Shock and Vibration

Volume 2018, Article ID 3739690, 14 pages

https://doi.org/10.1155/2018/3739690

## Sensor Placement Strategies for the Seismic Monitoring of Complex Vaulted Structures of the Modern Architectural Heritage

Department of Structural, Geotechnical and Building Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy

Correspondence should be addressed to Rosario Ceravolo; ti.otilop@olovarec.oirasor

Received 28 March 2018; Accepted 28 June 2018; Published 1 August 2018

Academic Editor: Emanuele Reccia

Copyright © 2018 Erica Lenticchia et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Effective diagnostic and monitoring systems are highly needed in the building and infrastructure sector, to provide a comprehensive assessment of the structural health state and improve the maintenance and restoration planning. Vibration-based techniques, and especially ambient vibration testing, have proved to be particularly suitable for both periodic and continuous monitoring of existing structures. As a general requirement, permanent systems must include a sensing network able to run a continuous surveillance and provide reliable analyses based on different information sources. The variability in the environmental and operating conditions needs to be accounted for in designing such a sensor network, but it is mainly the structural typology that governs the optimal sensor placement strategy. Architectural heritage consists of a great variety of buildings and monuments that significantly differ from each other in terms of typology, historic period, construction techniques, and materials. In this paper, the main issues regarding seismic protection and analysis of the modern architectural heritage are introduced and applied to one of the vaulted structures built by Pier Luigi Nervi in the Turin Exhibition Centre. The importance of attaining an adequate level of knowledge in historic structures is also highlighted. After an overview of the Turin Exhibition Centre and its construction innovations, this paper focuses on Hall B, describing the structural design conceived by Pier Luigi Nervi. A seismic assessment of the structures of Hall B is then presented, considering the potential seismic damage to nonstructural elements. Subsequently, the application of an optimal sensor placement strategy is described with reference to two different scenarios: the first one corresponding to the undamaged structure and the second one that considers a possible damage to the infill walls. Finally, a novel damage-scenario-driven sensor placement strategy based on a combination of the two above mentioned is proposed and discussed. One of the major conclusions drawn from the analyses performed is that nonstructural elements undergoing seismic damage or degradation may significantly affect the global dynamic response and consequently the optimal sensing configurations.

#### 1. Introduction

Optimal sensor placement techniques play a significant role in assuring a reliable positioning of sensors for Structural Health Monitoring (SHM). This is particularly true in the case of complex systems or configurations, in which a large number of possible positions and degree of freedoms are present. In the case of architectural heritage, these issues are even more relevant due to the uncertainties of the building construction technologies and the diversity of architectural configurations. These uncertainties entail significant complexities in the design of a possible dynamic monitoring system. Indeed, architectural heritage consists of a great variety of buildings and monuments, which differ from each other in terms of typology, historic period, construction techniques, and materials and very often are characterized by the occurrence in time of several changes in the structural design and in the end use. The architectural heritage of the modern movement makes no exception, and its conservation is perhaps one of the most controversial frontiers in the field of architectural preservation. Presently, much of the world’s heritage from this period is unrecognized or undervalued, and therefore, it is at risk and in need of analysis and protection. This vulnerable situation can be attributed to multiple factors: 20th century buildings still struggle to be considered part of a heritage; moreover, their original functions have substantially changed, and their technological innovations have not always endured long-term stresses.

Vibration-based structural health monitoring techniques for the control and diagnosis of structures have been applied for years and have now become an important tool for the preservation of either antique or modern architectural heritage [1, 2]. Dynamic tests are particularly appreciated in this field because they are a nondestructive technique and provide information about the whole-body response of the structure and its overall structural integrity.

However, the dynamic monitoring of architectural heritage structures still raises different unresolved issues, including (i) the complex optimisation problems due to the spatial characters of architectural heritage; (ii) the need for distributed sensing systems with corresponding optimisation of their configurations; and (iii) the possible effects of damage degradation on the sensing system’s design.

Based on the above-reported considerations, in this paper, an iconic structure of modern architectural heritage was analysed, that is, the Turin Exhibition Centre, designed and built by Pier Luigi Nervi. Its halls, with their vaulted roofing systems, represent a structural masterpiece of the period and are admired worldwide for their challenging and innovative conception.

Despite its remarkable historical and architectural relevance, the Turin Exhibition Centre has been abandoned for a long time, and the lack of maintenance is starting to induce serious preservation problems. In addition, its halls were built without accounting for seismic actions, but only for static configurations, in accordance with the technical standards of the time. Therefore, it is of crucial importance to assess the dynamic behaviour of these structures in order to understand their vulnerability and plan their correct preservation measures. These structures represent a challenging example, especially in view of defining their optimal sensor configurations.

Numerical simulations under different damage scenarios were conducted, in order to evaluate the influence of nonstructural elements, such as the infill walls, on the behaviour of the building and thus on the optimal sensor placement. In fact, sensor placement strategy, in such complex structures, has to consider also the effect of possible damage in nonstructural elements. Therefore, in this study, the objective function of the algorithm was modified in order to account for progressive damage in the infill walls. The numerical analyses demonstrated that these elements, when subjected to seismic damage or degradation, may significantly affect the global dynamic response and consequently the optimal monitoring configurations.

