Remote Assessment of the Serviceability of Infrastructural Assets

Abstract

The continued serviceability of structures and infrastructural assets over time is a very important component of design and construction. Traditionally, structural health monitoring techniques utilize sensors and field inspections to capture distress and defects in structural members to allow for repairs and retrofitting prior to catastrophic collapse. However, these processes are usually quite expensive (financially and time wise), making it difficult to assess all assets. Rather, it necessary to identify specific assets requiring field investigations. To do this, an ability to remotely compute the real time serviceability of these structures and periodically update their condition to determine the criticality of field inspections is important. Several methods and processes have been proposed for this purpose with respect to different loading conditions and type of structures. This chapter will offer insight into remote monitoring of structures and infrastructure over time as they sustain damage from varied loading conditions.

1. Introduction

Structures are primarily designed to have the capacity to withstand certain loads they can be expected to bear. Over their design lives, structural members can be expected to deteriorate, with an attendant decrease in their capacities. This is generally as a result of exposure to environmental factors, aging of the constituent materials, as well as the residual effects of loading conditions. Such degradation of structures occurs in a number of ways including fatigue, corrosion, cracking, and scour. Thus, maintaining infrastructure to ensure its continued ability to fulfill design criteria is very important for the safety and security of a society. To this end, accurate knowledge of the in-service state of infrastructural assets cannot be trifled with. This brings to the fore, the pertinence of periodic inspection and maintenance for these assets, especially those designed to last for a long time, to ensure they continue to meet specified design requirements.

The process of inspecting or monitoring structures with a view to identifying and assessing damage to them is referred to as structural health monitoring (SHM). Principally, the inspection aspect is carried out by visual means. However, such visual inspections have a number of shortcomings including subjectivity of the inspecting personnel, the ability to only capture surface damage in visible locations, and the limitation of the inspection to damage without a congruent monitoring of loads applied to the structure. In addition, the sheer volume of infrastructural assets requiring such inspections and maintenance precludes the possibility of thorough inspections being carried out regularly on most, increasing the possibility of critical information getting missed during cursory examinations. For example, the Federal Highway Administration specifies biennial routine inspections for every bridge within its purview. These inspections are primarily designated to be carried out via visual inspection, with more advanced equipment and methods only deployed for more in-depth inspection if deemed necessary. However, with about 600,000 bridges included in this inspection regime, rigorous visual inspection of each bridge becomes a very difficult task to achieve within the projected time frame, leading to increased risks of failure.

With the unreliability of such conventional lifetime assessment methods [1, 2], SHM has become a very important tool for assessing the lifetime of a structure. To curtail the stated shortcomings in the inspection and maintenance process, it became necessary to expand the original scope of SHM frameworks. In redefining the SHM process, Ref. [3] asserted that a monitoring system should include four operations namely acquisition, validation, analysis and management. Ideally, a single SHM system would collect information on both loads and system response to the loading. In addition to monitoring duties, an ideal SHM system would also incorporate some prognostic methods that will allow for the damage levels to be evaluated and the in-situ health of the structures to be determined. This will allow for an analysis of the present and future performance of the infrastructural assets. Integrating a variety of disciplines including material science, non-destructive evaluation, fracture and fatigue mechanics, structural dynamics and structural design, SHM frameworks can be designed to collect information on deflections and strains, system behavior, thresholds of systems and members, input values for lifetime assessment, and maintenance planning [1]. To this end, SHM frameworks originally designed for capturing and assessing the initiation and propagation of damage, have been expanded to collect other information related to the performance of the structure [1, 4]. To prevent damage to structures, the monitoring or data acquisition stage of SHM is carried out principally using non-destructive evaluation (NDE) techniques. These techniques allow for the evaluation of the integrity of materials and structures without compromising their continued abilities to meet design criteria. Used widely for detecting and characterizing defects and damage in infrastructure, NDE techniques have been extensively researched and offer a useful means of collecting information for SHM to adequately characterize the in-situ health of infrastructure.

