**2.2 Prognostication of structural health**

Beyond identifying the existence and type of damage, it is vital for SHM processes to adequately characterize the damage to determine the continued serviceability of the structure in the presence of these defects/damages. Determining the continued health of the structure and its constituent members involves analysis of the captured damage, and its effect on structural capacity. This requires the identification/development of damage models that accurately represent the initiation and propagation of the identified damage, and the degradation of capacity due to the damage propagation. Ref. [13] opined that a typical SHM scheme for development of damage models includes six principal steps including identification of the damage mechanism, identification of structural parameters affected, modeling of structure, sensitivity studies on the model, modeling of the damage mechanism, and sensitivity studies of variations of different parameters.

There are four possible levels of analyzing data collected from a SHM system to characterize the health of the structure. These are inferences using the raw data, analyzing the data to detect damage, deterioration or changes in structural behavior, localizing and quantifying the damage and/or changes, and predicting future performance based on current condition [5]. The first two levels do not usually require very rigorous levels of analysis, beyond quite straightforward determination of a deviation from the original state of the structure as an indication of damage. The last two levels on the other hand usually require an extensive examination of the data in a bid to determine the condition of the structure, the level of damage and distress, its residual capacity and the future performance that can be expected of it. To determine these levels, reliability analysis (level 3) and Bayesian updating (level 4) are used to make inferences from the data collected.

#### *2.2.1 Reliability analysis*

A very important aspect of structural health monitoring involves the use of the damage incurred by, and capacity of the structure to estimate its remaining useful life i.e. the residual capacity for specific loading scenarios. The determination of deterioration levels and changes in structural capacity, require both a characterization of damage as well as a proper determination of the effect of the damage on the structural capacity. Several studies have offered methods into using damage models to estimate residual capacities for structures and their members. These include estimation of remaining fatigue life [30, 31], post impact capacity [32], residual capacity post corrosion initiation [33], etc. In these studies, the computation of the residual capacities is done in either a deterministic or a probabilistic manner. Deterministic estimations of residual capacity are quite straightforward, and relatively uncomplex. However, with the presence of uncertainties in both loads, material properties and geometry of structural members, such deterministic estimations may not offer an accurate estimate of the damage and residual capacity of a structure.

To curtail the disadvantages of deterministic computations, probabilistic methods have been developed which consider the uncertainties associated with the different parameters involved in the load and resistance of structures. Two types of uncertainties are commonly encountered namely aleatory and epistemic uncertainties [34]. Aleatory uncertainty refers to uncertainties that cannot be reduced or minimized such as uncertainties associated with material or geometric properties. Epistemic uncertainties on the other hand refer to uncertainties which can be minimized as more knowledge is gained of the system and more care is taken in modeling it to closer reflect its actual state. Uncertainties from sensor measurements can be said to be epistemic, and can be reduced with the development or acquisition of more precise instrumentation.

Structural reliability in utilizing a probabilistic approach to define the performance of a structure, takes cognizance of uncertainties relating to different aspects of design and construction, thus improving the accuracy of analytically deduced performance of the structure [35, 36]. Fundamentally, reliability analysis sets out to determine the likelihood of a structure's performance failing to live up to its design criteria [37]. This analysis principally revolves around the definition and evaluation of a limit state. Limit states are commonly designed around safety, serviceability or durability criteria and define the boundary for acceptable performance and failure [3]. These limit states are evaluated to determine the likelihood that a structure or structural member fails to meet a specific design criterion (probability of failure). This probability of a system failing to meet the specific performance criterion is defined generically as shown in Eq. (1) below [38].

$$P\_f = Pr[\mathbf{g}(\mathbf{x}) < \mathbf{0}] \tag{1}$$

where: *Pf* is the probability of failure, *g(x)* is a performance or limit state function and *x* is a vector of all the random variables included in the limit state function.

In reliability analysis, the reliability of a structure is quantified using a reliability index. This index, is a measure of structural reliability and captures the inherent

#### *Remote Assessment of the Serviceability of Infrastructural Assets DOI: http://dx.doi.org/10.5772/intechopen.109356*

influence of parameter uncertainties [39]. In a SHM framework, this reliability index becomes a quantified measure of the structure's likely performance under the loading scenario in question, and allows for more informed decision making on the structure. Used as a defining parameter for condition assessment, a reliability index can be defined as a decision criterion for structural performance, with the dropping of a structure's performance below this limit indicative of a need for immediate inspection and possible remedial actions. Inculcating a reliability analysis into the SHM framework will thus bridge the gap between capturing damage and distress, and extrapolating the effects of these captured damages on the performance of the structure.

These probabilistic methods have been used to good effect in several studies to characterize the expected behavior of structures under expected loading over the lifetimes of these structures [33, 40–43]. However, some of these studies assume the initial state of the structure is undamaged and do not update the probabilistic model to account for damage and eroding capacity during its design life. Others that do account for eroding capacity utilize specific models for certain time dependent loads that cannot be extrapolated to other loading types. In addition, although useful for estimating the performance of a structure at the set point in time, reliability analysis on its own does not give a good indication of future performance. Model updating i.e. the updating of the models describing a structure and its performance with new information collected from the structure is needed to do this. A commonly used model updating method is Bayesian updating.

#### *2.2.2 Bayesian updating*

Structural model updating involves the adjustment of a theoretical model to reflect the responses garnered from the actual structure, and thus improve the ability of the model to characterize the behavior and response of the structure to applied loads. For a model updating procedure to be useful in practice, it must be able to handle noisy data, relatively small datasets, errors in the model, incorporate existing knowledge about the structural system performance, and be insensitive to distributions of model parameters [44]. Bayesian techniques are particularly advantageous for model updating as they meet these criteria, thus making them ideal for use in SHM.

