The Gray-Box Approach to Sensor Data Analysis

In an effort to address this problem, we present a new method called the gray-box method. It is called a “gray box” because a deterministic model of the system, i.e., a “white box,” is used to filter the data and generate a residual, while a stochastic model, i.e., a “black-box,” is used to describe the residual. Instead of setting a threshold on the residual, the residual is modeled by a three-tier stochastic model. The linear and nonlinear components of the residual are described by an autoregressive process and a time-delay feed-forward neural network, respectively. The last component, the noise, is characterized by its moments.