A Survey on Non-Intrusive Load Monitoring Methodies and Techniques for Energy Disaggregation Problem

This is the first step for any NILM algorithm and it involves acquiring aggregated load measurement at an adequate rate so that distinctive load patterns can be identified. Several power meters such as Yomo [11] and c-meter [12] have been designed to measure the aggregated load of the building. A cost efficient approach for acquiring aggregate power data is to use smart meters which are currently being deployed as the requirement of smart-grid.

The aggregate power signal from these meters can be recorded at different sampling rate. The sampling frequency is determined by the measurements and electrical characteristics used by NILM algorithm [9]. The sampling frequency can either be high-frequency or low-frequency.

High-frequency is when sampling rate is in a range of $10\text{\,}\mathrm{MHz}100\text{\,}\mathrm{MHz}$ for the quantity whose electrical characteristics is to be determined. Power meters for this range are often custom-built and expensive due to sophisticated hardware [9]. Smart meters belong in the low sampling rate of the power signal which is less than $1\text{\,}\mathrm{Hz}$.

The NILM algorithm needs to detects the appliance operations status (e.g ON and OFF) from the power measurements.  The changes in power levels (like ON/OFF) is done by the detection module.  It is a complex process because of different types of appliance in buildings and the different status to be detected like simple ON/OFF, finite state, constantly ON, and continuously variable status as identified in [8]. Based on different event-detection strategies, the current NILM approaches can be classified as event-based or state-based.

Effective NILM algorithm requires unique features or signatures that characterize appliance behaviour. All appliances type have a unique energy consumption pattern often termed as “appliance signatures”. This unique energy consumption pattern is often used to uniquely identify and recognize appliance operations from the aggregated load measurements [9]. According to [8], appliances features are measured parameter of total load that give information about nature or operating state of an individual appliance in the load. It is unique consumption pattern intrinsic to each individual electrical appliance [24]. There are two main classes of appliance signatures used by NILM research for appliances identification namely transient features and steady-state features.

In this stage the extracted appliances signature are analysed in order to classify an appliance specific states and estimate its corresponding power consumption. The learning algorithms are used to learn the model parameters while the inference algorithms are employed to infer appliance states from observed aggregate power data and estimate their corresponding power consumption. The algorithm for learning in NILM can be supervised or unsupervised.

Supervised NILM techniques require a training phase in which both the aggregate data and the individual appliance consumption are used. In that case, sub-metered appliances data or labeled observations must be collected from the target building. The process of collecting these data is expensive, time-consuming and limit the scalability of NILM systems [31]. Several existing works have focused on supervised learning techniques such as Support Vector Machine(SVM)[32, 33], Nearest Neighbour(k-NN) [16] and some forms of HMM [34].

Unlike supervised NILM, unsupervised NILM techniques do not require pre-training and thus suitable for real time NILM application. Unsupervised NILM approaches do not require individual appliance data, the models parameters are captured only using the aggregated load, without the user intervention [35]. Current NILM research has focused on building unsupervised learning models which are less costly and more reliable [35, 9].

Unsupervised NILM approaches can further be grouped into three subgroups as suggested by [15]; First are the unsupervised approaches that require unlabelled training data to build appliance model or populate appliances database. They are usually based on HMM and the appliance models are either generated manually [21] or automatically [20] during the training phase. Most of these approaches can not be generalized into unseen buildings.

The Second groups includes unsupervised approaches that use labelled data from known house to build appliances models which are then used for disaggregation in unknown (unseen) building. These approaches require sub-metered appliances data to be collected from the training or known house. These data are used to build generic appliance models which is then used in unseen buildings. Most deep learning based NILM techniques such as in [36] fall in this category.

Lastly are the unsupervised approaches that do not require training before energy disaggregation takes place. These approaches can perform energy disaggregation without the need of sub-metered data or the prior knowledge [15, 37].

