IDENTIFICATION OF SYSTEM PARAMETERS OF MULTI- STOREY BUILDINGS WITH LIMITED SENSORS

I declare that the work presented in the thesis entitled "Identification of System Parameters of Multi-Storied Buildings with Limited Sensors" in fulfillment of the requirement for the degree of Doctor of Philosophy is an authentic record of my own work. at the Department of Civil Engineering of the Institute. Nripen Kalita, the technical staff of the laboratory for constant help in preparing and experimenting with test models.

ABSTRACT

Studies on laboratory test models with and without infill walls were carried out separately. Modal analyzes of all numerical models were performed to evaluate the natural frequencies.

LIST OF TABLES

139 Table 5.11 Peak ground accelerations of different models 141 Table 5.12 Modal frequencies of the numerical model of the W-I test model for. 143 Table 6.1 Distribution of sensors on different floors of the model building 148 Table 6.2 Peak acceleration values of recorded responses corresponding to.

Table 5.9 First storey stiffness in (10 6 ) N/m of test model with equivalent diagonal strut using various recommendations

4.11(A) Response at first floor and roof levels of initial numerical models due to El Centro (1940): Comp – 180 earthquake input.

Fig. 6.1 Pictorial view of the BSNL building 147

LIST OF SYMBOLS AND ABBREVIATIONS

K Global stiffness matrix for a symmetrically designed shear structure KT Global stiffness matrix for a torsionally coupled shear structure , , , , , Stiffness submatrices .. kd Stiffness of diagonal brace .. kD Stiffness of diagonal brace with opening kl Lateral stiffness of infill wall. M Global mass matrix for symmetrically designed shear structure MT Global mass matrix for torsionally coupled shear structure Mi Ground mass submatrix i.

INTRODUCTION AND LITERATURE REVIEW

INTRODUCTION

Conventional Nondestructive Testing (NDT) Technique
Vibration Characterization Based Technique

SHM helps identify structural damage by identifying changes in structural properties. Changes in the modal properties of structures play an important role in identifying damage to structures.

Table 1.1 Classification of structural health monitoring techniques [Rytter 1993]

LITERATURE REVIEW

Traditional Damage Detection Techniques
Conventional Techniques Based on Vibration Characteristics
System Identification Based Techniques

NExT and ERA were used to identify the natural frequencies and mode shapes of the structures. In the second phase, the identification of the second-order dynamic modal parameters from the realized state space model was carried out.

OBJECTIVES AND SCOPES OF STUDY

Identification of system parameters for an existing symmetrical multi-storey building with limited sensors. Identification of system parameters for an existing asymmetrical multi-storey building through system identification.

OVERVIEW OF THE THESIS

Then, the comparison of the identified system parameters of the laboratory test models with those obtained from the corresponding ones. Then, the results of identifying the system parameters of a torsionally coupled multi-story shear building using multidirectional acceleration histories are presented.

DESCRIPTION OF SELECTED SYSTEM IDENTIFICATION TECHNIQUES

INTRODUCTION

Fundamental Equations
Extraction of Normal Modes for Symmetric-Plan Shear Building
Extended Random Decrement Method for Obtaining RANDOMDEC
Ibrahim Time Domain Identification Technique
Least Squares Solution of Eigenvalue Problem
Least Square Solution of Eigenvalue Problem

In the case of a torsion-coupled building, the response matrices are constructed using free decay responses from the recorded floor responses of the building. One of the measures used to study the stability of a system is discussed in this chapter. Aψψψψ = λ The matrix AAAA is called system matrix and contains information about modal parameters of the system.

They obtained satisfactory results in most cases by setting 2(∆t) 3 equal to half the value of (∆t). Thus, the iterative approach can be used to determine the eigenvectors, eigenvalues and stiffness of the structure.

Fig. 2.1 A dynamic system with inputs, outputs and disturbances [Overschee and Moor, 1996]

STABILITY OF SYSTEMS

The system dynamics can be represented graphically by plotting their locations on the complex z-plane, whose axes represent the real and imaginary parts of the complex variable z. The amplitude is related to the damping values and the phase of will generate complex coefficients in the polynomial(z)=0.. either real or appear in complex conjugate pairs. can be represented graphically by drawing their locations on the plane, whose axes represent the real and imaginary parts of the complex wn as pole-zero plots. Many computer programs poles and zeros of a system from either the transfer function The poles can be projected in z-plane of any system and the stability of the system can be checked as in Fig.

