Aalborg Universitet

Structural Time Domain Identification (STDI) Toolbox for Use with MATLAB

Kirkegaard, Poul Henning; Andersen, P.; Brincker, Rune

Publication date:1996

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Citation for published version (APA):Kirkegaard, P. H., Andersen, P., & Brincker, R. (1996). Structural Time Domain Identification (STDI) Toolbox forUse with MATLAB. Dept. of Building Technology and Structural Engineering, Aalborg University. Fracture andDynamics, No. 95, Vol.. R9642

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INSTITUTTET FOR BYGNINGSTEKNIK DEPT. · OF BUILDlNG TECHNOLOGY AND STRUCTURAL ENGINEERING AALBORG UNIVERSITET • AAU • AALBORG • DANMARK

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FRACl'URE & DYNAMICS PAPER NO. 95

Aalborg Universitetsbibliotek 530005830604

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To be presented at the 15th International Modal Analysis Conference Orlando, Florida, USA, February 3-6, 1997

P. H. KIRKE·GAARD, P. ANDERSEN & R. BRINCKER STRUCTURAL TIME DOMAIN IDENTIFICATION (STDI) TOOLBOX FOR USE WITH MATLAB OCTOBER 1996 ISSN 1395-7953 R9642

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The FRA.CTU:RE AND ;.IrYNAMIQS pap€~s are, issued for early dissemination of rese­aFch æ~ults ftcvin the Strm:tu.ral ·Fract.m::e aRd Dynamics Group at the Department of Bbt.ilding Technology and Structural En:gineerirrg, U:r~iversity ~f Aalbbrg. These papers are geiierally submitted to scientific meetings; t:c;niferenc€s or journals and should there­føre n~t b e wi<.del~ di~trib'Utecl~ Whenever pos~1ble referep.ce should be given to the final public~tiQns (.pr0:~eediBg.s;jom:hals ; etc.) · ~nd not to the Fract~re and Dyrrarnics papers.

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INS'riTUTTET FOR BYGNINGSTEKNIK DEPT. OF BUILDING TECHNOLOGY AND STRUCTURAL ENGINEERING AALBORG UNIVERSITET • AAU • AALBORG • DANMARK

FRACTURE & DYNAMICS PAPER NO. 95

To be presented at the 15th International Modal Analysis Conference Orlando, Florida, USA, February 3-6, 1997

P. H. KIRKEGAARD, P. ANDERSEN & R. BRINCKER STRUCTURAL TIME DOMAIN IDENTIFICATION (STDI) TOOLBOX FOR USE WITH MATLAB OCTOBER 1996 ISSN 1395-7953 R9642

STRUCTURAL TIME DOMAIN IDENTIFICATION (STDI) TOOLBOXFOR USE WITHMATLAB

P.H. Kirkegaard, P. Andersen & R. Brincker Aalborg University

De partment o f Building Technology and Structural Engineering Sohngaardsholmsvej 57, DK-9000 Aalborg, Denmark

ABSTRAGT

The Structural Time Domain ldentification (STOl) toolbox for use with MATLABrM is developed at Aalborg University, Denmark, based on the system identification research performed during recent years. By now, a reliable set of tunetions offers a wide spectrum of services for all the important steps of multivariate time domain system identifica­tion of time-variant as well as time-invariant civil engineering structures from ambient testing data. A graphical user interface (GUl) is also developed to make the toolbox more user friendly .