HMM is a Markov model whose states are not directly observed instead each state is characterised by a probability distribution function modelling the observation corresponding to that state [18, 41]. There are two variables in HMM: observed variables and hidden variables where the sequences of hidden variables form a Markov process. In the context of NILM, the hidden variables are used to model appliances states (ON,OFF, standby etc) of individual appliances and the observed variables are used to model the electric usage. HMMs has been widely used in most of the recently proposed NILM approach because it represents well the individual appliance internal states which are not directly observed in the targeted energy consumption.

A typical HMM is characterised by the following: The finite set of hidden states $S$ (e.g ON, stand-by, OFF, etc.) of an appliance, $S=\{S_{1},S_{2}....,S_{N}\}$. The finite set of observable symbol $Y$ per states (power consumption) observed in each state, $Y=\{y_{1},y_{2}....,y_{T}\}$. The observable symbol $Y$ can be discrete or a continuous set. The transition matrix A $=\{a_{ij},1\leq i,j\geq N\}$ represents the probability of moving from state $S_{i}$ to $S_{j}$ such that: $a_{ij}=P(q_{t+1}=S_{j}\mid q_{t}=S_{i})$, with $a_{ij}\leq 0$ and where $q_{t}$ denotes the state occupied by the system at time $t$. The emission matrix B$=P(y_{t}\mid S_{j})$ representing the probability of emission of symbol $y_{t}$ $\epsilon$ $Y$ when system state is $S_{j}$. The initial state probability distribution is $\bm{\pi}=\{\pi_{i}\}$ indicating the probability of each state of the hidden variable at $t=1$ such that, $\pi_{i}=P(q_{1}=s_{i}),1\leq i\geq N$. The set of all HMM model parameters is represented by $\bm{\lambda=\{\pi,A,B\}}$.

When applying HMM to a real world problem, two important problem must be solved. First how to learn the model parameter $\bm{\lambda}$ given the sequences of observable variable $\bm{Y}$. Second, given the model parameter $\bm{\lambda}$ and the sequences of observable variable $\bm{Y}$ how to infer the optimal sequences of hidden state $\bm{S}$. These problems are referred to as learning and inference problems. Various algorithms such as Baum-Welch algorithm and the Viterbi algorithm have been proposed to solve these problems.

The factorial HMM (FHMM) is an extension of HMM with multiple independent hidden state sequences and each observation is dependent upon multiple hidden variables [42]. In FHMM, if we consider $\bm{Y}=\{y_{1},y_{2},.....y_{T}\}$ to be the observable sequences then $\bm{S=\{S^{(1)},S^{(1)},.....S^{(M)}\}}$ represents the set of hidden state sequences where $\bm{S^{(i)}}=\{S^{(i)}_{1},S^{(i)}_{2},.....S^{(i)}_{T}\}$ is the hidden state sequence of the chain $i$ as shown in Figure 2.

FHMM are preferred to HMMs for modelling time series generated by the interaction of several independent process. However, the computational complexity of both learning and inference is greater for FHMMs compared to HMMs. In addition, the inference techniques for FHMM based approach is highly susceptible to local optima [9].

Several HMMs based NILM algorithms for energy disaggregation at low sampling rate has been proposed in the literature. In [18] unsupervised technique for energy disaggregation using a combination of four FHMM variants is proposed. The authors use low-frequency real power feature and assume a binary state of appliances (ON and OFF state only). To learn model parameters, Kim’s approach uses Expectation Maximasation (EM) algorithm and employ Maximum Likelihood Estimation(MLE) algorithm to infer load states. The performance of Kim’s technique is limited to few number of appliances, require appliances to be manually labelled after disaggregation and suffer from high computational complexity which makes it unsuitable for real-time applications [43].

The work presented in [19] propose a new inference algorithm for unsupervised energy disaggregation called Additive Factorial Approximate MAP (AFMAP) that is computationally efficient and does not suffer from local optima. The AFMAP algorithm is used to perform approximate inference over the additive FHMM. However, the model requires appliances to be manually labelled after off-line disaggregation and have a low performance for electronics and kitchen appliances.

Parson et al. [20], introduce an approach that use difference HMM from [19] as Bayesian network for disaggregation of active power with $60\text{\,}\mathrm{s}$ sampling rate. To perform inference, the authors use an extension of viterbi algorithm and propose an EM training process to build a generic appliance model for learning the model parameters. This generic model is then tuned to specific appliance instances using only aggregate data from home in which NILM is being applied. The active tuning process requires a training window of data where no other appliance changes state. For the cyclic types of appliance such as fridges, this is easy since it is often the only appliance running at night, but it is generally difficult for other appliances [44].

A fully unsupervised NILM framework based on non-parametric FHMM using low-frequency real power feature is presented in [37]. They use the combination of slice sampling and Gibbs sampling to do inference that simultaneously detect number of appliances and disaggregate the power signal from the composite signal. However, for larger disaggregation problems this inference algorithm becomes a limitation as it may stuck in local optima [45]. Besides it difficult to see this algorithm runs in real-time owing to complexity problem of FHMM.

Makonin et al. [21] present another NILM algorithm for low-frequency sampling rate that uses a super-state HMM in which a combination of modeled appliances states is represented as one super state. The authors propose a new variant of viterbi algorithm called sparse Viterbi algorithm. This algorithm perform computationally efficient exact inference instead of relying on approximate inference method like in FHMM based approach. Makonin’s approach preserves dependencies between appliances, can disaggregate appliances with complex multi-state power signatures and can run in real-time on an inexpensive embedded processor. Although the reported approach can disaggregate large number of super-state, there is still a limitation in time and space since number of super-states grow exponentially with the number of appliances.

Despite the fact that HMM-based NILM approaches have been widely used in energy disaggregation they require an expert knowledge to set a-priori values for each appliance state. Their performance are thus limited by how well the generated models approximate appliance true usage [15]. Moreover, HMM-based approaches have better performance for controlled multi-state appliances like refrigerator, but their performance degrades for uncontrolled multi-state and variable appliances [22].

Graph Signal Processing (GSP) or signal processing on graph is an emerging field that extends classical signal processing theory to data indexed by general graphs [46]. GSP represents a dataset using a graph signal defined by a set of nodes and a weighted adjacency matrix [30]. Each node in the graph corresponds to an element in the dataset while the adjacency matrix define all directed edges in the graph and their weights, where assigned weights reflects degree of similarity or correlation between the nodes [38]. GSP is the powerful, scalable and flexible signal processing approach that is suitable for machine learning and data mining problems. In particular, GSP is suitable for data classification problems in which training periods are short and inefficient to build appropriate class models [47].

Given a set of aggregate power measurement $X$ we define a graph $G=\{\mathcal{V},A\}$ where $\mathcal{V}$ is the set of nodes corresponding to the acquired measurements and $A$ is the weighted adjacency matrix of a graph which define the edge of a graph. Each element $x_{i}\in X$ corresponds to a node $\mathit{v_{i}}\in\mathcal{V}$ and each weight $A_{ij}$ of the edge between nodes $\mathit{v_{i}}$ and $\mathit{v_{j}}$ reflects the degree of relation between $x_{i}$ and $x_{j}$. The weight of a node $A_{ij}$ is usually defined using gaussian kernel weighting function, the most used kernels in machine learning for expressing similarities between dataset defined by equation 2.

$$A_{ij}=\exp\Big{[}-\frac{(x_{i}-x_{j})^{2}}{\rho^{2}}\Big{]}$$

(2)

where $\rho$ is a scaling factor [17]. A graph signal is then defined as a map from the map on the graph nodes $\mathcal{V}$ to the set of complex number $\mathbf{s}$ where each element $s_{i}\in\mathbf{s}$ is indexed by nodes $v_{i}\in\mathcal{V}$ [46]. In the context of energy disaggregation, each vertex $v_{i}\in\mathcal{V}$ is associated to aggregate power variation signal between adjacent power reading one sample $\Delta X_{t},$ where $\Delta X_{t}=X_{t+1}-X_{t}$. For further literature on GSP, interested reader may refer to [46].

