# Some Considerations about the Incorporation of Dynamic Parameters in the Structural Health Monitoring Systems of Bridges

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## Abstract

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## Featured Application

**Design and implementation of structural health monitoring systems for bridges.**

## Abstract

## 1. Introduction

## 2. Some References of Interest about the Dynamic Monitoring of Structures

## 3. Materials and Methods

#### 3.1. E-1 Structure

^{−6}g at frequencies lower than 10 Hz, installed on each road), 2 anemometers and 2 wind vanes (on the left road). These accelerometers were located on each roadway as follows: three vertical accelerometers in the haunches of the arch (two in the south haunch and one in the north haunch) and two accelerometers in the key of the arch, one of them vertical and the other transversal. In all cases, they were inside the arch box, on the lower side. The instrumentation was completed with a total of 37 thermometers and 2 laser distance meters to measure the movement of the expansion joints of the structure. The monitoring period in which there are dynamic records is between the months of March and September 2010. The range of ambient temperature recorded throughout this period was between 10 and 40 °C, which allowed us to detect its influence over dynamic parameters, as explained in the following sections.

#### 3.2. E-2 Structure

^{−6}g at frequencies lower than 100 Hz), 12 of which were vertical, 2 longitudinal, and 1 transversal. All these devices were inside the box section, either on the central axis or the lateral extremes, but in all cases, on the lower side. The structure was monitored between the months of June 2008 and December 2009 [36,37]. The range of temperatures recorded throughout this period was between 4 and 29 °C.

#### 3.3. Parameters under Study

- Accelerations, registered in the experimental accelerograms;
- Eigenfrequencies, obtained by the analysis of the accelerograms in the frequency domain and modes of vibration associated with these natural frequencies;
- Modal damping ratios calculated from the accelerograms after filtering in the neighbourhood of the eigenfrequencies.

## 4. Results

## 5. Discussion

#### 5.1. About the Structural Typology

#### 5.2. About the Type of Instrumentation

#### 5.3. About the Analysis of the Accelerations

#### 5.4. About the Analysis of the Natural Frequencies and Vibration Modes

#### 5.4.1. Study of the Available Background Information: Computational Models and Load Test

#### 5.4.2. Possible Correction of Values

^{2}) of up to a value of 0.90 in the case of the natural frequency f

_{exp 6}, as shown in Figure 6, where the relationship with the ambient temperature is represented, as it is the variable that, independently, had a greater correlation.

#### 5.5. About the Analysis of the Modal Damping Ratio

#### 5.5.1. Study of the Modal Damping Ratio Values

#### 5.5.2. Possible Correction of Values

- Although, a priori, the mechanical properties of the materials could vary depending on the temperature, in the E-1 structure, no relationship was observed between the variations recorded in the modal damping ratio neither with the ambient temperature nor the arch temperature.
- On the other hand, some correspondence was seen (coefficients of determination R
^{2}of the order of 0.20 and 0.30) in the case of two of the natural frequencies and the average wind speed. The justification for this fact may be that the modal damping ratio has an aerodynamic component, although this contribution is usually very small. - Finally, the relationship with the maximum vertical and transverse accelerations was also analysed since it is a measure of the degree of excitation of the structure. However, in this case, no clear relationships were obtained.

#### 5.5.3. About the Calculation Method of the Modal Damping Ratio

_{exp 5}= 1.675 Hz), its study in the frequency domain, the filtered wave, and the values of the modal damping ratio obtained as a result of applying different calculation methods. As can be seen, there is an important variation in the results, which in this case ranges from the 0.18% value obtained through the methods of logarithmic decrement, adjustment to the theoretical curve, and the RDT combined with the logarithmic decrement, to the value of 0.30% obtained through the RDT method combined with curve fitting. Therefore, in SHM systems, it is essential to know which modal damping ratio calculation method has been used and to maintain the same criterion throughout the monitoring period.

#### 5.5.4. Relationship between Modal Damping Ratios and Natural Frequencies

_{0}= 0.02272472 and α

_{1}= 0.00020197 result. The recorded modal damping factors (green points), their average values (blue points), and the adjustment obtained by applying the formulation indicated in this section (orange curve) have been represented in Figure 8. It can be seen how the values obtained with the instrumentation reasonably adjust in this case to the Rayleigh hypothesis.

#### 5.6. About the Set of Thresholds

## 6. Possible Future Lines of Research

- Firstly, the extension of this type of study to other real bridges with more actual results, which analyse the dynamics of structures of different typologies, given that, although there are more and more studies in the field of SHM systems, there are relatively few that relate the behaviour of real structures.
- Likewise, due to the enormous influence that the calculation method adopted can have on the values of the modal damping ratio, an in-depth study must be carried out on this issue, both on a theoretical and experimental level, which also analyses the possibility of introducing improvements in the mentioned procedures.
- Thirdly, it is necessary to explore the physical modelling of the correlations observed during the experimental analysis, especially in the case of the variation of the natural frequencies as a function of the ambient temperature, as well as the damping factor for certain natural frequencies as a function of the average wind speed.
- Fourth and last, more studies should be carried out on the variation in dynamic parameters as a consequence of specific damage having occurred, both through computational models, which will allow analysing of the behaviour, especially in terms of frequencies, and in scale tests, which will make it possible to see the behaviour both in terms of frequencies and the modal damping ratio.

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**Influence of the circulation speed on the maximum vertical accelerations obtained with the computational model of the E-1 structure.

**Figure 5.**Analysis of the natural frequencies in an event of the E-2 structure, accelerometer AV011: (

**a**) Accelerogram; (

**b**) Spectrum.

**Figure 7.**Calculation of the modal damping ratio in a dynamic event of the E-1 structure: (

**a**) Registered accelerogram; (

**b**) Spectrum; (

**c**) Filtered accelerogram; (

**d**) Modal damping ratios obtained by applying different calculation methods.

**Figure 8.**Example of the study of the relationship between natural frequencies and modal damping ratio under the Rayleigh hypothesis in structure E-1.

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**MDPI and ACS Style**

López-Aragón, J.-A.; Astiz, M.-Á.
Some Considerations about the Incorporation of Dynamic Parameters in the Structural Health Monitoring Systems of Bridges. *Appl. Sci.* **2024**, *14*, 33.
https://doi.org/10.3390/app14010033

**AMA Style**

López-Aragón J-A, Astiz M-Á.
Some Considerations about the Incorporation of Dynamic Parameters in the Structural Health Monitoring Systems of Bridges. *Applied Sciences*. 2024; 14(1):33.
https://doi.org/10.3390/app14010033

**Chicago/Turabian Style**

López-Aragón, Juan-Antonio, and Miguel-Ángel Astiz.
2024. "Some Considerations about the Incorporation of Dynamic Parameters in the Structural Health Monitoring Systems of Bridges" *Applied Sciences* 14, no. 1: 33.
https://doi.org/10.3390/app14010033