1. INTRODUGTION

The MATLAB™ program (Mathworks Ine.) is a High-Perfor­mance Numeric Camputalions and Visualization Software. MATLAB integrates numerical analysis, matrix computation, signal processing, and graphics in an easy-to-use environ­ment where problems and solutions are expressed just as they are written mathematically - without traditional program­ming . The name MATLAB stands for matrix laboratory. MATLAB was originally written to provide easy access to matrix software developed by the LINPAGK and EISPAGK projects, which together represent the state of the art in software for matrix computation. MATLAB is an interactive system whose basic data element is a matrix that does not require dimensioning. MATLAB has evolved over a period of years with input from many users. In university environments, it has become the standard instructional tool for introductory courses in applied linear algebra, as well as advanced courses in other areas. In industrial settings, MATLAB is used for research and to salve practical engineering and mathematical problems. Typical uses inelude general purpose numerical computation, algorithm prototyping, and special purpose problem salving with matrix formulations that arise in disciplines such as automatic control theory, statistics, digital signal processing (time-series analysis), etc. MATLAB also features a family of application-specific solu­tions that are called toolboxes. Very important to most users of MATLAB, toolboxes are comprehensive calleetions of MATLAB functions (m-files) that extend the MATLAB environ­ment in order to salve particular classes of problems. Areas in which toolboxes are available inelude signal processing, controlsystems design, dynamic systems simulation, systems identification, neural networks, and others. This allows one to create own applications without writing a single line of C, Fortran or other low-level code.

For system identification several toolboxes exist. System identification is a way to find a mathematical model for a physical system (like an electric motor, or even a financial market) based only on a record of the inputs and outpuls of that system. The System ldentification toolbox, Ljung [1] features a flexible Graphical User Interface (GUl) as well as identification tunetions that implement both parametric and nonparametric identification techniques. Written by Dr. Lennart Ljung, [2] a recognized leader in the field of system identification, the toolbox contains carefully implemented algorithms to ensure efficiency and reliable numerical results. All the data sets and models created with the GUl are represented by icons. An entire session of data and models, along with relevant diaries, can be saved for reloading at a later time. The Frequency Domain System ldentification Toolbox, Kellår [3], Kailår et al. [4], contains tools for accurate modeiling of linear systems with or without delay. The modelsaretransfer tunetions in the s-domain or in the z-domain . The procedures inelude excitation signal design, data preprocessing, parame­ter estimation, graphical presentalion of results, and model validation (tests, uncertainty bounds, modeiling errors). The two menticned toolboxes are official , sold by Mathworks Ine, while the foliowing system identification toolboxes mentione are unofficial. The SSID toolbox, Mckelvey [5] provides identification routines for identification of multivariable state-s pace models from input/output data. The main feature of the toolbox is that the models do not use the standard identifyable state-space parameterizations but a full parametrization of all state-space matrices. In arder to use the SSID-toolbox the System ldentification Toolbox, Ljung [1] , is required. The SENSTOOLS toolbox, Knudsen [6], is a toolbox for direct estimation of physical/continuous-time parameters in linear and nonlinear systems from input-output measurements. The m-files are tunetions for input signal design , parameter estimation and model validation. The NNSYSID toolbox [7] is a neural network based nonlinear system identification toolbox which contains a large number of tunetions for training and evaluation of multilayer perceptron type neural networks. The main focus is on the use of neural networks as a generic model structure for the identification of nonlinear systems. However, in order to use the above-mentioned toolboxes for identification of structural systems one is missing tunetions for the estimation of the modal parameteres and mode shapes. Recently, same MATLAB toolboxes made for solving structural engineering identification problems have been presented.

