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Monitoring historical masonry structures with operational modal analysis: Two case studies
ARTICLE IN PRESS Mechanical Systems and Signal Processing 24 (2010) 1291–1305
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Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/jnlabr/ymssp
Monitoring historical masonry structures with operational modal analysis: Two case studies L.F. Ramos a,, L. Marques a, P.B. Lourenc- o a, G. De Roeck b, A. Campos-Costa c, J. Roque d a
~ ISISE, University of Minho, Department of Civil Engineering, 4800-058 Guimaraes, Portugal Catholic University of Leuven, Department of Civil Engineering, Belgium c ´rio Nacional de Engenharia Civil, Portugal NESDE, Laborato d Polytechnic Institute of Braganc- a, Braganc- a, Portugal b
a r t i c l e in fo
abstract
Article history: Received 2 May 2008 Received in revised form 9 December 2009 Accepted 31 January 2010 Available online 4 February 2010
The paper addresses two complex case studies of modal and structural identification of monuments in Portugal: the Clock Tower of Mogadouro and the Church of Jero´nimos Monastery, in Lisbon. These are being monitored by University of Minho with vibration, temperature and relative air humidity sensors. Operational modal analysis is being used to estimate the modal parameters, followed by statistical analysis to evaluate the environmental effects on the dynamic response. The aim is to explore damage assessment in masonry structures at an early stage by vibration signatures, as a part of a health monitoring process that helps in the preservation of historical constructions. The paper presents the necessary preliminary dynamic analysis steps before the monitoring task, which includes installation of the monitoring system, system identification and subsequent FE model updating analysis, automatic modal identification and investigation of the influence of the environment on the identified modal parameters. & 2010 Elsevier Ltd. All rights reserved.
Keywords: Damage identification Experimental testing Modal analysis Masonry structures
1. Introduction Preservation of the architectural heritage is a fundamental issue in the cultural life of modern societies. This heritage is accumulating damage due to deterioration of materials, repeated loading and exceptional events. This means that conservation, repair and strengthening are often necessary. In this process, monitoring and non-destructive (ND) testing play a major role, providing information on the building condition and existing damage, and allowing to define adequate remedial measures. The paper must be therefore understood in a general framework of damage identification by using Global and Local techniques. Vibration-based damage identification methods, usually defined as Global methods, can alert for the presence of damage and define its location (e.g. [1]), but they might not give sufficiently accurate information about the type and extent of the damage. Visual inspections or experimental non-destructive tests like the acoustic or ultrasonic methods, magnetic field methods, radiography, eddy-current methods and thermal field methods (e.g. [2]), also called as Local methods, can be preceded by a global method that indicates that damage is present. Local methods are certainly more accurate to localize and describe the damage.
Corresponding author.
E-mail address: [email protected] (L.F. Ramos). 0888-3270/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ymssp.2010.01.011
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Nomenclature
x
s o j f
p j00 jexp Aq
damping coefficient estimated standard deviation eigen frequency or resonant frequency mass-non-scaled mode shapes mass-scaled mode shapes objective function mass-non-scaled curvature mode shapes measured modal displacement scalar of the ARX model
Bq E q ro rj
scalar matrix of the ARX model Young’s modulus delay operator vector of frequency residuals vector of mode shape residuals
2 r^ xy R^ xy
coefficient of determination
u W
covariance input in the ARX model weighting factors
2. Damage identification Historical masonry structures exhibit usually a complex geometry and successive past interventions. In addition, the constituting materials tend to exhibit significant variations in properties and internal structure. The damage on masonry structures mainly relates to cracks, foundation settlements, material degradation and deformations. When cracks occur, they are generally localized, splitting the structures in macro-blocks. The use of dynamic-based methods to assess the damage is an attractive, but complex, tool to apply to this type of structures due to requirements of possible remedial measures: unobtrusiveness, minimum intervention and respect of the original construction. The assumption that damage can be linked to a decrease of stiffness seems to be reasonable to this type of structures, as for structures with other materials. Many methods and applications have been presented in the literature for damage identification based on vibration signatures, see e.g. [3–9], but there are only a few papers related to masonry-like structures. It is also noted that the usage of these techniques for monitoring and damage identification requires elimination of the environmental effects [10]. Fig. 1 presents an overview of different methods organized according to the level of damage identification, the required data, and
Classification
Modal data (ω and/or ϕ and/or ϕ″)
Methods
Model Based
Data
Damage Identification
• Frequency Shifts (Level 1); • COMAC (Level 2); • Mode Shape Curvature (Level 2); • Parameter Method (Level 2); • Damage Index (Level 2); • Changes in Flexibility Matrix (Level 2); • Direct Stiffness Calculation (Level 2 and Level 3).
Non-Model Based
Time data
• FE Model Updating Techniques (Level 2 and Level 3)
• Wavelet Analysis (Level 1 and Level 2)
Reference scenario is not required (Non-Reference Based)
Reference scenario is required (Reference Based) Fig. 1. General overview of the damage identification methods [12]. Level 1 is detection, Level 2 is localization and Level 3 is assessment.
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the need of a reference scenario. Still, at the moment, there is no method based on vibration signatures that gives accurate results for all levels of damage and for all types of structural systems. This is still a challenge for the next decades [5,8]. 3. Monitoring procedures The current practices of structural health condition are based mainly on periodic visual inspections or condition surveys but, during the last decade, software and hardware developments made continuous monitoring possible [8]. Typically, one can install hundreds of sensors in a structure and read the data in real time. The attention now seems to be focused on what type of information is important from the structural point of view and how the data should be processed and stored for damage analysis [13]. The developments in Micro Electro Mechanical Systems (MEMS) and Wireless Sensor Networks (WSN) are promising technologies in this field, in particular for historical masonry structures [14]. The process leading to monitoring of historical masonry structures can be divided in four phases: 1. The first phase is the data collection of the structure, including the historic information, geometrical and topographic survey, damage survey, mechanical materials characterization with ND tests, global dynamic modal test and a numerical model analysis for static and dynamic validation. This is the first approach to the structural behaviour in the assumed condition at time ‘‘zero’’. 2. In the second phase the health monitoring plan can be performed with a limited number of sensors (e.g. a pair of reference accelerometers, strain gauges at critical sections, temperature and humidity sensors, etc.). Data should be stored periodically and the monitoring system should be able to send the proper alarms. Environmental effects should be studied and the presence of damage should be observed by the global modal parameters. 3. In the third phase, should it be required by the first two phases, or by a life cycle cost analysis, or by the importance of the structure, a full-scale dynamic survey with more sensors and measuring points should be performed. In this phase the ‘‘health condition’’ of a structure is studied with more detail. Damage identification methods should be applied to the structure after filtering the environmental effects. The aim of the dynamic methods is to confirm and locate the (possible) damage in a global way. 4. In the last phase, a local approach with visual and complementary ND tests should be performed to locally assess the damage and classify it. The global and local approach should be considered as complementary tasks. For the case of historical constructions these two approaches seem to be suitable, since they are ND procedures to evaluate the health conditions. The following sessions present two complex case studies, in which the first two phases of the preceding methodology were already applied. Here, a dynamic identification monitoring system is used to detect cracks in masonry structures at early stage, the possible breakage or loss of anchorage in a tie, or changes in the boundary conditions. 4. Case study I—Mogadouro Clock Tower The Mogadouro Clock Tower is located inside the castle perimeter (see Fig. 2) of Mogadouro, a small town in the Northeast of Portugal. The tower was built after the year 1559. It has a rectangular cross section of 4.7 4.5 m2 and a height of 20.4 m. Large granite stones were used in the corners and rubble stone with thick lime mortar joints were used in the central part of the walls. The thickness of the walls is about 1.0 m. In 2004, the tower was severely damaged, characterized by large cracks, material deterioration and loss of material in some parts, see Fig. 2a and b. A geometrical survey of the structure was performed and the existing damage was mapped.
Fig. 2. Mogadouro Clock Tower: (a, b) before the rehabilitation works and (c, d) after the rehabilitation works.
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S7 S8 S9
E10
S4 S5 S6
E11 E13 E12
E5 E6
W13 W15 W16 E14 W12 W14
E8 E9
S1
S2
E1 E2
S3
E4 E3
W9
W7 W8
E7
W1
W11 W10
W3 W5 W6
N12 N14 N15 N13
N11
N6
N4
N9 N10
N5 N7 N8 N1
N2 N3
W2 W4
Fig. 3. Dynamic tests and example of sensor locations: (a) south, east, west and north fac- ade measuring points, respectively; (b) measurements before rehabilitation works and (c) after rehabilitation works.
Table 1 Dynamic response before and after the rehabilitation. Mode shape
1st 2nd 3rd 4th 5th 6th 7th Average values
Before
After
Do
Before
After
Dx
o (Hz)
CVo (%)
o (Hz)
CVo (%)
(%)
x (%)
CVx (%)
x (%)
CVx (%)
(%)
2.15 2.58 4.98 5.74 6.76 7.69 8.98 –
1.85 1.05 0.69 1.56 1.13 2.94 1.21 1.49
2.56 2.76 7.15 8.86 9.21 15.21 16.91 –
0.21 0.30 0.27 0.47 0.21 2.24 1.40 0.73
+19.28 + 6.70 +43.67 +54.37 +36.13 +97.87 +88.27 +49.47
2.68 1.71 2.05 2.40 2.14 2.33 2.30 2.23
219.51 94.02 65.33 24.27 31.74 55.98 46.39 76.75
1.25 1.35 1.20 1.31 1.16 2.54 1.49 1.47
0.13 0.17 0.14 0.13 0.12 0.24 0.23 0.17
53.26 21.00 41.32 45.72 45.65 + 9.11 35.07 40.34*
* Average value calculated only with negative differences.
