Effective prognostics and health management of modern engines relies on accurate turbine gas temperature predictions and robust uncertainty quantification to ensure reliability and safety. This paper investigates five major approaches for constructing prediction intervals -- namely the Delta method, Bayesian Monte Carlo Dropout, Bootstrap method, Lower-Upper Bound Estimation, and Mean-Variance Estimation -- as a means of capturing the uncertainty in neural network predictions of turbine gas temperature. Each approach is implemented within a unified experimental framework that employs cross-validation for hyperparameter selection, repeated train-test splits for performance robustness, and multiple metrics to evaluate both the accuracy and tightness of the intervals. In particular, Coverage Probability, Normalized Mean Prediction Interval Width, and the Coverage Width-based Criterion are measured to comprehensively assess each method's reliability and sharpness. Experiments conducted on a representative turbine gas temperature dataset reveal distinct trade-offs among the five methods in terms of interval coverage, width, and stability. These findings provide a practical guide for selecting and tuning prediction interval methods in engine health management and prognostics, ensuring both interpretability and precision in real-world applications.

翻译：现代发动机的有效预测与健康管理依赖于准确的涡轮气体温度预测和稳健的不确定性量化，以确保可靠性和安全性。本文研究了五种构建预测区间的主要方法——即Delta方法、贝叶斯蒙特卡洛丢弃法、Bootstrap方法、下上界估计法和均值方差估计法——作为捕获神经网络预测涡轮气体温度中不确定性的一种手段。每种方法都在统一的实验框架中实现，该框架采用交叉验证进行超参数选择、重复训练-测试分割以确保性能稳健性，并使用多个指标来评估区间的准确性和紧凑性。具体地，衡量了覆盖率概率、归一化平均预测区间宽度和基于覆盖率宽度的准则，以全面评估每种方法的可靠性和锐度。在代表性涡轮气体温度数据集上进行的实验揭示了五种方法在区间覆盖率、宽度和稳定性方面的不同权衡。这些发现为发动机健康管理和预测中预测区间方法的选择和调优提供了实用指南，确保了实际应用中的可解释性和精确性。