A holistic monitoring system must be able to provide sufficient information for users to make decisions on the continued serviceability of the structure, and on maintenance, repair and replacement regimens. With the plethora of tools developed for capturing damage and structural response, the determination of the presence of damage has become a relatively trivial task. However, the extrapolation of the effect of the damage on the serviceability of the structure remains a relatively complicated undertaking. Currently, most systems deployed for SHM of infrastructural assets are essentially either sensor arrays or other equipment used to identify the existence of damage or distress in the structures under investigation, without requisite provision for quantifying the damage and defining the residual capacities of the structures. Thus, while providing good data on the loading of a system, and the damage incurred, these systems do not provide information on its continued serviceability, making manual inspections in the SHM process irreplaceable. To this end, SHM systems remain a precursor to physical inspections, giving inspectors an idea of the state of infrastructure and a basis for the determination of inspection and maintenance schedules. This brings to the fore the importance of accurately analyzing the data collected from the SHM systems.

Two approaches are used for the analysis and interpretation of the data collected, and primarily differ in the use or avoidance of a physics-based model for analyzing the behavior of the structure [5]. Model based approaches involve updates to models that capture damage and eroding capacity with respect to applied loads to reflect changes in the structural parameters observed from collected data [6, 7, 8]. In analyzing the strengths and weaknesses of the approaches, Ref. [5] determined that rather than being considered alternatives, both systems should be considered to be complementary, depending on the needs and requirements of the SHM system. Although well established, these methods are developed using idealizations of the structural behavior, without taking into considerations uncertainties in materials, geometry and loading conditions in analyzing the data collected. These uncertainties could lead to discrepancies between projected structural behavior and the actual behavior, possibly creating incorrect assumptions on the state of a structure. To this end, such deterministic methods remain at best approximations of the condition of a structure and must be used with caution. To overcome this shortcoming, a probabilistic process that accounts for these uncertainties, thus allowing for a more realistic estimation of the state of the structure, and its reliability can be applied. This inclusion of reliability methods in SHM processes, enhances the ability of monitoring systems and components in real time, and allows for the introduction of predefined alert levels to trigger specified actions once a value dips below a critical reliability index [5].

Beyond the use of reliability methods, Bayesian updating processes have become a popular means for updating the state of structures in SHM frameworks. These processes, utilize the data collected alongside prior knowledge on the performance of the structure to make inferences on its current state and future performance. The incorporation of Bayesian updating processes, moves SHM frameworks from being monitoring systems to becoming more holistic systems, inculcating both monitoring and analysis into making decisions on the condition and future performance of infrastructural assets.

Some steps are important for such SHM frameworks. These are obtaining data on the loading and response of structures, characterizing damage or distress from this information, analyzing the information, and making conclusions based on the characterizations. These steps are carried out to get a good grasp of the state of the structure, prior to full on-site inspections. However, with the cost of permanent sensors, it is quite unfeasible to instrument all infrastructural assets. The alternative, periodic inspections are also impractical due to the number and geographical spread of these assets. To counteract these challenges, this chapter proposes a trade-off between both. This alternative involves the use of existing and regularly updated data such as wind speeds, traffic information and ground motion from seismic events to extrapolate the condition of infrastructural assets exposed to these conditions, and update their conditions, allowing for the optimization of an inspection regimen. To this end, the objectives of this chapter include:

1. The identification of loading scenarios with readily available data and the extrapolation of such data to site specific conditions for the locations of infrastructural assets.

2. The development of a procedure for the use of these loading conditions to determine the in-service state of the structures.

3. The determination of a methodology that will allow for periodic updating of the state of these assets using the collected information and prior knowledge of the performance of the assets.

To meet these objectives, the rest of the chapter is designed to begin with a background and overview of the SHM process, and then focuses on a methodology designed to meet each objective. A case study example of traffic signal structures is included to demonstrate the use of the proposed methodology.