Rehabilitation works carried out in 2005 reinstated the tower safety, see Fig. 2c and d, including lime injection for the consolidation of the walls, replacement of material with high level of degradation, filling of voids and losses, and installation of ties (or steel belt) at two levels.
4.1. Modal identification before and after the rehabilitation works Two dynamic modal identification tests were performed before and after the works. The same test planning was adopted in the two conditions by using the same measuring points, see Fig. 3a. Fig. 3b and c presents images of the execution of the ambient dynamic tests carried out before and after the works. The dynamic acquisition system was composed by 4 uniaxial piezoelectric accelerometers, with a bandwidth ranging from 0.15 to 1000 Hz (5%), a dynamic range of 70.5 g, a sensitivity of 10 V/g, 8 mg of resolution and 210 g of weight, connected by coaxial cables to a front-end data acquisition system with a 24-bit ADC, provided with anti-aliasing filters. The front-end was connected to a laptop by an Ethernet cable. The accelerometers were bolted to aluminum plates that were glued with epoxy to the stones. A preliminary FE dynamic analysis estimated 10 frequencies between 2 and 15 Hz. Therefore, and for each test campaign, a sampling frequency of 256 Hz was chosen to acquire the response with ambient excitation. The total sampling time of each setup was equal to 10 min and 40 s (2000 times the highest period). Table 1 presents the first seven estimated natural frequencies, damping ratios, and Coefficient of Variation (CV), estimated by the Stochastic Subspace Identification (SSI) method [10] (Principal Component), implemented in ARTeMIS [11], Fig. 4 shows the corresponding mode shapes. Analyzing the two structural conditions, on average the frequencies increased 50% with the consolidation works, while the damping decreased 40% for all modes, with exception of sixth mode. As expected, by closing the cracks the stiffness increased and the energy dissipation decreased, directly affecting the frequencies and damping, respectively. Concerning the modal displacements, local protuberances can be observed in the areas close to the cracks and in the upper part of the
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After Rehabilitation
Before Rehabilitation
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1st mode
2nd mode
3rd mode
4th mode
5th mode
6th mode
7th mode
2.15 Hz
2.58 Hz
4.98 Hz
5.74 Hz
6.76 Hz
7.69 Hz
8.98 Hz
2.56 Hz
2.76 Hz
7.15 Hz
8.86 Hz
9.21 Hz
15.21 Hz
16.91 Hz
y
z x
y
z x
Fig. 4. Experimental mode shapes and MAC values before and after rehabilitation works.
tower, before the works. This is due to the presence of severe damage. On the contrary, the structure behaves monolithically after the rehabilitation. Taking into account the previous results, it is possible to conclude that the structure suffered a significant structural intervention and the strengthening works were efficient. One can also conclude that the presence of damage changed the dynamic behaviour significantly with respect to the possible original structure. The challenge now is to verify if the cracks were stabilized with the intervention by means of a dynamic monitoring system. 4.2. Structural assessment For the structural assessment, a 3D FE model was built. The model updating analysis was performed with the aim to assess the tower dynamic behaviour in its actual condition (after the retrofitting). The non-linear least-squares method implemented in MatLab [15] was used together with DIANA [16] to compute the numerical modes. The objective function p to be minimized is composed by the residuals formed with calculated and experimental frequencies and mode shapes, given by [17] 2 3 N N X m X 1 4X p¼ r þ r 5 ð1Þ 2 i ¼ 1 o;i i ¼ 1 j ¼ 1 j;i;j with N denoting the number of eigenfrequencies, m denoting the number of degrees of freedom in each eigenvector, and ro and rj denoting the vectors of eigenfrequency residuals and of mode shape residuals, respectively. The residuals ro and rj are given by !2 2 o2i o2i;exp ro;i ¼ Wo;i ; rj;i;j ¼ Wj;i jji jji;exp ð2Þ 2
oi;exp
where the subscript exp indicates experimental values, and Wo, and Wj are the weighting factors for frequencies and mode shapes, respectively. The weighting factors can have different values according to the engineering judgement of the user. Note that mode shapes are scaled in a way that the maximum value in any vector component is equal to one. With this scaling, frequencies and mode shapes differences are in the same order of magnitude and can be compared in the same equation. The first attempt to tune the numerical model was carried out in a series of analysis using shell element models, see [12] for details. Due to the unrealistic updating results obtained, it was concluded that the structure needed to be modelled with 3D brick elements, mainly to better represent the corners stiffness and the geometry of the upper part of the tower. The optimization parameters were selected taking into account the possible differences between the material properties and the modulus of elasticity of the different parts was chosen as updating parameters. Fig. 5 shows the final 3D model where eight updating parameters can be observed. Table 2 shows the updating analysis results, including the initial and final values for each updating parameter, the average frequency error, the average Modal Assurance Criterion (MAC) value, the average Normalized Modal Difference (NMD) value, and the average Co-ordinate Modal Assurance Criterion (COMAC) value. With respect to Young’s modulus variation, the South and North fac- ades have values around 2 GPa, and the East and West fac- ades have values around 1 GPa.
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Fig. 5. Updating parameters for the brick elements model.
Table 2 Results for the model updating analysis after rehabilitation. Updating parameters
Initial values (GPa)
Final values (GPa)
E1 E2 E3 E4 E5 E6 E7 E8
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
1.974 2.210 1.075 0.804 3.875 1.210 0.195 5.997
(south) (north) (west) (east) (corners) (columns) (roof) (foundation)
Average o error (%)
Average MAC
Average NMD
Average COMAC
|2.10|
0.98
0.12
0.98
The differences from one to two are acceptable, if the heterogeneity of masonry is taken into account. The material at the corners has higher stiffness, about 4 GPa, and the areas with better masonry type have values of the same order of the masonry walls in general. The roof has a lower value around 0.2 GPa and the foundation 6 GPa, which is acceptable due to the lack of information on the foundations, the likely higher vertical stress at the base, the possible enlargement of the foundation at the base and the soil confinement. Fig. 6 presents the tuned modes and the frequency values, where it is possible to observe that the upper part of the structure has a flexible behaviour due to the presence of the windows. The discussion on the tower structural behaviour, by means of FE model updating techniques, demonstrates that the correct definition of the structure, including the foundations, is critical for having a good correlation between the experimental and numerical modal results. 4.3. Dynamic monitoring system From the beginning of April 2006, and after the rehabilitation, a dynamic monitoring system was installed in the tower, see Fig. 7. The aim is to evaluate the environmental effects of temperature and relative air humidity on the dynamic behaviour of the tower, and to detect any possible non-stabilized phenomenon in the structure (damage). Three piezoelectric accelerometers connected to an USB data acquisition card with 24 bits resolution are recording each hour ten minutes of ambient vibrations. In parallel a combined sensor is recording the ambient temperature and relative air humidity. This task is performed in several campaigns (test series), in different periods of the year. During each
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z
1297
y x
y x Mode 1 (2.54 Hz)
Mode 2 (2.68 Hz)
Mode 3 (7.33 Hz)
Mode 4 (8.62 Hz)
Mode 5 (9.36 Hz)
Fig. 6. Numerical mode shapes after rehabilitation.
A1
Level 5
North
Level 4 Level 3 A1
TH
A2
D Level 2 TH D
A2
y x
Level 1
North
z
South
y
Fig. 7. Dynamic monitoring system: Dynamic monitoring system: (a) location of measuring positions, datalogger (D) and environmental sensor (TH); (b) measured directions for accelerations; (c) installation of accelerometer at position A1; (d) accelerometers at position A2 and (e) datalogger and environmental sensor.
campaign 600 records of ten minutes at every hour are stored in a laptop. No triggering was applied. Ten series were completed in the period from April 2006 until December 2007. For modal estimation, an automatic procedure based on the SSI/Ref method [18] was implemented in MatLab [15]. However, the automatic procedure needs a preliminary manual estimation of a few numbers of events to better establish limit values for the automatic estimation. In the manual identification, six to ten data files were selected to better analyze the modal results. A maximum statespace model order equal to 50 is fixed. This number corresponds to 25 structural vibration modes and is expected to
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exceed the true model order significantly. Although this parameter does not have a direct repercussion on the analysis results, selecting a relatively large number helps to visualize and to define trends in the stabilization diagrams. Next, eigenfrequency intervals, damping intervals and a reference mode shape vector are established. Normally, the damping coefficient interval for all the modes was between 0.5% and 3%. Finally, the automatic procedure is applied to all the events with the same range of model order. To avoid unrealistic modes, for every event file the selection of the correct model order in the stabilization diagram is carried out by selecting the model that gives the frequencies and the damping values in the expected intervals, and gives the best MAC values (always greater than 0.95).
