Building management system with system identification using multi-step ahead error prediction
A building management system includes a controller configured to control building equipment by providing a control input to the building equipment for each of the plurality of time steps and generate a set of training data for a system model for the building. The training data includes input training data and output training data for each of the plurality of time steps. The controller is further configured to perform a system identification process to identify parameters of the system model. The system identification process includes predicting, for each time step, a predicted value for one or more of the output variables for each of a plurality of subsequent time steps, generating a prediction error function by comparing the output training data to the predicted values, and optimizing the prediction error function to determine values for the parameters of the system model that minimize the prediction error function.
1. A building management system comprising:
building equipment operable to heat or cool a building;
one or more sensors configured to measure a variable state of the building at a plurality of time steps; and
a controller configured to:
control the building equipment by providing a control input to the building equipment for the plurality of time steps; and
generate a set of training data for a system model for the building, the training data comprising system input data and system output data for the plurality of time steps, the system input data for a given time step comprising values at the given time step for one or more input variables of the system model including the control input provided to the building equipment, and the system output data for the given time step comprising values at the given time step for one or more output variables of the system model including a variable measured by the one or more sensors; and
perform a system identification process to identify one or more parameters of the system model, the system identification process comprising:
generating a multi-step ahead prediction error function by comparing the system output data for multiple time steps subsequent to the given time step to predicted values of the one or more output variables for the multiple time steps subsequent to the given time step, wherein the predicted values are generated using the system model based on the system output data for the given time step and without requiring the system output data for the multiple time steps subsequent to the given time step; and
optimizing the prediction error function to determine values for the one or more parameters of the system model; and
generate additional control inputs for the building equipment by performing a model predictive control process that uses the system model with the one or more parameters identified by the system identification process; and
cause the building equipment to operate in accordance with the additional control inputs.
2. The building management system of claim 1 , wherein comparing the system output data for the multiple time steps subsequent to the given time step to the predicted values of the one or more output variables for the multiple time steps subsequent to the given time step comprises:
calculating differences between the predicted values of the one or more output variables for the multiple time steps and the system output data for the multiple time steps;
weighting the differences based on a weighting function to generate weighted differences; and
summing the weighted differences.
3. The building management system of claim 2 , wherein calculating the differences comprises:
subtracting the predicted values of the one or more output data variables from the system output data to generate difference vectors;
taking 2-norms of the difference vectors; and
squaring the 2-norms of the difference vectors to generate the differences.
4. The building management system of claim 1 , wherein optimizing the prediction error function comprises minimizing the prediction error function over a set of allowable parameter values for the one or more parameters.
5. The building management system of claim 1 , wherein the controller is further configured to refine the set of training data by:
determining whether an operating capacity of the building equipment is in a non-transient region for a threshold amount of a time period upon determining that an error exists for the time period;
in response to a determination that the operating capacity is in the non-transient region for at least the threshold amount of the time period, indicating the time period as a saturation period; and
removing data for the saturation period from the set of training data.
6. The building management system of claim 1 , wherein:
the system identification process comprises a first stage and a second stage;
the first stage comprises determining at least one of thermal parameters or HVAC parameters of the system model; and
the second stage comprises augmenting the system model with an integrating disturbance and determining one or more Kalman gain parameters.
7. The building management system of claim 1 , wherein the control input is varied with an excitation signal to generate the set of training data.
8. The system of claim 1 , wherein generating the multi-step ahead prediction error function comprises a plurality of iterations of shifting the given time step forward in time and repeating comparing the system output data for the multiple time steps subsequent to the given time step to the predicted values of the one or more output variables for the multiple time steps subsequent to the given time step.
9. A method comprising:
operating building equipment to heat or cool a building;
measuring, by one or more sensors, a variable state of the building at a plurality of time steps;
controlling the building equipment by providing a control input to the building equipment for the plurality of time steps; and
generating a set of training data for a system model for the building, the training data comprising system input data and system output data for the plurality of time steps, the input data for a given time step comprising values at the given time step for one or more input variables of the system model including the control input provided to the building equipment, and the system output data comprising values for one or more output variables of the system model including a variable measured by the one or more sensors; and
performing a system identification process to identify one or more parameters of the system model, the system identification process comprising:
generating a multi-step ahead prediction error function by comparing the system output data for multiple time steps subsequent to the given time step to predicted values of the one or more output variables for the multiple time steps subsequent to the given time step, wherein the predicted values are generated using the system model based on the system output data for the given time step and without requiring the system output data for the multiple time steps subsequent to the given time step; and
optimizing the prediction error function to determine values for the one or more parameters of the system model; and
generating additional control inputs for the building equipment by performing a model predictive control process that uses the system model with the one or more parameters identified by the system identification process; and
controlling the building equipment in accordance with the additional control inputs.
10. The method of claim 9 , wherein comparing the system output data for the multiple time steps subsequent to the given time step to the predicted values of the one or more output variables for the multiple time steps subsequent to the given time step comprises:
calculating differences between the predicted values of the one or more output variables for the multiple time steps and the system output data for the multiple time steps;
weighting the differences based on a weighting function to generate weighted differences; and
summing the weighted differences.
11. The method of claim 10 , wherein calculating the differences comprises:
subtracting the predicted values of the one or more output variables from the system output data to generate difference vectors;
taking 2-norms of the difference vectors; and
squaring the 2-norms of the difference vectors to generate the differences.
12. The method of claim 9 , wherein optimizing the prediction error function comprises minimizing the prediction error function over a set of allowable parameter values for the one or more parameters.
13. The method of claim 9 , further comprising refining the set of training data by:
determining whether an operating capacity of the building equipment is in a non-transient region for a threshold amount of a time period upon determining that an error exists for the time period;
in response to a determination that the operating capacity is in the non-transient region for at least the threshold amount of the time period, indicating the time period as a saturation period; and
removing data for the saturation period from the set of training data.
14. The method of claim 9 , wherein the control input is varied with an excitation signal to generate the set of training data.
15. The method of claim 9 , wherein:
the system identification process comprises a first stage and a second stage;
the first stage comprises determining at least one of thermal parameters or HVAC parameters; and
the second stage comprises augmenting the system model with an integrating disturbance and determining one or more Kalman gain parameters.
16. The method of claim 9 , wherein generating the multi-step ahead prediction error function further comprises a plurality of iterations of shifting the given time step forward in time and repeating comparing the system output data for multiple time steps subsequent to the given time step to the predicted values of the one or more output variables for the multiple time steps subsequent to the given time step.