#### 2. Optimal Sensor Placement

##### 2.1. Optimisation Algorithms for Optimal Sensor Placement

When designing a SHM system, it is necessary to first perform an accurate analysis of the structural behaviour, in order to select the most significant and sensitive parameters. One of the most critical issues in the design of a dynamic monitoring system is the deployment of the sensors, usually in the form of accelerometers, especially when testing complex structures. In fact, in the case of structures that present a simple geometry, the optimal location of sensors can be considered a trivial problem that can be solved by simply relying to the experience of the operator. On the contrary, in the case of complex structures, as it often happens with architectural heritage, it is recommended to recur to more sophisticated strategies, such as optimal sensor placement (OSP) [3].

Optimal sensor placement techniques play a significant role in enhancing the quality of modal data in SHM. This is particularly true for large civil structures, where a limited number of sensors are normally available to monitor a huge number of movements. The accelerometers must be placed in order to obtain all the relevant features of the dynamic response during the course of the test, and, at the same time, the resulting sensor configuration must be optimal such that testing resources are conserved [4].

The problem of locating sensors on a structure can be driven by the aim of maximising the data information in order to fully characterize the structural dynamic behaviour. In this case, the primary objective is the enhancement of the modal testing results. Several studies have been carried out to cope with this problem using the a priori information derived by a FE model of the structure.

Although many different sensor placement algorithms can be implemented to optimise the number and location of sensors on the structure, a general common criterion of information maximisation is recognizable. The knowledge of the expected type of damage represents an important discriminating element. If the purpose is fault detection and classification, the problem of determining the best number of sensors and their locations is mainly an optimisation problem. Recently some optimisation methods based on analogies with biology and physics have been introduced. Artificial Neural Networks (ANNs), Pattern Search (PS), and Evolutionary Strategies (ES), such as the Genetic Algorithms (GA) [5], the Particle Swarm Optimization (PSO) [6], and the Covariance-Matrix Adaptation Evolution Strategy (CMA-ES), are only some of the countless examples present in the literature [7].

A popular OSP approach is the one proposed by Kammer [8] and consists in a minimisation of the norm of the Fisher information matrix. The method of Effective Independence (EI) was developed to assure the spatial independence and to maximise the signal strength of a certain number of targeted mode shapes. The algorithm is iterative: at each step, as the lowest ranked sensor is removed, the determinant of the Fisher information matrix is maintained, resulting in a suboptimal optimisation which ends when the required number of sensors is obtained.

Another way to solve the problem is the modal kinetic energy-based method as proposed by Salama et al. [9] and Chung and Moore [10] as a means of ranking the importance of candidate sensor locations. The Kinetic Energy Method (KEM) looks for the sensor placement configuration whose positions are the points of maximum kinetic energy for the modes of interest in order to maximise their observability. The procedure to derive the best sensors positions is similar to that implemented in the EI method with the difference that the Fisher information matrix is substituted by the KE matrix.

A third approach that uses the mass-to-stiffness ratio associated with each candidate sensor location was proposed by [11]. A more detailed review of OSP methods with particular emphasis on vibration measurements can be found in [12–15].

In the aforementioned methods, the definition of a certain number of target mode shapes is required. This number can be selected as the number of modes which are expected to be identified by the modal testing. Finally, it must also be stressed that due to economic considerations, the number of available sensors is generally limited and sometimes even insufficient to fulfil the requirements of the optimal sensor placement techniques.

In order to overcome this limit, it is common to use different overlaying setups during a dynamic testing campaign. The identified measuring positions are split into two groups: the points belonging to the first group are assumed as reference and kept fixed in every acquisition carried out on the structure, and the other points are moved around the structure defining a number of setups sufficient to investigate all the identified locations [3, 16]. The positions selected as reference points should correspond to the points which undergo the largest modal displacements and definitely not coincide with the nodes of the structural mode shapes.

##### 2.2. Genetic Algorithms for OSP

A special family of optimisation strategies for OSP relies on the use of Genetic Algorithms (GAs), offering simple and robust criteria for the solution of the problem of optimal placement of accelerometers.

GAs are a popular bioinspired approach, with many examples of their use appearing in the engineering literature [17], as their use is known to reduce the probability to incur in local minima. According to [12], the first pioneering studies on using GAs for the sensor placement problems date back to the early nineties [18]. For the exposed reasons, and due to their simplicity, GAs are highly recommended also in the case of complex civil structures and, in fact, were chosen to define the OSP for the vaulted halls in the Turin Exhibition Centre.

GAs are optimisation algorithms which evolve solutions in a manner analogous to the Darwinian principle of natural selection, where members of the population compete to survive and reproduce while the weaker ones die out [19]. Each individual is assigned a fitness value according to how well it meets the objective of solving the problem and, in this paper, to identify the optimal position of the sensors. Each possible solution, that is, each set of possible parameters in solution space, is encoded as a gene. Having decided on a representation, the next step is to randomly generate an initial population of possible solutions. The number of genes in a population depends on several factors, including the size of each individual gene, which itself depends on the size of the solution space [12].

