E. Torroja's bridge: Tailored experimental setup for SHM of a historical bridge with a reduced number of sensors

UNCORRECTED PROOF Engineering Structures xxx (2018) xxx-xxx Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com E. Torroja’s bridge: Tailored experimental setup for SHM of a historical bridge with a reduced number of sensors Pablo Pachón⁠a⁠, ⁠⁎, Rafael Castro⁠b, Enrique García-Macías⁠c, Víctor Compan⁠a, Esther Puertas⁠d aDept. of Continuum Mechanics, Universidad de Sevilla, Avenida Reina Mercedes, 41012 Sevilla, Spain bDept. of Mechanics, Universidad de Córdoba, Campus de Rabanales, 14071 Cordoba, Spain cDepartment of Continuum Mechanics and Structural Analysis, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Seville, Spain dDept. of Mechanical Structures and Hydraulic Engineering, Universidad de Granada, Avenida Fuentenueva, 18001 Granada, Spain ARTICLE INFO Keywords: Ambient vibration Cultural heritage Genetic algorithm Historical constructions Operational modal analysis Optimal sensor placement Structural Health Monitoring ABSTRACT This paper presents the design of an experimental setup with a reduced number of sensors for the structural health monitoring of the historical bridge of Posadas (Córdoba, Spain), designed by the eminent engineer Eduardo Torroja in 1957. The motivation of this study stems from the need for safeguarding this piece of cultural heritage. In particular, the singularity of this historical construction, a steel–concrete composite typology consisting of a concrete deck slab and inverted bowstring steel trusses, makes continuous in-service condition assessment essential for its maintenance. Nevertheless, the application of existing continuous monitoring systems to such large-scale structures entails considerable investments as well as complex signal processing algorithms. Whereby the optimization of the number of sensors and their location is of the utmost interest. In this line, this work presents the application of an Optimal Sensor Placement (OSP) methodology to tailor an experimental setup for a cost-efficient continuous monitoring of the E. Torroja’s bridge. Due to the fact that most OSP approaches are model-based, it is essential to count on a sufficiently accurate numerical model. To this aim, an extensive vibration-based operational modal analysis is first conducted with a large number of accelerometers. Afterward, a three-dimensional finite element model of the E. Torroja’s bridge is updated on the basis of the experimentally identified dynamic properties with a genetic optimization algorithm. Finally, an optimal sensor placement methodology is utilized to design an experimental setup with a limited number of sensors for long-term monitoring purposes. The results demonstrate that few sensors are needed to accurately assess the main resonant frequencies and mode shapes. 1. Introduction Historical bridges constitute a key piece of cultural heritage, inasmuch as they bear witness to the course of history and hold an important social, cultural, and artistic value. There exists a great concern about their conservation and, therefore, the assessment of their health condition is absolutely crucial. Structural Health Monitoring (SHM) encompasses the application of Non-Destructive Testing (NDT) and damage detection in order to extend the life-cycle of structures. In particular, Operational Modal Analysis (OMA) is considered one of the most suitable methods to assess the condition of structures through their vibrational properties [1,2]. OMA is performed under conditions of service without the need for artificial excitations, feature that is essential to monitor historical structures where the use of stronger modal exciters, such as instrumented hammers or shakers, is often inadmissible. Nevertheless, OMA usually requires a large number of sensors to properly characterize the dynamic properties, fact that limits the scalability of long-term OMA-based SHM to large-scale structures. Given the high cost of such systems, it is essential to count on techniques that allow for tailoring experimental setups in such a way that only a reduced number of sensors can accurately identify the vibrational properties of structures. Plenty of studies on Finite Element Modeling (FEM) and experimental investigation of historical bridges can be found in the literature. A noteworthy contribution was done by Chiara Pepi et al. [3] who studied the structural performance of an ancient bridge located in Todi (Umbria, Italy), through the integration of geometric survey proce ⁎Corresponding author. Email address: [email