4.4. Environmental effects The data series were analyzed and they allowed concluding that the environmental effects significantly change the dynamic response of the structure. Mainly, the water absorption of the walls in the beginning of the raining seasons changes the frequencies about 4%. The significant influence of moisture inside the walls on the dynamic response of masonry structures is not reported in literature, as the changes are always attributed to others environmental effects or loading conditions, such as temperature and excitation level. The series presented in Fig. 8 was recorded during October and November, 2006, which is linked to the first strong raining event at the site. As no damage was observed in the structure, the humidity influence can be observed by a shift in the linear relation between frequency and temperature by a transition series (gray dots in Fig. 8a). The ambient temperature, the relative air humidity and the excitation level, by means of the Root Mean Square (RMS) of the signal, were correlated to the resonant frequencies. Multiple linear regression models were compared with AutoRegressive outputs with eXogeneous input models, also known as ARX models [19], in order to evaluate the environmental and loading effects. ARX models with Multiple Inputs and a Single Output (MISO models) were computed in MatLab [15], to model each frequency value. The multivariable ARX model with n inputs u and one output y is given by Aq y^ k ¼ Bq uenv knk þ ek
ð3Þ
First two Frequencies versus Temperature 3.0
Frequency [Hz]
2.8 2.6 2.4 2.2 2.0 0
5
10
15 20 Temperature [ºC]
25
30
35
First two Frequencies versus Humidity 3.0
Frequency [Hz]
2.8 2.6 2.4 2.2 2.0 0
10
20
30
40 50 60 Humidity [%]
70
80
90
100
Fig. 8. Environmental effects: (a) temperature and (b) relative air humidity. Black dots correspond to the first frequency, white dots to the second frequency, and gray dots to the transition period of each frequency.
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where Aq is a scalar with the delay operator q 1, Bq is a matrix 1 n, and e are the unknown residuals. For convenience, to model the response and to establish the confidence intervals, an approach similar to the one used by Peeters [10], with the appropriate changes, was used. The methodology includes the following steps: 1. Normalized inputs and outputs: uenv k;Temp ¼
uenv;m u 1 k;1
su;1
;
uenv k;RMS ¼
uenv;m u 2 k;2
su;2
;
uenv k;Hum ¼
uenv;m u 3 k;3
su;3
and
yk;o ¼
ym k y
sy
ð4Þ
where uenv;m and ym k are the measured values for the environmental parameters and the dynamic response, respectively, k;i u i and y are the average values and su,i and sy are the standard deviations. 2. Estimate ARX models and their statistical properties (e.g. ARX[0, 1 2 3, 0 0 0], i.e. an ARX model for one output and three inputs, with zero order for the autoregressive part, three different orders for the exogeneous part and with no delays). 3. Select the ‘‘best’’ model based on quality criteria, such as the loss function V with is the average quadratic error, the Akaike’s Final Prediction Error (FPE) which measures the model quality by simulating the situation where the model is 2 tested on a different data set, see [19], and the coefficient of determination r^ xy , given by !2 N R^ xy 1X 1þ d=N 2 V¼ e2k ; FPE ¼ V ð5Þ ; and r^ xy ¼ s^ x s^ y N 1d=N k¼1
where d is the number of estimated parameters and R^ xy is the estimated covariance. 4. Simulate the expected response with the previous selected model. 5. Calculate the simulation error and its statistics e^ k ¼ yk y^ k
and
R^ xy
ð6Þ
6. Establish the confidence intervals ci and detect the outliers qffiffiffiffiffiffiffi qffiffiffiffiffiffiffi y^ k zð1a=2Þ R^ xy ; y^ k þzð1a=2Þ R^ xy
ð7Þ
where z is found from a statistical table of Student’s t-distribution (e.g. to compute 95% confidence interval, a = 0.05 and z (for a large number of data points) is equal to 1.96. Fig. 9a shows the fitting models through the normalized frequency and simulated errors with the 95% confidence intervals ci, and Fig. 9b shows the simulated error. In general, the model is able to replicate the frequency variation, but does not takes into account the water absorption phenomenon, because the relative humidity variation does not totally represent that change. Nevertheless, by observing Fig. 9 no damage was detected because the simulated error does not go significantly further than the confidence intervals. This fact was visually confirmed in the tower, as no damage was found during the monitoring period. The results indicate that ARX models can simulate the natural frequencies, but sensors to measure the water absorption inside the walls are necessary in this case to better simulate the dynamic response and to detect the presence of damage. A proposal for new humidity sensors was made in [12]. To monitor this phenomenon, humidity sensors should be placed inside the four fac-ades, at different elevation levels. In order to better study the distribution of the humidity inside the walls, on each measuring point three sensors should be placed along the thickness of the walls. Additionally, to evaluate the tower mass change due to rain, load cells or flat jacks test equipment can be also installed at the bottom of the walls in order to measure the changes in the compressive stresses. For these sensors, a measuring periodicity of one sample per hour will be enough to follow the water absorption phenomenon.
3 2
Simulation Error
Normalized Frequency
4
1 0 -1 -2 -3 -4
0 100 200 300 400 500 600 700 800 900 Events
5 4 3 2 1 0 -1 -2 -3 -4 -5
0 100 200 300 400 500 600 700 800 900 Events
Fig. 9. ARX model [3, 2 2 4, 0 0 0] (i.e. an ARX model for one output and three inputs, with order three for the autoregressive part, with orders two, two and four for the exogeneous part and with no delays) for mode shape 1 with 95% confidence intervals: (a) normalized frequency and (b) simulation error.
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5. Case study II—Church of Monastery of Jero´nimos The Monastery of Jero´nimos, located in Lisbon, is one of the most famous Portuguese monuments (see Fig. 10). The Portuguese ‘‘Manuelino’’ architectural style of the XVI Century makes the monument very attractive for tourists. The church of the monastery, Santa Maria de Bele´m church, has considerable dimensions: a length of 70 m, a width of 40 m and a height of 24 m.
5.1. Modal identification of the main nave The main nave of the church was tested using output-only modal identifications techniques, which provided the modal parameters: resonant frequencies, mode shapes and damping coefficients. Two techniques were applied to compare the experimental dynamic parameters obtained and have more accurate results. The Enhanced Frequency Domain Decomposition (EFDD) [20] and the Stochastic Subspace Identification (SSI) method. Thirty points on the top of the main nave were selected to measure the acceleration response, see Fig. 11. Ten points are located on the top of the external walls with the purpose of measuring the nave boundaries and also the global dynamic response of the church. The other points are located either on the top of the columns or on the top of the vault keys. Table 3 summarizes six natural frequencies, damping ratios and MAC values estimated by two different output-only system identification techniques. The natural frequencies range from 3.7 to 12.45 Hz and no significant differences could be found between the two methods. For the damping coefficients, differences up to 140% can be observed. The reasons for such large differences in damping can be explained by the effect of the noise in the data or the low excitation level in the nave. Moreover, although in the EFDD technique the natural frequencies and damping ratios are, in general, estimated with a good accuracy, when the deterministic signals are close to the natural frequencies, the fitting SDOF Bell functions of the EFDD method can give deviations in the modal parameters, mainly for damping coefficients. Finally, the MAC values are only higher than 0.95 for the first two modes as a consequence of the difficulty in exciting this heavy structure. Fig. 12 shows the shape of the first two modes. The dynamic response of the main nave is influenced by the slenderness of the columns and the modes are composed by components mostly in y (North–South) and z (vertical) directions.
y x
C
B
A
A
C
z
B 0.0
25.0 m
x
Fig. 10. Church of Monastery of Jero´nimos: (a) inside view of the choir; (b) aspect of the three naves; (c) plan and (d) section A–A.
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P11
P10
P30
P22
P9
P23
P21
P24
y x
P25
P15
P2
P3
P26
P14
P13
P4
P27
P19 P17
P16 P29
P7
P8
P20
1301
P18 P1
P12
P28
P5
P6
Fig. 11. Measurement points: (a) in plan location and (b) the reference transducer.
Table 3 Comparison with the estimated modal parameters of the main nave.
o (Hz)
Mode shape
Mode Mode Mode Mode Mode Mode
1 2 3 4 5 6
EFDD
SSI
EFDD
SSI
3.69 5.12 6.29 7.23 9.67 12.45
3.68 5.04 6.30 7.29 9.65 12.51
2.34 1.11 1.00 0.77 1.10 1.25
1.26 2.68 0.82 1.44 1.45 1.19
y
z y
z x
x
y x
0.99 0.92 0.67 0.67 0.62 0.71
y y
z
z
MAC
x (%)
z
x
z x
y x
Fig. 12. Experimental mode shape results from EFDD method: (a) first mode shape at 3.7 Hz and (b) second mode shape at 5.1 Hz.
Nevertheless, this modal identification seems to be acceptable if the structural complexity of the main nave is taking into account. Even if the mode shape and damping coefficients estimation is not very accurate for the higher modes, their natural frequencies seem accurately extracted by the two output-only techniques. The use of the two output-only techniques helped in the results discussion and validation. For masonry-like structures, the robust results obtained, together with simplicity, the low cost, the non-destructiveness and low interference with operating conditions make these techniques an attractive tool to assess historical constructions. One disadvantage is the fact that the mode shapes are not scaled with respect to the structure mass matrix.
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5.2. Structural assessment Due to the high level of complexity of the structure a beam FE model was manually tuned to the dynamic experimental results. The adoption of a relatively ‘‘simple’’ model is due to the fact that the model is to be used in subsequent non-linear time integration analysis, including a parametric study using a set of mechanical properties, different return period scenarios and strengthening possibilities, see also [21]. Nevertheless, it should be stressed here that for a correct updating analysis the complexity of the structure needs a FE model with volume elements to accurately reproduce the dynamic response, similarly to what was carried out for the case of the Mogadouro Tower presented in Section 4.2. The updating parameters were the modulus of elasticity of the columns and the main nave, and the boundary conditions of the columns. The dynamic response is mostly governed by the slender columns, as many local modes appear in the results. The first mode shape of the numerical model is presented in Fig. 13. Table 4 shows the first six frequencies after tuning for the first frequency. The results obtained for the modulus of elasticity were 30 GPa for the columns and 12 GPa for the masonry. The high value for the columns can be explained by the very high compression stresses present due to the small cross section, and the fact that solid drums and very thin joints are used.