2. Overview of structural health monitoring

Designed principally to determine and assess structural integrity, structural health monitoring has continued to evolve with improvements in the technology and processes used in achieving the said goals. Some fundamental bases of SHM include an assumption that all materials have inherent flaws, and the necessity of at least two system states in order to assess damage. As an important tool for assessing the condition and lifetime performance of a structure, Ref. [9] opined that systems which only include sensors deployed on structures without a definition or classification system for the damage cannot truly be classified as SHM systems. The study stated that a true SHM system would include a quantifiable and pre-established definition of damage to be detected by the sensors. Also, in the development and deployment of a SHM system, a classification process for the identification of damage and assessment of its extent needs to be defined [9]. To improve the practice of SHM for infrastructure, Ref. [3] proposed a condition-based assessment framework for the management of bridges. This process, would ideally provide information on damage to the structure and erosion of structural resistance, as well as the probability of the structure’s performance falling below a set standard and an estimation of the remaining useful service life. An SHM system encompassing these parts would arm inspectors with adequate information on the service condition of these infrastructural assets, allowing them to make decisions on the repairs/retrofitting, while drastically cutting down on the need for periodic manual inspections. There are five principal steps in a SHM process. These are detection, localization, classification, assessment and prediction [9, 10]. While the first two steps involve utilizing sensors and other equipment for monitoring via non-destructive evaluation of the structure under investigation, the last 3 steps involve analyses of the data collected from the monitoring process. Thus, it can be said that an optimal SHM process consists of monitoring of structural behavior, and analyzing this data for a proper prognostication of structural health.

2.1 System monitoring

Monitoring of structures for SHM involves use of instrumentation and processes for the detection and localization of damage. With the inability of sensors to measure damage, the data collection at the system monitoring stage is qualitative in nature, giving useful information on the presence and type of damage present in a structure, but not offering quantitative information on the extent of the damage and the remaining useful life of the structure or structural member. Most sensor systems deployed for the purpose of SHM consist principally of this monitoring process, without going further to quantify the damage and predict remaining useful life of the structures [9]. Although only one part of a holistic SHM process, the importance of proper deployment of sensors and instrumentation towards damage detection and monitoring cannot be overestimated. With sensing systems, there is a trade-off between sensitivity to damage of a sensing system and its noise rejection capability, and also the size of damage detectable is inversely proportional to the frequency range of excitation [9]. Generally, the length and time associated with the initiation and evolution of damage dictates the properties of the sensing system to be used. Non-destructive evaluation techniques have been widely investigated for this purpose. These techniques can be deployed in an online manner for continuous monitoring, or in an offline manner for inspection purposes. NDE methods researched and deployed for SHM include vibration-based methods [11, 12, 13], optical based methods [14], radiography [15], ultrasonic testing [16, 17], acoustic emission [18, 19], electromagnetic methods [20, 21, 22], magnetic particle inspection [23, 24] and thermographic methods [25, 26, 27, 28]. These methods are usually used to capture damage in either continuous monitoring schemes or in inspection regimes. Several types of damage are usually the targets of such non-destructive evaluation processes. Ref. [13] in a follow up of a study by Ref. [29], determined that the material and geometric changes that can be characterized as damage by these systems include cracks, corrosion, buckling, creep, fastener loosening and loss of preload, debonding, delamination, microstructural degradation, and pull-out.

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].

$$P_f=\mathit{Pr}\left[g\left(\mathit{x}\right)<0\right]$$E1

where: P_f 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 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, 41, 42, 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.

3. Methodology

The methodology for the remote asset management is very similar to that for any SHM process, and can be divided into two parts namely data collection and data analysis. The data collection process is relatively straightforward, and begins with an identification of the requisite information needed for the assessment. This data comes in form of historic information on the loading patterns, collected from monitoring stations within the vicinity of the location of interest. Cleaning the data and aggregating the information into a usable form specific to the location of interest can then be carryout using processes specific to the type of data. Data analysis on the other hand requires extensive knowledge about geometry of the structure, material properties and model parameters as detailed in the following sections. The overall process is as follows:

1. Determine the load and damage mechanism to be investigated.

2. Identify monitoring stations collecting the needed data in the vicinity of the site in question.

3. Collect the data and aggregate into site specific data.

4. Compute the damage using probabilistic methods.

5. Periodically update the reliability using Bayesian methods and timely information from monitoring stations.

6. Schedule inspections once the reliability falls below a predetermined threshold.

7. Update the reliability models with results from inspections and/or maintenance processes.

Details on each step in the process are laid out in the following sections.

