current conditions, the mean and variance of the residual error from a multi-stage model are extracted to calculate the probability density function (PDF) based on the assumption of a normal distribution, which is then used to determine the fusion weights for the establishment of a fusion model...
Kitagawa, G.: Monte Carlo filter and smoother for non-Gaussian nonlinear state space models. J. Comput. Gr. Stat. 5(1), 1–25 (1996) MathSciNet Google Scholar Klenke, A.: Probability Theory: A Comprehensive Course, 2nd edn. Springer, London (2014) Book MATH Google Scholar Kloeden,...
State Bayes' theorem for a partition (F1, F2) and an event E. Consider a discrete random variable Y with Y(omega) = {0, 1, ..., 8} and probability mass function: where a is some fixed number between 0 and 1 and c...
Considering the high accuracy, high computing speed, and excellent performance of deep learning algorithm, Chen et al. [10] applied a deep belief network (DBN) to predict the flank wear of a cutting tool in milling. To describe the time-variant transition probability of tool wear states and ...
One of the most exciting tools that have entered the material science toolbox in recent years is machine learning. This collection of statistical methods has already proved to be capable of considerably speeding up both fundamental and applied research.
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Then, the classical inference problem of a probability distribution via graphical models [16] also leads to a maximum entropy estimation. Density operators naturally encompass classical probability distributions on the finite-dimensional setup; therefore, when considering direct correlations between the sub...
This method is robust to data time lag and abnormal signals by dynamically updating the model based on Bayes’ theorem, allowing for continuous improvement as new data are collected. Unlike traditional methods, BMLR can handle sparse sensing points and short-term observation data, making it ...
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Rather than giving a single estimated output on the current system health, it gives a probability distribution of possible likely options [22]. In this way, the Bayesian method can present the current state of the system, but can also evaluate future trends before a given threshold. Stochastic...