Figure 4. Monitoring system: (a) and (b) sensors location; and (c) logger software.

The LabView (2006) software was used to measure and acquire accelerations, see Figure 4c. In parallel, a combined sensor connected to the laptop through serial cable is recording the ambient temperature and relative air humidity. The environmental data is acquired in the laptop by interface software provided by the supplier of the combined sensor.

Every hour, 10 minutes of ambient vibrations in the three channels with a sampling frequency of 100 Hz are acquired without any triggering. The data is then saved in ASCII files.

Finally and for modal estimation, an automatic procedure based on SSI/Ref method (Peeters and De Roeck, 1999) was implemented in MatLab.

The second phase of the proposed approach is the dynamic monitoring task, which can be performed with a limited number of sensors. This task has been carried out since April, 2006, in the Mogadouro Clock Tower. The aim is to evaluate the environmental and loading effects and to detect any possible non stabilized phenomena in the structure (damage), by studying the global dynamic parameters.

A low-cost monitoring system was chosen for this task. The system is composed by three piezoelectric accelerometers, connected by coaxial cables to a USB data acquisition card with 24 bits resolution, provided with anti-aliasing filters, which is connected to a Pentium IIĀ® laptop with an uninterruptible power supply device.

Two points (A1 and A2) were selected in the middle of Level 2 to acquire accelerations in three directions, see Figure 4a and b. In this way, all the mode shape components of the first five eigenfrequencies can be studied, including the torsion mode. The environmental measurements are acquired in the point TH, close to the datalogger (D).

4.1 Filtering the environmental and loading effects for damage detection

The study of the environmental and loading effects was initially based on the assumption that the modal response is changed by three independent variables: temperature, relative air humidity and the level of excitation. For the later and for every event, it was decided to use the average Root Mean Square (RMS) value of the three acceleration channels.

In general, there is a positive relation between temperature and frequency, and a negative relation between humidity and frequency and between level of excitation and frequency.

Here it should be stressed that a significant frequency shift related to the walls water absorption happens twice a year. Figure 5 presents the first resonant frequency variation compared with the environmental variables along short period. During this period the temperature did not change significantly, while the relative air humidity after 18th of October is close to 100%, i.e. the first raining season on the site.

Figure 5. Environmental effects of the dynamic response.

Figure 6. Numerical simulation: (a) ARX model; and (b) the residuals distribution.

Figure 5. Environmental effects of the dynamic response.

After 22nd of October the frequency values decrease linearly with humidity almost constant. This indicates that the structure absorbs water and the mass changes, reducing the frequency values because the two quantities are inverse related. It can also occur that water leads to a stiffness reduction, at least in the lime mortars. The inverse drying phenomenon also happens during the hot period.

Since the environmental and the loading variables are changing the modal parameters of the tower, an attempt to model the dynamic response according to the three variables was carried out. It was decided to use a procedure similar to the one used by Peeters (2000) with AutoRegressive output with an eXoge-neous input parts models (ARX models). Here, ARX models with multiple inputs and a single output (MISO models) were computed in MatLab (2006), function arx, to model each frequency value. The multivariate ARX model with n inputs u and one output y is presented by:

where Aq is a scalar with the delay operator q-1, Bq is a matrix 1 x n, and e is the unknown residuals. For damage detection, confidence intervals were establish and by analyzing the outliers is possible to detect damage.

Figure 6 shows for the first natural frequency the fitting model through the normalized frequency and simulated errors with the 95% confidence intervals ci. In general, the model represents the frequency

Figure 6. Numerical simulation: (a) ARX model; and (b) the residuals distribution.

variation, but it doesn't account the water absorption phenomenon, because the relative humidity variation does not totally represent that change. Furthermore, the damage is detected by frequency shifts that significantly go outside the confident intervals ci.

Concerning the numerical frequency simulation, it should be stressed that the calibration period of one year might be not enough for having a tuned model. A longer period of, at least, three years should be used for calibration in order to have a reliable model for frequency prediction.

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