3.1 Data analysis

In SHM, two levels of analyzing information collected on the state of a structure require extensive examination of said data. These are the levels of quantifying damage/changes to the structure and that of predicting future performance based on the latest information on condition [5]. Reliability analysis can be used for the first level, and Bayesian updating off the results from the reliability analyses used for the second.

Carrying out a reliability analysis of the structure in question requires a number of steps. To begin with, a limit state equation including both resistance and damage models needs to be ascertained. These models should ideally be models that include measurable parameters, which can be captured via a site inspection. As such, when a structure is flagged for inspection, measurements made during said inspection can be used in eventually updating the condition of the structure for future estimation of its condition.

After determination of a limit state, a method of solving the probabilistic problem needs to be decided upon. Popular methods for solving such problems include first order reliability method (FORM), second order reliability method (SORM), Monte Carlo simulations, Markov Chain Monte Carlo simulations, Hasofer-Lind procedure, and Rackwitz- Fiessler procedure. These methods each has its pros and cons and a determination of which would be ideal for the particular set of circumstances is needed. The process for the reliability analysis is as follows:

• Identify a limit state equation including both capacity and demand models appropriate to the scenario under investigation.

• Identify all nondeterminate variables in the limit state, their distributions and parameters.

• Compute the reliability index or probability of failure using these parameters and the limit state function in one of the methods mentioned above.

The relationship between the probability of failure and reliability index can be described using the normal cumulative function as shown in Eq. (2) [35, 38].

$${\mathrm{P}}_{\mathrm{f}}=\mathrm{\Phi }\left(-\mathrm{\beta }\right)$$E2

where Φ is the standard normal cumulative function.

The reliability analysis giving a probability of failure and a reliability index for the structure offers insight into the reliability parameters correlating to the point-in-time condition of the structure i.e. a Level 3 type assessment of the state of the structure.

Bayesian updating using the prior information on historic loadings, as well as fresh information from either the reliability analysis or from inspections can then be used to update the reliability models for a prediction of the possible future performance of the structure given the point-in-time knowledge of its condition. Based on the Bayes’ theorem of conditional probability, the underlying idea can be used to update a quantified characteristic state of a structure, using the Bayesian framework as shown in Eq. (3) [48].

$$p_f\left(b|a\right)=\frac{p_f\left(a+b\right)-p_f\left(a\right)}{1-p_f\left(a\right)}$$E3

where $p_f\left(b|a\right)$ is the probability of failure in b subsequent years given that it has survived a number of years, and $p_f\left(a+b\right)$ and $p_f\left(a\right)$ are the probabilities of failure in time a + b and a respectively.

Updating the probability of failure using timely information on loading, and /or from inspections, would allow for continuous monitoring of the condition, and prediction of future performance, offering a cheap and quick way to remotely obtain insights into the condition of infrastructural assets.

3.2 Case study

To demonstrate the laid-out methodology, a case study is presented. This illustrative example involves two traffic signal structures placed in different orientations at the same location. Selected from the cases presented in Ref. [30], these represent structures at a location which showed significant damage from wind forces in the aforementioned study. Installed in 1997, these traffic signal structures are in a location with significant wind loads a explained in Ref. [30]. To this end, the analysis carried out in the study, showed that each is expected to have degraded significantly, making them good candidates to test the remote assessment strategy laid out in this study. Both traffic signal structures are cantilevered structures, with the mast arm extending from a single pole, which also has a luminaire post over it.

3.2.1 Loading model

The first step in the methodology involved collecting data pertinent to the structure under investigation. For the traffic signal structure, the principal type of load affecting its performance relates to the wind forces acting on it. To this end, wind speeds were collected from different weather monitoring stations in the vicinity of the traffic structures. A process laid out in Ref. [30] for cleaning the data to get rid of outliers, incomplete data and erroneous readings was then used to obtain a dataset that representative of the historic wind speeds in the general area. These were then converted into hourly wind data using the Durst curve. Next, these wind data were aggregated into site specific wind data using the process described in Ref. [31]. The equation used in obtaining the wind data specific to the site is as shown in Eq. (4).

$$S_d=\frac{{\sum }_{i=1}^n\frac{S_{d,i}}{R_i}}{{\sum }_{i=1}^n\frac{1}{R_i}}$$E4

where S_d is the wind parameter for a specific time period d, n is the number of weather stations used in the interpolation process, S_d,i is the wind parameter for the time period d at the weather station i, and R_i is the distance of weather station i from the site of interest.

