FEM UPDATING OF EXISTING STRUCTURES BASED ON AMBIENT VIBRATION MEASUREMENTS Elena Dumova-Jovanoska*1, Goran Markovski*2, Sergey Churilov*3 *
University “Ss. Cyril and Methodius”, Faculty of Civil Engineering Skopje/Macedonia 1
[email protected],
[email protected],
[email protected]
Abstract This paper presents methodology for FEM updating and definition of genuine calculation model for existing structures based on estimation and identification of structural modal parameters by ambient vibration measurements. Obtained experimental results are used for modal updating of material parameters of the initial finite element calculation model with the help of extracted natural frequencies and mode shapes. Manual model updating by variation of several key material parameters was performed. Thereby, a model which reflects real bearing capacity of the building was obtained. Keywords - Ambient vibration, model, existing structure, capacity.
1
INTRODUCTION
The design and construction of complex structures and the new trend of predicting damage in existing structures stimulate structural engineers to develop appropriate experimental tools to evaluate the structural behavior over time using monitoring techniques (process called Structural Health Monitoring). In the short, medium or long term monitoring processes, static and dynamic data are collected, which can then be used for numerical analysis, such as in a process of model updating or damage identification. The aim of static monitoring is to observe phenomena with small variations on time, such as displacement variations during construction, a crack or tilt progress, or monitor environmental conditions. On the other hand, the aim of dynamic monitoring is to observe fast time-dependant phenomena. Dynamic monitoring systems also allow modal identification in terms of identifying resonance frequencies, damping and mode shapes. Static monitoring is beyond the scope of this work and only dynamic monitoring will be addressed next. For structural dynamic monitoring, depending on the excitation source, two different groups of techniques are currently used, namely, Input-Output and Output-Only techniques. InputOutput techniques are based on the estimation of a set of Frequency Response Functions (FRFs) relating an applied force to the corresponding response at several points along the structure. Testing civil engineering structures with forced vibration generally requires a large amount of specialized equipment and trained personnel, making the tests difficult and expensive. Additionally, when automated health monitoring systems are implemented, force vibration tests are not a suitable alternative. For these reasons, simpler tests in which the structures are excited just by ambient vibration, called Output-Only techniques, are desirable and often used.
During the last years, the technological developments in the field of sensors made feasible the accurate measurement of low levels of dynamic responses strongly stimulating the development of the Output-Only identifications methods, also called Operational Modal Analysis (OMA). Output-Only methods are based on the premise that wind, traffic and human activities can adequately excite structures. The main assumption of the Output-Only identification methods is that the ambient excitation input is a Gaussian white noise stochastic process in a frequency range of interest. Due to the nature of the excitation, the response includes not only the modal contributions of the ambient forces and the structural system, but also the contribution of the noise signals from undesired sources. In this way the measurements reflect the response from the structural system and also from the ambient forces, meaning that the identification techniques must have the ability to separate them. Output-Only modal identification methods are divided in two groups, namely, nonparametric methods, essentially developed in frequency domain, and parametric methods, developed in time domain. Calculation models based on finite element method (FEM) usually used for dynamic analysis of buildings are idealized models constructed in a suitable way to represent structure’s behaviour under different dynamic loads, like: earthquakes, strong winds, explosions and etc. They can be controlled by experimental tests on buildings in real size through ambient and forced vibrations (Ivanović et al., 2000). Both methods can be used to identify the dynamic properties of the structural system of the building, namely: natural frequencies, damping coefficients and mode shapes. Ambient vibration tests (AVT) are used to describe the structural behaviour in the linear range because the amplitudes of vibrations are small. These tests can be used to determine the structural behaviour of damaged buildings and their components, and also to develop structural models and time and amplitude dependant analysis algorithms for structural health monitoring and structural control studies. The basic advantage of ambient vibration tests over forced based tests is the light and mobile equipment used to perform the tests and the small number of operators involved in the process. The most common sources of ambient vibrations are: wind, soil micro tremors and different local periodical or random excitations (traffic or heavy machinery). Forced vibration tests are performed by attracting large forces acting on the inspected buildings which can produce useful response amplitudes. These forces are created with vibration devices usually positioned on the top of the building. This causes significant excitation of modes of oscillation with greater amplitudes at the higher levels of the building. Ambient vibration tests are conducted in Macedonia for more than 30 years. Generally, they are performed on structures with significant cultural, historical, political and economical values: historic monuments, dams, bridges and etc. Buildings were rarely tested, except buildings which according to “Code of Technical Regulations for the Design and Construction of Buildings in Seismic Regions” (PIOVSP, 1981) are classified in out-ofcategory and category I. Buildings classified in other categories were never tested. Today’s development of measuring equipment, ambient vibration tests and modern technologies for data transfer and monitoring of measured results allows easy and simple application of this method to regular building structures. Such system developed by American company Digitexx Data Systems Inc. was applied to an existing building in Macedonia. The system is composed of portable electronic device for data acquisition (PDAQ), laptop computer and acceleration sensors connected with high quality cables.