5.3. Dynamic monitoring system Since April of 2005, a dynamic monitoring system was installed in the church within the scope of the Euro-Indian research project ‘‘Improving the Seismic Resistance of Cultural Heritage Buildings’’. The monitoring system is composed of two strong motions recorders (R) with 18 bits AD converters connected to two triaxial force balance accelerometers, see Fig. 14. One accelerometer (A1) was installed at the base of the structure near the chancel and the other (A2) at the top of the main nave (extrados), between two consecutive columns, and in the location with higher signal levels obtained in the dynamic modal identification analysis. The two recorders are connected by an enhanced interconnection network, which allows a common trigger and time programmed records. The recorder connected to sensor A1 is the master recorder, which enables synchronization and updates the internal clock of the slave recorder connected to sensor A2. The monitoring task is mainly processed by the master recorder, with a trigger armed for low-level signals corresponding to microtremors occurring at the site. In parallel, every month, dynamic data are registered during 10 min. Also seasonally, to study the environmental effects, 10 min are recorded every hour during one complete day.
y y x
x
Fig. 13. First mode numerical mode shape at 3.79 Hz: (a) transversal section and (b) plan view.
Table 4 Comparison experimental and numerical frequencies of the two columns. Modes
1 2 3 4 5 6
Experimental
Numerical
o (Hz)
Comment
o (Hz)
Comment
3.68 5.04 – – – –
Main nave (x) Main nave (x) – – – –
3.79 5.06 5.20 5.34 5.76 6.13
Main nave (x) Tower (x) Tower (y) Columns and main nave (x)
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y x
A1, R A2
0.0
25.0 m
Fig. 14. Dynamic monitoring system: (a) location of the sensors; (b) battery of recorders and the base accelerometer and (c) accelerometer on the main nave.
Frequency versus Temperature
Temperature
50 40 30 20 10 0
Frequency [Hz]
Frequency
Temperature [ºC]
4.2 4.1 4.0 3.9 3.8 3.7 3.6 3.5
Feb-05 Apr-05 Jun-05 Aug-05 Oct-05 Dec-05 Feb-06 Apr-06 Jun-06 Aug-06 Oct-06 Dec-06 Feb-07 Apr-07
Frequency [Hz]
Temperature Effect on the First Frequency
4.2 4.1 4.0 3.9 3.8 3.7 3.6 3.5 0
5
10
15
20
25
30
35
40
Temperature [ºC]
Date Fig. 15. Results for the first mode shape: (a) frequency and temperature variation and (b) frequency versus temperature.
The dynamic monitoring system is complemented by a static one, which measures temperatures and rotation of the columns at several points in the structure. Additional sensors for relative air humidity and wind velocity were recently added to this system.
5.4. Environmental effects For the study of the environmental and loading effects all data acquired in the strong motion recorders were used. Up to now, 1300 events were acquired: 28% of which correspond to programmed events with ten minutes of total sampling duration, and 72% correspond to triggered events, with an average sampling duration of 1 min and 15 s. To estimate the modal parameters, the procedure described previously for the Mogadouro Clock Tower was again adopted. It should be stressed that in the modal parameter estimation only the first, the third and the fourth mode shapes of the nave were successful estimated. The majority of the triggered events occurred during working hours, due to the road traffic, special events inside the church (like mass or concerts), and minor earthquakes. With respect to programmed events, it is noted that it was more difficult to estimate the modal parameters during the night period, due to the low ambient excitation level. Observing Fig. 15a, it can be concluded that for the case of the nave the temperature effect is significant, because the first frequency values can follow the temperature along the time. This effect turns clear when plotted the temperature values against frequency, see Fig. 15b. With later figure, a trend for linear relation between temperature and frequency was found, with a possible apex for a temperature about 18 1C. This trend occurs for all the estimated frequencies. As no continuum series were recorded in the monitoring system, modelling of thermal inertia is difficult and only static regression models were used. From the observed bilinear trend, two linear regressions for temperature values lower and higher than 17.5 1C were adopted. Fig. 16a shows the static models for the first estimated frequency by correlating the two quantities, temperature and frequency with the 95% ( 72s) confidence intervals. The results show that the bilinear static model follows the evolution of the frequencies but a significant number of outliers can be observed in Fig. 16b, where the residuals between the first natural frequency and the simulated frequency are shown. This indicates that others environmental effects need to be studied to better model the dynamic response. Finally, it should be stressed that in 12 February 2007, at 10:35 am a 5.8 magnitude earthquake, with a Modified Mercalli intensity V, occurred in the Southwest of Lisbon. The permanent staff of the monument felt the ground shake. No visitors were inside the church because on Mondays the church is closed to public. The strong motions recorders acquired the signals, as can be observed in Fig. 17a. The peak of the frequency contents of the elastic response spectra was in the
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Oct-07
Jun-07
Aug-07
40
Feb-07
35
Apr-07
30
Oct-06
15 20 25 Temperature [ºC]
Dec-06
10
-0.45 Jun-06
5
-0.30 Aug-06
0
0.00 -0.15
Feb-06
3.5
0.15
Apr-06
3.7 3.6
0.30
Oct-05
3.9 3.8
Residuals for the First Frequency
0.45
Dec-05
Frequency Residuals [Hz]
Frequency [Hz]
Static Regression for the First Frequency 4.2 4.1 4.0
Aug-05
1304
Date
Fig. 16. Static regression for the first mode: (a) temperature influence and (b) residuals history.
Acceleration [mg]
10 8 6 4 2 0 -2 0 -4 -6 -8 -10
Nave (A2) Base (A1)
25
50
75
100
125
150
Acceleration [mg]
Accelerograms in the x Direction
Elastic Response Spectra (ξ = 5%)
15.0 12.5 10.0 7.5 5.0 2.5 0.0
x
0
Time [s]
y
z
5 10 15 20 25 30 35 40 45 50 Frequency [Hz]
Fig. 17. Small earthquake in February, 2007: (a) the accelerograms in the x direction (transversal) at the base and at the nave and (b) the elastic response spectra of the seismic event.
range of the estimated natural frequencies, see Fig. 17b, but the estimated natural frequencies did not suffer any significant shift, as can be observed through Fig. 16b. Therefore, no damage in the structure occurred due to this minor earthquake. 6. Conclusions A methodology based on operational modal analysis is presented for masonry structures, aiming at detecting damage at an earlier stage. The methodology comprises four phases, namely data collection, simplified health monitoring, detailed health monitoring and local non-destructive testing. As an illustration, the first two phases were applied to two complex Portuguese monuments. For these monuments, the modal identification results, the development of structural model with model updating techniques, for subsequent assessment with FE models, the installation of monitoring systems and the automatic parameter retrieval were presented. From the experience with the two cases, the proposed methodology for damage identification seems to be useful and applicable to masonry-like structures, especially to complex historical constructions. In particular, the frequency monitoring seems to be a reliable quantity for damage detection. Analysis of the environmental effects on the dynamic behaviour through autoregressive models was carried out. An important conclusion emerging from the results is the non-negligible influence of the humidity on the dynamic behaviour of masonry-like structures subjected to rain, besides the well-known influence of the temperature. Finally, apparently no damage was observed in the two monuments by global modal parameters changes during the monitoring period.
Acknowledgements The authors would like to thank Edwin Reynders for his kind support in the automatic system identification. The activities on Monastery of Jero´nimos were partly funded by the EU-India Economic Cross Cultural Programme ‘‘Improving the Seismic Resistance of Cultural Heritage Buildings’’, Contract ALA-95-23-2003-077-122. References [1] P.C. Chang, A. Flatau, S.C. Liu, Review paper: health monitoring of civil infrastructure, Structural Health Monitoring 2 (3) (2003) 257–267. [2] J.E. Doherty, Nondestructive evaluation, in: A.S. Kobavashi (Ed.), Handbook on Experimental Mechanics, Society for Experimental Mechanics, 1987 (Chapter 12). [3] S.W. Doebling, C.R. Farrar, M.B. PrimeD. Shevitz, Damage Identification and Health Monitoring of Structural and Mechanical Systems from Changes in their Vibration Characteristics: A Literature Review, Los Alamos National Laboratory, New Mexico, NM, 1996 132 pp.
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[4] C.R. Farrar, S.W. Doebling, Damage detection and evaluation II—field applications to large structures, in: Ju´lio Silva, Nuno Maia (Eds.), Modal Analysis and Testing, NATO Science Series E, vol. 363, Kluwer Academic Publishers, London, 1998, pp. 345–378. [5] S.W. Doebling, C.R. Farrar, M.B. Prime, A summary review of vibration-based damage identification methods, The Shock and Vibration Digest (1998) 91–105. [6] S. Choi, S. Park, N. Stubbs, Non-destructive damage detection in structures using changes in compliance, International Journal of Soils and Structures 42 (2005) 4494–4513. [7] O.S. Salawu, Detection of structural damage through changes in frequency: a review, Engineering Structures 19 (9) (1997) 718–723. [8] P.C. Chang, A. Flatau, S.C. Liu, Review paper: health monitoring of civil infrastructure, Structural Health Monitoring 2 (3) (2003) 257–267. [9] D. Montalva~ o, N.M.M. Maia, A.M.R. Ribeiro, A review of vibration-based structural health monitoring with special emphasis on composite materials, The Shock and Vibration Digest 38 (4) (2006) 295–324. [10] B. Peeters, System identification and damage detection in civil engineering, Ph.D. Thesis, Catholic University of Leuven, Belgium, 2000. [11] SVS, ARTeMIS Extractor Pro User Manual, Release 3.5, Structural Vibration Solutions, Aalborg, Denmark, 2006. [12] L.F. Ramos, Damage identification on masonry structures based on vibration signatures, Ph.D. Thesis, University of Minho, Portugal. Available from /www.civil.uminho.pt/masonryS, 2007. [13] J. Maeck, Damage assessment of civil engineering structures by vibration monitoring, Ph.D. Thesis, Catholic University of Leuven, Belgium, 2003. [14] J.P. Lynch, An overview of wireless structural health monitoring for civil structures, Journal of Philosophical Transactions of the Royal Society of London Series A, Mathematical and Physical Sciences (2007) 345–372. [15] MATLAB, MATLAB User Manual, Release 7.2, The MathWorks, USA, 2006. [16] DIANA, DIANA-9 Finite Element Analysis, User’s Manual-Release 9, TNO, Netherlands, 2006. [17] A. Teughels, Inverse modelling of civil engineering structures based on operational modal data, Ph.D. Thesis, Catholic University of Leuven, Belgium, 2004. [18] B. Peeters, G. Roeck, Reference-based stochastic subspace identification for output-only modal analysis, Mechanical Systems and Signal Processing (1999) 855–878. [19] L. Ljung, System Identification: Theory for the User, second edition, Prentice-Hall, Upper Saddle River, NJ, USA, 1999. [20] R. Brincker, L. Zhang, P. Andresen, Modal identification from ambient responses using frequency domain decomposition, in: Proceedings of the 18th International Seminar on Modal Analysis, San Antonio, Texas, 7–10 February, 2000. [21] J.A. Roque, P.B. Lourenc- o, D.V. Oliveira, Towards a Methodology for Seismic Assessment of Monuments. The Case Study of Santa Maria of Bele´m Church, Studies on Historical Heritage, Antalya, Turquia, 2007, p. 551–558.
Contents lists available at ScienceDirect
Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/jnlabr/ymssp
Monitoring historical masonry structures with operational modal analysis: Two case studies L.F. Ramos a,, L. Marques a, P.B. Lourenc- o a, G. De Roeck b, A. Campos-Costa c, J. Roque d a
~ ISISE, University of Minho, Department of Civil Engineering, 4800-058 Guimaraes, Portugal Catholic University of Leuven, Department of Civil Engineering, Belgium c ´rio Nacional de Engenharia Civil, Portugal NESDE, Laborato d Polytechnic Institute of Braganc- a, Braganc- a, Portugal b
a r t i c l e in fo
abstract
Article history: Received 2 May 2008 Received in revised form 9 December 2009 Accepted 31 January 2010 Available online 4 February 2010
The paper addresses two complex case studies of modal and structural identification of monuments in Portugal: the Clock Tower of Mogadouro and the Church of Jero´nimos Monastery, in Lisbon. These are being monitored by University of Minho with vibration, temperature and relative air humidity sensors. Operational modal analysis is being used to estimate the modal parameters, followed by statistical analysis to evaluate the environmental effects on the dynamic response. The aim is to explore damage assessment in masonry structures at an early stage by vibration signatures, as a part of a health monitoring process that helps in the preservation of historical constructions. The paper presents the necessary preliminary dynamic analysis steps before the monitoring task, which includes installation of the monitoring system, system identification and subsequent FE model updating analysis, automatic modal identification and investigation of the influence of the environment on the identified modal parameters. & 2010 Elsevier Ltd. All rights reserved.
Keywords: Damage identification Experimental testing Modal analysis Masonry structures
1. Introduction Preservation of the architectural heritage is a fundamental issue in the cultural life of modern societies. This heritage is accumulating damage due to deterioration of materials, repeated loading and exceptional events. This means that conservation, repair and strengthening are often necessary. In this process, monitoring and non-destructive (ND) testing play a major role, providing information on the building condition and existing damage, and allowing to define adequate remedial measures. The paper must be therefore understood in a general framework of damage identification by using Global and Local techniques. Vibration-based damage identification methods, usually defined as Global methods, can alert for the presence of damage and define its location (e.g. [1]), but they might not give sufficiently accurate information about the type and extent of the damage. Visual inspections or experimental non-destructive tests like the acoustic or ultrasonic methods, magnetic field methods, radiography, eddy-current methods and thermal field methods (e.g. [2]), also called as Local methods, can be preceded by a global method that indicates that damage is present. Local methods are certainly more accurate to localize and describe the damage.
Corresponding author.
E-mail address: [email protected] (L.F. Ramos). 0888-3270/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ymssp.2010.01.011
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Nomenclature
x
s o j f
p j00 jexp Aq
damping coefficient estimated standard deviation eigen frequency or resonant frequency mass-non-scaled mode shapes mass-scaled mode shapes objective function mass-non-scaled curvature mode shapes measured modal displacement scalar of the ARX model
Bq E q ro rj
scalar matrix of the ARX model Young’s modulus delay operator vector of frequency residuals vector of mode shape residuals
2 r^ xy R^ xy
coefficient of determination
u W
covariance input in the ARX model weighting factors
2. Damage identification Historical masonry structures exhibit usually a complex geometry and successive past interventions. In addition, the constituting materials tend to exhibit significant variations in properties and internal structure. The damage on masonry structures mainly relates to cracks, foundation settlements, material degradation and deformations. When cracks occur, they are generally localized, splitting the structures in macro-blocks. The use of dynamic-based methods to assess the damage is an attractive, but complex, tool to apply to this type of structures due to requirements of possible remedial measures: unobtrusiveness, minimum intervention and respect of the original construction. The assumption that damage can be linked to a decrease of stiffness seems to be reasonable to this type of structures, as for structures with other materials. Many methods and applications have been presented in the literature for damage identification based on vibration signatures, see e.g. [3–9], but there are only a few papers related to masonry-like structures. It is also noted that the usage of these techniques for monitoring and damage identification requires elimination of the environmental effects [10]. Fig. 1 presents an overview of different methods organized according to the level of damage identification, the required data, and
Classification
Modal data (ω and/or ϕ and/or ϕ″)
Methods
Model Based
Data
Damage Identification
• Frequency Shifts (Level 1); • COMAC (Level 2); • Mode Shape Curvature (Level 2); • Parameter Method (Level 2); • Damage Index (Level 2); • Changes in Flexibility Matrix (Level 2); • Direct Stiffness Calculation (Level 2 and Level 3).
Non-Model Based
Time data
• FE Model Updating Techniques (Level 2 and Level 3)
• Wavelet Analysis (Level 1 and Level 2)
Reference scenario is not required (Non-Reference Based)
Reference scenario is required (Reference Based) Fig. 1. General overview of the damage identification methods [12]. Level 1 is detection, Level 2 is localization and Level 3 is assessment.
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the need of a reference scenario. Still, at the moment, there is no method based on vibration signatures that gives accurate results for all levels of damage and for all types of structural systems. This is still a challenge for the next decades [5,8]. 3. Monitoring procedures The current practices of structural health condition are based mainly on periodic visual inspections or condition surveys but, during the last decade, software and hardware developments made continuous monitoring possible [8]. Typically, one can install hundreds of sensors in a structure and read the data in real time. The attention now seems to be focused on what type of information is important from the structural point of view and how the data should be processed and stored for damage analysis [13]. The developments in Micro Electro Mechanical Systems (MEMS) and Wireless Sensor Networks (WSN) are promising technologies in this field, in particular for historical masonry structures [14]. The process leading to monitoring of historical masonry structures can be divided in four phases: 1. The first phase is the data collection of the structure, including the historic information, geometrical and topographic survey, damage survey, mechanical materials characterization with ND tests, global dynamic modal test and a numerical model analysis for static and dynamic validation. This is the first approach to the structural behaviour in the assumed condition at time ‘‘zero’’. 2. In the second phase the health monitoring plan can be performed with a limited number of sensors (e.g. a pair of reference accelerometers, strain gauges at critical sections, temperature and humidity sensors, etc.). Data should be stored periodically and the monitoring system should be able to send the proper alarms. Environmental effects should be studied and the presence of damage should be observed by the global modal parameters. 3. In the third phase, should it be required by the first two phases, or by a life cycle cost analysis, or by the importance of the structure, a full-scale dynamic survey with more sensors and measuring points should be performed. In this phase the ‘‘health condition’’ of a structure is studied with more detail. Damage identification methods should be applied to the structure after filtering the environmental effects. The aim of the dynamic methods is to confirm and locate the (possible) damage in a global way. 4. In the last phase, a local approach with visual and complementary ND tests should be performed to locally assess the damage and classify it. The global and local approach should be considered as complementary tasks. For the case of historical constructions these two approaches seem to be suitable, since they are ND procedures to evaluate the health conditions. The following sessions present two complex case studies, in which the first two phases of the preceding methodology were already applied. Here, a dynamic identification monitoring system is used to detect cracks in masonry structures at early stage, the possible breakage or loss of anchorage in a tie, or changes in the boundary conditions. 4. Case study I—Mogadouro Clock Tower The Mogadouro Clock Tower is located inside the castle perimeter (see Fig. 2) of Mogadouro, a small town in the Northeast of Portugal. The tower was built after the year 1559. It has a rectangular cross section of 4.7 4.5 m2 and a height of 20.4 m. Large granite stones were used in the corners and rubble stone with thick lime mortar joints were used in the central part of the walls. The thickness of the walls is about 1.0 m. In 2004, the tower was severely damaged, characterized by large cracks, material deterioration and loss of material in some parts, see Fig. 2a and b. A geometrical survey of the structure was performed and the existing damage was mapped.
Fig. 2. Mogadouro Clock Tower: (a, b) before the rehabilitation works and (c, d) after the rehabilitation works.
