Low-rate non-intrusive load monitoring approaches via graph signal processing

The large-scale roll-out of smart metering worldwide brings many new application possibilities. One promising application is appliance-level energy feedback based on identifying individual loads from aggregate measurements. Driven by high application potentials, the research in this area has intensified. In particular, non-intrusive load monitoring (NILM), that is, estimating appliance load consumption from aggregate readings, using software means only, has attracted a lot of attention, since it does not require any additional hardware to be installed. This thesis first proposes two Graph Signal Processing (GSP)-based approaches for disaggregation of total energy consumption down to individual appliances used. The first approach uses the Graph Laplacian Regularisation (GLR) minimiser results as a starting point, adding further refinement via Simulated Annealing (SA). The second approach applies data segmentation and associates data segments with graph nodes. A Dynamic Time Warping (DTW) distance is applied for evaluating weights between graph nodes. GLR minimiser is again used for clustering. Finally, a generic optimisation based approach is proposed for improving the accuracy of existing NILM by minimising the difference between the measured aggregate load and the sum of estimated individual loads with the difference from original NILM approaches' results as regularisation. For all proposed methods, the competitive performance are demonstrated in terms of both accuracy and effciency compared to state-of-the-art approaches, using the public Personalised Retrofit Decision Support Tools For UK Homes Using Smart Home Technology (REFIT) dataset and Reference Energy Disaggregation Dataset (REDD) electrical load datasets.The large-scale roll-out of smart metering worldwide brings many new application possibilities. One promising application is appliance-level energy feedback based on identifying individual loads from aggregate measurements. Driven by high application potentials, the research in this area has intensified. In particular, non-intrusive load monitoring (NILM), that is, estimating appliance load consumption from aggregate readings, using software means only, has attracted a lot of attention, since it does not require any additional hardware to be installed. This thesis first proposes two Graph Signal Processing (GSP)-based approaches for disaggregation of total energy consumption down to individual appliances used. The first approach uses the Graph Laplacian Regularisation (GLR) minimiser results as a starting point, adding further refinement via Simulated Annealing (SA). The second approach applies data segmentation and associates data segments with graph nodes. A Dynamic Time Warping (DTW) distance is applied for evaluating weights between graph nodes. GLR minimiser is again used for clustering. Finally, a generic optimisation based approach is proposed for improving the accuracy of existing NILM by minimising the difference between the measured aggregate load and the sum of estimated individual loads with the difference from original NILM approaches' results as regularisation. For all proposed methods, the competitive performance are demonstrated in terms of both accuracy and effciency compared to state-of-the-art approaches, using the public Personalised Retrofit Decision Support Tools For UK Homes Using Smart Home Technology (REFIT) dataset and Reference Energy Disaggregation Dataset (REDD) electrical load datasets

Post-processing for event-based non-intrusive load monitoring

Most current non-intrusive load monitoring (NILM) algorithms disaggregate one appliance at a time, remove the appliance contribution towards the total load, and then move on to the next appliance. On one hand, this is effective since it avoids multi-class classification, and analytical models for each appli- ance can be developed independently of other appliances, and thus potentially transferred to unseen houses that have different sets of appliances. On the other hand, however, these methods can significantly under/over estimate the total consumption since they do not minimise the difference between the measured aggregate readings and the sum of estimated individual loads. By considering this difference, we propose a post-processing approach for improving the accuracy of event-based NILM. We pose an optimisation problem to refine the original disaggregation result and propose a heuristic to solve a (combinatorial) boolean quadratic problem through relaxing zero-one constraint sets to compact zero-one intervals. We propose a method to set the regularization term, based on the appliance working power. We demonstrate high performance of the proposed post-processing method compared with the simulated annealing method and original disaggregation results, for three houses in the REFIT dataset using two state-of-the-art event-based NILM methods

Non-intrusive load disaggregation using graph signal processing

With the large-scale roll-out of smart metering worldwide, there is a growing need to account for the individual contribution of appliances to the load demand. In this paper, we design a Graph signal processing (GSP)-based approach for non-intrusive appliance load monitoring (NILM), i.e., disaggregation of total energy consumption down to individual appliances used. Leveraging piecewise smoothness of the power load signal, two GSP-based NILM approaches are proposed. The first approach, based on total graph variation minimization, searches for a smooth graph signal under known label constraints. The second approach uses the total graph variation minimizer as a starting point for further refinement via simulated annealing. The proposed GSP-based NILM approach aims to address the large training overhead and associated complexity of conventional graph-based methods through a novel event-based graph approach. Simulation results using two datasets of real house measurements demonstrate the competitive performance of the GSP-based approaches with respect to traditionally used Hidden Markov Model-based and Decision Tree-based approaches