The synthesized wind data collected and interpolated for the location as described above led to the computation of approximate historic wind information for the site, and thus the wind forces the structures located therein are expected to have borne over their service lives. With the historic wind forces acting on the structure collected, the next step involved the determination of stresses from these forces at critical locations, and the response of the structure to these loadings.

Assuming that the cyclic wind forces on the structure will lead to fatigue at certain critical locations on the structure, the stresses at identified critical locations due to the wind forces were computed. The base of the mast arm and the base of the pole were selected as critical fatigue locations as a number of studies have pinpointed these locations to be fatigue critical given the concentration of stresses there. The deterioration of the connections at these locations were then analyzed and used as a defining parameter for the service states of the traffic signal structures.

3.2.2 Deterioration model

To ensure ease in updating using information gleaned from site inspections, it is imperative that the structural degradation model used includes measurable degradation parameters. Prior studies on wind fatigue degradation of similar structures made use of the Miner’s rule for cumulative fatigue damage in analyzing the fatigue damage. Although a valid process for estimating fatigue damage, this process does not give observable parameters, and would not be updateable using results from site inspections. To this end, a fracture mechanics approach for crack propagation is used in this study instead, and a limit state function defined related to the crack propagation through the weld at both critical locations as shown in Eq. (5) [50].

$$g\left(X,t\right)={\int }_{a_i}^{a_f}\frac{\mathit{da}}{(Y\left(a\right){\sqrt{\mathit{\pi a})}}^B}-C{S}_R^{B}N\le 0$$E5

where $a_i$ is the initial crack length, $a_f$ is the crack size associated with failure, Y(a) is a geometry function accounting for shape of specimen and mode of failure, C is a material property, B is an equivalent damage material property, S_R is the equivalent stress range, and N is the number of stress cycles.

The limit state equation was then evaluated using the statistical parameters for the random variables shown in Table 1. This process was used to compute the annual reliability and probabilities of failure for the traffic signal structures. These can be expressed as the point in time probabilities of failure which do not consider the previous year’s probability of failure. Next, an updated probability of failure for each year is computed using a Bayesian updating process as expressed in Eq. (3).

Parameter	Mean	Coefficient of Variation	Distribution
Thickness of Pole	0.18	0.25	Normal
Initial crack length	0.004–0.01	1	Normal
Stress	Variable	0.1	Normal
C	1.294 × 10^−12	0.5	Lognormal

Table 1.

Random variables used in the limit state equation.

3.2.3 Results

Cumulative probabilities of failure are obtained for the 25 year span the traffic structures have been in service. For the reliability analyses, failure is deemed to have occurred if the crack in the weld extends to the thickness of the tubular pole or mast arm. Assuming prior knowledge of the existing level of deterioration of the structure via a knowledge of an existing crack and the corresponding lengths, Figures 1 and 2 show the annual reliabilities of the traffic structure, as a function of the service age. The influence of time on the reliabilities can be seen with the continual degradation of the reliability indices over time, irrespective of the initial size of the crack. However, the initial size of the defect (ai) also has a telling effect on the structures and the time until they require inspections and/or maintenance. For example, for the pole to baseplate connection o traffic structure 2, assuming a reliability index of 3 is the determined point at which an inspection becomes necessary, the traffic structure would be due for inspection in year 16 assuming an initial crack size of 0.08 to 0.1 inches, but would only be due for inspection in year 19 for an initial crack size of 0.04 inches. However, post inspection, these point-in-time reliabilities are not updated with the results of the inspection/possible maintenance, and thus they will no longer represent ground truth.

Figure 1.