protected] (P. Pachón) https://doi.org/10.1016/j.engstruct.2018.02.035 Received 26 September 2017; Received in revised form 5 January 2018; Accepted 9 February 2018 Available online xxx 0141-0296/ © 2017. UNCORRECTED PROOF P. Pachón et al. Engineering Structures xxx (2018) xxx-xxx dures, dynamic testing and numerical modeling. Conde et al. [4] conducted ambient vibration tests on the Vilanova bridge, a masonry structure located in Galicia (Spain), and whose origin dates back to the 13–14th centuries. Those authors presented a multidisciplinary approach for the structural assessment of masonry arch bridges by using NDT techniques and three-dimensional numerical modeling. Gentile and Saisi [5] conducted the dynamic characterization of two historic structures, namely the Collegiata of San Vittore bell tower (Arcisate, Italy), and the San Michele bridge (Milan, Italy), an arch bridge built in 1889. In the latter case, those authors investigated the variation of the dynamic characteristics of the bridge under different traffic conditions. Finally, it is also worth noting the work done by Altunisik et al. [6] on a mid-nineteenth century bridge in Turkey, the Mikron arch. Those authors reported about the definition of a three-dimensional FEM of the bridge, an OMA campaign, and the updating of the FEM on the basis of the experimentally identified modal properties. Overall, despite great efforts have been put into the implementation of these techniques to the conservation of historical constructions, the elevated costs of these systems still remain an important obstacle. This paper is aimed at presenting a methodology to tailor a cost-ef- ficient experimental set-up with a reduced number of sensors for the long-term SHM of the E. Torroja’s bridge. This bridge was constructed in 1951 over the Guadalquivir river by the renowned civil engineer Eduardo Torroja (Fig. 1). The cultural and historical importance of this bridge justifies the implementation of a long-term SHM system, so that preventive actions can be taken in order to prevent or mitigate structural aging and accidental damages. Following the previous discussions, the present methodology proposes the use of a limited number of sensors which are placed at optimal locations determined by means of an OSP algorithm. OSP algorithms, which are typically based on a numerical model of the structure, maximize the modal information with a reduced number of degrees of freedom and, therefore, a limited number of sensors. Hence, the suitability of the tailored experimental set-up is critically determined by the accuracy of the numerical model. A thorough ambient-vibration test with a large number of sensors is first conducted to assess the vibrational properties of the structure and to serve as a basis for the updating of the preliminary numerical model. Afterward, the discrepancies between the theoretical and experimental results are minimized by updating different variables of the numerical model through a genetic optimization algorithm. Once the numerical model is properly tuned, the optimal locations of a reduced set of sensors are determined by an OSP algorithm. The results demonstrate that few sensors are needed to accurately assess the main resonant frequencies and mode shapes. The remainder of this paper is organized as follows. Section 2 concisely describes the historical evolution of the bridge and its geometric configuration. Section 3 introduces the preliminary FE model of the bridge. Section 4 presents the dynamic characterization of the bridge by means of an experimental OMA campaign. Section 5 details the up dating process of the preliminary FE model. Section 6 overviews the theoretical formulation of the utilized OSP technique and reports the proposed optimal set-up for a long-term SHM of the E. Torroja’s bridge. Finally, Section 7 draws the main conclusions of this study. 2. E. Torroja’s bridge: Construction and evolution Eduardo Torroja Miret (1899–1961) is considered one of the major figures of Spanish civil engineering, with a fundamental contribution to the design of thin-shell concrete structures. In his book “Razón y Ser de tipos estructurales”[7], his oeuvre is conceived as a quest for structural truth, a concept through which E. Torroja advocates that beauty lies in rationality and not in artificial ornamentation. With this in mind, E. Torroja developed new ways of designing structures whereby aesthetics arises from the rationality of the different structural members. Furthermore, E. Torroja showed interest in fundamental art forms and are present in most of his structures. Nowadays, numerous bridges designed by this eminent engineer are