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The purpose of the Structural Dynamics Toolbox, Balmes (8] is to provides low cost , modular, and versatile access to methods in experimental and analytical structural dynamic modelling. The toolbox ineludes tunetions for experimental modal analysis , Finite Element analysis and Finite Element design and update. A GUl provides a layer of predefined operations for Frequency Response Function visualization and analysis, identification and 3-D deformation animation. The X-modal modal analysis software package, Phillips et al. (9], was delveloped as a collaboration between the University in Cincinnati and the industry. The software is basedon The Unified Matrix Polynomia Approach (UMPA), Fladung et al. [1 O] . The unified approach to modal parameter estimation within the context of X-modal invloves not only the formulation of the algorithms, but also the presentalion of their controiling parameters. This software package was programmed using the MATLAB language, The 'C' language and the X windows system. However, a MATLAB toolbox consisting of only m-files for structural system identification based on time domain techiques is to the authors' knowledge not available. Therefore the members of the Structural Time Domain Edentification group at Aalborg University, Denmark, decided to develop the STOl toolbox, Andersen et al. [11] based on the system identification research performed during recent years. By now, a reliable set of tunetions offers a wide spectrum of services for all the i m partant steps of multivariate time domain system identification o f time-invariant as well as time-variant civil engineering structures from ambient testing data. These tunetions have mainly been developed as a part of the research presented in Andersen [12], Kirkegaard et al. (13] and Kirkegaard et al. [14] Since the STOl toolbox is mainly developed for identification of civil engineering structures a large part of the tunetions is implemented from a civil engineering point ofview, i.e. nearly all the implemented parameter estimation algorithms only use output data (ambient testing). Same of the alorithms also work on input - output data. The tunetions are usable either as stand-alane tunetions or through a menu driven GUl, for frequent and infrequent users, respectively. l.e. the GUl is a compiement rather than an alternative: all tunetions can either be run in command mode or in GUl mode, and one can freely mix the two modes. The goal is, however, that the typical user should be able to run any application en: •ly in GUl mode if he or she prefers that. The whole toolbox IS entirely written as MATLAB m-files, so it can be executed from any platform that is supported by MATLAB. Windows-MATLAB is required in arder to use the developed GUl . The toolbox is not dependent on other MATLAB toolboxes. The aim of the present paper is to present an overview of the STOl toolbox.

2. AN OVERVIEW OF STOl FUNCTIONS

This section describes of the type of tunetions in the Structural Time Domain ldentification Toolbox by listing tunetion-types grouped by subject area. The overall objective of developing the STOl toolbox has been to make a set of tunetions for system identification of civil enginering. However, the aim has also been to make tunetions to facilitate the system identification process. The first step in the identification process is to "book-keep" the identification step and acquire data. Figure 1 shows that STOl offers tunetions for "book-keeping", structural geometry

preprocessing (nessary for showing mode shapes) and algorithms for making the interface to data acquisition PC plug-in cards.

For preprocessing of the data the STOl toolbox contains a whole range of functions, see tigure 2. The preprocessing makes the measured signals suitable for . identification. Further, the preprocessing fucntions can be used to show and to estimate statistical charateristics of the measured data. For identification the STOl to9lbox ineludes algorithms for identification of time-invariant systems, see tigure 3 ::; s well as time-variant multivariate systems, see tigures 3 and 4. Apart from the well-known system identification techniques also a subspace identification algorithm (N4SID), Van Overschee et al. [15] is implemented. The acronym N4SI D stands for Numerical algorithm for Subspace State Space System ldentification. For assessing the "quality" of the identified models the STOl toolbox offers several functions, see tigure 5 such as FPE and AIC criteria, plot of the poles and zeroes, plot of the match of the power spectrum obtained by a Fast Fourier Transformation and the spectrum obtained from the identified model. Also tunetions to make plots of the spectrum and autocerrelation of the residual time series are given, and tunetions to compare the model output with recorded output. After model validation, or combined with model validation, one has to select a model. The STOl toolbox gives several tunetions for model selection, mainly stabilization diagrams, see tigure 6. When a model has been selected and the modal parameters have been estimated it is important to be able to qunatify the uncertainty of the estimated parameters. Thi s is possible for same of the identification algorithms in the STOl toolbox, see tigure 7. After an appropriate model has been validated and selected the system identification results have to be exported. Here the STOl toolbox offers functions, see tigure 8, for making data tables with modal parameters and plots of e.g. mode shapes and measured data etc. Sesides the tunetions directly used in the identification process, a lot of auxiliary tunetions are implemented , e.g. tunetions for : transformation between continuous models and discrete models, handling and evatuating state- space systems, Random Decrement estimation, matrix polynomia calculations etc.

Project book-keeping (load, save .. .. )

Structural geometry preprocessing

Data acquisition (Interface to Data Translation plug-in AD-baards, load/save data files acquired in other data acquistion enviroments)

Figure l Information Importing.