2
USED METHODOLOGY FOR FEM UPDATING
This paper describes in details a methodology for FEM updating and definition of genuine calculation model of an existing building with the help of ambient vibration measurements and experimental modal analysis. Within the suggested methodology a calculation model is obtained which fully represents the real structural behaviour. The updated model can be used for different linear and nonlinear, dynamic and seismic analyses and with great efficiency can be used to determine structural vulnerability and possible needs for retrofit. If used in permanent or periodical monitoring this system can detect possible damage of the structural system. The experimental modal analysis uses "Output-only modal identification" which is utilized when the modal properties are identified from measured responses only. "Output-only modal identification" is also known by the terms "ambient identification" or "ambient response analysis" within the field of civil engineering. The basic principle in modal identification is the determination of modal parameters from experimental data. The usual modal parameters are natural frequencies (the resonance frequencies), damping ratios (the degree to which the structure itself is able of damping out vibrations) and mode shapes (the way the structure moves at a certain resonance frequency). The common way is to use input-output modal identification where the modal parameters are found by fitting a model to a Frequency Response Function, a function relating excitation and response. When modal identification is based on the measured response (output) only, things become more complicated for several reasons: the excitation (input) is unknown and the measured response (output) is often noisy. Output-only modal identification is used for analyzing large civil engineering structures, operating machinery or other structures that are not easily excited artificially. Large civil engineering structures are often excited by natural loads that cannot easily be controlled, for instance wave loads (offshore structures), wind loads (buildings) or traffic loads (bridges). For operating machinery the problems are the same. They are also excited by natural sources like noise from bearings or vibrations from the environment around the structure. In these cases, it is an advantage to use output-only modal identification. Instead of exciting the structure artificially and dealing with the natural excitation as an unwanted noise source, the natural excitation is used as the excitation source. The unknown loading conditions of the structure are assumed to be produced by a virtual system loaded by white noise. The white noise is assumed to drive both the real structural system and the virtual loading system as a total system and not only the structural system (Ibsen and Liingaard, 2006). A flow chart describing the methodology is presented in Fig. 1. The methodology is established on dynamic-based assessment which involves analytical and operational modal analysis. The analytical modal analysis consists of identification of dynamic properties using FE method. The FE model is created according available geometry and material data. Operational modal analysis considers extraction of modal parameters (natural frequencies, damping and mode shapes) from output-only experimental data obtained by AV tests. The need for model updating is checked by comparing the difference between FEA and OMA results. If the difference is less than certain established criteria, than the FE model is optimal. On contrary, the model needs updating. Usually it is done by modifying selected parameters in FE model until calculation results do not match experimental. The following list summarizes the used methodology in FEM updating process of existing structures with all necessary steps: -
Development of a FEM of the structure under consideration;
-
o
Through survey of the design project documentation if available;
o
By destructive tests of samples taken out of the building;
o
By non-destructive testing: ultrasonic, magnetic particle testing, resonance method, thrust hardness test and etc.
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Numerical analysis of FE model by modal analysis to obtain dynamic properties of the building: natural frequencies and mode shapes.