Recently, researchers have proposed different GSP-based approach for NILM. The first GSP-NILM approach that is neither state-based nor event-based was presented in [38]. The authors, leverage on the work by [47] to perform low-complexity multi-class classification of the acquired active power readings without the need for event detection to detect appliance changing states. However, this approach is supervised and employs GSP only for data classification [30].

Zhao et al. [30, 15] propose a blind, low-rate and steady state event-based GSP approach that does not require any training. The proposed GSP-NILM disaggregate any aggregate active power dataset without any prior knowledge and relay upon the GSP to perform adaptive threshold, signal clustering and pattern matching [30, 15]. Zhao’s approach work well if the average load of each appliance is distinct enough from other appliances load and if the power of each load does not fluctuate much. This is not a typical case in most building and thus limit the performance of Zhao’s algorithm. Additionally, the proposed GSP approach require appliances to be manually labelled after disaggregation, highly affected by noise and it’s performance is also limited by the event detection performed via adaptive thresholding [47].

Deep learning is the machine learning approach that has drawn heavily on the knowledge of the human brain (artificial neural networks), statistics and applied mathematics [48]. It is the artificial neural networks (ANN) that are composed of many layers. For a comprehensive survey and more details on deep-learning interested reader should refer to [49, 48].

In recent years, deep learning has made substantial improvements in several fields such as computer vision [50], speech recognition [51] and machine translation [52]. This is mainly due to more powerful computers, larger datasets and techniques to train deeper networks. In addition, deep learning models are flexible (enabling similar models to be used in wide range of problems) [49]. Recently, different deep learning architecture such as Recurrent Neural Network (RNN) [39], Convolutional Neural Network (CNN) [39, 53, 40], Auto encoder [39] and a combination of deep learning and HMM [53, 54, 44] has been employed to the energy disaggregation problem.

A deep learning novel approach for energy disaggregation that identifies additive sub-components of the power signal in an unsupervised way is presented in [55]. The approach uses high-frequency measurements of current, assume two-state appliances models and requires buffering of all the data until inference. Barsim et al. [29] propose neural network ensembles approach to address NILM problem. The ensemble of neural networks are used in appliance identification problem from the raw high-resolution current and voltage waveforms. The work by Kelly et al. [36], adapted three neural network architectures to low-frequency energy disaggregation problem. In [40], Paulo et al. present a comparison of variety of CNN and RNN for energy disaggregation across a number of appliances.

The work presented by [44] uses CNN network to extract appliance features which are then used as observations to a hidden semi Markov model (HSMM). Huss’s model performed considerably better than a CNN alone with reduced computational cost. In [22], Mauch et al. propose a novel combination of HMM with deep neural network (DNN) for load disaggregation. Mauch’s approaches trains HMM with two emission probabilities, one for single load to be extracted which is modelled as a Gaussian distribution and other for the aggregate signal in which DNN is used. Despite the fact that Mauch’s DNN-HMM models outperformed FHMM, it was trained using few data (20.7 days REDD data). Deep learning models require lots of data in order to be well generalized.

Zhang et al. [53] propose a sequence-to-point learning with CNN for energy disaggregation in which a single-midpoint of an appliance window is treated as classification outputs of a neural network with the mains window being the input. This differ from the work presented in [39] in which a given window of the main sequence is treated as input and a sequence of target appliance as the output of the neural network. The authors further integrate CNN and AFHMM using logarithmic opinion pool method. Zhang approach was found to outperform HMM based approaches [19, 56] and deep learning approach by Kelly et al. [39] with reduced computational cost.

NILM researchers use several performance metrics to evaluate energy disaggregation algorithms. To measure how well an algorithm can predict how an appliance is running in each state(switching ON or OFF), several NILM researchers use accuracy metric defined in (3).

$$Acc.=\frac{correct\_matches}{total\_possible\_matches}$$

(3)

Since appliance usages in a house is a relative rare event, accuracy metric is sometimes misleading. Accuracy metric is not descriptive for an appliance that is mainly OFF [44, 18]. For example, if a TV is ON 10% of the time, an algorithm that predict that the TV is always off will have 90% accuracy without any ability to predict its usage. As results, classification accuracy measures, such as F-Measure ($F_{M}$) has been used [32, 57, 38].

