NIALM as a factorial hidden Markov model

After considering various heuristic approaches towards NIALM, it is clear that a more principled probabilistic approach is required. The approach would need to recognise that premise-level power readings are sequentially drawn from a continuous time series, and are not independent of each other. In fact, intuition tells us that in general appliances are far more likely to stay in their current state, and that state changes are comparatively rare. NIALM can also be considered as an online-learning problem, in which disaggregation must occur after each individual premise-level power value has been received. These two assumptions map directly on to the modelling of such a problem as a factorial hidden Markov model.

In a factorial hidden Markov model, there are multiple independent chains of hidden variables, which in this case are the current operating state of each appliance. At each time slice, there is also an observed variable conditional on the states of all of the corresponding hidden variables, which in the case is the premise-level power value. Below is a diagram of a factorial hidden Markov model.

where:

• Z - hidden (latent) variable, subscript - time slice, superscript - variable number
• X - observed variable, subscript, time slice

NIALM solutions are interested in evaluating the state of appliances, and given a look-up table of appliance state power values, can therefore evaluate the power of each appliance at each time slice. We are therefore interested in modelling the probability of an appliance being in a certain state, given the appliance's state in the previous time slice and the observed variable for that time slice:

This is an approach I will be investigating over the following weeks, after reading up on the relevant theory on sequential data and expectation-maximisation.