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# Conditioned Fully Convolutional
Denoising Autoencoder for Energy
Disaggregation

Diego García<fnref n="1" />(✉), Daniel Pérez<fnref n="2" />, Panagiotis Papapetrou<fnref n="3" />, Ignacio Díaz<fnref n="1" />,
Abel A. Cuadrado<fnref n="1" />, José Maria Enguita<fnref n="1" />, Ana González<fnref n="1" />,
and Manuel Domínguez<fnref n="2" />

**Abstract.** Energy management increasingly requires tools to support decisions for improving consumption. This is achieved not only obtaining feedback from current systems but also using prior knowledge about human behaviour. The advances of data-driven models provide techniques like Non-Intrusive Load Monitoring (NILM) which are capable of estimating energy demand of appliances from total consumption. In addition, deep learning models have improved accuracy in energy disaggregation using separated networks for each device. However, the complexity can increase in large facilities and feedback may be impaired for a proper interpretation. In this work, a deep neural network based on a Fully Convolutional denoising AutoEncoder is proposed for energy disaggregation that uses a conditioning input to modulate the estimation aimed to one specific appliance. The model performs a complete disaggregation using a network whose modulation to target the estimation can be steered by the user. Experiments are done using data from a hospital facility and evaluating reconstruction errors and computational efficiency. The results show acceptable errors compared to methods that require various networks and a reduction of the complexity and computational costs, which can allow the user to be integrated into the analysis loop.

**Keywords:** energy dissaggregation · NILM · convolutional neural networks

## 1 Introduction

Energy efficiency has gained substantial attention not only in the promotion of sustainable products and generation technologies that aim to save energy but also in the study of current systems in order to obtain knowledge about how the

<footnote n="1">¹ Department of Electrical Engineering, University of Oviedo, Gijón 33204, Spain
{garciaperdiego,idiaz,cuadradoabel,jmenguita,gonzalezmunana}@uniovi.es</footnote>

<footnote n="2">² SUPPRESS Research Group, University of León, 24007 León, Spain
{dperl,manuel.dominguez}@unileon.es</footnote>

<footnote n="3">³ Department of Computer and Systems Sciences, Stockholm University, Kista,
Stockholm SE-164 07, Sweden

panagiotis@dsv.su.se</footnote>
energy is consumed. Frequently, this consumption is reported as an overview of the total demand in a certain period of time. However, the perception of detailed representations of the energy allows users to obtain feedback that encourages them to take actions to improve overall consumption [9, 11].

The development of data-driven models focused on energy disaggregation has provided the capacity to extract detailed information. One kind of these models is known as *Non-Intrusive Load Monitoring* (NILM), where the energy consumption of a facility (commonly residential) is decomposed by estimating the energy demands of specific appliances using only the measurements from the main energy demand. In contrast to other intrusive methods, NILM is able to provide complete energy disaggregation using few measuring devices and, therefore, reducing costs and complexity.

Different solutions for NILM systems have been reviewed in the literature [2, 28], mainly using real electrical power data from public datasets [18, 21]. Firstly, signatures on total consumption were defined in the seminal work of Hart [14] focusing on transitions between steady-states through finite state machines. Later, other techniques based on *Hidden Markov Models* (HMM) [20] were applied, achieving acceptable results while suffering limitations in computing models for several appliances that include multiple operating states. These results have been remarkably improved thanks to the advancement of *Deep Neural Networks* (DNN) [17, 25]. Examples of these architectures are *recurrent neural networks* [19, 22], *convolutional neural networks* [5, 13] or *denoising autoencoders* [4, 13] which are able to extract individual energy consumption accurately. Nevertheless, a set of trained networks are required to disaggregate each individual consumption separately so that the design and computation of these models can be difficult to deploy in complex facilities.

However, it is not only the performance of NILM models that is relevant but also the interpretation of their outcome since they facilitate users to improve the overall efficiency by reducing energy waste thanks to the knowledge gained from NILM feedback [3, 31]. In this sense, several solutions have emerged allowing the user to interact with the outcome of NILM models in interactive data visualizations [1, 12, 29]. Although users are able to manipulate the visualizations and select the sequences of total consumption to be disaggregated, fluid interaction pathways which modulate the behavior of NILM models according to the user's intentions are not commonly supported.