Scaling and trend removal

Removal of outliers

Show measured data

Show FFT/Autocoriance functions of measured data

Estimates of moments (mean, standard deviation .. )

Low, high or bandpass filtering

Decimalion and resampling

Split up into identification and validalien data sets

Figure 2 Preprocessing.

2-stage LS estimation of an ARMAV model

Non-linear LS estimation of an ARMAV model

LS estimation of an ARV model

Eigensystem Realizalien Algorithm (ERA, ERAIDC)

Matrix block Hankel (MBH)

Subspace Methods (N4SID)

Figure 3 Parameter Estimation.

Recursive non-linear LS estimation of an ARMAV model

Recursive pseudo-linear estimation of an ARMAV model

Recursive least-square estimation of an ARV model

Kaiman filtering

Recursive instrumental variable method

Figure 4 Recursive Parameter Estimation.

FPE - Final Prediction Error Criterion

Al C - Akaike's Information Theoretic Criterion

Plot prediction errors

Plot measured and predicted response

Plot poles and zeros

Compares spectral densities of one or several istructures with response data

Figure 5 Model V alidation .

Modal Assurance Criterion

Coordinated Modal Assurance Criterion

Modal Confidence Factor

Eigenfrequency stabilizalien diagram

Damping ratio stabilizalien diagram

Mode shape stabilizalien diagram

Modal stabilizalien diagram

Figure 6 Mode Selection Functions.

Returns the covariance matrix of the estimated parame­ters

Compule the uncertainties of the modal parameters

Figure 7 Assessing Model Uncertainty.

Tables with the estimated modal parmaters

Mode Shape Animation

Documentation (final report generating)

Figure 8 Information Exporting.

3. THE STOl GUl

All the tunetions presented in section 2 are stand-alone tunetions which can run in command-line mode. However, to make a more user-friendly toolbox, the STOl toolbox ineludes a Graphical User Interface (GUl). Recently, GUl toolboxes for system identification have been presented, see Ljung [14] and OeMoor et al. [16]. The latter is not written for use with MATLAB but Xmath. A GUl system identification toolbox belongs to a third generation software with the foliowing benefits , see OeMoor et al. [16]

- the user can tackle much more serious problems because helshe is releaved from programming subtleties ( atmost all o f the interaction with the software happens via the mouse button s)

- implies that book-keeping of tasks, models, data sets and interconnections, becomes relative/y straightforward

- there is quite some user guidance by the GU/ in terms of options and defaults that can be chosen

- GU/s a re user friend/y and one c an team to work with them in a couple of minutes, without the necessity of going through thick manuals

To motivate the use of GUl for system identification a short history of user-interfaces is given in OeMoor et al . [16]. They split the user interfaces up in the three stages: Program User Interface, Command-line User Interface and Graphical User Interface. The Program User Interface is the era of lower level programming (Fortran, Pascal and C). Typically, the user­input consisted of programs with low level commands. The Command-line Interface allows the user to enter commands at the command-line. Contrary to the previous generation, the effect of the commands could immediately be inspected. The Graphical User Interface is made up of graphicl objects such as menus, buttons and plots. Using it is straightforward since it only requires manipulation of the three mouse buttons an at rare accasios, typing in the name of an object or data file. An overview of the discussion of user interfaces in OeMoor et al. [16] is given in table 1. The cernbination of powerful numerical algorithms for system identification and an GUl leads to intelligent and user-friendly identification software. The GUl in the STOl toolbox makes it possible to run the identification process entirely in GUl mode, or a cernbination of GUl modes and command-line mode. The GUl is developed to handle the different kinds of tunetions presented in figures 1 - 8. An example of an GUl is hsown in figure 9. This GUl can be used to animate mode shapes atter a model has been established.

4. CONCLUSIONS

The present paper gives an overview of the GUl based Structural Time Oomain ldentification (STOl) toolbox for use with MATLAB™ is developed at Aalborg University, Oenmark. The toolbox offers a reliable set of tunetions for all the important steps of multivariate time domain system identifica­tion of time-variant as well as time-invariant civil engineering structures. Further, the paper decribes how user-friendly identification software is obtained by combing numerical algorithms for identification with an GUl.

