摘要: This paper presents an approach to data-driven modeling of unknown system dynamics or parameters from real-time operation data of physical processes or systems based on the known physical knowledge about the system. Specifically, ... 展开 This paper presents an approach to data-driven modeling of unknown system dynamics or parameters from real-time operation data of physical processes or systems based on the known physical knowledge about the system. Specifically, this solution is a data-driven parameter learning process to iteratively update the predefined model equations based on physics-guided machine learning at runtime. The learning process starts with deriving the differential and algebraic equations that can be determined beforehand about the system dynamics. These equations can represent the partial dynamics and behavior of the system under consideration, and additional dynamics (including equations and parameters) will need to be learned from operational data. An iterative process, which is similar to training a neural network, will be designed to update the model equations and parameters from the training data. The training process primarily includes: 1) estimating the output from a defined model structure (with pre-designed equations and tunable parameters) based on the prior known physical knowledge, 2) defining and calculating a loss function or objective function based on the error (or difference) between the predicted output and actual measurement, 3) computing the gradients of the loss function with respect to the model parameters (i.e. the parameters in the physical equations), 4) updating the estimated model parameters according to the gradients, and 5) finalizing the learning process if the total error falls within a tolerance or the maximum epoch is reached. In addition, the learning process may also apply to quantify the uncertainty in the entire or partial system dynamics, while portions of the physical system dynamics are given or known. The probability density functions can be used to represent the uncertainty and variations in the system model (input-output relationships) or parameters, and the respective probability distribution curves can be learned from operation data as well. The learned stochastic models together with the learned physical models can then be used in control design for planning, operation and optimization, for instance, as one component in a model predictive controller for integrated dynamic systems. This paper provides technical details about the novel machine learning concept, and as an example, a case study about the application of data-driven physics-based modeling. The initial results from the case study can demonstrate the potential to learn the unknown dynamics, parameters, or uncertainty and predict the system behavior based on historical and real-time operational data. A plan for future work will also be identified. 收起