Dents are one of the common integrity threats of long-distance transmission pipelines. The current CSA Z662 standard assesses dents based on the dent depth. However, the severity of dent features is a function of many factors. Most recently, numerical modeling via finite element analysis (FEA) has been utilized to assess dent severity, however the approach is computationally expensive. Recently, the authors’ research group developed a robust but much simplified analytical model to evaluate the strains in dented pipes based on the geometry of the deformed pipe. When the strain distribution predicted using the analytical model is benchmarked against the strains by nonlinear FEA they showed a good agreement with certain error. The procedure, however, predicts more conservative results in terms of the maximum equivalent plastic strain (PEEQ). In order to estimate the accuracy in the recently developed model, a series of nonlinear FEA pipe indentation simulations were conducted using the finite element analysis tool, ABAQUS and compared with the analytical prediction.
This paper presents an application of a Bayesian machine learning method named Gaussian Process Regression (GPR) for the accuracy assessment of the developed analytical model for dent strain assessment, quantifying the error in comparison with the FEA in terms of the maximum PEEQ. The Gaussian Process (GP) model holds many advantages such as easy coding, prediction with probability interpretation, and self-adaptive acquisition of hyper-parameters.
By varying the dent depth and the indenter radius, this paper provides a model that quantifies the error in the developed analytical model. The proposed model can be utilized to rapidly determine the severity of a dent along with the accuracy of the prediction. This analysis method can also serve as a reference for other analytical expressions.