System and method for modeling conditional dependence for anomaly detection in machine condition monitoring

A computer-implemented method of predicting sensor output values of a machine sensor monitoring system, comprising the steps of:

• providing a set of input sensor data X and a set of output sensor data Y for a plurality of sensors the monitor the performance of a machine;
• providing a functional relationship y=f(x, u)=Ax+Bu that maps the input sensor data y to the output sensor data x, wherein x and y are N and M dimensional vectors of the input sensor data X and the output sensor data Y, respectively, u is a K-dimensional vector representing unknown hidden input values, and A and B are unknown matrix parameters of the functional relationship, wherein a conditional probability of y given x for the functional relationship f(x, u)=Ax+Bu is P(y|x)=N(y|Ax, BBT+σ2IM) wherein N is a Gaussian distribution of mean Ax and standard deviation BBT+σ2IM wherein IM is an M×M identity matrix;
• estimating A from A=(YXT)(XXT)−1;
• estimating B from the first K eigenvectors of (Y−AX) (Y−AX)T/L;
• and
• calculating σ2 from an average variance of the remaining L-K minor components of (Y−AX) (Y−AX)T/L.

A program storage device readable by a computer, tangibly embodying a program of instructions executable by the computer to perform the method steps for predicting sensor output values of a machine sensor monitoring system, the method comprising the steps of:

• providing a set of input sensor data X and a set of output sensor data Y for a plurality of sensors the monitor the performance of a machine;
• learning a functional relationship that maps the input sensor data to the output sensor data by maximizing a logarithm of a marginalized conditional probability function P(Y|K) wherein a dependence of the output sensor data Y with respect to unknown hidden machine inputs u has been marginalized;
• providing another set of input sensor data X′;
• and
• calculating expected values of the output sensor data Y′using the input sensor data X′ and the marginalized conditional probability function P(Y|X), wherein the calculated expectation values reflect the dependence of the output sensor data Y″ with respect to the unknown hidden machine inputs u.