Machine Learning for Industrial Anomaly Detection using Bivariate Gaussian Probability Density Function: A Case Study

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 Bivariate Gaussian Probability Density Function (PDF) enables the simultaneous evaluation of two 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, specifically within server room environments, by transitioning from rigid, static threshold systems to a framework of probabilistic intelligence. By integrating multidimensional statistical baselines and correlation coefficients, the model can distinguish between benign stochastic fluctuations and genuine early-stage hardware malfunctions with high granularity. The study demonstrates that by understanding how sensors dance together through covariance, systems can identify contextual anomalies that individually appear normal but statistically violate the learned operational relationship.