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S7 S8 S9
E10
S4 S5 S6
E11 E13 E12
E5 E6
W13 W15 W16 E14 W12 W14
E8 E9
S1
S2
E1 E2
S3
E4 E3
W9
W7 W8
E7
W1
W11 W10
W3 W5 W6
N12 N14 N15 N13
N11
N6
N4
N9 N10
N5 N7 N8 N1
N2 N3
W2 W4
Fig. 3. Dynamic tests and example of sensor locations: (a) south, east, west and north fac- ade measuring points, respectively; (b) measurements before rehabilitation works and (c) after rehabilitation works.
Table 1 Dynamic response before and after the rehabilitation. Mode shape
1st 2nd 3rd 4th 5th 6th 7th Average values
Before
After
Do
Before
After
Dx
o (Hz)
CVo (%)
o (Hz)
CVo (%)
(%)
x (%)
CVx (%)
x (%)
CVx (%)
(%)
2.15 2.58 4.98 5.74 6.76 7.69 8.98 –
1.85 1.05 0.69 1.56 1.13 2.94 1.21 1.49
2.56 2.76 7.15 8.86 9.21 15.21 16.91 –
0.21 0.30 0.27 0.47 0.21 2.24 1.40 0.73
+19.28 + 6.70 +43.67 +54.37 +36.13 +97.87 +88.27 +49.47
2.68 1.71 2.05 2.40 2.14 2.33 2.30 2.23
219.51 94.02 65.33 24.27 31.74 55.98 46.39 76.75
1.25 1.35 1.20 1.31 1.16 2.54 1.49 1.47
0.13 0.17 0.14 0.13 0.12 0.24 0.23 0.17
53.26 21.00 41.32 45.72 45.65 + 9.11 35.07 40.34*
* Average value calculated only with negative differences.
Rehabilitation works carried out in 2005 reinstated the tower safety, see Fig. 2c and d, including lime injection for the consolidation of the walls, replacement of material with high level of degradation, filling of voids and losses, and installation of ties (or steel belt) at two levels.
4.1. Modal identification before and after the rehabilitation works Two dynamic modal identification tests were performed before and after the works. The same test planning was adopted in the two conditions by using the same measuring points, see Fig. 3a. Fig. 3b and c presents images of the execution of the ambient dynamic tests carried out before and after the works. The dynamic acquisition system was composed by 4 uniaxial piezoelectric accelerometers, with a bandwidth ranging from 0.15 to 1000 Hz (5%), a dynamic range of 70.5 g, a sensitivity of 10 V/g, 8 mg of resolution and 210 g of weight, connected by coaxial cables to a front-end data acquisition system with a 24-bit ADC, provided with anti-aliasing filters. The front-end was connected to a laptop by an Ethernet cable. The accelerometers were bolted to aluminum plates that were glued with epoxy to the stones. A preliminary FE dynamic analysis estimated 10 frequencies between 2 and 15 Hz. Therefore, and for each test campaign, a sampling frequency of 256 Hz was chosen to acquire the response with ambient excitation. The total sampling time of each setup was equal to 10 min and 40 s (2000 times the highest period). Table 1 presents the first seven estimated natural frequencies, damping ratios, and Coefficient of Variation (CV), estimated by the Stochastic Subspace Identification (SSI) method [10] (Principal Component), implemented in ARTeMIS [11], Fig. 4 shows the corresponding mode shapes. Analyzing the two structural conditions, on average the frequencies increased 50% with the consolidation works, while the damping decreased 40% for all modes, with exception of sixth mode. As expected, by closing the cracks the stiffness increased and the energy dissipation decreased, directly affecting the frequencies and damping, respectively. Concerning the modal displacements, local protuberances can be observed in the areas close to the cracks and in the upper part of the
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Before Rehabilitation
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1st mode
2nd mode
3rd mode
4th mode
5th mode
6th mode
7th mode
2.15 Hz
2.58 Hz
4.98 Hz
5.74 Hz
6.76 Hz
7.69 Hz
8.98 Hz
2.56 Hz
2.76 Hz
7.15 Hz
8.86 Hz
9.21 Hz
15.21 Hz
16.91 Hz
y
z x
y
z x
Fig. 4. Experimental mode shapes and MAC values before and after rehabilitation works.
tower, before the works. This is due to the presence of severe damage. On the contrary, the structure behaves monolithically after the rehabilitation. Taking into account the previous results, it is possible to conclude that the structure suffered a significant structural intervention and the strengthening works were efficient. One can also conclude that the presence of damage changed the dynamic behaviour significantly with respect to the possible original structure. The challenge now is to verify if the cracks were stabilized with the intervention by means of a dynamic monitoring system. 4.2. Structural assessment For the structural assessment, a 3D FE model was built. The model updating analysis was performed with the aim to assess the tower dynamic behaviour in its actual condition (after the retrofitting). The non-linear least-squares method implemented in MatLab [15] was used together with DIANA [16] to compute the numerical modes. The objective function p to be minimized is composed by the residuals formed with calculated and experimental frequencies and mode shapes, given by [17] 2 3 N N X m X 1 4X p¼ r þ r 5 ð1Þ 2 i ¼ 1 o;i i ¼ 1 j ¼ 1 j;i;j with N denoting the number of eigenfrequencies, m denoting the number of degrees of freedom in each eigenvector, and ro and rj denoting the vectors of eigenfrequency residuals and of mode shape residuals, respectively. The residuals ro and rj are given by !2 2 o2i o2i;exp ro;i ¼ Wo;i ; rj;i;j ¼ Wj;i jji jji;exp ð2Þ 2
oi;exp
where the subscript exp indicates experimental values, and Wo, and Wj are the weighting factors for frequencies and mode shapes, respectively. The weighting factors can have different values according to the engineering judgement of the user. Note that mode shapes are scaled in a way that the maximum value in any vector component is equal to one. With this scaling, frequencies and mode shapes differences are in the same order of magnitude and can be compared in the same equation. The first attempt to tune the numerical model was carried out in a series of analysis using shell element models, see [12] for details. Due to the unrealistic updating results obtained, it was concluded that the structure needed to be modelled with 3D brick elements, mainly to better represent the corners stiffness and the geometry of the upper part of the tower. The optimization parameters were selected taking into account the possible differences between the material properties and the modulus of elasticity of the different parts was chosen as updating parameters. Fig. 5 shows the final 3D model where eight updating parameters can be observed. Table 2 shows the updating analysis results, including the initial and final values for each updating parameter, the average frequency error, the average Modal Assurance Criterion (MAC) value, the average Normalized Modal Difference (NMD) value, and the average Co-ordinate Modal Assurance Criterion (COMAC) value. With respect to Young’s modulus variation, the South and North fac- ades have values around 2 GPa, and the East and West fac- ades have values around 1 GPa.
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Fig. 5. Updating parameters for the brick elements model.
Table 2 Results for the model updating analysis after rehabilitation. Updating parameters
Initial values (GPa)
Final values (GPa)
E1 E2 E3 E4 E5 E6 E7 E8
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
1.974 2.210 1.075 0.804 3.875 1.210 0.195 5.997
(south) (north) (west) (east) (corners) (columns) (roof) (foundation)
Average o error (%)
Average MAC
Average NMD
Average COMAC
|2.10|
0.98
0.12
0.98
The differences from one to two are acceptable, if the heterogeneity of masonry is taken into account. The material at the corners has higher stiffness, about 4 GPa, and the areas with better masonry type have values of the same order of the masonry walls in general. The roof has a lower value around 0.2 GPa and the foundation 6 GPa, which is acceptable due to the lack of information on the foundations, the likely higher vertical stress at the base, the possible enlargement of the foundation at the base and the soil confinement. Fig. 6 presents the tuned modes and the frequency values, where it is possible to observe that the upper part of the structure has a flexible behaviour due to the presence of the windows. The discussion on the tower structural behaviour, by means of FE model updating techniques, demonstrates that the correct definition of the structure, including the foundations, is critical for having a good correlation between the experimental and numerical modal results. 4.3. Dynamic monitoring system From the beginning of April 2006, and after the rehabilitation, a dynamic monitoring system was installed in the tower, see Fig. 7. The aim is to evaluate the environmental effects of temperature and relative air humidity on the dynamic behaviour of the tower, and to detect any possible non-stabilized phenomenon in the structure (damage). Three piezoelectric accelerometers connected to an USB data acquisition card with 24 bits resolution are recording each hour ten minutes of ambient vibrations. In parallel a combined sensor is recording the ambient temperature and relative air humidity. This task is performed in several campaigns (test series), in different periods of the year. During each
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y x
y x Mode 1 (2.54 Hz)
Mode 2 (2.68 Hz)
Mode 3 (7.33 Hz)
Mode 4 (8.62 Hz)
Mode 5 (9.36 Hz)
Fig. 6. Numerical mode shapes after rehabilitation.
A1
Level 5
North
Level 4 Level 3 A1
TH
A2
D Level 2 TH D
A2
y x
Level 1
North
z
South
y
Fig. 7. Dynamic monitoring system: Dynamic monitoring system: (a) location of measuring positions, datalogger (D) and environmental sensor (TH); (b) measured directions for accelerations; (c) installation of accelerometer at position A1; (d) accelerometers at position A2 and (e) datalogger and environmental sensor.
campaign 600 records of ten minutes at every hour are stored in a laptop. No triggering was applied. Ten series were completed in the period from April 2006 until December 2007. For modal estimation, an automatic procedure based on the SSI/Ref method [18] was implemented in MatLab [15]. However, the automatic procedure needs a preliminary manual estimation of a few numbers of events to better establish limit values for the automatic estimation. In the manual identification, six to ten data files were selected to better analyze the modal results. A maximum statespace model order equal to 50 is fixed. This number corresponds to 25 structural vibration modes and is expected to
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exceed the true model order significantly. Although this parameter does not have a direct repercussion on the analysis results, selecting a relatively large number helps to visualize and to define trends in the stabilization diagrams. Next, eigenfrequency intervals, damping intervals and a reference mode shape vector are established. Normally, the damping coefficient interval for all the modes was between 0.5% and 3%. Finally, the automatic procedure is applied to all the events with the same range of model order. To avoid unrealistic modes, for every event file the selection of the correct model order in the stabilization diagram is carried out by selecting the model that gives the frequencies and the damping values in the expected intervals, and gives the best MAC values (always greater than 0.95).
