[Paper Review] Interleaved Factorial Non-Homogeneous Hidden Markov Models for Energy Disaggregation

Mingjun Zhong, Nigel Goddard+1 more|arXiv (Cornell University)|Jun 30, 2014

Smart Grid Energy ManagementEngineering13 references18 citations

TL;DR

This paper proposes the Interleaved Factorial Non-Homogeneous Hidden Markov Model (IFNHMM) to improve energy disaggregation in ultra-low frequency household electricity data. By enforcing non-homogeneous state transitions to model diurnal usage patterns and a one-at-a-time state change constraint, the IFNHMM reduces identifiability issues and achieves the lowest normalized squared error (0.847 ± 0.289) across 100 households, outperforming baseline models.

ABSTRACT

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.

Motivation & Objective

• To address the challenge of energy disaggregation in ultra-low frequency household electricity data, where readings are taken every two minutes.
• To reduce the identifiability problem in blind source separation of aggregated energy signals by imposing structural constraints on hidden Markov chains.
• To model diurnal variations in appliance usage through non-homogeneous Markov chains.
• To improve disaggregation accuracy by enforcing that at most one appliance state changes at any time step.
• To evaluate model performance on a large-scale, diverse dataset of 251 UK households to assess generalization and variability across households.

Proposed method

• Proposes the Interleaved Factorial Non-Homogeneous Hidden Markov Model (IFNHMM), combining non-homogeneous HMMs with a one-at-a-time state change constraint.
• Uses a non-homogeneous transition probability matrix where transition probabilities vary by time of day, capturing diurnal usage patterns.
• Imposes a constraint such that only one hidden chain can change state at any time step, modeled via conditional transition probabilities dependent on a switching variable Zt.
• Employs a chainwise Viterbi algorithm to infer the most likely hidden states S* and switching variable Z* that maximize the posterior P(S,Z|Y).
• Estimates model parameters via maximum likelihood on supervised training data, using 20–30 days for training and 5–10 days for evaluation.
• Evaluates performance using normalized squared error (E = Σ(ŷit - xit)² / Σxit²) across 100 households from the UK Household Energy Survey (HES).

Experimental results

Research questions

• RQ1 Can a non-homogeneous HMM better capture diurnal appliance usage patterns in low-frequency electricity data?
• RQ2 Does enforcing a one-at-a-time state change constraint improve disaggregation accuracy and reduce identifiability issues?
• RQ3 How does model performance vary across diverse households, and does this variability exceed differences between models?
• RQ4 Can the IFNHMM outperform standard FHMM and FNHMM in ultra-low frequency energy disaggregation settings?
• RQ5 To what extent does the variability in household energy usage patterns limit the generalization of disaggregation models?

Key findings

• The IFNHMM achieved the lowest normalized squared error of 0.847 ± 0.289 across 100 households, outperforming the FHMM (1.024 ± 0.396), FNHMM (0.947 ± 0.368), and IFHMM (0.892 ± 0.334).
• The coefficient of variation in disaggregation error across households was 0.389 for the IFNHMM, indicating high inter-household variability that rivals the performance gap between models.
• The high standard deviation in error (0.289) underscores that household-specific usage patterns significantly affect model performance, highlighting a key challenge for future research.
• The model performs well on some households (e.g., household A in Figure 1) but poorly on others (e.g., household B), indicating sensitivity to individual household behavior.
• The one-at-a-time constraint and non-homogeneous transitions together reduce identifiability issues, improving disaggregation accuracy compared to less constrained models.
• The results suggest that future disaggregation research must prioritize large-scale, diverse datasets to address variability across households.