Multivariate Gaussian Probability Density Function in Machine Learning for Industrial Anomaly Detection

In the field of Machine Learning (ML), transitioning from univariate monitoring to a multivariate framework allows for a sophisticated analysis of complex industrial systems. While a univariate model analyzes a single feature, such as temperature, in isolation, the Multivariate Gaussian Probability Density Function (PDF) enables the simultaneous evaluation of multiple related sensors, such as temperature and humidity, to establish a dynamic mathematical baseline for operational normality. This research presents a paradigm shift in industrial monitoring by transitioning from rigid, static threshold systems to a framework of probabilistic intelligence. By integrating multidimensional statistical baselines, the model can distinguish between benign stochastic fluctuations and genuine early-stage hardware malfunctions with high granularity.