4.4. Environmental effects The data series were analyzed and they allowed concluding that the environmental effects significantly change the dynamic response of the structure. Mainly, the water absorption of the walls in the beginning of the raining seasons changes the frequencies about 4%. The significant influence of moisture inside the walls on the dynamic response of masonry structures is not reported in literature, as the changes are always attributed to others environmental effects or loading conditions, such as temperature and excitation level. The series presented in Fig. 8 was recorded during October and November, 2006, which is linked to the first strong raining event at the site. As no damage was observed in the structure, the humidity influence can be observed by a shift in the linear relation between frequency and temperature by a transition series (gray dots in Fig. 8a). The ambient temperature, the relative air humidity and the excitation level, by means of the Root Mean Square (RMS) of the signal, were correlated to the resonant frequencies. Multiple linear regression models were compared with AutoRegressive outputs with eXogeneous input models, also known as ARX models [19], in order to evaluate the environmental and loading effects. ARX models with Multiple Inputs and a Single Output (MISO models) were computed in MatLab [15], to model each frequency value. The multivariable ARX model with n inputs u and one output y is given by Aq y^ k ¼ Bq uenv knk þ ek
ð3Þ
First two Frequencies versus Temperature 3.0
Frequency [Hz]
2.8 2.6 2.4 2.2 2.0 0
5
10
15 20 Temperature [ºC]
25
30
35
First two Frequencies versus Humidity 3.0
Frequency [Hz]
2.8 2.6 2.4 2.2 2.0 0
10
20
30
40 50 60 Humidity [%]
70
80
90
100
Fig. 8. Environmental effects: (a) temperature and (b) relative air humidity. Black dots correspond to the first frequency, white dots to the second frequency, and gray dots to the transition period of each frequency.
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where Aq is a scalar with the delay operator q 1, Bq is a matrix 1 n, and e are the unknown residuals. For convenience, to model the response and to establish the confidence intervals, an approach similar to the one used by Peeters [10], with the appropriate changes, was used. The methodology includes the following steps: 1. Normalized inputs and outputs: uenv k;Temp ¼
uenv;m u 1 k;1
su;1
;
uenv k;RMS ¼
uenv;m u 2 k;2
su;2
;
uenv k;Hum ¼
uenv;m u 3 k;3
su;3
and
yk;o ¼
ym k y
sy
ð4Þ
where uenv;m and ym k are the measured values for the environmental parameters and the dynamic response, respectively, k;i u i and y are the average values and su,i and sy are the standard deviations. 2. Estimate ARX models and their statistical properties (e.g. ARX[0, 1 2 3, 0 0 0], i.e. an ARX model for one output and three inputs, with zero order for the autoregressive part, three different orders for the exogeneous part and with no delays). 3. Select the ‘‘best’’ model based on quality criteria, such as the loss function V with is the average quadratic error, the Akaike’s Final Prediction Error (FPE) which measures the model quality by simulating the situation where the model is 2 tested on a different data set, see [19], and the coefficient of determination r^ xy , given by !2 N R^ xy 1X 1þ d=N 2 V¼ e2k ; FPE ¼ V ð5Þ ; and r^ xy ¼ s^ x s^ y N 1d=N k¼1
where d is the number of estimated parameters and R^ xy is the estimated covariance. 4. Simulate the expected response with the previous selected model. 5. Calculate the simulation error and its statistics e^ k ¼ yk y^ k
and
R^ xy
ð6Þ
6. Establish the confidence intervals ci and detect the outliers qffiffiffiffiffiffiffi qffiffiffiffiffiffiffi y^ k zð1a=2Þ R^ xy ; y^ k þzð1a=2Þ R^ xy
ð7Þ
where z is found from a statistical table of Student’s t-distribution (e.g. to compute 95% confidence interval, a = 0.05 and z (for a large number of data points) is equal to 1.96. Fig. 9a shows the fitting models through the normalized frequency and simulated errors with the 95% confidence intervals ci, and Fig. 9b shows the simulated error. In general, the model is able to replicate the frequency variation, but does not takes into account the water absorption phenomenon, because the relative humidity variation does not totally represent that change. Nevertheless, by observing Fig. 9 no damage was detected because the simulated error does not go significantly further than the confidence intervals. This fact was visually confirmed in the tower, as no damage was found during the monitoring period. The results indicate that ARX models can simulate the natural frequencies, but sensors to measure the water absorption inside the walls are necessary in this case to better simulate the dynamic response and to detect the presence of damage. A proposal for new humidity sensors was made in [12]. To monitor this phenomenon, humidity sensors should be placed inside the four fac-ades, at different elevation levels. In order to better study the distribution of the humidity inside the walls, on each measuring point three sensors should be placed along the thickness of the walls. Additionally, to evaluate the tower mass change due to rain, load cells or flat jacks test equipment can be also installed at the bottom of the walls in order to measure the changes in the compressive stresses. For these sensors, a measuring periodicity of one sample per hour will be enough to follow the water absorption phenomenon.
3 2
Simulation Error
Normalized Frequency
4
1 0 -1 -2 -3 -4
0 100 200 300 400 500 600 700 800 900 Events
5 4 3 2 1 0 -1 -2 -3 -4 -5
0 100 200 300 400 500 600 700 800 900 Events
Fig. 9. ARX model [3, 2 2 4, 0 0 0] (i.e. an ARX model for one output and three inputs, with order three for the autoregressive part, with orders two, two and four for the exogeneous part and with no delays) for mode shape 1 with 95% confidence intervals: (a) normalized frequency and (b) simulation error.
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5. Case study II—Church of Monastery of Jero´nimos The Monastery of Jero´nimos, located in Lisbon, is one of the most famous Portuguese monuments (see Fig. 10). The Portuguese ‘‘Manuelino’’ architectural style of the XVI Century makes the monument very attractive for tourists. The church of the monastery, Santa Maria de Bele´m church, has considerable dimensions: a length of 70 m, a width of 40 m and a height of 24 m.
5.1. Modal identification of the main nave The main nave of the church was tested using output-only modal identifications techniques, which provided the modal parameters: resonant frequencies, mode shapes and damping coefficients. Two techniques were applied to compare the experimental dynamic parameters obtained and have more accurate results. The Enhanced Frequency Domain Decomposition (EFDD) [20] and the Stochastic Subspace Identification (SSI) method. Thirty points on the top of the main nave were selected to measure the acceleration response, see Fig. 11. Ten points are located on the top of the external walls with the purpose of measuring the nave boundaries and also the global dynamic response of the church. The other points are located either on the top of the columns or on the top of the vault keys. Table 3 summarizes six natural frequencies, damping ratios and MAC values estimated by two different output-only system identification techniques. The natural frequencies range from 3.7 to 12.45 Hz and no significant differences could be found between the two methods. For the damping coefficients, differences up to 140% can be observed. The reasons for such large differences in damping can be explained by the effect of the noise in the data or the low excitation level in the nave. Moreover, although in the EFDD technique the natural frequencies and damping ratios are, in general, estimated with a good accuracy, when the deterministic signals are close to the natural frequencies, the fitting SDOF Bell functions of the EFDD method can give deviations in the modal parameters, mainly for damping coefficients. Finally, the MAC values are only higher than 0.95 for the first two modes as a consequence of the difficulty in exciting this heavy structure. Fig. 12 shows the shape of the first two modes. The dynamic response of the main nave is influenced by the slenderness of the columns and the modes are composed by components mostly in y (North–South) and z (vertical) directions.
y x
C
B
A
A
C
z
B 0.0
25.0 m
x
Fig. 10. Church of Monastery of Jero´nimos: (a) inside view of the choir; (b) aspect of the three naves; (c) plan and (d) section A–A.
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P11
P10
P30
P22
P9
P23
P21
P24
y x
P25
P15
P2
P3
P26
P14
P13
P4
P27
P19 P17
P16 P29
P7
P8
P20
1301
P18 P1
P12
P28
P5
P6
Fig. 11. Measurement points: (a) in plan location and (b) the reference transducer.
Table 3 Comparison with the estimated modal parameters of the main nave.
o (Hz)
Mode shape
Mode Mode Mode Mode Mode Mode
1 2 3 4 5 6
EFDD
SSI
EFDD
SSI
3.69 5.12 6.29 7.23 9.67 12.45
3.68 5.04 6.30 7.29 9.65 12.51
2.34 1.11 1.00 0.77 1.10 1.25
1.26 2.68 0.82 1.44 1.45 1.19
y
z y
z x
x
y x
0.99 0.92 0.67 0.67 0.62 0.71
y y
z
z
MAC
x (%)
z
x
z x
y x
Fig. 12. Experimental mode shape results from EFDD method: (a) first mode shape at 3.7 Hz and (b) second mode shape at 5.1 Hz.
