**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:


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:


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].

$$\mathbf{P\_{f}} = \Phi(-\mathfrak{P}) \tag{2}$$

where Φ is the standard normal cumulative function.

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

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-intime 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].

$$p\_f(b|a) = \frac{p\_f(a+b) - p\_f(a)}{1 - p\_f(a)}\tag{3}$$

where *pf*ð Þ *b*j*a* is the probability of failure in b subsequent years given that it has survived a number of years, and *pf*ð Þ *a* þ *b* and *pf*ð Þ *a* 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).

$$\mathcal{S}\_d = \frac{\sum\_{i=1}^n \frac{S\_{d,i}}{R\_i}}{\sum\_{i=1}^n \frac{1}{R\_i}} \tag{4}$$

where Sd is the wind parameter for a specific time period d, n is the number of weather stations used in the interpolation process, Sd,i is the wind parameter for the time period d at the weather station i, and Ri 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].

$$\log(X, t) = \int\_{a\_i}^{a\_f} \frac{da}{\left(Y(a)\sqrt{\pi a}\right)^B} - \text{CS}\_R^B \text{N} \le \mathbf{0} \tag{5}$$

where *ai* is the initial crack length, *af* 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, SR 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).

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


#### **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,

#### **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.*

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.

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.

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

#### **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.*

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

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.