-
Ambient vibration tests to obtain experimental dynamic properties: natural frequencies, damping ratio and mode shapes. This step requires:
-
-
3
Selection of material properties for FE model based on existing data:
o
Proper selection and location of measuring points;
o
Use of sophisticated testing equipment and trained personnel;
Analysis of experimental data by performing Operational modal analysis (OMA) to identify modal properties of the building. This step requires: o
Selection of appropriate method for analysis in time and/or frequency domain;
o
Application of reliable software program to estimate frequency and mode shapes.
FEM updating to calibrate the calculation model to experimentally obtained modal parameters.
DESCRIPTION OF THE BUILDING
The analysed building is operational and a primary school “Vojdan Chernodrinski” is located in their premises. This building was selected for research and application of the developed methodology as a typical example of a building from the city of Skopje from several reasons. The building was constructed before catastrophic 1963 Skopje earthquake and according PIOVSP’81 it is classified in category I. For such buildings it is extremely important to survive future earthquakes without serious damage of the structural system and to protect the lives of the residing young children. In order to execute dynamic analysis of an existing building with real calculation model it is necessary to have the geometry data available, as well as data for construction material and mass distribution in layout and along the height. Therefore, design project documentation for the building was discovered from the Archives of Macedonia. Although incomplete, it was useful to determine some necessary data. It was discovered that the building was constructed in 1952; it consists of ground floor and 2 upper floors with rectangular shape in layout and dimensions 53.58 x 10.18 m, see Fig. 2. From the available documentation it was found out that the structural system is confined masonry composed of solid brick units and mortar with unknown properties and regularly spaced reinforced concrete (RC) columns made from concrete class MB16 and certain number of RC beams from MB22 which connect few columns while others are located over openings. The floors were designed and constructed as ribbed slabs from concrete MB22. The building was designed taking into account vertical gravitational loads only as seen in the design documentation. Typical views on the building are given in Fig. 3.
AMBIENT VIBRATION TESTING
FINITE ELEMENT ANALYSIS (FEA)
OPERATIONAL MODAL ANALYSIS (OMA)
FEA Responses (natural frequencies, mode shapes)
OMA Responses (natural frequencies, mode shapes)
Difference R between FEA and OMA MODEL UPDATING
No
Min R?
Yes
OPTIMAL MODEL
Fig. 1. Dynamic-based assessment for existing structure. With the purpose for determination of the real geometry, detailed on-site measurements were performed which confirmed many design parameters, but also notified some significant differences of the actual building configuration from the original documentation. The survey of the documentation and the current state of the building verified presence of RC columns which function as a confinement of the masonry, while the floors were assessed to have sufficient in-plane rigidity and can be treated as rigid diaphragm in the analysis. Complete information about the properties of the construction material was missing, except very few parameters given in the original documentation. Because it was impossible to perform destructive tests and extract test samples from the building, the only possible method to find out the material properties was to conduct non-destructive tests and to use ambient vibration measurements to determine the bearing capacity of the building. Therefore, series of ambient vibration measurements were carried out and these results were used to update the FE model of the building.
Fig. 2. Typical building layout.
Fig. 3. a) North-West and b) West-East view of the building.
4
FE MODELING AND IDENTIFICATION OF DYNAMIC PROPERTIES
Initial 3D calculation FE model of the building based on geometry survey was developed prior performing the AV tests, see Fig. 4. Masonry and floor slabs were modelled with 4-node shell FE, while RC beams and columns with frame elements. To obtain proper mass distribution in the model and to correctly represent openings in the masonry walls relatively large number of FE was used. In creation of the model several assumptions were followed. It was assumed that the model is fully fixed at the supports, masonry was assumed to have constant unit weight of 19.6 kN/m3 and Poisson ratio of 0.15, while the Young’s modulus was taken as 2800 MPa. RC elements were modelled with material properties according to their design class. Floor slabs were modelled as absolute rigid in their plane. In order to determine the dynamic properties of the structure, modal analysis was performed. Beside the mass from the self-weight of the structural elements, additional mass from the dead load calculated according the design project specification was applied. Calculated natural frequencies and periods for the first 6 mode shapes of the initial calculation model are given in Table 1.
а)
b) Fig. 4. 3D calculation FE model: (a) South-East view, (b) North-West view.