Nevertheless, this modal identification seems to be acceptable if the structural complexity of the main nave is taking into account. Even if the mode shape and damping coefficients estimation is not very accurate for the higher modes, their natural frequencies seem accurately extracted by the two output-only techniques. The use of the two output-only techniques helped in the results discussion and validation. For masonry-like structures, the robust results obtained, together with simplicity, the low cost, the non-destructiveness and low interference with operating conditions make these techniques an attractive tool to assess historical constructions. One disadvantage is the fact that the mode shapes are not scaled with respect to the structure mass matrix.
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5.2. Structural assessment Due to the high level of complexity of the structure a beam FE model was manually tuned to the dynamic experimental results. The adoption of a relatively ‘‘simple’’ model is due to the fact that the model is to be used in subsequent non-linear time integration analysis, including a parametric study using a set of mechanical properties, different return period scenarios and strengthening possibilities, see also [21]. Nevertheless, it should be stressed here that for a correct updating analysis the complexity of the structure needs a FE model with volume elements to accurately reproduce the dynamic response, similarly to what was carried out for the case of the Mogadouro Tower presented in Section 4.2. The updating parameters were the modulus of elasticity of the columns and the main nave, and the boundary conditions of the columns. The dynamic response is mostly governed by the slender columns, as many local modes appear in the results. The first mode shape of the numerical model is presented in Fig. 13. Table 4 shows the first six frequencies after tuning for the first frequency. The results obtained for the modulus of elasticity were 30 GPa for the columns and 12 GPa for the masonry. The high value for the columns can be explained by the very high compression stresses present due to the small cross section, and the fact that solid drums and very thin joints are used.
5.3. Dynamic monitoring system Since April of 2005, a dynamic monitoring system was installed in the church within the scope of the Euro-Indian research project ‘‘Improving the Seismic Resistance of Cultural Heritage Buildings’’. The monitoring system is composed of two strong motions recorders (R) with 18 bits AD converters connected to two triaxial force balance accelerometers, see Fig. 14. One accelerometer (A1) was installed at the base of the structure near the chancel and the other (A2) at the top of the main nave (extrados), between two consecutive columns, and in the location with higher signal levels obtained in the dynamic modal identification analysis. The two recorders are connected by an enhanced interconnection network, which allows a common trigger and time programmed records. The recorder connected to sensor A1 is the master recorder, which enables synchronization and updates the internal clock of the slave recorder connected to sensor A2. The monitoring task is mainly processed by the master recorder, with a trigger armed for low-level signals corresponding to microtremors occurring at the site. In parallel, every month, dynamic data are registered during 10 min. Also seasonally, to study the environmental effects, 10 min are recorded every hour during one complete day.
y y x
x
Fig. 13. First mode numerical mode shape at 3.79 Hz: (a) transversal section and (b) plan view.
Table 4 Comparison experimental and numerical frequencies of the two columns. Modes
1 2 3 4 5 6
Experimental
Numerical
o (Hz)
Comment
o (Hz)
Comment
3.68 5.04 – – – –
Main nave (x) Main nave (x) – – – –
3.79 5.06 5.20 5.34 5.76 6.13
Main nave (x) Tower (x) Tower (y) Columns and main nave (x)
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y x
A1, R A2
0.0
25.0 m
Fig. 14. Dynamic monitoring system: (a) location of the sensors; (b) battery of recorders and the base accelerometer and (c) accelerometer on the main nave.
Frequency versus Temperature
Temperature
50 40 30 20 10 0
Frequency [Hz]
Frequency
Temperature [ºC]
4.2 4.1 4.0 3.9 3.8 3.7 3.6 3.5
Feb-05 Apr-05 Jun-05 Aug-05 Oct-05 Dec-05 Feb-06 Apr-06 Jun-06 Aug-06 Oct-06 Dec-06 Feb-07 Apr-07
Frequency [Hz]
Temperature Effect on the First Frequency
4.2 4.1 4.0 3.9 3.8 3.7 3.6 3.5 0
5
10
15
20
25
30
35
40
Temperature [ºC]
Date Fig. 15. Results for the first mode shape: (a) frequency and temperature variation and (b) frequency versus temperature.
The dynamic monitoring system is complemented by a static one, which measures temperatures and rotation of the columns at several points in the structure. Additional sensors for relative air humidity and wind velocity were recently added to this system.
5.4. Environmental effects For the study of the environmental and loading effects all data acquired in the strong motion recorders were used. Up to now, 1300 events were acquired: 28% of which correspond to programmed events with ten minutes of total sampling duration, and 72% correspond to triggered events, with an average sampling duration of 1 min and 15 s. To estimate the modal parameters, the procedure described previously for the Mogadouro Clock Tower was again adopted. It should be stressed that in the modal parameter estimation only the first, the third and the fourth mode shapes of the nave were successful estimated. The majority of the triggered events occurred during working hours, due to the road traffic, special events inside the church (like mass or concerts), and minor earthquakes. With respect to programmed events, it is noted that it was more difficult to estimate the modal parameters during the night period, due to the low ambient excitation level. Observing Fig. 15a, it can be concluded that for the case of the nave the temperature effect is significant, because the first frequency values can follow the temperature along the time. This effect turns clear when plotted the temperature values against frequency, see Fig. 15b. With later figure, a trend for linear relation between temperature and frequency was found, with a possible apex for a temperature about 18 1C. This trend occurs for all the estimated frequencies. As no continuum series were recorded in the monitoring system, modelling of thermal inertia is difficult and only static regression models were used. From the observed bilinear trend, two linear regressions for temperature values lower and higher than 17.5 1C were adopted. Fig. 16a shows the static models for the first estimated frequency by correlating the two quantities, temperature and frequency with the 95% ( 72s) confidence intervals. The results show that the bilinear static model follows the evolution of the frequencies but a significant number of outliers can be observed in Fig. 16b, where the residuals between the first natural frequency and the simulated frequency are shown. This indicates that others environmental effects need to be studied to better model the dynamic response. Finally, it should be stressed that in 12 February 2007, at 10:35 am a 5.8 magnitude earthquake, with a Modified Mercalli intensity V, occurred in the Southwest of Lisbon. The permanent staff of the monument felt the ground shake. No visitors were inside the church because on Mondays the church is closed to public. The strong motions recorders acquired the signals, as can be observed in Fig. 17a. The peak of the frequency contents of the elastic response spectra was in the
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Oct-07
Jun-07
Aug-07
40
Feb-07
35
Apr-07
30
Oct-06
15 20 25 Temperature [ºC]
Dec-06
10
-0.45 Jun-06
5
-0.30 Aug-06
0
0.00 -0.15
Feb-06
3.5
0.15
Apr-06
3.7 3.6
0.30
Oct-05
3.9 3.8
Residuals for the First Frequency
0.45
Dec-05
Frequency Residuals [Hz]
Frequency [Hz]
Static Regression for the First Frequency 4.2 4.1 4.0
Aug-05
1304
Date
Fig. 16. Static regression for the first mode: (a) temperature influence and (b) residuals history.
Acceleration [mg]
10 8 6 4 2 0 -2 0 -4 -6 -8 -10
Nave (A2) Base (A1)
25
50
75
100
125
150
Acceleration [mg]
Accelerograms in the x Direction
Elastic Response Spectra (ξ = 5%)
15.0 12.5 10.0 7.5 5.0 2.5 0.0
x
0
Time [s]
y
z
5 10 15 20 25 30 35 40 45 50 Frequency [Hz]
Fig. 17. Small earthquake in February, 2007: (a) the accelerograms in the x direction (transversal) at the base and at the nave and (b) the elastic response spectra of the seismic event.
range of the estimated natural frequencies, see Fig. 17b, but the estimated natural frequencies did not suffer any significant shift, as can be observed through Fig. 16b. Therefore, no damage in the structure occurred due to this minor earthquake. 6. Conclusions A methodology based on operational modal analysis is presented for masonry structures, aiming at detecting damage at an earlier stage. The methodology comprises four phases, namely data collection, simplified health monitoring, detailed health monitoring and local non-destructive testing. As an illustration, the first two phases were applied to two complex Portuguese monuments. For these monuments, the modal identification results, the development of structural model with model updating techniques, for subsequent assessment with FE models, the installation of monitoring systems and the automatic parameter retrieval were presented. From the experience with the two cases, the proposed methodology for damage identification seems to be useful and applicable to masonry-like structures, especially to complex historical constructions. In particular, the frequency monitoring seems to be a reliable quantity for damage detection. Analysis of the environmental effects on the dynamic behaviour through autoregressive models was carried out. An important conclusion emerging from the results is the non-negligible influence of the humidity on the dynamic behaviour of masonry-like structures subjected to rain, besides the well-known influence of the temperature. Finally, apparently no damage was observed in the two monuments by global modal parameters changes during the monitoring period.
Acknowledgements The authors would like to thank Edwin Reynders for his kind support in the automatic system identification. The activities on Monastery of Jero´nimos were partly funded by the EU-India Economic Cross Cultural Programme ‘‘Improving the Seismic Resistance of Cultural Heritage Buildings’’, Contract ALA-95-23-2003-077-122. References [1] P.C. Chang, A. Flatau, S.C. Liu, Review paper: health monitoring of civil infrastructure, Structural Health Monitoring 2 (3) (2003) 257–267. [2] J.E. Doherty, Nondestructive evaluation, in: A.S. Kobavashi (Ed.), Handbook on Experimental Mechanics, Society for Experimental Mechanics, 1987 (Chapter 12). [3] S.W. Doebling, C.R. Farrar, M.B. PrimeD. Shevitz, Damage Identification and Health Monitoring of Structural and Mechanical Systems from Changes in their Vibration Characteristics: A Literature Review, Los Alamos National Laboratory, New Mexico, NM, 1996 132 pp.
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