Modeling and Calculation of Dent Based on Pipeline Bending Strain

The bending strain of long-distance oil and gas pipelines can be calculated by the in-line inspection tool which used inertial measurement unit (IMU). The bending strain is used to evaluate the strain and displacement of the pipeline. During the bending strain inspection, the dent existing in the pipeline can affect the bending strain data as well. This paper presents a novel method to model and calculate the pipeline dent based on the bending strain. The technique takes inertial mapping data from in-line inspection and calculates depth of dent in the pipeline using Bayesian statistical theory and neural network. To verify accuracy of the proposedmethod, an in-line inspection tool is used to inspect pipeline to gather data.The calculation of dent shows themethod is accurate for the dent, and the mean relative error is 2.44%.The newmethod provides not only strain of the pipeline dent but also the depth of dent. It is more benefit for integrity management of pipeline for the safety of the pipeline.


Introduction
With the development of the oil and gas production, the longdistance buried pipeline is used to the transport the production of oil and gas [1,2].Due to the reasons of time accumulated or construction, defects such as corrosion, gouge, dent, and displacement seriously threat the safety operation of the pipeline.In order to reduce the risk of these defects, the pipeline company usually selects in-line inspection tool to inspect the defects for body of pipeline.The magnetic flux leakage (MFL) and ultrasonic tool are used to inspect metal loss of pipeline such as corrosion, crack, and gouge.
Dent is another common defect in long-distance buried oil and gas pipeline.A lot of dents have been found in the pipeline due to the construction of mechanical damage.Dents can deform the pipeline and affect the integrity of body for the pipeline [3][4][5][6].Specifically, the dent located in the weld of pipeline or the dent that is very sharp can lead to the serious leak consequence.The information about the severity of the damage to a pipe due to dents is very important for the pipeline industry.The defect of dent is the radial deformations of the pipe wall.Generally, these dents can be measured by in-line inspection tools named geometry tool which equipped with instrumentation and mechanical fingers is able to provide data on the pipe wall geometry deformation.However, this tool only inspects the size (length, depth, and width) of the dent.In order to assess the hazard for the dent, the technical requires a complex modeling and computes the strain or other information.Another method for dent testing can be using the profile gauge to measure the depth, width, and length of the gouge or scratch damage.This method also can be used to determine the extent of damage and determine if any sharp edges are present.Recently, 3D laser scanner is used to map and measure the dent.This technology can more accurately measure the dimensions of the dent by the laser scan.However, the method for dent testing of profile gauge and 3D laser scan only use dents which have been dug.They are the verification for dents which are inspected by geometry tool.
Nowadays, another Pipeline In-Line Inspection tool which installed inertial measurement unit (IMU) is used to inspect the pipeline [7][8][9][10].As shown in Figure 1, this tool, which consists of a Data Acquisition System (DAS), an IMU, some weld detectors, and odometers, is driven to move through the pipeline and collect data regarding dents, bends, and navigation.Petrochina Pipeline Company has developed an IMU system based on a navigation system, which is suitable for a geometry PIG.The IMU can be used to record the attitude data for the tool during the inspection.A method of calculation for pipeline centerline is proposed by fusion for multisensors.Czyz et al. [11,12] developed a pure geometry-based algorithm for the bending strain of a pipeline.Another pipeline strain testing method is using the strain gauge to be installed on the surface of pipeline.Two types of strain gauge, resistance and optical fiber, are used to measure the strain of pipeline.The strain gauge of optical fiber is more precise for measuring the strain.These two methods can be used to monitor the strain changes of the pipeline.But the limit for these two methods is only used to measure the part sections of pipeline.They cannot inspect the whole strain for long-distance buried pipeline.
The bending strain can be reported for the whole pipeline when the tool runs for once.Generally, the technical just uses the bending strain to detect the position of pipeline enduring the extra strain larger than the operation requirement and assessing the displacement for local pipeline.However, it is found that the bending strain can be affected by the dent [13][14][15][16].In this paper, a method for modeling and computation of dent which is based on bending strain is proposed.The technique takes Bayesian statistical theory and neural network to improve a new method to compute the depth of the dent.It is more useful to assess the dent for the pipeline integrity.