In this article, an alternative perspective of DNN-based NILM models is proposed, where a multi-task approach based on conditioned *Fully Convolutional denoising AutoEncoder* (FCN-dAE) is used to estimate several individual consumptions using a single network, instead of training a DNN model per individual consumption to be disaggregated. The suggested multi-task approach allows users to steer the intermediate activations of the network according to the target individual consumption indicated by a conditioning input. Special layers based on *feature-wise linear modulation* (FiLM) [27] are integrated in our model in order to modulate the intermediate activations from the conditioning input. The multi-task NILM approach allows a fluid integration of the user's intent-
tions in the analysis by steering the energy disaggregation model by means of the FiLM modulations and the conditioning input. This facilitates the integration of NILM into interactive applications and provide a more actionable and meaningful feedback to the user.

The remaining sections of the article are organized as follows: in Sect. 2, the DNN-based NILM models are defined; in Sect. 3, the conditioning paradigm and FiLM framework are presented; in Sect. 4, the FiLM approach is adapted to the NILM problem to define the proposed mul-titask FCN-dAE disaggregator; in Sect. 5, the performance, the computational efficiency and the interpretability of the proposed method are evaluated using real energy demand data from a hospital. Finally, the conclusions and future work are presented in Sect. 6.

## 2 DNN-based NILM Models

In the NILM problem, the disaggregation is computed from a sequence of the whole-facility energy consumption, which is commonly denoted as $\mathbf{P}$. This sequence is the sum of all the appliance-specific loads in the facility:

$$ \mathbf{P} = \sum_{m=1}^{N} \mathbf{p}_{m} \qquad (1) $$

where $\mathbf{p}_m$ represents a sequence—with the same length as $\mathbf{P}$—from the $m$-th individual load and $N$ is equal to the number of individual consumptions of the facility. An energy disaggregator $D_m$ is a function that extracts the $m$-th individual energy consumption from $\mathbf{P}$:

$$ D_m : \mathbf{P} \rightarrow \hat{\mathbf{p}}_m \qquad (2) $$

Most approaches estimate individual consumptions by means of a set of $N$ disaggregators $\{D_m\}$ $m = 1, 2, \dots, N$. Complex DNN models have been recently proposed as suitable energy disaggregation functions $D_m$ in the literature [4, 5, 13, 16].

All the aforementioned models rely on a previous windowing operation that divides the whole sequence of total energy consumption (daily/monthly sequence) into smaller input sequences. This operation is defined by the window length $L$ and the stride $M$ between contiguous windows. The performance of the resulting disaggregators is notably affected by $M$ and $L$, as they determine the amount of context used to train the energy disaggregators.

Once the windowing operation is applied, the resulting training windows of total and individual consumptions $\{\mathbf{P}^{(i)}, \mathbf{p}_m^{(i)}\}$ are used to minimize the reconstruction loss function $\mathcal{L}$ in order to optimize the parameters $\theta$ of the architecture:
$$ \theta^* = \arg \min_{\theta} \frac{1}{n} \sum_{i=1}^{n} \mathcal{L}(\mathbf{p}_m^{(i)}, D_m(\mathbf{P}^{(i)}, \theta)) = \arg \min_{\theta} \frac{1}{n} \sum_{i=1}^{n} \mathcal{L}(\mathbf{p}_m^{(i)}, \hat{\mathbf{p}}_m^{(i)}) \quad (3) $$

where $\hat{\mathbf{p}}_m^{(i)}$ is the estimated individual consumption sequence for the $i$-th training sample and $\theta^*$ the optimized weights. Reconstruction error functions, such as RMSE or MSE, are often employed as loss functions in DNN-based NILM models.

After training, each disaggregator $D_m$ estimates individual sequence $\hat{\mathbf{p}}_m$ from a sequence of total consumption $\mathbf{P}$. In practice, this approach entails excessive memory usage and long latencies in the analysis because a total of $N$ DNN-based models must be loaded and executed to obtain all individual consumptions. In addition, interacting with the model, beyond varying the input sequence, is not straightforward.

## 3 Conditioning Mechanisms for NILM

Recent conditioning techniques for DNN-based models [7,15] can be integrated into the aforementioned NILM models to enhance their computational efficiency and to make them steerable by users. These techniques are able to modulate the intermediate activations of a DNN-based model by means of an auxiliary input or conditioning input. Thus, energy disaggregators $D_m$ can be conditioned by adding a user-driven input $S_D$, as it is shown in Fig. 1.

<figure><img src="image_2.png" /><figcaption>Fig. 1. