基于Kriging代理模型的造斜率预测方法研究

造斜率受导向工具结构、类型、钻井参数、井眼轨迹、地层和钻头等因素的影响,构成了一个多变量影响的非线性耦合体系。造斜率预测呈现一定的模糊性、随机性和非线性特点,难以用显性的定量关系式来精确刻画造斜率与其影响因素之间的函数关系。从回归分析预测法的角度,提出一种采用Kriging代理模型构建预测功能函数,进行造斜率预测的新方法。该方法基于空间插值理论,以造斜率预测值为输出目标。首先选取造斜率主要影响因素作为输入参数,确定训练样本和测试样本;然后,计算Kriging模型中的最优超参数,并构建该预测模型。最后,以测试样本为基准,计算模型预测性能指标,完成对Kriging代理模型的造斜率预测性能评价。通过现场案例研究表明,与常见的多元回归模型和径向基函数模型(radial basis function,RBF)相比,基于Kriging代理模型的造斜率预测方法在均方根误差(root-mean-square error,RMSE)、最大绝对误差(maximum absolute error,MAE)和平均绝对误差(average absolute error,AAE)3个常见的定量指标上表现了更佳的预测性能。预测结果更稳健,计算量更小,对造斜率的预测精度较高,能克服几何法预测精度不高或力学法计算量大等缺点。在工程应用中能节约计算成本和提高预测效率,便于推广应用。

Research on Prediction Method of Build-up Rate of Deflecting tools Based on Kriging Surrogate Model

Build-up rate is affected by various factors, such as the deflecting tool structure and type, drilling parameters, well trajectory and geographic formation, drill bit, etc. It constitutes a multivariable nonlinear coupling system. As a result, prediction of the build-up rate has the characteristics of vagueness, randomness and non-linearity, and it is difficult to use explicit quantitative formula to accurately portray a function between build-up rate and its influence factors. From regression analysis point of view, a novel method is proposed, which uses the Kriging surrogate model to build the predictive performance function to predict the build-up rate. The method is based on the theory of spatial interpolation and derives the build-up rate prediction value as the output target. Firstly, the input parameters are assured by selecting the main influence factors on build-up rate, and then the train samples and test samples are determined. Secondly, the optimal super-parameters are calculated, and the Kriging surrogate model is constructed. Finally, based on the test samples, the build-up rates are predicted and the prediction errors are calculated to evaluate prediction performance of the Kriging surrogate model under the test samples. The effectiveness of the proposed methodology is validated through a field drilling example. In comparison with the commonly used multiple regression model and Radial Basis Function model (RBF), the Kriging surrogate model exhibits better performance in terms of the three performance indicators, i.e. root-mean-square error (RMSE), maximum absolute error (MAE)and average absolute error (AAE). The proposed Kriging surrogate model in this paper has better prediction performance, more robust prediction results, less calculation and more efficient. It can not only overcome the shortcomings of low prediction accuracy of Geometric method and much calculation of Mechanical method, but also reduce the computing cost for predicting buid-up rate and improve prediction efficiency in drilling engineering. Furthermore, the proposed prediction method is not influenced by the structure of a deflecting tool and hence it is easily to be applied in oilfields.