considered as historical constructions, such as the Muga bridge (Fig. 2a) or the Pedrido bridge (Fig. 2b). After the Spanish civil war, E. Torroja was commissioned to substitute the bridge over the Guadalquivir river in Posadas (Córdoba, Spain) which had been seriously damaged in the conflict. The original structure, which consisted of reinforced concrete arches, was replaced by five isostatic steel-concrete composite spans of 43m (Fig. 3). The new solution was defined with a 7m width reinforced concrete deck and two inverted bowstring steel trusses, whose bottom chords were defined as parabolic arches with a maximum rise of 6m. Fig. 4 shows two photographs of the original bridge under construction. In 1983, some new deck repairs were conducted, including the construction of new dilatation joints, injections, as well as repairs of the piles’and abutments’walls. In addition, some damaged steel components were replaced and, eventually, the metallic structure and the handrails were repainted. Nonetheless, the structural typology was kept unaltered (see Fig. 5). In 1991, E. Torroja’s grandson, Antonio Torroja, was entrusted to carry out an extension of the deck width from 6.5m (Fig. 6(a)) to 11m (Fig. 6(b)). To this end, two new arches were added and connected to the original ones by a tubular truss structure. The original deck had to be completely removed because new upper reinforcements were needed to bear the transverse negative moments (Fig. 7). It should be noted that all the modifications experienced by the structure entail a high level of uncertainty, affecting both the material properties and the structural behavior. Moreover, due to the singular geometry that characterizes the bridge, the metallic part of the structure is not physically accessible (Fig. 8) and, therefore, the experimental modal characterization of the bridge must be carried out on the road. In this sense, the numerical model represents a fundamental tool to evaluate the current state of conservation of the bridge in general and the steel structure in particular. Fig. 1. E. Torroja’s bridge in Posadas, Córdoba (Spain). 2 UNCORRECTED PROOF P. Pachón et al. Engineering Structures xxx (2018) xxx-xxx Fig. 2. Views of (a) Muga bridge, 1939 (Girona, Spain), and (b) Tordera bridge, 1939 (Barcelona, Spain). Fig. 3. Front view of E. Torroja’s bridge (dimensions in m). Fig. 4. Photographs of the original bridge under construction (1940–1951). Fig. 5. Photographs of the original bridge in service (1966). 3. Finite element modal analysis This section details the preliminary FEM of the E. Torroja’s bridge. Firstly, to provide some insight into the structural evolution of the bridge, the results reported in a previously published work by the authors [8] on the study of the variation of the dynamic properties of the bridge along its history are briefly presented. Then, the preliminary three-dimensional FEM of the bridge, which serves as a basis for the following updating process, is presented in detail. 3.1. Structural evolution of the bridge As previously indicated, the bridge has experienced important modifications since its construction. Some of the original elements were preserved, whilst some others were later incorporated. In order to shed 3 UNCORRECTED PROOF P. Pachón et al. Engineering Structures xxx (2018) xxx-xxx Fig. 6. Cross sections of the bridge (dimensions in m). Fig. 7. Views of (a) initial and (b) final operations of deck’s width increment (1992). Fig. 8. Views of the current bridge in service. some light on the evolution of the structural behavior of the bridge, the authors carried out a preliminary research that was presented at the International Modal Analysis Conference (IMAC 2015) [8]. In that study, both the original and the current designs of the bridge (see Fig. 6) were simulated by preliminary FEMs. Then, a comparison of both models in terms of their dynamic properties was made in order to aid in the understanding of the structural evolution. Beam elements were used for all the components except for the deck for which thick shell elements were utilized. Finally, the resonant frequencies of both structures were computed by modal analysis, and it was observed that only small differences are found in the first five natural modes. This fact indicates that, despite the considerable modifications experienced by the structure, the dynamic behavior of the bridge has not been significantly altered. Therefore, it was concluded that the increase in the stiffness of the bridge has been counteracted by a similar increase in its mass, where the change of weight of steel per area of the deck from 66.22 to 79.33kg/m⁠2 is indicative of this conclusion. It was also concluded that, since the dynamic characteristics have not been apparently altered, the different operations conducted in the bridge may have introduced uncertainties derived from differential aging processes. 