Input programs command- graphical line

Output text variables graphical

Element low Level high level window

Start Level very high high lo w

Flexibility lo w high high

User gui- none Jimited high dance

Syntax complex complex simple

Expertise high high Jimited

Computer simple simple fast

Date 1960- 1982-1990 1990-? 1982

Table 1 Comparison of the distinct stages in the history of identification and control software, OeMoor et al. [16].

Figure 9 A Graphical User Interface for mode shape anima­tion.

_ FRACTURE AND DYNAMICS PAPE'RS . .

PA:PER NO. 59: P. H. Kirkegaard & A. Rytter: A Comparative Study of Three Vibr{Ltion Based Damage Assessment Techni·ques. ISSN 090Q-7513 R943·5.

PAPE.R NO. 60: p_. H. Kirkegaard, J. C. Asmussen, P. Andersen & R. ~rincker: An Experimenta,l Study of an Offshore Pl'atform. ISSN 090Q-7513 R9441.

PAPER NO. 61: R. Brincker, P. Andersen, P. H. Kirkegaard, J . P. Ulfkjær: Damage Detection in Labaratory Concrete Beams. ISSN 0902-7513 R9458.

PAPE.R NO. 62: R. BriFH.:ker, J. Simonsen, W. Hansen: $om€ Aspecis of Formati·on of Cracks in FRC with Main Reinforcement. ISSN 0902-7513 R9506.

PAPE.R NO. 63: R. Brincker, J. P. Ulfkjær, P. Adamsen, L. Langvad, R. Toft: . Analytical Model for Hook An.chor Pull-out. ISSN 0902-7513 R9511.

PAPER NO. _64: P. S. Skjærbæk, S. R. K. Nielsen, A. ~- Qakmak: Assessment 4 Damage in Seismically Excited RC-Structures from a Single Measured Response. ISSN 1395-7953 R9528.

PAPER NO. 65: J. C. Asmussen, S. R. Ibrahim, R. Brincker: ·Random Decrement ·and Regressi'On Analysis of Traffie Respønses of Bridges. ISSN 1395-7953 R9529.

PAPER NO. 66: R. Brincker, P. Andersen, M. E. Martinez, F. Tallav6: Modal Analy­sis of an Offshore Platform using Two Different AR~A Approaches, ISSN 1395-7953 _ R9531.

PAPER NO. 67: J. C. Asmussen, R. Bri:ncker: Estimation of Frequency Respons.e Fun­ctions by Random Decrement. ISSN 1395-7953 R9532.

PAPER NO. 68: P. H. Kirkegaard, P. A,o.dersen, R. Brincker: Identification of an Equivalerd Linear Model for a Non-Linear Time- Variant RC-Structure. ISSN 1395-7953 R9533.

PAPER NO : 69: P. H. Kirkegaard, P. Andersen, R. Brincker: Identificalion of the Skirt Pil ed Gullfaks C Gravity Platf?rm using ARMA V M od els. ISSN 1395-7953 R9534.

PAPER NO. 70: P. H. Kirkegaard, P. Andersen, R. Brincker: Identification of Civil Engineering Structures using Multivariate ARMAV and RARMAV Models. ISSN 1395-7953 R9535.

PAPER NO. 71: P. Andersen, R. :Srincker, P. H. Kirkegaard: Theory of Co·variance Equivalent ARMAV Models of Civil Engineering Structures . . ISSN 1395-7953 R9536.

PAPER NO. 72: S. R. Ibrahim, R. Brincker, J. C ~ Asmussen: Modal Parameter Iden­tification from Respønses of General Unknown Random lnp~·ts.ISSN 1395-7953 R9544.

PAPER NO. 73: S. R. K. Nielsen, P. H. Kirkegaa.Fd: Active Vibration C~ntrol ofa Monopile Offshore Structure. Part One - Pilot Proje_ct. ISSN 1395-7953 R960@.

PAPER NO. 74: J. F. Ulfkjær, L. Pilegaard Hansen, S. 'Qvist ; S. H. Maasen: Fracture . Energi; o f Plain Concrete Beams at Different Rates . o f Loading. ISSN 13.95~ 7953 R9610.

