## Abstract

This work proposes a sampling inspection framework for point measurement non-destructive testing of pipelines to improve its time and cost efficiencies. Remaining pipe wall thickness data from limited dense inspection are modelled with spatial statistics approaches. The spatial dependence in the available data and some subjective requirements provide a reference for selecting a most efficient sampling inspection scheme. With the learned model and the selected sampling scheme, the effort of inspecting the residual part of the same pipeline or cohort will be significantly reduced from dense inspection to sampling inspection, and the full information can be reconstructed from samples while maintaining a reasonable accuracy. The recovered thickness map can be used as an equivalent measure to the dense inspection for subsequent structural analysis for failure risk estimation or remaining life assessment.

## INTRODUCTION

In the water industry, quality, performance, efficiency and productivity are all major concerns in asset and service management (Marques 2008). For water industry organisations that usually own and maintain a large volume of pipelines, non-destructive testing (NDT) inspection and the prediction of a pipe's remaining life are important procedures in developing effective renewal programs aimed at reducing the incidence of catastrophic failures (Misiunas 2005; Costello *et al.* 2007; Liu & Kleiner 2013). A common practice in the NDT of pipelines is to measure remaining pipe wall thicknesses with internal or external point measurement tools. An intense thickness map providing full coverage of a pipe segment can be evaluated through stress analysis (Ji *et al.* 2015, 2017), and the minimum value of the thickness of a segment is an indication of the time to through-wall penetration (Wiersma *et al.* 2007). However, depending on the tool being utilised, dense inspection can be costly and time consuming, or even infeasible in some cases (Schneider 2009; Rizzo 2010; Liu & Kleiner 2013). Therefore, various research has been undertaken with the aim of taking full advantage of limited data, for the prediction of maximum pit depth (Aziz 1956; Khalifa *et al.* 2013) or the evaluation of pipe integrity (Ostrowska 2006; Kishawya & Gabbar 2010). In the authors’ perspective, the purposes of sampling inspection are two-fold: (1) extrapolating the pipe condition information to the unseen area in the same pipeline based on dense local inspection data (De Silva *et al.* 2006; Terpstra 2009; Shi *et al.* 2016); (2) utilising the local data dependency information to minimise the effort in the local inspection process (Ostrowska 2006; Gomez-Cardenas *et al.* 2015). The focus of this research is on the second aspect.

This research aims to address the following three questions: (1) How much redundancy is there in the pipe wall thickness map? (2) How can we develop and determine a guided sampling inspection scheme to improve the efficiency of NDT inspection? (3) How can we robustly reconstruct a dense thickness map from its sampling inspection? To the best knowledge of the authors, none of the current sampling inspection frameworks have systematically considered various practical requirements, targeted at recovering the original data, and been comprehensively evaluated with real data.

The rest of this paper is arranged as follows. The Material and methods section presents a review of related work regarding sampling inspection and modelling pipe condition assessment data, describes the proposed framework, and explains the experimental setup. The experimental results are demonstrated and discussed in the Results and discussion section, followed by the Conclusions.

## MATERIAL AND METHODS

In the water industry, it is a common practice in the management of buried critical water mains to study the condition of an asset in a three-step process: selection of a target pipeline based on a desktop study, coarse condition assessment screening, followed by local NDT inspections to measure remaining pipe wall thickness (Shi *et al.* 2017). The local inspections are usually conducted using ultrasonic or electromagnetic point measurement sensors, and a common interpretation of the pipe condition is remaining pipe wall thickness map (Ulapane *et al.* 2014; Vidal-Calleja *et al.* 2014). The objective of this research is to minimise the required amount of point measurements through data correlation driven sampling inspection, in order to improve the cost-efficiency of local inspections with manageable information loss. In addition, it is the objective that the omitted data are statistically inferable so that the original information can be reconstructed to the best capability of the framework.

Various spatial sampling strategies exist in the literature within the context of improving the efficiency of NDT whilst preserving the information for pipe integrity analysis. The most straightforward inspection strategy is the regular inspection scheme which predefines the pattern for data collection, but appropriate prior knowledge about the defects distribution is essential in designing such a scheme (Ostrowska 2006). The link between acquiring the prior knowledge and the regular inspection scheme has not been well-established in the literature. Therefore, instead of designing more complicated inspection schemes like adaptive strategies, we suggest modelling the available dense local inspection data to establish the prior knowledge which can provide guidance to sampling inspection scheme selection and data reconstruction.