The Calculation Method of the Pipeline Bending Strain
In this section, the calculation method of the pipeline bending strain is described.Several factors such as internal pressure, temperature differential, external loads, and boundary conditions are affecting the strain.The strain can be consisted of two primary components: longitudinal and hoop strain [17][18][19].The bending strain is one of the components for longitudinal strain.It can be described by the following formula: where  is the total bending strain,  is the total curvature,  V is vertical curvature, and  ℎ is horizontal curvature.
The total curvature of the centerline of a pipe is described at each point along the pipeline by the curvature vector.In order to calculate the pipeline curvature, the centerline of a pipe is considered as a 3D parametric curve described in a Cartesian system by a vector V(), which is a function of a distance () along the curve [20,21]: Assume that the vector  is tangent of V(), separating the vertical and horizontal curvature components as shown in Figure 2. The calculation of the pipeline bending strain can be given as where the pitch () and azimuth () of the pipeline centerline can be measured by the PIG.
Assume that the vector  is the curvature vector of a 3D curve at a given point, and  consists of the vertical curvature  V and the horizontal curvature  ℎ , which can be given as The above equation can be written separately for each component of the curvature vector in the Cartesian system: Based on ( 1)-( 4), the components of the defined curvature vector can be calculated as follows: The vertical curvature  V and the horizontal curvature  ℎ can be given as From ( 7), it can be seen that the pipeline bending strain can be calculated with the attitude data, which can be acquired with a PIG.

Modeling and Computation of Dent
In Section 2, a computation of the pipeline bending strain is discussed.The total of the features such as displacement and dent based on bending strain can be computed and identified.However, it is difficult to obtain the depth of dent by the bending strain measurement.Because of the lots of factors, it is hard to find a simple relationship between bending strain and size of dent.Neural network is a good solution for this practical project.It is based on complex connection of large number of neurons and deal with difficult language of the modeling information by self-learning, self-organized, and nonlinear dynamics.

BP Neural Network.
The BP neural network consists of an input layer, a hidden layer, and a linear output layer.Each layer is composed of several neurons [22][23][24].The most basic three-layer BP neural network structure is shown in Figure 3.It is assumed that each layer consisted of "" processing elements; the training set included "" samples mode for (  ,  ).For the "" training sample, the sum of total input is   for  element.If the output is   , it follows where   is the weight for neurons between  and . is the function as The error of neural network is as follows: where   is expect output of the  output for input of .If the learning rule used a method for gradient descent, the weights can be changed by error function.The modified function is as follows: where  is the times of learning,  is the learning factor, and  is the value of modified error.  is the modify error for output and    is the modified error for hidden layer.

