Method for monitoring a nonlinear dynamic process and a computing system
View Patent ↗A method for monitoring a nonlinear dynamic process and a computing system are provided. The method includes training a model based on sample data, wherein the model comprises: a first layer, wherein the first layer is configured to linearize the sample data using one or more dimension lifting techniques; a second layer, wherein the second layer is configured to extract reduced-dimension dynamic latent variables (DLVs) from the linearized sample data using a reduced-dimension model; and a third layer, wherein the third layer is configured to parameterize the extracted reduced-dimension DLVs using a latent state space model; and inputting data from the nonlinear dynamic process into the trained model for monitoring the nonlinear dynamic process.
1 . A method for monitoring a nonlinear dynamic process, comprising:
training a model based on sample data, wherein the model comprises:
a first layer, wherein the first layer is configured to linearize the sample data using one or more dimension lifting techniques;
a second layer, wherein the second layer is configured to extract reduced-dimension dynamic latent variables (DLVs) from the linearized sample data using a reduced-dimension model; and
a third layer, wherein the third layer is configured to parameterize the extracted reduced-dimension DLVs using a latent state space model; and
inputting data from the nonlinear dynamic process into the trained model for monitoring the nonlinear dynamic process.
2 . The method of claim 1 , wherein linearizing the sample data comprises nonlinearly mapping the sample data into a high-dimensional feature space.
3 . The method of claim 1 , wherein the one or more dimension lifting techniques comprises one or more kernel methods.
4 . The method of claim 1 , wherein the reduced-dimension model comprises a weight matrix.
5 . The method of claim 1 , wherein the latent state space model comprises system matrices.
6 . The method of claim 5 , wherein the system matrices comprise a latent state transition matrix, an emission matrix and a Kalman gain matrix.
7 . The method of claim 1 , wherein:
the reduced-dimension model comprises a weight matrix;
the latent state space model comprises system matrices; and
the method further comprises updating the weight matrix and the system matrices using an alternating optimization algorithm.
8 . The method of claim 1 , wherein the first layer is further configured to compute reconstruction residuals, and wherein the second layer and the third layer are further configured to compute DLVs prediction residuals.
9 . The method of claim 1 , wherein the model further comprises a fault label matrix configured to identify a fault condition in the nonlinear dynamic process.
10 . A computing system, comprising:
at least one processor;
a non-transitory computer-readable storage medium coupled to the at least one processor and storing programming instructions for execution by the at least one processor, the programming instructions instruct the at least one processor to:
train a model based on sample data, wherein the model comprises:
a first layer, wherein the first layer is configured to linearize the sample data using one or more dimension lifting techniques;
a second layer, wherein the second layer is configured to extract reduced-dimension dynamic latent variables (DLVs) from the linearized sample data using a reduced-dimension model; and
a third layer, wherein the third layer is configured to parameterize the extracted reduced-dimension DLVs using a latent state space model; and
input data from the nonlinear dynamic process into the trained model for monitoring the nonlinear dynamic process.
11 . The computing system of claim 10 , wherein linearizing the sample data comprises nonlinearly mapping the sample data into a high-dimensional feature space.
12 . The computing system of claim 10 , wherein the one or more dimension lifting techniques comprises one or more kernel methods.
13 . The computing system of claim 10 , wherein the reduced-dimension model comprises a weight matrix.
14 . The computing system of claim 10 , wherein the latent state space model comprises system matrices.
15 . The computing system of claim 14 , wherein the system matrices comprise a latent state transition matrix, an emission matrix and a Kalman gain matrix.
16 . The computing system of claim 10 , wherein:
the reduced-dimension model comprises a weight matrix;
the latent state space model comprises system matrices; and
the programming instructions further instruct the at least one processor to update the weight matrix and the system matrices using an alternating optimization algorithm.
17 . The computing system of claim 10 , wherein the first layer is further configured to compute reconstruction residuals, and wherein the second layer and the third layer are further configured to compute DLVs prediction residuals.
18 . The computing system of claim 10 , wherein the model further comprises a fault label matrix configured to identify a fault condition in the nonlinear dynamic process.