the growth factor Eample: y =
More informationIntroduction to Systems Analysis and Decision Making Prepared by: Jakub Tomczak
Introduction to Systems Analysis and Decision Making Prepared by: Jakub Tomczak 1 Introduction. Random variables During the course we are interested in reasoning about considered phenomenon. In other words,
More informationSpatial Analysis I. Spatial data analysis Spatial analysis and inference
Spatial Analysis I Spatial data analysis Spatial analysis and inference Roadmap Outline: What is spatial analysis? Spatial Joins Step 1: Analysis of attributes Step 2: Preparing for analyses: working with
More informationBayesian Semi-supervised Learning with Deep Generative Models
Bayesian Semi-supervised Learning with Deep Generative Models Jonathan Gordon Department of Engineering Cambridge University jg801@cam.ac.uk José Miguel Hernández-Lobato Department of Engineering Cambridge
More informationINDIAN INSTITUTE OF SCIENCE STOCHASTIC HYDROLOGY. Course Instructor : Prof. P. P. MUJUMDAR Department of Civil Engg., IISc.
INDIAN INSTITUTE OF SCIENCE STOCHASTIC HYDROLOGY Course Instructor : Prof. P. P. MUJUMDAR Department of Civil Engg., IISc. Course Contents Introduction to Random Variables (RVs) Probability Distributions
More informationChapter 27 Summary Inferences for Regression
Chapter 7 Summary Inferences for Regression What have we learned? We have now applied inference to regression models. Like in all inference situations, there are conditions that we must check. We can test
More informationWavelets bases in higher dimensions
Wavelets bases in higher dimensions 1 Topics Basic issues Separable spaces and bases Separable wavelet bases D DWT Fast D DWT Lifting steps scheme JPEG000 Advanced concepts Overcomplete bases Discrete
More informationVibration based Fatigue Damage Assessment of Cantilever Beams
5 th National Conference on Machines and Mechanisms NaCoMM-8 Vibration based Fatigue Damage Assessment of Cantilever Beams N. Harish Chandra, A.S. Sekhar Abstract This paper explores to relate total fatigue
More information