Training a mathematical model for a device using a smart plug

A system for training a mathematical model for a first device, the system comprising:

• at least one computer comprising at least one processor and at least one memory, the at least one computer configured to:
• receive a smart-plug power monitoring signal, wherein the smart-plug power monitoring signal indicates an amount of power provided by a smart plug to one or more devices, the one or more devices comprising the first device;
• identify a plurality of turn-on times corresponding to the smart-plug power monitoring signal transitioning from zero power to non-zero power;
• identify a plurality of turn-off times corresponding to the smart-plug power monitoring signal transitioning from non-zero power to zero power;
• obtain a first-main power monitoring signal using measurements from a sensor that measures an electrical property of a first electrical main of a building;
• identify power events in the first-main power monitoring signal, wherein each power event corresponds to an event time;
• cluster the power events into a plurality of clusters;
• select a first cluster of the plurality of clusters using (i) the plurality of turn-on times and (ii) event times of power events of the first cluster;
• select a second cluster of the plurality of clusters using (i) the plurality of turn-off times and (ii) event times of power events of the second cluster;
• train a first transition model for the first device using one or more of the power events of the first cluster;
• train a second transition model for the first device using one or more of the power events of the second cluster;
• and
• identify state changes of devices using the first transition model and the second transition model.

One or more non-transitory, computer-readable media comprising computer executable instructions that, when executed, cause at least one processor to perform actions comprising:

• receiving a smart-plug power monitoring signal, wherein the smart-plug power monitoring signal indicates an amount of power provided by a smart plug to one or more devices, the one or more devices comprising a first device;
• identifying a plurality of turn-on times corresponding to the smart-plug power monitoring signal transitioning from zero power to non-zero power;
• identifying a plurality of turn-off times corresponding to the smart-plug power monitoring signal transitioning from non-zero power to zero power;
• obtaining a first-main power monitoring signal using measurements from a sensor that measures an electrical property of a first electrical main of a building;
• identifying power events in the first-main power monitoring signal, wherein each power event corresponds to an event time;
• clustering the power events into a plurality of clusters;
• selecting a first cluster of the plurality of clusters using (i) the plurality of turn-on times and (ii) event times of power events of the first cluster;
• selecting a second cluster of the plurality of clusters using (i) the plurality of turn-off times and (ii) event times of power events of the second cluster;
• training a first transition model for the first device using one or more of the power events of the first cluster;
• training a second transition model for the first device using one or more of the power events of the second cluster;
• and
• identifying state changes of devices using the first transition model and the second transition model.