3.2. Preliminary FEM of the E. Torroja’s bridge In order to incorporate all the geometrical details of the structure, a sophisticated three-dimensional FEM of the E. Torroja’s bridge is developed. Due to the large size of the bridge, including five simply supported spans, a FEM of the complete structure would result in an excessive computational cost. Moreover, since there is no structural connection between adjacent spans, each span of the bridge behaves independently of the others. Therefore, only one single span is modeled as 4 UNCORRECTED PROOF P. Pachón et al. Engineering Structures xxx (2018) xxx-xxx common practice in the study of this type of bridges. Only shell elements are defined in such a way that the connections between the steel arches and the concrete desk can be accurately simulated (Fig. 9). The horizontal braces are defined as built-up sections with UPN-120 profiles and batten plates of dimensions 400×50×8mm every 50cm. The arches are also built-up sections with IPN-200 profiles and batten plates of dimensions 210×50×8mm every 50cm. With regard to the numerical definition of the structural members, 4-node triangular shell elements are used for the concrete slab and all the steel members. Overall, the complete model has 374.928 elements, 388.679 nodes and 2.332.074 degrees of freedom. The boundary conditions are defined as constrained displacements and free rotations, as can be observed in the details of Fig. 9. Table 1 summarizes the material properties used in the modeling. Note that all the selected properties are common values for the design of this type of structures, with the exception of the mass density of steel, whose value is increased by 1.9% with respect to the standard value of 7850kg/m⁠3. This decision is taken to account for all those factors that have not been explicitly included in the numerical model, such as welds, bolts, and other ancillary elements. The weight of the battens and the pavement is also included in terms of added mass. Afterward, the modal properties of the structure are computed by a modal analysis in Abaqus CAE [9]. The first eight mode shapes are shown in Fig. 10. It is observed that the bridge exhibits a narrow band of low resonant frequencies with natural modes that are highly coupled, what makes the dynamic features of the structure quite complex. 4. Ambient vibration test and operational modal analysis The dynamic testing of the structure can provide an accurate prediction of its global modal parameters. In order to ensure an efficient identification of the modal properties of the bridge, an extensive ambient vibration campaign with a large number of sensors was first performed on March 14, 2017, on the E. Torroja’s bridge. In this way, the experimentally identified dynamic properties serve as a basis for the updating of the preliminary FEM of the bridge. 4.1. Ambient vibration test The experimental layout of the preliminary ambient vibration test is schematically represented in Fig. 11. Accelerations were registered in three orthogonal directions with the aim of identifying the vibration modes in the lateral, longitudinal and vertical directions of the bridge. Twelve set-ups were defined with four mobile sensors, whilst one was kept fixed as a reference (placed at point 6, Fig. 11), what amounted to a total of 36 measuring points. The position of the reference acceleration sensor was chosen according the results provided by the numerical model [10]. In each one of these set-ups, a sampling time of 10min and a sampling rate of 100Hz were selected, taking into ac Fig. 9. FEM of the E. Torroja’s bridge. 5 UNCORRECTED PROOF P. Pachón et al. Engineering Structures xxx (2018) xxx-xxx Table 1 Material properties used in the FEM. Property Unit Value Mass of security barriers kg/m 14.66 Mass of asphalt kg/m⁠2 110 Young’s modulus of concrete slab MPa 30,000 Poisson’s ratio of concrete slab –0.2 Density of concrete slab kg/m⁠3 2500 Young’s modulus of steel MPa 210,000 Poisson’s ratio of steel –0.3 Density of steel kg/m⁠3 8000 count the empirical rule proposed by J. Rodrigues in his Phd Thesis [11]. These assumptions ensure that frequencies from 1 to 50Hz are properly recorded. The equipment used in the tests included five self-contained recorder instruments manufactured by the company GeoSIG Measuring Systems. These instruments have three internal