Amplitude is related to damping values and phase. The system is similar. Thus, the pole plot in the z-plane can be used to show the stability of the identification system.

INDICES FOR DAMAGE IDENTIFICATION

Modal Assurance Criterion

If two mode shapes are not linearly correlated, the MAC factor will be zero. In much literature, the MAC is used to see the shifts in the order of mode shapes between two measurements.

CONCLUDING REMARK

Lower MAC values for the same mode shape between measurements a and b indicate that the structure has changed, possibly due to damage. These can be used to develop an oversized mathematical model using time shifting technique, after which modal parameters can be identified. The stiffness of a building system can be easily evaluated via the least squares solution of an eigenvalue problem.

However, the results are accurate when the full modal matrix and its associated modal frequencies are used. The MAC compares the mode shapes of a damaged structure with corresponding mode shapes of the same structure in an undamaged state.

DETAILS OF EXPERIMENTAL ARRANGEMENT FOR SYSTEM IDENTIFICATION STUDY

INTRODUCTION
DETAILS OF EXPERIMENTAL ARRANGEMENT FOR LABORATORY TEST MODELS

Laboratory Shake Table
Sensors and Data Acquisition System (DAS)
Details of Sample Ground Motions for Shake Table Test

INSTRUMENTATIONS OF EXISTING MULTI-STOREY BUILDINGS

Sensors and Data Acquisition System (DAS)
Details of Earthquake Excitations

PROCESSING OF RECODED DATA
CONCLUDING REMARK

DAS manufactured by Kinemetics Inc., USA (Model: Altus K2) was selected for recording and storing acceleration data measured by the accelerometers at different floor levels of the selected sample buildings. Using only useful portion of data helps to increase the efficiency of the identification process. However, the test models can only be excited in one direction using the available Uniaxial Shaking Table test facility in the laboratory.

The high-amplitude parts of the recorded excitation responses are used in the proposed identification models. The sampling frequency of the data set in DAS sometimes turns out to be much higher than the system frequency.

Fig. 3.1 Schematic diagram of instrumentation for laboratory test models

IDENTIFICATION OF SYSTEM PARAMETERS OF SCALED LABORATORY TEST MODELS

INTRODUCTION

STUDIES ON LABORATORY TEST MODELS

Similitude and Scaling
Modeling Process
Bare Frame Scaled Laboratory Test Models
Material Properties of Test Models
Scaled Time Histories
Compensating Mass for Scaled Test Models
Shake Table Test
Characteristics of Recorded Responses
Modal Parameter Identification of Laboratory Test Models
Stability of Identified System
Mode Shapes
Structural Parameter Identification

Peak acceleration values were found to increase from base to roof of each of the test models. The frequency content of the floor responses of the same test patterns is found to be almost similar. Similarly, the FFTs of the recorded data of Model II and III are examined to observe the pattern frequencies.

Identifications of modal parameters for Test Model I have been performed with responses obtained for all four different earthquake excitations separately. The geometric and material properties of the columns are taken into account according to tables 4.2 and 4.3 respectively.

Fig. 4.1 Construction of laboratory test model

STUDY OF NUMERICALLY SIMULATED MODELS OF TEST MODELS The laboratory testing of structural models are quite involved and hence any repetition of

Description of Bare Frame Numerical Models
Modal Analysis of Numerical Models and Updating of the Models
Responses of Numerically Developed Models of the Test Models

Modal and time history analyzes of the numerical models were performed to obtained modal frequencies. Furthermore, the evaluated modal parameters were compared with the identified results of the corresponding test models. It was observed that the obtained modal frequencies of all the models are slightly higher than the identified frequencies of the corresponding test models.

The frequencies based on the modal analyzes from the three updated numerical models are found to agree well with the identified frequencies of the corresponding test models. The acceleration time histories recorded at the base level of the laboratory test models presented in 4.2.8 were considered for the time history analysis of all numerical models.