Spatial statistics approaches like spatial processes have been previously employed in terrain and surface modelling (Vasudevan *et al.* 2009; Kroese & Botev 2013). In this study, we propose modelling the remaining pipe wall thickness map from limited dense inspections with Gaussian processes to capture and approximate the data dependence with a specifically designed, composite, anisotropic covariance function (Shi *et al.* 2015, 2016). The model can be regarded as a multivariate distribution which models the distribution of the thickness values and the spatial correlation between thickness values at any two locations. The model by itself has the capability of inferring the original dense data from the sample data (Rasmussen & Williams 2006), and the correlation strength pattern contained in the model provides guidance for designing the regular sampling inspection schemes.

The flow chart of the proposed sampling inspection approach is depicted in Figure 1, and explained in more detail as the following procedure:

- a.
Carry out a pilot survey on the targeted pipeline (a few dense local inspections). In this stage, an improved efficiency has not been achieved.

- b.
Based on the local inspection results from (a):

- b.1
Build a spatial statistics model (Shi

*et al.*2015, 2016) and assess the spatial correlation pattern, with the objective of learning from available data. - b.2
Determine the optimised sampling inspection scheme for the subsequent inspections, considering:

Spatial correlation of thickness values

Distribution consistency of thickness values

The worst-case scenario error on the minimum wall thickness (

**T**)_{min}The worst-case scenario error on the maximum corrosion patch size (

**P**)._{max}

Some of these considerations like maximum pit depth (Khalifa

*et al.*2013), minimum remaining pipe wall thickness (Schneider 2009), and critical patch (Ji*et al.*2015, 2017) arise from practical concerns in analysing the inspection data. - b.1
- c.
In the subsequent inspections, apply the sampling inspection scheme (b.2) on any pipe segment belonging to the residual part of the same pipeline or cohort (i.e. a grouping of pipes that are expected to exhibit similar characteristics in terms of material, year laid, thickness, lining, etc. (Osman & Bainbridge 2011)). The improvement in efficiency is achieved through the reduction of the required amount of point measurements.

- d.
Apply the spatial statistics model (b.1) on the data collected in sampling inspection (c) to recover the original data for the subsequent analysis, e.g. stress prediction (Ji

*et al.*2017).

The evaluation is carried out on ground truth data which consist of the thickness maps of 12 pipe segments extracted from a 1.5 km long DN600 cement lined cast iron (CICL) pipe at Strathfield, NSW, Australia. These data were provided by Sydney Water as a test-bed for the Advanced Condition Assessment and Pipe Failure Prediction Project (Valls Miro *et al.* 2014). Pipe wall thickness profiles are produced by processing high-resolution geometric 3D laser scans of both the outer and inner surfaces of exhumed segments (Skinner *et al.* 2014). Each thickness map is 800 mm (pipe length) by 2050 mm (pipe circumference). In order to reflect the real-world situation of NDT local inspection, the reference data are averaged out at a spatial resolution of 50 mm by 50 mm to mimic the output of an external NDT sensor (Ulapane *et al.* 2014).

The study was done in a cross-validation manner to guarantee a fair test (Hastie *et al.* 2009). The thickness maps of the 12 pipe segments, as shown in Figure 2, are divided into three batches according to the stages in which they were excavated. In each cross-validation round, one batch (four pipe segments, dense inspection) is used as the pilot survey result and the two remaining batches (eight pipe segments) are treated as the test data on which inspections are performed.

Specifically, experiments are performed to find the optimised sampling inspection scheme with which the sample data and the recovered data satisfy the following requirements:

When applying the determined sampling inspection scheme on the same pipe segment, and considering all possible different starting points, any two collected non-overlapping datasets are from the same continuous thickness distribution (with regard to a hypothesis test).

For the same pipe segment, when comparing the minimum remaining pipe wall thickness (

**T**) in the original thickness map and all possible recovered thickness maps, the worst-case absolute error <3 mm (about 10% of the nominal wall thickness)._{min}For the same pipe segment, when comparing the identified maximum patch size (

**P**) in the original thickness map and all possible recovered thickness maps, the worst-case absolute error <150 mm (about three times the length of the spread of the sensor's footprint – 50 mm × 50 mm)._{max}For the same pipe segment, when comparing the root-mean-square error (

**RMSE**) (Shi*et al.*2015) between the original thickness map and all possible recovered thickness maps, the worst-case absolute error <2 mm (about 5% of the nominal wall thickness).