PAPERNO 75: J. P. Ulfkjær, M. S. Henriksen, B. Aarup: Experimental Investigation of th€ Fracture Behaviour of Reinforced Ultra High Str€ngth Concrete. ISSN 1'395-7953 R9611. .

FRACTURE AND DYNAMICS PAPERS

PAPER NO. 76: J. C. Asmussen, P. Andersen: Identification of EURO-SEIS Test Structure. ISSN 13~5-791»3 R9612.

PAPER NO. 77: P. · S. Skjærbæk, S. R. K. Ni~lsen, A. S. Qakmak: Identification of Damage in RC-$tructures from Earthqua,ke Records - Optimal Location· of Sensors. lSSN l395-7953 R9614.

PAPER NO. 78: P. Andersen, P. H. Kirkegaard, R. Brincker: System Identification of ,, Civil En(Jineering Structures using State Space and ARMAV Models. ISSN 1395-7953

R9618.

PAPER NO. 79: P. H. Kirkegaard, P. S. Skjærbæk, P. Andersen: Identification of Time Varying Civil Engineering Structures using Multivariate Recursive Time Domain Models. ISSN ·1395-7953 R9619.

PAPER NO. 80: J.: C. Asmussen, R. Brincker: Estimation of Correlation Functions by Random Decrement. ISSN 1395-7953 R9624.

PAPER NO. 81: M. S. ·Henriksen, J. P. Ul:fkjær, R. Brincker: Scale Effects and Tran­sitional Failure Ph(momena of Reinforced concrete Beams in Flexure. Part 1. ISSN 1395-7953 R9628. ·

PAPER NO. 82: P. Andersen, P. H. Kirkegaard, R. Brincker: 'Filtering out Environ­mental Effects in Damage Detection of Civil Engineering Structures. ISSN 1395-7953 R9e33.

PAPER NO. 83: P. S. Skjærbæk, S. R. K. Nielsen, P. H. Kirkegaard, A. S. Qakmak: Case Study of Local Damage Indicators for a 2-Bay, 6-Storey R C-Frame · subject to Earthquakes. ISSN 1395-7953 R9639.

PAPER NO. 84: P. S. Skjærbæk, S. R. K. Nielsen, P. H. Kirkegaard, A. S. Qakmak: Modal Identification of a Time-Invariant 6-Storey Model Test RC-Frame from Free De­cay Tests using Multi- Variate Models. ISSN 1395~7953 R9640 .

. PAPER NO. 91: P. S. Skjærbæk, P. H. Kirkegaard, G. N. Fouskitakis, S. D. Fassois: Non-Sta-tionary Modelling and Simulation of Near-Source Earthquake Ground Motion: ARMA and Neural Network Methods. ISSN 1395-7953 R9641.

PAPER NO. 92: J. C. Asmussen, S. R. Ibrahim, R. Brincker: Application of Vector Triggering Random Decrement. ISSN 1395-7953 R9634.

PAPER NO. 93: S. R. Ib:rahim, J. C. Asmussen, R. Brincker: Theory of Vector Trigge­ring Ra.ndom Decrement. ISSN 1395-79153 R9635.

PAPER NO. 94: R. Bri11cker, J. C. Asmussen: Rand·om Decrement ·Based FRF Esti­mation. ISSN 1395-7953 R9636.

PAPER NO. 95: P. H. Kirkegaard, P. Andersen, R. Brincker: Structuml Time Domain Identification (STD9 Toolbox for Use with MATLAB. ISSN 1395-7953 R9642.

PAPER NO. 96: P. H. Kirkegaard, P, Andersen: State Space, Identzfication of Civil Engineering S truetures from Output M easurements. ISSN 1395-7953 R9643.

Department of BuHding Technology and Structural Engineering Aalborg URive,rsity, Sohngaarclsholmsvej 57, DK 900Q Aalborg Telephøne: +45 98 15 85 22 Telefax: +45 98 14 82 43