Prognostic Algorithms Design Based on Predictive Bayesian Cramér-Rao Lower Bounds

Unified Evaluation Framework for Stochastic Algorithms Applied to Remaining Useful Life Prognosis Problems

“…Among the huge variety of uncertainty propagation methods available in the literature [17,21,33], the proposed one is a sampling based method called Monte Carlo prediction [33]. In Monte Carlo prediction, samples from the input distributions are drawn randomly and simulated until the desired event is reached (EOL event), predicting like this the RUL of each sample.…”

“…For that, every author uses different evaluation metrics. The metrics that appear the most on this kind of studies quantify the estimation error, such as the Absolute Error (AE) [6][7][8], the Mean Absolute Error (MAE) [9][10][11], the Mean Squared Error (MSE) [12], the Mean Absolute Percentage Error (MAPE) [13][14][15], the Relative Predicting Error (RPE) [4], the Root Mean Squared Error (RMSE) [5,8,16], the Relative Accuracy (RA) [17,18], the Score [19], the Skill Score (SS) [20], the Bayesian Cramér-Rao Lower Bounds (BCRLB) [21] and their variations considering their mean value [5], maximum value [16], normalized value [22] or their variance [5,23]. In addition to this, metrics that represent the precision on estimating the RUL are also used, such as the probability density function width (PDF width) [24] or the probability on estimating the real RUL [25].…”

“…Besides all this, there are many key design concepts on the stochastic algorithms that change completely their performance and that are not always completely described or taken into account. As a general trend, authors don't specify the method used on the parameterization of the algorithm [5,21,23,26] even though the chosen parameters have a big influence on the final results [3]. In addition, authors rarely specify the method applied to quantify the uncertainty (the probability distribution) of RUL predictions [37] even though it is known that any prediction would be meaningless for effective decision-making unless uncertainty is carefully accounted for [33].…”