In this study, to make the statement that two datasets are from the same thickness distribution, hypothesis tests such as two-sample Kolmogorov-Smirnov test (Massey 1951) are applied to the two datasets to examine whether the null hypothesis (i.e. they are from the same continuous distribution) will be rejected at 5% significance level.

A patch is defined as an elliptical approximation of an isolated area where the thickness values are under 15 mm (about 50% of the nominal wall thickness). Please note that the criteria parameters are selected based on recent research findings on remaining life prediction for older cast iron critical water mains, instead of referring to a particular standard (Kodikara *et al.* 2016; Ji *et al.* 2017). According to the definition of a patch, an automatic patch extraction algorithm is developed to detect the maximum patch size (i.e. the maximum length of the major axis of the fitted ellipses) from the thickness data. For example, within the ground truth data, patches are identified in five out of the 12 thickness maps, as shown in Figure 3.

## RESULTS AND DISCUSSION

Various experiments on the pilot survey stage on the available data indicate the following:

- (1)
From the available remaining pipe wall thickness data, the spatial correlation plot (the strength of correlation vs. distances in the axial and circumferential directions respectively) of thickness measurements suggests that the correlation decays slower in the axial direction and faster in the circumferential direction (Shi

*et al.*2015). An example of the spatial correlation plot is visualised in Figure 4. The point in the centre represents any thickness measurement and the change of the colour illustrates how the correlation strength decays with distance. Therefore, ideally, the circumferential direction needs to be sampled more frequently than the axial direction, because given the same distance between two point measurements, the data dependency in the circumferential direction is weaker than in the axial direction. - (2)
At least 10% of the original data is required to be sampled so that by following certain inspection patterns, any two non-overlapping datasets sampled from the same thickness map are from the same continuous thickness distribution.

- (3)
The worst-case error on the minimum remaining pipe wall thickness (

**T**) <3 mm appears to be the most challenging requirement. Based on the pilot survey, at least 50% of the original data needs to be sampled so that by following certain inspection patterns, the requirement on the worst-case T_{min}_{min}error can be satisfied.

Figure 5 shows three regular inspection schemes for sampling 50% of the original data. In the pilot survey stage and with cross-validation, Scheme A succeeds in meeting all requirements for most of the cases and Schemes B and C succeed in all cases; Scheme C shows slightly better performance than the other two schemes, respectively. In addition, according to the correlation pattern, Schemes B and C are more reasonable choices in comparison to Scheme A which samples less frequently in the circumferential direction.

The worst-case performances of the selected inspection schemes on the test data (the data which were not used in the pilot survey) are presented quantitatively in Table 1. In this experiment, through cross-validation each worst case represents the worst case of 48 tests.

Inspection scheme . | Maximum worst case absolute T_{min} error (mm)
. | Maximum worst case absolute P_{max} error (mm)
. | Maximum worst case RMSE (mm) . |
---|---|---|---|

A | 3.8 | 520 | 1.1 |

B | 2.4 | 97 | 1.0 |

C | 2.4 | 60 | 0.9 |

Inspection scheme . | Maximum worst case absolute T_{min} error (mm)
. | Maximum worst case absolute P_{max} error (mm)
. | Maximum worst case RMSE (mm) . |
---|---|---|---|

A | 3.8 | 520 | 1.1 |

B | 2.4 | 97 | 1.0 |

C | 2.4 | 60 | 0.9 |

Although Scheme A is not a satisfactory choice, as the results do not meet the requirements set out in the previous section, the results are still produced for comparison purposes. According to Table 1, Scheme C demonstrates more competitive performance than Scheme B, even though they both meet the set requirements. In practice, both Scheme B and Scheme C have their own advantages: Scheme C is likely to provide more accurate results while Scheme B is more efficient, as it requires less localisation effort to achieve the inspection pattern.

As Table 1 is a summary of a series of iterative tests with cross-validation, an example of more detailed test results is provided in Table 2. In this particular test set, data from batch 1 (G11, G12, G13 and G14) serve as the pilot survey results to determine the inspection scheme, and Scheme C (assuming it was selected) is applied on the rest of the eight thickness maps. Table 2 shows the evaluation results by comparing the recovered data (from the sample data) against the original data. For example, on pipe segment G21, considering all possible datasets collected with sampling Scheme C, in the worst case the recovered thickness maps have an absolute T_{min} error of 1.1 mm and/or an absolute P_{max} error of 58 mm.