F-Measure is the harmonic mean of precision (PR), the positive predictive values and recall (RE) which is the true positive rate or sensitivity defined by equations 4 to 6

	$\displaystyle PR$	$\displaystyle=\frac{TP}{(TP+FP)}$		(4)
	$\displaystyle RE$	$\displaystyle=\frac{TP}{(TP+FN)}$		(5)
	$\displaystyle F_{M}$	$\displaystyle=\frac{2\times PR\times RE}{(PR+RE)}$		(6)

where true positive (TP) presents the correctly detected state of ON or OFF, false positive (FP) represents an incorrect detection that is predicted appliance was ON while OFF, and false negative (FN) indicates that the appliance used was not identified i.e. was ON but not detected. However, F-measure is limited to binary appliances (OFF/ON) and not applicable for multi-state appliances [58].

To account for multi-state appliances, Makonin et al. [58] introduce a finite-state F-Measure (FS-$F_{M}$) by adapting the work by [18]. Their approach split TP into two: inaccurate true-positives (ITP) and accurate true-positives (ATP). The ITP is a partial penalization measure which converts the binary nature of TP into a misclassification that is not binary in nature defined by equations 7 to 8

	$\displaystyle ITP$	$\displaystyle=\frac{\sum_{t}^{T}\mid\hat{s}_{t}^{i}-s_{t}^{i}\mid}{K^{i}}$		(7)
	$\displaystyle ATP$	$\displaystyle=1-ITP$		(8)

where $\hat{s}_{t}^{i}$ is the estimated state from appliance $i$ at time $t$, $s_{t}^{i}$ is the ground truth state, and $K^{i}$ is the number of states for appliance $i$. To take account for these partial penalizations, [18] redefined precision (PR) and recall (RE) stated as equations 9 to 10.

	$\displaystyle PR$	$\displaystyle=\frac{ATP}{(ATP+ITP+FP)}$		(9)
	$\displaystyle RE$	$\displaystyle=\frac{ATP}{(ATP+ITP+FN)}$		(10)

The FS-$F_{M}$ remains the harmonic mean of the new precision and recall. Accuracy and F-Measure are called classification metrics because they only measure how accurately NILM algorithms can predict what appliance is running in each state.

To measure how well NILM algorithm is able to estimate and assign the power consumed by each appliance different measures have been used. Root mean square error (RMSE) is one of such estimation accuracy measure that NILM researchers use [59, 20, 2]. The RMSE between the estimated power $\hat{y}_{t}^{i}$ consumed at time $t$ for appliance $i$ and the ground truth power $y_{t}^{i}$ consumed at time $t$ for appliance $i$ is given by equation 11

$$RMSE=\sqrt{\frac{1}{T}\sum_{t}(\hat{y}_{t}^{i}-y_{t}^{i})}$$

(11)

where $T$ denotes the number of samples recorded. Using RMSE measure is hard to compare how the disaggregation of one appliance performed over another since this measure is not normalized [60]. To address this issue, other researchers [19, 61, 59] use the normalized disaggregation error that provides a normalized measure of the difference between the actual and the estimated power consumptions of the $i^{th}$ appliance given by equation equation 12.

$$de=\displaystyle\sqrt{\frac{\displaystyle\sum_{t,i}||\hat{y}_{t}^{i}-y_{t}^{i}||^{2}}{\displaystyle\sum_{t,i}||y_{t}^{i}||^{2}}}$$

(12)

The estimation accuracy proposed by [62] can be used to evaluate the overall performance of the NILM algorithm and is defined by equation 13

$$E_{Acc}=\displaystyle\Bigg{[}1-\frac{\sum_{t=1}^{T}\sum_{i=1}^{N}|\hat{y}_{t}^{i}-y_{t}^{i}|}{2\sum_{t=1}^{T}\sum_{i=1}^{N}|y_{t}^{i}|}\Bigg{]}$$