Table 1. Natural frequencies and periods of the initial calculation model. Mode 1 2 3 4 5 6
Frequency (Hz) 5.33 6.58 7.80 8.78 12.34 12.98
Period (sec) 0.19 0.15 0.13 0.11 0.08 0.08
The building responds with translation oscillation in north-south direction in the first mode and small rotation which originates from the stiffness difference of the structure in the part where classrooms are located and the stairways. In second mode the structure oscillates with torsion, while translation in east-west direction is dominated in the third mode. The first 3 mode shapes are shown in Fig. 11.
5
TEST DESCRIPTION AND METHOD FOR ANALYSIS
Three series of AV tests were conducted on August 18, 2011. Each series contains results from acceleration sensors of each floor, while fixed reference sensors (T1) were located on the top floor. Calibration of the sensors was applied prior each measurement. Total recording time was 212 sec, and sampling frequency was fixed to 200 Hz.
5.1
Test equipment
To measure ambient vibration effects on the building, Digitexx PDAQ Premium portable system with physical dimensions 457 x 330 x 170 mm as shown in Fig. 5 was used. This system supports data acquisition and analysis from distance. Main characteristics of the system are: 16 channels, 24 bits, local and remote real time data analysis, FFT, transfer functions, interstorey drift based on FEMA 351 and 274 seismic safety standards, hysteresis curve for the interstorey drift, computation of acceleration, velocity and displacement. This system is best option for permanent structural health monitoring for a period up to 6 months. The main characteristics of the acceleration sensors are: uni- and tri-axial micro electro-mechanical capacity sensors with wide dynamic range
+/- 3g, perfect band and ultra low noise, which make them ideal for structural health monitoring, Fig. 6.
5.2
Arrangement of the test equipment and measurement
AV tests were accomplished with uniaxial (U) and triaxial (T) acceleration sensors and measurements in 9 points on each floor. Fig. 7 schematically presents the layout and arrangement of the sensors on the second floor, cable disposition and measurement direction of the sensors. The arrangement of the test equipment on the other floors is identical, while the roof floor was not measured due to its inaccessibility. PDAQ device was transferred on each floor prior the measurements. All sensors were placed carefully and levelled on the hard ‘terazzo’ flooring, except sensors U2 and U7 which were placed over hard wood flooring. A view of the PDAQ and sensor location in school hallway is presented in Fig. 8. While the measurements were on their way, there were no other people present in the building, apart from the test operators who stayed still during the recording time. There were no active heating and cooling devices turned on, and the running water in the building was stopped. The recording was carried out between 10 am and 2 pm. The outside temperature was in the range 26-330C. Total number of measurement points from all three series were accelerations were recorded was 27. The recorded analog signals were digitized and saved in ASCII format on the hard disk of the computer used for data acquisition.
Fig. 5. Digitexx PDAQ Premium.
Fig. 6. Digitexx D110-T triaxial sensor.
Fig. 7. Sensor location in the second floor.
Fig. 8. PDAQ and U1 sensor location.
5.3
Methods for analysis of the measured data
For analysis of the complex non-stationary nature of the measured excitations it is necessary to use techniques for identification of the dynamic properties based on Output-Only experimental data, like: Frequency Domain Decomposition (FDD), Enhanced Frequency Domain Decomposition (EFDD) and Stochastic Subspace Identification (SSI) methods (ElBorgi et al., 2005). These methods were successfully applied to buildings and bridges and are implemented in ARTeMIS software (ARTeMIS, 2011). The essence of the FDD technique is to perform an approximate decomposition of the measured system response into a set of responses of independent single degree of freedom (SDOF) systems, one for each mode. The decomposition is performed by a Singular Value Decomposition (SVD) of each of the spectral density matrices obtained from the measurements. The results of the decomposition are a set of singular values and associated singular vectors. The singular values are estimates of the auto spectral density of the component SDOF systems, and the singular vectors are estimates of the mode shapes. A further refinement of the FDD, the Enhanced Frequency Domain Decomposition method in ARTeMIS, uses the modal estimates from the FDD technique to identify the bell-shaped spectral functions of the SDOFs. From these functions, it estimates additional modal parameters such as modal damping (El-Borgi et al., 2005). The time domain estimation is based on Stochastic Subspace Identification technique. In the SSI techniques a parametric model is fitted directly to the raw time series data obtained from the accelerometers. The parametric models are characterized by the assumption of a mathematical model constructed from a set of parameters, where the mathematical model is a linear and time-invariant system of differential equations. The task of the SSI technique is to adjust the parameters in order to change the way the model fits to the data. In general the objective is to estimate a set of parameters that will minimize the deviation between the predicted system response (predicted transducer signal) of the model and measured system
response (transducer signal) (Ibsen and Liingaard, 2006). This method has great advantage over frequency domain methods because the modal density can became very high due to occurrence of close mode shapes with high damping values. Further details about analysis methods can be found in the cited references.