Improving the Neural Network Based on Bayesian Theory.
The traditional neural network has difficulty in controlling its model complexity, leading to network overfitting, long time training, and network model low stability [25,26].However, the Bayesian neural network based on Bayesian reasoning can solve these problems effectively through correcting network training performance function.
In the actual complex system, the input quantity includes given input quantity and unknown disturbance quantity such as (noise signals), and normally the unknown disturbance quantity has an effect on the system output [27,28].Let  = [ 1 ,  2 , . . .,   ] as an observable given input; then the relationship between system output quantity  and input quantity  can be described by the following formula: where  represents the effect of input on the output and the random quantity submitting to some distribution.The training performance function of neural network adopts mean square error function.Assume error function is as follows: where  is the sample numbers,  is the neural network output numbers,   is the expectation output, and    is the network actual output.Generally the not unique  0 solution may lead the neural network training to fall into partial minimum value.To solve this problem, a constraint item can be introduced to make function () have interpolation ability, and then the solution for  0 is stable.The condition that () has interpolation ability is that () is smooth.While the square sum of network weight and threshold is small, its output is smoother.Therefore constraint item should represent smooth constraint, and the objective function is expressed as follows: is the neural network weight and threshold numbers,  is network weight and threshold,  net () is the square sum of weight and threshold,  net () is the square sum of network actual output and objective expectation value residual, and  and  are hyperparameter which decide the value size of the neural network objective performance function and control the distribution form of weight and threshold.Through using new objective performance function, the network weight and threshold are as little as possible, on condition that the network training error is as small as possible.According to Bayesian, posterior distribution probability of  and  meets the following formula: = {(), ()} is a sample data set which consists of  samples,  ℎ is neural network hidden layer number, (,  |  ℎ ) is hyperparameter prior probability, ( |  ℎ ) is normalization factor, and ( | , ,  ℎ ) is likelihood function.After partial derivatives to , , the most salient hyperparameter can be carried out: is the number that can reduce parameters numbers (0-W) in performance index function parameters in network.  is the weight and threshold when  ALL is minimum. is the subscript for .  is the weight and threshold when  ALL is minimum.After working out the most salient hyperparameter ,  determine whether  ALL is convergence again.Through iterative judgment, the best and most salient neural network model can be obtained.
Relative to traditional neural network, the Bayesian neural network is focused on the probability distribution of the whole parameter space, and the predicted results are based on the statistical average of parameters posterior distribution.A single model is corresponding to one point in the space; all models are corresponding to the whole parameter space.Therefore the Bayesian neural network guarantees network stronger generalization in theory.Figure 3.The horizontal axis represents the dent length along the pipeline and the vertical axis is the bending strain for dent, respectively.The bending strain can be represented for the severity for the dent.To the identity of the dent feature, the input can be related to the bending strain information for the dent.The output selected the actual depth of the dent from the site measurement.

Modeling and Computation for Dent by Bending
According to the relationship for the bending strain and dent as shown in Figure 3, pattern in a plot of bending strain against distance shows the characteristic of environmentally induced deformation for dent.The pattern is caused by a primary action in the center, with a reaction (bending strain in the opposite direction) on both sides.In the case of a dent the central deformation is an underbend with overbends at either end.The main influencing parameters are including the beginning bending strain  1 and ending bending strain  3 which is related to the reaction area of dent along the pipeline, respectively.The largest bending strain  2 is related to the deepest of the dent. 1 is the distance for reaction of the beginning bending strain for dent. 2 is the distance for primary action for dent. 3 is the distance for another reaction of the ending bending strain for dent.The process of modeling and computation for the dent based on Bayesian theory neural network is shown in Figure 4.   Figure 5) with the proposed method is used to inspect oil pipeline, which is about 150 kilometers.About 150 dents have been dug to measure and verify depth gauge in past five years.These actual data can be selected to be used for sample for the proposed algorithm.

Field Test and Data Analysis
The IMU pipeline ILI tool mainly consists of the following sensors to be used to calculate the bending strain and position of the pipeline: (1) Inertial measurement unit is the main device to gather the ILI data.Three gyroscopes and three accelerometers orthogonally mounted on the IMU to measure the attitude and positon for ILI tool.These gathered data can be used to calculate the pipeline bending strain with other sensors mounted on the ILI tool.
(2) Two odometers mounted on the ILI to measure the distance and instantaneous and average speed, which can be used to modify the inertial system errors.
(3) Two weld detector sensors are used to measure and record time of passing each girth weld for tool.They can use the alignment for every spool for repeat inspection.
As is known, most domestic oil pipelines are heating transportation and pass through mountains, hills, rivers, and other complex environmental areas [29]; the technical and safety requirements of electrical equipment are extremely strict.To safely inspect the actual pipeline, the IMU should meet not only the technical performance, but also the actual situation of the pipe and the external environment should be considered.Technical performances of inertial devices, which are used in the field test, are shown in Table 1.