Table 4.11 Comparison of natural frequencies of numerically simulated building

CONCLUDING REMARK

EVALUATION OF INFILL WALL CONTRIBUTION THROUGH SYSTEM IDENTIFICATION

INTRODUCTION

STUDIES BASED ON LABORATORY TEST MODELS

Description of Test Models with Infill Walls
Properties of Brick Masonry used for Test Models
Sizes of Openings in Walls
Shake Table Test
Stability of Identified System
Mode Shapes
Structural Parameter Identification
Evaluation of Contribution of Infill Walls
Correlation between Sizes of Wall Opening and Stiffness
Existing Recommended Methods for Infill Wall Contribution

Different sizes of openings in infill wall have been considered to study its influence on the stiffness of the model. The openings are made by cutting the infill walls of the test models from the central area. Comparison of the identified storey stiffness of test model W-I with full infill wall and those of a bare frame model is shown in Fig.

The increase in lateral stiffness due to the infill wall can be resolved along the diagonal direction to determine the stiffness of the idealized diagonal brace. Stiffness of first floor for all cases of wall openings was compared with stiffness of the corresponding bare frame models.

Fig. 5.1 Three test models with infill wall at first storey

2sin

Modal Analysis of Numerical Models

The infill walls on the first floor of the W-I test model were separately modeled with a GAP element using the recommendations given in Table 5.9 and the proposed expression. The modal frequencies corresponding to the modal shapes in the shorter direction of the model were extracted and given in Table 5.12. The estimated modal frequencies corresponding to the modal shape in the shorter direction of the building were scaled according to the similarity requirements.

The scaled modal frequencies of the full-size building with different openings have been compared with the corresponding modal frequencies of the model of test model I. A very good agreement can be observed between the scaled natural frequencies of the model of the full-size building with the corresponding modal frequencies of the numerical model of the scaled test model.

Table 5.10 Natural frequencies corresponding to mode shapes of different numerical models with different cases of wall openings

CONCLUDING REMARKS

In addition, it was observed that the stiffness of the floors decreases with the increase in the size of the opening in the infill wall. The contribution of the infill wall was found to be insignificant when the size of the wall opening becomes 45% of the total wall size. Considering the infill wall as an equivalent diagonal strut, a simple expression was proposed to estimate the stiffness of the strut.

The system identification scheme, N4SID, has proven to be an effective tool for determining the infill wall contribution for prototype buildings. The derived empirical relationships (based on data from laboratory test models) representing wall contributions as well as the influence of openings in infill walls have been observed to be independent of the scale of the building and can be very easily applied to the modeling of existing existing building.

IDENTIFICATION OF SYSTEM PARAMETERS OF AN EXISTING MULTI-STOREY SYMMETRIC-PLAN SHEAR BUILDING

INTRODUCTION

Description of the Sample Building
Details of Instrumentations
Modal Parameters Identification
Stability of the Identified System

The material characteristics of the building related to this study are presented in Appendix – A [Table A – 3]. Uni-axial accelerometers are fixed on selected floors in both the X (longest) and Y (shortest) directions of the building. Therefore, FFT plots of the recorded structural responses are obtained to observe the frequency content.

The poles of the transfer functions are drawn on the complex plane using polar coordinates according to. It can be observed that the identified frequencies of the building converged, as estimated on the basis of the measured ones.

Fig. 6.1 Pictorial view of the BSNL building

NUMERICALLY SIMULATED MODEL OF THE SAMPLE MULTI-STOREY BUILDING

Damage Identification Index
Time history analysis of the Numerical Model
Sensitivity of the Sensor Locations

The frequencies from the modal analysis were found to be lower than the identified frequencies of the existing building, as shown in Table 6.5. The acceleration responses in all floors of the numerical model in the longer and shorter directions were compared with the corresponding acceleration responses of the existing building. The comparison shows that the acceleration responses at different floors of the simulated building are very similar to the corresponding acceleration responses of the existing building.

Comparing these peak acceleration values with the peaks of correspondingly recorded acceleration responses of the existing building (Table 6.2), a very close agreement is observed. FFTs for some of the acceleration responses from the simulated building are also shown in Fig.

CONCLUDING REMARKS

However, it can be noted that the system is unstable for all the cases with single output data (Case-7). The sensor allocation case actually used for the sample building is designated as X and corresponding PIs are also shown in Fig. A very consistent estimate of the modal parameters and structural stiffness made for an existing building, which is equipped with a limited number of sensors.

It is observed that the iterative approach adopted for the identification of the entire modal matrix and the stiffness of the system for the limited sensor case is very effective. The simulated model was used to study the suitability of a limited number of sensors placed in the building.

IDENTIFICATION OF SYSTEM PARAMETERS OF TORSIONALLY COUPLED SHEAR BUILDING

INTRODUCTION

Description of Scaled Laboratory Test Model