6
RESULTS
Fig. 9 illustrates average of the normalized singular values of spectral density matrices (ANPSD) for all test setups estimated with EFDD method implemented in ARTeMIS software. The singular values in this figure correspond to identified frequencies. Fig. 10 presents the stabilization diagram obtained with Crystal Clear SSI® method. The analysis with both methods was performed to identify the natural frequencies in the frequency range of 0-20 Hz.
Fig. 9. ANPSD for EFDD method
Fig. 10. Stabilization diagram for Crystal Clear SSI® method
6.1
Comparison of results
Table 2 shows estimated values of the measured natural frequencies for the first 3 mode shapes obtained with both methods for analysis. This table also contains values of the calculated natural frequencies with the initial calculation model. It can be concluded that both methods yield similar results for natural frequencies taking into account the first three modes.
Table 2. Estimated values for natural frequencies and damping coefficients and calculated frequencies with the initial calculation model. Mode
1 2 3
EFDD (Hz) 4.50 5.13 6.25
Estimated by measurements Damping SSI Damping (%) (Hz) (%) 1.19 4.49 2.56 2.05 5.16 4.02 1.55 6.87 2.90
Calculated frequencies (Hz) 5.33 6.58 7.80
Relative error EFDD/SSI (%) 16 / 16 22 / 22 20 / 12
The relative errors of the estimated frequencies for both methods in regard to calculated with the initial model are in the range of 12-22%. The bigger difference of 90-115% was registered for damping values which results from the different approach for damping estimation. Fig. 11 shows a comparison of the mode shapes of the structure in the first three modes calculated by initial FE model and identified with SSI method in ARTeMIS. Good agreement of mode shapes was achieved.
7
FEM UPDATING
The basic principle of FEM updating technique is contained in the process of changing certain critical parameters in the model until calculated dynamic properties do not match the experimental results. The updated FE model assures better analytical representation of the dynamic response of the structure and serves as calibration tool for prediction of the seismic response (Lord et al., 2004). The main goal of the updated model is to achieve acceptable correlation between calculated dynamic properties and measured experimentally. This operation comprehends sensitivity analysis of the stiffness matrix of the model in correlation with changing values of certain predefined parameters (Ventura et al., 2005). To improve the correlation of experimental and calculated results a correlation analysis of selected response parameters is executed. Usually, it is fulfilled by iterative change of selected parameters until the correlation coefficients do not satisfy convergence criteria. FEM updating can be achieved by manual or automatic modification of parameters. Automatic updating has advantage over manual in the iterative modification of several parameters at a time, while the comparison of the frequencies is made by controlling the relative error of the calculated and measured frequencies. The relation of the calculated and measured mode shapes is estimated by MAC criterion (Allemang and Brown, 1982). This study uses manual FEM updating.
f=5.33 Hz
f=4.49 Hz
f=6.58 Hz
f=5.16 Hz
f=7.80 Hz
f=6.87 Hz
Fig. 10. The first 3 mode shapes calculated with the initial FE model (left column) and identified with SSI method (right column). First step of FEM updating was to change the absolute rigid diaphragm behaviour of the floor slabs to flexible behaviour by using real material parameters. In absence of reliable data for mechanical and strength properties for masonry, in the second step it was selected to modify the Young’s modulus and unit weight of the masonry. Several manual iterations were done and Table 3 shows values for the natural frequencies of the first three mode shapes calculated with the initial calculation model. Also, the table contains estimated frequencies based on AVT and calculated with the updated FE model. Table 4 summarizes the values of the masonry Young’s modulus and unit weight before and after FEM updating. The modification of the floor structural type from absolute rigid to flexible has significant impact on the natural frequencies. They differ from the estimated about 3-5% which on one side is result of the good engineering assessment for masonry material properties in the initial model. FEM updating of the selected parameters further improves the determined parameters.