Optimal detection and error exponents for hidden semi-Markov models

We study detection of random signals corrupted by noise that over time switch their values (states) between a finite set of possible values, where the switchings occur at unknown points in time. We model such signals as hidden semi-Markov signals (HSMS), which generalize classical Markov chains by introducing explicit (possibly non-geometric) distribution for the time spent in each state. Assuming two possible signal states and Gaussian noise, we derive optimal likelihood ratio test and show that it has a computationally tractable form of a matrix product, with the number of matrices involved in the product being the number of process observations. The product matrices are independent and identically distributed, constructed by a simple measurement modulation of the sparse semi-Markov model transition matrix that we define in the paper. Using this result, we show that the Neyman-Pearson error exponent is equal to the top Lyapunov exponent for the corresponding random matrices. Using theory of large deviations, we derive a lower bound on the error exponent. Finally, we show that this bound is tight by means of numerical simulations

Improving event-based non-intrusive load monitoring using graph signal processing

Large-scale smart energy metering deployment worldwide and integration of smart meters within the smart grid will enable two-way communication between the consumer and energy network, thus ensuring improved response to demand. Energy disaggregation or Non-intrusive load monitoring (NILM), namely disaggregation of the total metered electricity consumption down to individual appliances using purely algorithmic tools, is gaining popularity as an added-value that makes the most of meter data. However, NILM remains a challenging problem since NILM is susceptible to sensor noise, unknown load noise, transient spikes and fluctuations. In this paper, we tackle this problem using novel graph signal processing (GSP) concepts, applied at both, physical signal level via graph-based filtering and data level, via effective semi-supervised GSP-based feature matching. The proposed GSP-based method is generic and can be used to improve results of various event-based NILM approaches. We demonstrate significant improvement in performance using three state-of-the-art NILM methods, both supervised and unsupervised, and real-world active power consumption readings from the REDD and REFIT datasets, sampled at 1 and 8 seconds, respectively

Graph-based clustering for identifying region of interest in eye tracker data analysis

Localization of a viewer's region of interest (ROI) on eye gaze signal trajectories acquired by eye trackers is a widely used approach in scene analysis, image compression, and quality of experience assessment. In this paper, we propose a novel clustering approach for ROI estimation from potentially noisy raw eye gaze data, based on signal processing on graphs. The clustering approach adapts graph signal processing (GSP)-based classification by first cleverly selecting a starting data sample, and then classifying the remaining samples. Furthermore, Graph Fourier Transform is used to adjust GSP parameters on-the-fly to maximise accuracy. Experimental results show competitive clustering accuracy of our proposed scheme compared to Density-based spatial clustering of applications with noise (DB-SCAN), Distance-Threshold Identification (I-DT), and Mean-Shift on publicly available Shape Dataset and the potential of estimating ROI accurately on true eye tracker data

Undirected graphs : is the shift-enabled condition trivial or necessary?

With the growing application of undirected graphs for signal/image processing on graphs and distributed machine learning, we demonstrate that the shift-enabled condition is as necessary for undirected graphs as it is for directed graphs. It has recently been shown that, contrary to the widespread belief that a shift-enabled condition (necessary for any shift-invariant filter to be representable by a graph shift matrix) can be ignored because any non-shift-enabled matrix can be converted to a shift-enabled matrix, such a conversion in general may not hold for a directed graph with non-symmetric shift matrix. This paper extends this prior work, focusing on undirected graphs where the shift matrix is generally symmetric. We show that while, in this case, the shift matrix can be converted to satisfy the original shift-enabled condition, the converted matrix is not associated with the original graph, that is, it does not capture anymore the structure of the graph signal. We show via examples, that a non-shift-enabled matrix cannot be converted to a shift-enabled one and still maintain the topological structure of the underlying graph, which is necessary to facilitate localized signal processing

A generic optimisation-based approach for improving non-intrusive load monitoring

The large-scale deployment of smart metering worldwide has ignited renewed interest in electrical load disaggregation, or non-intrusive load monitoring (NILM). Most NILM algorithms disaggregate one appliance at a time, remove the estimated appliance contribution from the total load, and then move on to disaggregate the next appliance. On one hand, this is efficient since multi-class classification is avoided and analytical models for each appliance can be developed independently of other appliances with the benefit of being transferred to unseen houses that have different sets of appliances. On the other hand, however, these methods can significantly under- or over- estimate the total consumption since they do not minimise the difference between the measured aggregate load and the sum of estimated individual loads. Motivated by minimising the latter difference without losing the benefits of existing NILM algorithms, we propose novel post-processing approaches for improving the accuracy of existing NILM. This is posed as an optimisation problem to refine the final NILM result using regularisation, based on the level of confidence in the original NILM output. First, we propose a heuristic method to solve this (combinatorial) boolean quadratic problem through relaxing zero-one constraint sets to compact zero-one intervals. Convex-based solutions, including norm-1, norm-2 and semi-definite programming-based relaxation, are proposed trading off accuracy and complexity. We demonstrate good performance of the proposed post-processing methods, applicable to any event-based NILM, compared with 4 state-of-the-art benchmarks, using public REFIT and REDD electrical load datasets