Data Analysis.
According to Section 2, a typical bending strain for dent is shown in Figure 6, whose depth is 52.79 mm     for 6.5% of outer diameter measured with gauge in field.The bending strain for this dent is −0.4125% which is located in bottom of the pipeline.
For the method of Section 3, 120 data sets for bending strain of dent are selected for the input of the new neural network.Part of dents of training data are shown in Table 2.The input of neural network is consisted of  1 ,  2 ,  3 ,  1 ,  2 , and  3 introduced in Section 3.3.The output of neural network is the depth of the dent.
The measured data input into the BP neural network to calculate the result of the dent.Parts of sample data input into the network for training and the other sample data to verify the accuracy.The calculation is shown in Table 3 and Figure 7.The mean relative error for BP calculation and actual depth is 12.26%.Although the BP neural network can be used to calculate the depth from the bending strain, the accuracy degree is low to assess the dent.
To verify the accuracy of the proposed method, all of data input into the modified Bayesian neural network.The neural network can be trained by the sample data.Mean square error (MSE) is selected to assess the quality of the neural network.To adjust the parameter of neural network, the result of training is shown in Figure 8.The best validation performance of MSE for the method is 0.0040885 at the epoch 95.The calculation of modified neural network based on Bayesian is shown in Figure 9 and Table 4.It is clear to see the method can be used to calculate the depth of dent from bending strain.From Table 4, the mean relative error for calculation and actual depth is 2.44%.The accuracy of modified neural network is raised more than BP neural network.The calculation of modified Bayesian neural network can be used to calculate the depth of dent from dent.With this method, the pipeline company runs the IMU tool for once not only  to obtain the pipeline bending strain but also to calculate all of the depths of dent.The proposed method offers a useful method for pipeline integrity evaluation.

Conclusions
The in-line inspection tool, which loads the IMU, used to inspect the centerline of the pipeline.The attitude information can be used to compute the bending strain of the pipeline.However, there is no paper or report to research the relationship between the bending strain and dent.In this paper, based on the analysis of the calculation method of pipeline bending strain, we propose a method based on modified Bayesian neural network to calculate dent depths from bending strain.To test the proposed method experimentally, a PIG with the proposed method is used to inspect a 150 km pipeline.It can be obtained that (1) A new method is proposed to verify the relationship between pipeline bending strain and dent based on the calculation of bending strain.
(2) According to the characteristic of signal between dent and pipeline bending strain, a new model is presented in detail to be used for proposed calculation of algorithm.
(3) The calculation of modified Bayesian neural network is proposed to compute the depth dent with pipeline bending strain to compare with actual data.And traditional BP neural network is used to calculate the depth of dent.According to the result of calculation, the mean accuracy of calculation for modified Bayesian neural network is better than BP neural network for 9.82%.
(4) According to calculation, the proposed method is more accurate and suitable for the calculation of depth based on pipeline bending strain.The mean relative error for calculation of dent depth based the modified Bayesian neural network is 2.44%.
This paper provides a novel method for calculating dent depths from the pipeline bending strain.The dent can be evaluated by the bending strain not used to dig or use another tool to reinspect.The bending strain and calculation of dent depth is also useful to the evaluation of pipeline integrity.

Figure 1 :
Figure 1: Measurement system of in-line inspection of pipeline centerline.

Figure 3 :
Figure 3: A typical signal of dent feature from bending strain.

Figure 4 :
Figure 4: Dent modeling and computation based on Bayesian theory neural network.

4. 1 .
Equipment and Performance.To test the proposed method experimentally, an in-line inspection tool (shown in

Figure 6 :
Figure 6: Typical bending strain of a dent.

Figure 7 :
Figure 7: Calculation and error for BP neural network.

Figure 8 :
Figure 8: Training for modified neural network based on Bayesian.

Figure 9 :
Figure 9: Calculation and error for modified Bayesian neural network.

Table 1 :
Characteristics of sensors.

Table 2 :
Part of dents of training data.

Table 3 :
Calculation and error for BP neural network.

Table 4 :
Calculation and error for modified Bayesian neural network.