(13)

where $T$ is the time sequence or number of disaggregated readings and $N$ is the number of appliances. Using this metric, we can derive the estimation accuracy for each appliance by eliminating the summations over $N$ as in equation 14

$$E_{Acc}^{(i)}=\displaystyle\Bigg{[}1-\frac{\sum_{t=1}^{T}|\hat{y}_{t}^{i}-y_{t}^{i}|}{2\sum_{t=1}^{T}|y_{t}^{i}|}\Bigg{]}$$

(14)

The disaggregation error (de) in equation 12 and estimation accuracy for each appliance ($E_{Acc}^{(i)}$) in equation 14 measure how well the estimated power profiles match the actual power profiles overtime [63]. The low values of the disaggregation error or RMSE (high value of the estimation accuracy) imply an accurate disaggregation.

The work by [63] introduce another estimation metric called the estimated energy fraction index (EEFI) which provides the fraction of energy assigned to the $i^{th}$ appliance. The EEFI is defined by equation 15

$$EEFI=\displaystyle\frac{\sum_{t=1}^{T}\hat{y_{t}^{i}}}{\sum_{t=1}^{T}\sum_{i=1}^{N}\hat{y_{t}^{i}}}$$

(15)

and it should be compared with the actual energy fraction index (AEFI) which provides the actual fraction of energy consumed by the $i^{th}$ appliance defined by equation 16

$$AEFI=\displaystyle\frac{\sum_{t=1}^{T}y_{t}^{i}}{\sum_{t=1}^{T}\sum_{i=1}^{N}y_{t}^{i}}$$

(16)

The lack of efficient benchmarking framework is another major challenge in the field of NILM research. This has greatly attributed by the fact that there is no reference algorithms implementation. Hence, NILM researchers use different metrics, different datasets, and different pre-processing steps [36, 64]. It is therefore empirically difficult to perform direct comparison or to reproduce results of the state-of the art NILM algorithms. As the result, the newly proposed approaches are rarely use the same benchmarking algorithms and/or most of the comparison studies are sometime misleading or favour the work presented [44].

To address the above mentioned challenge, Batra et al. [64] and Kelly et al. [65] developed Non-Intrusive Load Monitoring Toolkit (NILMTK)⁹⁹9http://nilmtk.github.io/. NILMTK is an open-source NILM toolkit written in Python and designed specifically to enable the comparison of NILM algorithms across diverse data sets. It contains data set parsers, data set analysis statistics, preprocessors for reformatting data sets, benchmark disaggregation algorithms, accuracy metrics and rich metadata support via the NILM Metadata¹⁰¹⁰10https://github.com/nilmtk/nilm_metadata[66].

The NILMTK toolkit provides a complete pipeline from data sets to accuracy metrics, thereby lowering the entry barrier for researchers to implement a new algorithm and compare its performance against the current state of the art [64]. Several studies such as [39, 67, 68, 2, 3] have used this toolkit to implement and evaluate their NILM algorithms. The work presented in [69] use NILMTK to analyse and validate the UK-DALE dataset.

The release of NILMTK was followed by the NILM-Eval framework¹¹¹¹11https://github.com/beckel/nilm-eval developed by ETH Zurich distribution system research group¹²¹²12http://vs.inf.ethz.ch/. The NILM-Eval is a comprehensive evaluation framework for NILM algorithms written in MATLAB. It is designed to facilitate the design and execution of large experiments that consider several different parameter settings of various NILM algorithms [4]. The NILM-Eval framework allows new NILM researcher to replicate experiments performed by others or evaluate an algorithm on a new dataset and fine-tune configurations to improve the performance of an algorithm in a new setting [36]. In their study, [70] implemented the algorithms on MATLAB and evaluated the performance of their approach on the NILM-Eval framework.

Recently, [71] propose an approach that aim to help NILM researchers systematically evaluate and benchmark NILM technology across different datasets and performance metrics, using open source technologies and well-established performance metrics and evaluation techniques. However, the tool is limited to event-based approaches.