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Conversion of the correlated random variables into independent variables, especially into independent standard normal variables, is the common technology for estimating the statistical moments of response and evaluating reliability of random system, in which calculating the equivalent correlation coefficient is an important component. The purpose of this paper is to investigate an accurate, efficient and easy to implement estimation method for the equivalent correlation coefficient of various incomplete probability systems.

First, an approach based on the Mehler’s formula for evaluating the equivalent correlation coefficient is introduced, then, by combining with polynomial normal transformations, this approach is improved to be valid for various incomplete probability systems, which is named as the direct method. Next, with the convenient linear reference variables for eight frequently used random variables and the approximation of the Rosenblatt transformation introduced, a further improved implementation without iteration process is developed, which is named as the simplified method. Finally, several examples are investigated to verify the characteristics of the proposed methods.

The results of the examples in this paper show that both the proposed two methods are of high accuracy, by comparison, the proposed simplified method is more effective and convenient.

Based on the Mehler’s formula, two practical implementations for evaluating the equivalent correlation coefficient are proposed, which are accurate, efficient, easy to implement and valid for various incomplete probability systems.

The anomaly detection task for oil and gas pipelines based on acoustic signals faces issues such as background noise coverage, lack of effective features, and small sample sizes, resulting in low fault identification accuracy and slow efficiency. The purpose of this paper is to study an accurate and efficient method of pipeline anomaly detection.

First, to address the impact of background noise on the accuracy of anomaly signals, the adaptive multi-threshold center frequency variational mode decomposition method(AMTCF-VMD) method is used to eliminate strong noise in pipeline signals. Secondly, to address the strong data dependency and loss of local features in the Swin Transformer network, a Hybrid Pyramid ConvNet network with an Agent Attention mechanism is proposed. This compensates for the limitations of CNN’s receptive field and enhances the Swin Transformer’s global contextual feature representation capabilities. Thirdly, to address the sparsity and imbalance of anomaly samples, the SpecAugment and Scaper methods are integrated to enhance the model’s generalization ability.

In the pipeline anomaly audio and environmental datasets such as ESC-50, the AMTCF-VMD method shows more significant denoising effects compared to wavelet packet decomposition and EMD methods. Additionally, the model achieved 98.7% accuracy on the preprocessed anomaly audio dataset and 99.0% on the ESC-50 dataset.

This paper innovatively proposes and combines the AMTCF-VMD preprocessing method with the Agent-SwinPyramidNet model, addressing noise interference and low accuracy issues in pipeline anomaly detection, and providing strong support for oil and gas pipeline anomaly recognition tasks in high-noise environments.