Annual point-in-time reliabilities for pole to baseplate connection for (a) traffic structure 1, and (b) traffic structure 2.

Figure 2.

Annual point-in-time reliabilities for mast arm to baseplate connection for (a) traffic structure 1, and (b) traffic structure 2.

Annual reliability indices, computed with an inclusion of the influence of prior knowledge of the performance of the structure in the preceding years is shown in Figures 3 and 4. These indices are compared with those computed using the cumulative stress but without an inclusion of the previous performance shown in Figures 1 and 2 for an initial crack size e of 0.01 inches.

Figure 3.

Comparison of Bayesian updated reliabilities to annual point-in-time reliabilities for pole to baseplate connection for (a) traffic structure 1, and (b) traffic structure 2.

Figure 4.

Comparison of Bayesian updated reliabilities to annual point-in-time reliabilities for mast arm to baseplate connection for (a) traffic structure 1, and (b) traffic structure 2.

The results for the updated reliabilities show the effect of prior knowledge on the reliability of a structure. The reliability and probability of failure for each year includes the prior knowledge that the structure did not fail in the previous year. From the results in Figures 3 and 4, it can be observed that the annual point-in-time reliability indices are significantly less conservative than the Bayesian updated reliabilities. Similar to the conclusions drawn in Ref. [48], not taking prior performance into account results in conservative reliability indices which may not be truly reflective of the performance of the structure. For example, at 25 years, the reliability index of traffic structure 1 is 1.87 with a corresponding probability of failure of 0.03. Comparatively, the Bayesian updated reliability index at this time is 2.23 and the probability of failure is 0.013. Essentially, this means that while the point-in-time reliability predicts that the likelihood of the structure failing in the next year as 3%, the Bayesian updated reliability gives a less conservative estimate of 1.3% probability of the structure failing. This seemingly less conservative result is because known information about the prior performance of the structure (i.e. not failing in prior years), is used in the Bayesian updated reliability but is not used in the point-in-time reliability estimate. Thus, while giving seemingly unconservative results, the Bayesian updating method does offer a realistic insight into the condition of the structure, considering its known performance. In addition, this method offers the flexibility of incorporating post inspection information, into an updated reliability for the structure.

4. Future work

This study set out to offer a framework for remote asset monitoring and assessment. Although a framework is laid out, there is still significant work to be done for widespread use.

A critical aspect of this framework involves the use of easily accessible data pertaining to the loading conditions related to the location of the structure. Wind data is used in the case study presented. However, it is important to identify data related to other types of loading conditions that can be obtained conveniently and updated regularly. It should also be possible to extrapolate these data to reflect the conditions of the site of interest, and use them in damage/deterioration models for the structure.

Damage and capacity deterioration models which can be used with such easily accessible data and which also capture measurable damage need to be identified for different loading scenarios pertinent to infrastructural assets. In addition to utilizing collected data, these models need to characterize damage in a way that can be physically measured in order to allow for updates to be made to the model from field inspections and maintenance work carried out.

Although offering a handy way to remotely assess infrastructural assets and update their conditions, the damage and deterioration models used in this study as well as in other studies on using reliability analyses are commonly based on idealizations of the structural systems. More field data is needed to determine the correlation between the structural systems and these models, in order to improve their predictive capabilities.

5. Conclusions

In a bid to optimize the SHM process, this study set out to offer a framework for the remote monitoring of infrastructural assets prior to scheduling field inspections and maintenance programs. Based on a Bayesian updating process, a process of obtaining remotely accessible data, extrapolating site-specific conditions from this data, and computing the time dependent performance indices for a structure at a specific location was laid out. Using a pair of traffic signal structures as a case study, the Bayesian updated reliabilities and the point-in-time reliability indices were computed. The point-in-time reliability indices offered more conservative results, due to the indices not considering the prior performance of the structure. The Bayesian updated reliability indices on the other hand accounted for the past performance of the structure and it’s continued serviceability. Beyond determining its current serviceability, the Bayesian updating process also provides room for including results from field inspections and/or maintenance work in future performance indices, which the point-in-time reliability does not, further buttressing its value in remote assessment frameworks.