sensors, anti-aliasing filters, a bandwidth ranging from 0.01 to 250Hz, a dynamic range of 146dB, a sensitivity of 10V/g, and 4.70kg of weight (model GMSplus) (Fig. 12). The same conditions of temperature and humidity were taken into account during the whole campaign in order to avoid variations in the modal parameters [12]. In addition, the modal excitation of the bridge was always caused by environmental loads, such as wind or traffic (Fig. 13). Fig. 10. First eight numerical eigenmodes computed by the FEM of the E. Torroja’s bridge. Fig. 11. Plan view of the accelerometer locations (reference accelerometer in red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) 6 UNCORRECTED PROOF P. Pachón et al. Engineering Structures xxx (2018) xxx-xxx Fig. 12. Self-contained recorder instrument (GMSplus). Fig. 13. Time history of acceleration registered by accelerometer number two, 4th set-up. 4.2. Operational modal analysis The Artemis Software [13] is used to analyze the data obtained during the experimental campaign. The Enhanced Frequency Domain Decomposition (EFDD) technique [14,15] and the Stochastic Subspace Identification (SSI) method [16,17] are the two different identification methods used to obtain the modal parameters of the bridge (Fig. 14). With regard to the signal processing of the recordings, a decimation factor of 5 is applied in order to take into consideration that the expected natural frequencies are below 10Hz, according to the results of the numerical modal analysis previously shown in Fig. 10. In addition, Fig. 14. Experimental identification of the resonant frequencies by the EFDD and SSI techniques. 7 UNCORRECTED PROOF P. Pachón et al. Engineering Structures xxx (2018) xxx-xxx the resolution of the spectral density estimation is defined as 1024, what results in a frequency line spacing of 0.005Hz. Harmonic detection algorithms are also applied in order to check all the frequencies in the spectrum. In order to validate the identified modal parameters, the Modal Assurance Criterion (MAC) [18] is applied. Given two mode shapes, φjand φk, their MAC value writes: (1) where superindex T designates transposition. When the MAC value is higher than 0.80, a good correlation between the two modes is considered [18]. Finally, Table 2 presents the obtained results, including the standard deviation of modal frequencies and the damping ratios. As can be observed in Table 2, the first eight vibration modes in a frequency range up to 10Hz have been identified. The differences between the frequencies identified by the SSI and EFDD methods are al ways lower than 1.5%, taking the results of the SSI method as reference value. The results for the damping ratios show an higher variability, with average modal damping ratios of 0.61% and 1.64% for SSI and EFDD techniques, respectively. Such large differences are typically found in practice, fact that indicates the need for higher levels of excitation to accurately capture the damping ratios [19]. The damping values obtained by the EFDD method are even less reliable than those obtained by the SSI method, as can be extracted from their higher standard deviation values. Further, the MAC indicates a good correlation between the modes identified by both methods with values higher than 0.80. The first and the fourth modes are torsional modes, while the other modes correspond to bending modes of the bridge (see Fig. 15). 5. FEM updating On the basis of the experimentally identified dynamic properties, the preliminary FEM has been updated to reproduce the actual behavior of the bridge and assist the OSP methodology. Standard FEMs of this kind of buildings usually include uncertainties derived from un Table 2 OMA results: natural frequencies (f), damping ratios (ξ) and standard deviation (std). Mode N⁠o SSI EFDD MAC f(Hz) std(f)ξ(%) std(ξ)f(Hz) std(f)ξ(%) std(ξ) 1 3.28 0.02 0.85 0.40 3.31 0.01 1.46 0.66 0.92 2 3.68 0.07 0.79 0.46 3.72 0.03 2.14 1.17 0.94 3 3.80 0.04 0.78 0.31 3.84 0.07 1.60 1.01 0.82 4 5.14 0.01 0.60 0.17 5.16 0.01 0.63 0.22 0.98 5 5.61 0.10 0.38 0.27 5.68 0.09 2.78 1.16 0.81 6 5.64 0.05 0.41 0.26 5.69 0.07 2.01 1.22 0.80 7 7.79 0.05 0.58 0.31 7.68 0.14 1.70 1.06 0.86 8 8.02 0.02 0.49 0.27 8.07 0.05 0.84 0.39 0.84 Fig. 15. Experimentally identified natural vibration modes. 