低秩矩阵恢复模型改进及其在石油测井中的应用

发布时间：2018-04-15 09:06

本文选题：石油测井 + 数据去噪　；参考：《科学技术与工程》2017年02期

【摘要】：传统的低秩矩阵恢复模型在去噪过程中通过将观测矩阵分解为低秩部分和稀疏部分达到噪声去除的目的,但该模型要求噪声矩阵必须是稀疏的。然而石油测井所获得的数据中噪声来源复杂,并不能完全保证噪声分布满足稀疏性的要求,使该模型在去噪时表现出一定的局限性,去噪效果不稳定,进而导致后续的数据处理准确率降低。为此,提出将加权范数的思想应用于传统的低秩矩阵恢复模型中,并在惩罚项中将F范数与待恢复矩阵的核范数相结合,构造改进的低秩矩阵恢复模型,使其能够在保证解的稳定性的同时,可以更好地挖掘观测矩阵的低秩性以及增强稀疏矩阵的稀疏性。通过非精确的拉格朗日乘子法分别对改进前后的模型进行求解,并对两种模型去噪后的测井数据分别采用支持向量机(SVM)和相关向量机(RVM)进行油气层识别,结果表明经改进的低秩矩阵恢复模型去噪后的测井数据在保证了油气层识别效率的同时,识别准确率上有了明显提升。
[Abstract]:In the process of de-noising, the traditional low-rank matrix restoration model achieves the purpose of noise removal by decomposing the observation matrix into low-rank part and sparse part, but the model requires that the noise matrix must be sparse.However, the noise sources in the data obtained by petroleum logging are complex, which can not fully guarantee that the noise distribution can meet the requirements of sparsity, which makes the model show certain limitations in denoising, and the denoising effect is unstable.Then the accuracy of subsequent data processing is reduced.Therefore, the idea of weighted norm is applied to the traditional low rank matrix restoration model, and the improved low rank matrix recovery model is constructed by combining F norm with the kernel norm of the recovery matrix in the penalty term.It can not only guarantee the stability of the solution, but also better mine the low rank of the observation matrix and enhance the sparsity of the sparse matrix.The improved model is solved by the imprecise Lagrangian multiplier method, and the log data after denoising of the two models are identified by support vector machine (SVM) and correlation vector machine (RVM), respectively.The results show that the improved low rank matrix restoration model can ensure the efficiency of oil and gas reservoir identification and improve the recognition accuracy.
【作者单位】：河北工业大学电子信息工程学院和河北省大数据计算重点实验室;
【基金】：河北省自然科学基金(E2016202341)
【分类号】：TE319;TP311.13

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