Used in many fields for the updating prior probabilistic models with observed data, Bayesian updating provides a consistent framework for introducing new information into existing probabilistic models towards improving their accuracy. This technique, by balancing prior information with observed data, allows for the proper estimation of posterior distributions of uncertain parameters, ensuring that logically consistent inferences can be drawn, and used in prognostic models.

In SHM, Bayesian techniques allow information gleaned from inspections as well as monitoring regimes to be combined and used in better predicting future performance of structures [41]. Using a Bayesian framework, Ref. [45] proposed a process for model updating to reflect the changing state of structures as new information on their state is gleaned from sensors attached to them. In following other model updating procedures, this process makes three base assumptions. These are the existence of variations within the model parameters, the understanding that the models only approximate actual systems and their behaviors, and the knowledge that the model and its corresponding system may be more sensitive to some parameters than to others [45]. This approach to model updating has some peculiar advantages including its explicit consideration of uncertainties, as well as the ability to incorporate both prior information and newly obtained data into the prediction process [41]. This

Bayesian updating process requires knowledge of a number of compositional parts including quantifiable damage level of the structure, or a damage model that allows this quantified damage to be computed, a capacity model, and a relationship between the capacity and damage, defining the erosion of capacity with increasing damage.

To utilize this updating procedure, two approaches are generally considered. The first involves the implementation of a monitoring scheme to assess a quantifiable damage level, and using this in a reliability model to compute a probability of failure. The second method is the use of monitoring schemes to monitor the load exposure of the structure and then use this in a damage model to estimate the damage done prior to the determination of updated probabilities of failure from a reliability model. Ideally, both these methods require some level of monitoring to collect information on the structure under investigation. As such, the first step in designing a Bayesian updating scheme for the health of in-service structures is the determination of data collection on loads and/or system response to the loads.

#### **2.3 Remote assessment of serviceability state**

Data collection for use in a SHM Bayesian updating framework usually involves the use of set in place sensors or the periodic inspection of the structures using mobile equipment/tools. While permanent sensors to collect data on infrastructural assets is an appealing idea, the sheer cost and logistical challenge of installing these sensors and maintaining them for all infrastructural assets limits the possibility of the use, especially for relatively low-cost infrastructural assets. Similarly, periodic inspections while useful are curtailed by the aforementioned logistical and practical challenges. These shortcomings underscore the challenges of implementing such updating schemes. To this end, a remote monitoring regime utilizing information which can be collected without the installation of onsite monitoring tools, and used to assess the state of the infrastructure would be very beneficial. Such a regimen, can be used in optimizing inspection intervals, thus reducing the cost of inspection and maintenance while also minimizing risk of abrupt failures.

The development of such remote monitoring and assessment methods, requires some very specific information. It is necessary to first identify possible types of damage/loading which can be remotely assessed without onsite sensors or equipment. Two possible loading scenarios which can be monitored in such a manner are wind loads and seismic loads. Wind loads are determined from wind speeds, and stations capturing this phenomenon are quite common around towns and cities. Seismic loads are captured from seismological stations and are quite similar for relatively large areas. With the proliferation of locations with equipment collecting data on these load types, it is quite possible to collect data from various sources and aggregate this data into loading history for infrastructural assets at a site of interest, and then use this information to obtain the state of the infrastructure. Periodically carrying out this process, timely information can be obtained and the Bayesian updating process used to update the condition of the asset in question.

Some studies have offered ideas and proposed paths towards such remote assessment of infrastructure. Ref. [31] touted the possibility of aggregating wind speeds collected from stations around a site of interest into the wind speeds for the location, and using these wind speeds in analyzing the damage to traffic ancillary structures. Ref. [30] took this idea further in developing a framework using historic wind speed data gleaned from different locations into making predictions on the remaining useful fatigue lives of these traffic structures. Ref. [46] similarly utilized historic wind data

to determine the fatigue state of high mast illumination poles. Ref. [47] presented a framework for rapid assessment of seismic damage to bridges. This study combined probabilistic analysis with a machine learning algorithm to predict likely damage to bridges in the event of a seismic event, so as to optimize decision making on what to do about the said bridges after an earthquake. These studies aimed to help optimize inspection and maintenance regimes by offering a means of obtaining an idea of the state of these infrastructural assets and their remaining useful lives prior to scheduling inspections and repair/retrofitting actions. While offering cogent processes for the remote assessment of infrastructure, these studies stopped short of using a Bayesian updating process and thus while giving an estimate of the state, cannot be used to continually update the state of the structure over time.

Incorporating a Bayesian updating process into reliability-based decision analysis process for bridges, Ref. [48], determined that including prior information on the performance of the bridges had a telling effect on the resulting reliability analyses. Further buttressing the utility of a Bayesian updating process which incorporates such information in analyzing current and future performance [49], offered a process for estimating the remaining useful life of a structure after developing fatigue cracks using a Bayesian updating process. This study identified parameters leading to damage growth, and utilized simulations and Bayesian inference to identify unknown parameters that will allow for an accurate estimation of the fatigue growth rate.

In developing a framework for remote asset management, some criteria need to be met. These include the consideration of uncertainties in material and model parameters, the ability to leverage historic loading information in determining the condition of the structures, and beyond that, the ability to predict future performance based on the prior knowledge of the state, and updated information collected about the structure. To design a Bayesian updating framework for remote assessment, this study proposes laid out in the next section.