Table 3. Comparison of the first three natural frequencies before and after FEM updating. Mode
Initial FE model-stiff (Hz)
Estimated with tests -SSI (Hz)
Initial FE model-flexible (Hz)
Updated FE model-flexible (Hz)
Relative error (%)
1 2 3
5.33 6.58 7.80
4.49 5.16 6.87
4.38 5.44 7.26
4.17 5.10 6.78
7.7 1.2 1.5
Table 4. Comparison of the initial and actual values of the selected updating parameters.
8
Element
Type
Initial value
Actual value
Difference (%)
Wall Wall
Е γ
2800 19.6
2850 18.7
1.8 4.6
CONCLUSIONS
The characteristic natural frequencies and mode shapes of the building of the primary school “Vojdan Chernodrinski” were determined experimentally, with estimation based on ambient vibration measurements and with analytical model using finite elements. Within the frequency range 0–20 Hz, seven vibration modes were clearly identified. A very good agreement was found between the modal estimates obtained from the EFDD and the SSI techniques. Taking into account measured values, the initial FE model was updated and real calculation model which closely fits its dynamic properties to the existing building was obtained. Thus, the updated model is ready for additional detailed seismic or nonlinear analyses. This application offers an example of the used methodology for effective determination of genuine calculation model for building structures based on results from analysis for modal identification. It should be noted that it is up to the engineer to accept the changes suggested by the modal updating program and to justify these.
ACKNOWLEDGEMENTS The authors acknowledge Digitexx Data Systems, Inc. for excellent system setup, measuring and test results, the municipality of Karposh and primary school “Vojdan Chernodrinski” from Skopje for approval and exceptional work conditions for testing and Archives of Macedonia for allowance to search and copy the archived materials of the design project documentation.
REFERENCES Ivanović, S.S., Trifunac, M.D., Novikova, E.I., Gladkov, A.A., Todorovska, M.I. (2000), “Ambient vibration tests of a seven-story reinforced concrete building in Van Nuys, California, damaged by the 1994 Northridge earthquake”, Soil Dynamics and Earthquake Engineering, 19, pp. 391-411.
„Code of Technical Regulations for the Design and Construction of Buildings in Seismic Regions“,Official Gazette of SFRY 31/81, 49/82, 29/83, 21/88 and 52/90. El-Borgi, S., Choura, S., Ventura, C., Baccouch, M., Cherif, F. (2005), “Modal identification and model updating of a reinforced concrete bridge”, Smart Structures and Systems, vol. 1, no. 1, pp. 83-101. ARTeMIS Testor 5.2, ARTeMIS Extractor 5.3, Structural Vibration Solutions, Inc., ©19992011, Structural Vibration Solutions, Inc., Aalborg, Denmark, www.svibs.com. Ibsen, L.B., Liingaard, M. (2006), “Experimental modal analysis”, DCE Technical Report No. 10, Aalborg University. Lord, J.F., Ventura, C.E., Dascotte, E. (2004), “Automated Model Updating Using Ambient Vibration Data from a 48-storey Building in Vancouver”, Proceedings of the 22nd International Modal Analysis Conference, Dearborn, Michigan, USA. Ventura, C.E., Lord, J.F., Turek, M., Brincker, R., Andersen, P., Dascotte, E. (2005), “FEM updating of tall buildings using ambient vibration data”, Proceedings of Eurodyn Conference. Allemang, R.J., Brown, D.L. (1982), “A Correlation Coefficient for Modal Vector Analysis”, Proceedings of the 1st International Modal Analysis Conference (IMAC), Orlando (FL).
