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Related Concept Videos

Prediction Intervals01:03

Prediction Intervals

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
The...
Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor 't,' or...
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
Uncertainty: Overview00:59

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...
End Point Prediction: Gran Plot01:07

End Point Prediction: Gran Plot

A Gran plot is used to predict the equivalence volume or endpoint of a potentiometric or acid-base titration without reaching the endpoint. Typically, titration data is collected as a function of the titrant's volume up to a point less than the equivalence volume and then transformed into a linear format. The straight line is extended to the x-axis, indicating the necessary titrant volume to achieve the equivalence point.
For potentiometric titration, the Gran plot is created by plotting the...

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Related Experiment Videos

Interval Prediction of Remaining Useful Life Based on Uncertainty Quantification with Bayesian Convolutional Neural

Zhendong Qu1,2, Jialong He1,2, Yan Liu1,2

  • 1Key Laboratory of CNC Equipment Reliability, Ministry of Education, Jilin University, Changchun 130022, China.

Sensors (Basel, Switzerland)
|May 13, 2026
PubMed
Summary

This study introduces a Bayesian convolutional neural network (CNN) for more reliable Remaining Useful Life (RUL) predictions. The novel dual-output CNN effectively quantifies uncertainties, improving RUL interval prediction accuracy.

Keywords:
Bayesian deep learningconvolutional neural networkinterval predictionremaining useful life predictionuncertainty quantification

Related Experiment Videos

Area of Science:

  • Machine Learning
  • Reliability Engineering
  • Artificial Intelligence

Background:

  • Traditional Remaining Useful Life (RUL) prediction methods struggle with data scarcity and noise, leading to unreliable point estimates.
  • Existing approaches often fail to adequately capture the inherent uncertainties in RUL predictions.
  • The need for robust RUL estimation methods that account for various uncertainty sources is critical in engineering practice.

Purpose of the Study:

  • To develop an advanced RUL prediction method that addresses the limitations of current techniques, particularly concerning uncertainty quantification.
  • To propose a Bayesian convolutional neural network (CNN) model capable of providing reliable RUL interval predictions.
  • To enhance the accuracy and trustworthiness of RUL estimates by explicitly modeling both aleatoric and epistemic uncertainties.

Main Methods:

  • A Bayesian convolutional neural network (CNN) with dual-output units was designed for RUL interval predictions.
  • The negative log-likelihood was utilized as the loss function to guide the network's training.
  • Bayesian principles and the Bayes-by-backprop method were applied to reformulate the CNN, enabling the quantification of aleatoric and epistemic uncertainties.

Main Results:

  • The proposed Bayesian CNN effectively quantifies aleatoric uncertainty through its dual-output structure.
  • Epistemic uncertainty, arising from model inaccuracies and limited data, was successfully quantified by treating model parameters as random variables.
  • Experimental results on the IEEE PHM Challenge 2012 dataset showed superior prediction accuracy compared to existing state-of-the-art uncertainty-aware methods.

Conclusions:

  • The developed Bayesian CNN offers a more reliable approach to RUL prediction by effectively handling data uncertainties.
  • The method's ability to quantify both aleatoric and epistemic uncertainties enhances the practical applicability of RUL predictions in engineering.
  • This work advances the field of predictive maintenance by providing a robust framework for uncertainty-aware RUL estimation.