Interleaved Factorial Non-Homogeneous Hidden Markov Models for Energy Disaggregation

To reduce energy demand in households it is useful to know which electrical appliances are in use at what times. Monitoring individual appliances is costly and intrusive, whereas data on overall household electricity use is more easily obtained. In this paper, we consider the energy disaggregation problem where a household's electricity consumption is disaggregated into the component appliances. The factorial hidden Markov model (FHMM) is a natural model to fit this data. We enhance this generic model by introducing two constraints on the state sequence of the FHMM. The first is to use a non-homogeneous Markov chain, modelling how appliance usage varies over the day, and the other is to enforce that at most one chain changes state at each time step. This yields a new model which we call the interleaved factorial non-homogeneous hidden Markov model (IFNHMM). We evaluated the ability of this model to perform disaggregation in an ultra-low frequency setting, over a data set of 251 English households. In this new setting, the IFNHMM outperforms the FHMM in terms of recovering the energy used by the component appliances, due to that stronger constraints have been imposed on the states of the hidden Markov chains. Interestingly, we find that the variability in model performance across households is significant, underscoring the importance of using larger scale data in the disaggregation problem.Comment: 5 pages, 1 figure, conference, The NIPS workshop on Machine Learning for Sustainability, Lake Tahoe, NV, USA, 201

Latent Bayesian melding for integrating individual and population models

In many statistical problems, a more coarse-grained model may be suitable for population-level behaviour, whereas a more detailed model is appropriate for accurate modelling of individual behaviour. This raises the question of how to integrate both types of models. Methods such as posterior regularization follow the idea of generalized moment matching, in that they allow matching expectations between two models, but sometimes both models are most conveniently expressed as latent variable models. We propose latent Bayesian melding, which is motivated by averaging the distributions over populations statistics of both the individual-level and the population-level models under a logarithmic opinion pool framework. ln a case study on electricity disaggregation, which is a type of single channel blind source separation problem, we show that latent Bayesian melding leads to significantly more accurate predictions than an approach based solely on generalized moment matching

Signal aggregate constraints in additive factorial HMMs, with application to energy disaggregation

Blind source separation problems are difficult because they are inherently unidentifiable, yet the entire goal is to identify meaningful sources. We introduce a way of incorporating domain knowledge into this problem, called signal aggregate constraints (SACs). SACs encourage the total signal for each of the unknown sources to be close to a specified value. This is based on the observation that the total signal often varies widely across the unknown sources, and we often have a good idea of what total values to expect. We incorporate SACs into an additive factorial hidden Markov model (AFHMM) to formulate the energy disaggregation problems where only one mixture signal is assumed to be observed. A convex quadratic program for approximate inference is employed for recovering those source signals. On a real-world energy disaggregation data set, we show that the use of SACs dramatically improves the original AFHMM, and significantly improves over a recent state-of-the art approach

Domestic heating behaviour and room temperatures: Empirical evidence from Scottish homes

In this paper, we describe patterns of residential heating based on data from 255 homes in and around Edinburgh, Scotland, UK, spanning August 2016 to June 2018. We describe: (i) the room temperatures achieved, (ii) the diurnal durations of heating use, and (iii) common diurnal patterns of heating behaviour. We investigate how these factors vary between weekdays and weekends, over the course of the year, by external temperature, and by room type. We compare these empirical findings with the simplifying assumptions about heating patterns found in the UK’s Standard Assessment Procedure (SAP), a widely-used building energy performance model. There are areas of concurrence and others of substantial difference with these model assumptions. Indoor achieved temperatures are substantially lower than SAP assumptions. The duration and timings of heating use vary substantially between homes and along lines of season and outdoor temperature, whereas the SAP model assumes no such variation. Little variation is found along the lines of weekday vs. weekend, whereas the SAP model assumes differences, or between living space and other rooms, consistent with the SAP. The results are relevant for those interested in how SAP assumptions regarding household heating behaviours and achieved indoor temperatures concur with empirical data

Sequence-to-point learning with neural networks for nonintrusive load monitoring

Energy disaggregation (a.k.a nonintrusive load monitoring, NILM), a single-channel blind source separation problem, aims to decompose the mains which records the whole house electricity consumption into appliance-wise readings. This problem is difficult because it is inherently unidentifiable. Recent approaches have shown that the identifiability problem could be reduced by introducing domain knowledge into the model. Deep neural networks have been shown to be a promising approach for these problems, but sliding windows are necessary to handle the long sequences which arise in signal processing problems, which raises issues about how to combine predictions from different sliding windows. In this paper, we propose sequence-to-point learning, where the input is a window of the mains and the output is a single point of the target appliance. We use convolutional neural networks to train the model. Interestingly, we systematically show that the convolutional neural networks can inherently learn the signatures of the target appliances, which are automatically added into the model to reduce the identifiability problem. We applied the proposed neural network approaches to real-world household energy data, and show that the methods achieve state-of-the-art performance, improving two standard error measures by 84% and 92%