Confidence interval estimation of mixed oil length with conditional diffusion model

TL;DR

The paper tackles the problem of underestimating mixed oil length in multi-product pipelines by deriving confidence intervals that account for statistical variability. It leverages a conditional diffusion model to learn the distribution $p(Y|X)$ and generate pseudo-samples, enabling CI construction from upper and lower quantiles with level $\alpha$. The authors demonstrate that the CI upper bound minimizes underestimation probability (e.g., $P(y_i^{\alpha-up} \le y_i) \approx (1-\alpha)/2$), with empirical results showing 6.8% and 4.9% underestimation at $\alpha=0.90$ and $0.95$ respectively, and a mean pseudo-sample estimator improving RMSE, $R^2$, and MAE by notable margins. The approach, validated on SCADA data from three pipelines, yields competitive coverage and shorter intervals than alternatives, supporting its practical use for determining cutting margins and improving pipeline operations.

Abstract

Accurately estimating the mixed oil length plays a big role in the economic benefit for oil pipeline network. While various proposed methods have tried to predict the mixed oil length, they often exhibit an extremely high probability (around 50\%) of underestimating it. This is attributed to their failure to consider the statistical variability inherent in the estimated length of mixed oil. To address such issues, we propose to use the conditional diffusion model to learn the distribution of the mixed oil length given pipeline features. Subsequently, we design a confidence interval estimation for the length of the mixed oil based on the pseudo-samples generated by the learned diffusion model. To our knowledge, we are the first to present an estimation scheme for confidence interval of the oil-mixing length that considers statistical variability, thereby reducing the possibility of underestimating it. When employing the upper bound of the interval as a reference for excluding the mixed oil, the probability of underestimation can be as minimal as 5\%, a substantial reduction compared to 50\%. Furthermore, utilizing the mean of the generated pseudo samples as the estimator for the mixed oil length enhances prediction accuracy by at least 10\% compared to commonly used methods.

Figures (11)

• Figure 1: The description of oil mixing phenomenon.
• Figure 2: Comparison of point estimation and confidence interval estimation.
• Figure 3: Comparison of the outputs of point estimator and diffusion model.
• Figure 4: Left panel: estimated density functions of $C_{AC}$ in the training and testing sets. Right panel: estimated density functions of $C_{AC}-C_{AP}$ in the training and testing sets.
• Figure 5: The flow chart of our proposed method.