Having generated a population of random genes (the accelerometers), it is necessary to decide which of them are fittest in the sense of producing the best solutions to the problem (the vibration modes discerning). To do this, a fitness function is required which operates on the encoded genes and returns a single number which provides a measure of the suitability of the solution. These fittest genes will be used for mating to create the next generation of genes which will hopefully provide better solutions to the problem. Genes are picked for mating based on their fitness. The probability of a particular gene to be chosen is equal to its fitness divided by the sum of the fitnesses of all the genes in the population [12]. Once a sufficient number of genes have been selected for mating, they are paired up randomly, and their genes are combined to produce a new couple of genes. The most common method of combination used is called *crossover*.

With genetic methods, it is not always possible to say what the fitness of a perfect gene will be [12]. Thus, the iterative process is usually continued until the population is dominated by a few relatively fit genes. One or more of these genes will generally be acceptable as solutions.

The objective function used in the optimisation problem here analysed is based on the concept of Modal Assurance Criterion (MAC) [20, 21], a matrix containing element indices of the correspondence of two modal vectors. In fact, the elements of the matrix can take values between 0, which indicates vectors devoid of correlation, and 1, which indicates equal vectors. The generic term of MAC can be defined aswhere and are, respectively, the *i*th and *j*th column of matrix , which is the reduced modal matrix of the degrees of freedom corresponding to possible measurement positions.

The goal of the OSP is to minimise the elements outside the diagonal of the MAC matrix. The genetic algorithm searches for the best set of positions that allow to minimise each term MACij (*i* ≠ *j*). This allows to distinguish the modes to be monitored on the basis of a given number of accelerometers. The objective function used to solve the problem of the OSP is based on the above-stated definitions, as it derives from the simple subtraction of terms related to the MAC calculated using the modal matrix (MAC_R) with those of the ideal MAC (MAC_I) and divided by the number of the elements of the matrix with selected target modes extracted from the FE model:where (2) represents the objective function to be minimised and *n* is the number of elements of the matrix.

The above-referred OSP strategy will be hereinafter applied to determine the best sensor locations from a large set of possible candidates in Hall B of Turin Exhibition Centre.

#### 3. Finite Element Modelling and Analysis

##### 3.1. The Turin Exhibition Centre

As stated in the introduction, in recent years, there has been an increase in the recognition of the cultural significance of modern architecture. However, there are still challenges to secure its protection and conservation [22, 23]. An area of conservation that requires attention is seismic provision. In fact, modern architecture buildings were designed and built with no, or very limited, seismic provisions, due to the lack of reference technical standards at the time of their construction. With a view to the restoration and renewal of these complex structures, a careful assessment of their structural performance is a priority, especially when they are situated in a high seismic risk area.

Pier Luigi Nervi (1891–1979) was one of the greatest and most inventive structural engineers of the 20th century [24]. With his masterpieces, Nervi contributed to create a glorious period for structural architecture [25]. Nikolaus Pevsner, the distinguished historian of architecture, described him as “the most brilliant artist in reinforced concrete of our time” [26]. Between the thirties and the sixties, structural research, particularly into thin concrete shells for vaulted structures, achieved extraordinary results. Dating back from the thirties, thin-shell roofs in concrete were seen as “the starting point for the specific solution of the vaulting problems” [27], and vaulting forms were created taking inspiration by simple ideas grounded in the laws of nature [28] both empirically and mathematically. Researchers and designers of the time adopted a highly pragmatic approach to the industrialisation of construction systems, optimal use of materials, and structural analysis [29]. Pier Luigi Nervi was one of the leading structural designers of the period together with Eduardo Torroja, Anton Tedesko, and Nicolas Esquillan and many others. The vaulted structures in the Turin Exhibition Centre are among many spatial buildings that were built at the time.

For Pier Luigi Nervi, the Turin Exhibition represented the first possibility to apply the principle of structural prefabrication, combining with a single large-scale vaulted structure his patented ferrocement technique with the extensive use of prefabricated elements. This combined use of two different technologies for the construction of large concrete shells became later one of the distinctive traits of Nervi’s work.

In the construction of both halls of the Turin Exhibition Centre, Nervi used new construction procedures that he studied for some years before this project. In fact, he had already successfully used these procedures with his engineering firm Nervi and Bartoli, even on smaller experimental buildings, such as the small storehouse in the Magliana area in Rome (1946) [30], the wharf Conte Trossi in San Michele di Pagana (1947), and the ceiling of the pavilion at the Milan Fair (1947) [31].

The Turin Exhibition Centre (Palazzo di Torino Esposizioni) was built in 1948 for the 31st international Auto Show. The tender was committed to Nervi and Bartoli, whose project proposed a new construction system that combined prefabrication and the use of ferrocement. The building consists of the main Hall B and the smaller adjacent Hall C [32], both designed and constructed by Nervi (1947-1948 and 1950). A historical aerial view of the building is reported in Figure 1.