8 UNCORRECTED PROOF P. Pachón et al. Engineering Structures xxx (2018) xxx-xxx known material properties, existing damage, complex internal composition of structural elements, and modeling approximations. Therefore, the calibration of the model with the aid of experimental information becomes essential to appropriately model the actual behavior of the structure. Following the same procedure as in previous works by the authors [20], the FEM updating is performed by means of iterative methods [21], in which the user introduces changes directly on some of the physical parameters that define the structure. To this aim, a sensitivity study is first conducted to detect those structural parameters that have a greater influence on its dynamic behavior. In this work, the Young’s modulus (Ec) and the density of the concrete desk (ρc) are selected as design variables. Once the updating parameters of the numerical model are selected, and considering the good quality of the experimental measurements, the first three identified modes are selected as target modes in the updating process. Taking into account the values of the natural frequencies and the modal coordinates, a total of 111 residual components are adjusted and minimized throughout the model updating. In order to consider the greater credibility of the identified frequencies with respect to the modal displacements, a weight factor wf= 1.00 is defined for the resonant frequencies, whilst a smaller factor ws= 0.05 is assigned to the modal coordinates. Finally, the FEM updating is performed using a genetic algorithm in Matlab environment [22], according to an objective function defined as the relative differences between the experimental and the numerical modal parameters. This function is usually formulated as a least-squares problem as follows: (2) where are the values related to the physical parameters of the numerical model, θ(Ecand ρc), while the variables zEXP,jare the same magnitudes obtained from the experimental campaign. The differences between these variables are set as residues, . It must be noted that the number of residues, m=mf+ms(with mfbeing the number of considered natural frequencies, and msthe number of the coordinates of the considered vibration modes), is greater than the number of adjusted variables, θ. The weight factors, wj, are the values established for each residue. In the case of natural frequencies, the residues read: (3) where and fEXP,jare the values of the obtained frequencies from the numerical and experimental model. In a similar way, the residues in terms of mode shapes correspondingly write: (4) where and are the selected and reference component of the numerical mode j, while and are the same magnitudes obtained from experimental mode j. Then, in order to minimize this objective function, a genetic algorithm is applied. Fig. 16 shows the convergence of the fitness function using a genetic algorithm. A range of variation for every updating parameter (Table 3) is selected to prevent the algorithm from defining physically unrealistic estimates. In each iteration, a population of 1000 vectors is considered by using the principles of genetic algorithms (as implemented in Matlab software), and the objective function in Eq. (2) is minimized. Such calibration process finishes when the differences between the mean values (blue dots in Fig. 16) and the best values (green Fig. 16. Convergence of the fitness function using a genetic algorithm. Fitness value versus the number of generations. Blue points: Mean values of the objective function of all the population of the corresponding generation. Green point: Best values result of an individual of the population.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Table 3 Summary of updated parameters of the FEM by a genetic algorithm. Parameter Initial value Range of variation Updated value Lower Upper Ec(MPa) 25,000 20,000 30,000 27790.51 ρc(kg/ m⁠3) 2500 2000 4000 3774.71 dots in Fig. 16) of the fitness function of two iterations are less than 1×10⁠−3. Table 3 presents the summary of the updated parameters, where large differences can be observed between the updated and initial parameters. Table 4 shows the comparison between the experimental results and those provided by both the preliminary and the updated FEMs. Table 4 Comparison of the experimentally identified natural frequencies, fSSI, the numerical results by the preliminary FEM, , and those provided by the updated FEM, , as well the MAC values of the mode shapes determined by the experiments and the updated FEM, . Mode n⁠o fSSI (Hz) (Hz) (Hz) 1 3.28 3.52 (7.31%) 3.26 (0.60%) 0.96 2 3.68 3.82 (3.81%) 3.67 (0.27%) 0.93 3 3.80 4.55 (19.73%) 3.90 (2.63%) 0.83 4 5.14 5.91 (14.98%) 5.26 (2.33%) 0.94 5 5.61 5.92 (5.52%) 5.77 (2.85%) 0.88 6 5.64 6.15 (9.04%) 5.82 (3.19%) 0.82 7 7.79 9.14 (16.81%) 7.83 (0.51%) 0.92 8 8.02 9.40 (17.20%) 8.08 (0.74%) 0.84 The percentages in parenthesis correspond to the relative differences between frequencies. 9