Test data . | Real T_{min} (mm)
. | Real P_{max} (mm)
. | Predicted T_{min} (mm)
. | Worst case abs. T_{min} Err. (mm)
. | Predicted P_{max} (mm)
. | Worst case abs. P_{max} Err. (mm)
. | Worst case RMSE . |
---|---|---|---|---|---|---|---|

G21 | 14.7 | 0 | 13.8–15.8 | 1.1 | 0–58 | 58 | 0.5 |

G22 | 19.6 | 0 | 19.6–19.6 | 0.0 | 0–0 | 0 | 0.5 |

G23 | 9.7 | 522 | 9.7–10.1 | 0.5 | 510–540 | 18 | 0.6 |

G24 | 11.4 | 353 | 11.4–12.2 | 0.8 | 319–343 | 34 | 0.5 |

G31 | 15.6 | 0 | 15.2–15.6 | 0.5 | 0–0 | 0 | 0.5 |

G32 | 15.0 | 0 | 14.4–14.6 | 0.7 | 0–0 | 0 | 0.5 |

G33 | 16.1 | 0 | 16.1–16.1 | 0.0 | 0–0 | 0 | 0.6 |

G34 | 9.5 | 297 | 9.5–9.9 | 0.4 | 259–288 | 37 | 0.6 |

Test data . | Real T_{min} (mm)
. | Real P_{max} (mm)
. | Predicted T_{min} (mm)
. | Worst case abs. T_{min} Err. (mm)
. | Predicted P_{max} (mm)
. | Worst case abs. P_{max} Err. (mm)
. | Worst case RMSE . |
---|---|---|---|---|---|---|---|

G21 | 14.7 | 0 | 13.8–15.8 | 1.1 | 0–58 | 58 | 0.5 |

G22 | 19.6 | 0 | 19.6–19.6 | 0.0 | 0–0 | 0 | 0.5 |

G23 | 9.7 | 522 | 9.7–10.1 | 0.5 | 510–540 | 18 | 0.6 |

G24 | 11.4 | 353 | 11.4–12.2 | 0.8 | 319–343 | 34 | 0.5 |

G31 | 15.6 | 0 | 15.2–15.6 | 0.5 | 0–0 | 0 | 0.5 |

G32 | 15.0 | 0 | 14.4–14.6 | 0.7 | 0–0 | 0 | 0.5 |

G33 | 16.1 | 0 | 16.1–16.1 | 0.0 | 0–0 | 0 | 0.6 |

G34 | 9.5 | 297 | 9.5–9.9 | 0.4 | 259–288 | 37 | 0.6 |

Figure 6 provides two examples of the sampling, recovery and basic analysis results. These were the worst situations with respective sampling schemes on the original thickness maps which are shown in the first column. In Example 1, relatively large patches are captured in the recovered sampling inspection data, whereas in Example 2, the relatively small patch is better preserved only in Scheme C.

## CONCLUSIONS

This work presents and evaluates a sampling inspection framework for point measurement NDT of pipelines.

The contribution of this research work includes: (1) proposal of a sampling inspection framework, (2) proposal of a set of requirements for determining inspection schemes, (3) development of a data recovery mechanism, and (4) evaluation of the proposed framework with an actual dataset and a set of assessment requirements which are close to reality.

On a specific dataset, we determined that in order to recover the original data to a certain accuracy, the circumferential direction of the pipe needs to be sampled more frequently in comparison to the axial direction. The worst-case error on the minimum remaining pipe wall thickness is the most challenging requirement to meet. Eventually, 50% of the data and certain sampling inspection patterns are required to achieve a set of pre-defined requirements. This work demonstrates that the data dependency can be explored further to improve the efficiency of the current NDT condition assessment procedure.

The significance of this work lies in its potential of providing a theoretical basis and a practical procedure for determining an optimised sampling inspection scheme to improve the efficiency of NDT, and its reconstruction capability. Experimental results are presented to demonstrate the effectiveness of the proposed framework.

## ACKNOWLEDGEMENTS

This work is an outcome from the Critical Pipes Project funded by Sydney Water, Water Research Foundation USA, Melbourne Water, Water Corporation (WA), UK Water Industry Research Ltd, South Australia Water, South East Water, Hunter Water, City West Water, Monash University, University of Technology Sydney and University of Newcastle.

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Failure Monitoring and Asset Condition Assessment in Water Supply Systems