Results have shown that some basic parameters influence the rerounding depth, stress concentration and strain in the dent. These parameters include dent geometry, pipe geometry, pipe material and pressure range.
Study of the pipe response to denting have shown that the pipe geometry influences both the spring back and rerounding of the dent. The ratio of the initial dent depth to the elastic spring back increases with increasing D/t. Similarly, the ratio of the measured dent depth to final dent depth (after pressurisation) increases with a corresponding increase in the D/t. The dent geometry also influenced the spring back and rerounding. The ratio of the initial dent to the measured dent is higher for longer dents compared to shorter dents. This is an indication that elastic recovery is higher in longer dents compared to shorter dents. However, the ratio of the measured depth to the final depth reduces as the dent depth increases. This clearly shows that deeper dents have less elastic recovery than shallow dents. From the study, it is seen that the ratio of the measured depth to the final depth is higher for longer dents compared to shorter dents. On the contrary to spring back, the ratio of the measured to final depths increases as the dent depth increases.
The study also indicated that both the ratio of the initial to the measured depth and the ratio of the measured depth to the final depth increases with increasing pipe grades. This confirms that pipes with lesser strength exhibit less elastic spring back and rerounding compared to pipes with higher material strength. These results were validated with experimental data and a good agreement was observed between them. Results from the study of the effect of aforementioned parameters show that pipes with higher material strengths have higher notch stresses compared to the lower pipe grades. However, the ratio of the stress range over the pressure range ∆σ/∆p appears higher in the lower pipe grades compared to the higher pipe grades. The result also
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show that the difference in SCF between pipe grades are smaller for pipes with smaller D/t. However, the difference in SCF between pipes grades increases as D/t increases further. It can also be seen from the result that the difference is more for 50%SMYS pressure range compared to the 72% SMYS range. It has also shown that Stress concentration increases with increasing pipe D/t ratio of equal dent depth and material grade. From the result, bar dents show higher stress concentration compared to dome dents of similar dent depth. It is also clear from the result that dent with higher dent depth exhibit higher stress concentration factor. Furthermore, it can be seen from the result that SCF is higher in the 50% SMYS pressure range compared to the 72% SMYS pressure range. The results were validated with both experimental data and analytical solutions. A good correlation was seen in both when compared to the FE results. This is an indication that the FE models were accurate and the data generated can be confidently used for the ANN application
Results from the strain study has shown that circumferential strains are higher in circumferential dents compared to longitudinal strains and reduce as the diameter to thickness ratio increases. As such, longitudinal strains are higher in longitudinal dent compared to circumferential strains and reduce as D/t increases. Results have also showed that the difference between the circumferential and longitudinal strain is higher in circumferential dent compared to that of the longitudinal dent. It has also shown that the total strain in a dent is higher in a longitudinal dent compared to a circumferential dent. As the dent depth increases, there is a corresponding increase in the strain for both dent models. Pipes with higher material grades exhibits higher strain and the difference in strain level gets smaller as the Diameter to thickness (D/t) increases. The results when compared to the ASME B31.8 equation shows similarity in patterns in regards to how the parameters affect the strain, however, the ASME equation under- predicted the strain. This could be attributed to that fact that the ASME equation does not consider plane strain state and also not considering radial components as pointed out by Noronha et al[21]. The FE results were further validated with the equation proposed by Noronha et al and a good correlation was seen between them
The data generated from the above studies were fed into an artificial neural network ANN. The network was used to predict the rerounding depth, SCF and the maximum strain in the dent. Two models each are created to predict for longitudinal and
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circumferential dents. Each networks have one hidden layer. Different number of processing elements are varied for each result to determine the one that gives the best performance. The Levenberg-Marquardt function is used as it the most common training function and has be proven to give good fits. Two transfer functions (logarithmic sigmoid and hyperbolic tangent) is also varied to determine the one that gives the best fit. Each network has a model architecture consisting of three (3) layers; the input, hidden and output layers. The input layer consist of four variable parameters which include D/t, L/D, d/D% and SMYS.
For the rerounding prediction ANN analysis, the network architecture that gave the best performance for the dome model is the network with 10 processing elements and a tansig activation function. The network gave the minimal error with a coefficient of variation (COV) of 4.1 %. The linear correlation between ANN predicted reround depth and the FEA reround depth showed a good correlation with an R-square value of 0.99. Similarly for the bar model, the network with the best performance is the network with 15 hidden processing elements and a tansig activation function. The network has a mean square error value of 5.01E-06 and a coefficient of variation of 3.2. The linear regression between the predicted values and actual gives a good fit with R-square value of 0.99.
The same analysis was run to predict the SCF. For the dome model, the logsig activation function gave better performance with the best network having 5 hidden processing elements. The linear regression gives a good fit with an R-square value of 0.99 and a coefficient of variation of 4.7. The Bar model has a network with 5 processing elements and a logsig transfer function. This network has a mean squared error value of 8.86E-5. The linear regression gives good fit with an R-square value of 0.99 and a coefficient of variation of 3.5 %.
From the strain prediction study, the best network for the dome model is network with 10 processing elements and a logsig activation function. The network has a mean squared error value of 7.44 E-6. The regression is shown to give a good fit with an R- square value of 0.99 and a coefficient of variation of 4.9%. Similarly for the bar model, the network with the overall best performance has 15 processing element and logsig activation function. The means squared error of this network is 5.64 x 10-6 .The linear
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correlation shows a good fit with an R-square value of 0.98 and coefficient of variation of 8.8%.
In general, all the ANN models have shown very good performance as they all show a COV of less than 10% and good R-squared value. These models will eliminate the need for running an extensive finite element study or setting up expensive experimental program to get the stress and strain data for a given dent. Once the variable parameters are known, these models are able to predict the result with minimal errors. By reason of its efficiency and possibly potential for further expansion, the technique will be attractive to pipeline operators to effectively determine the severity of dents in pipeline.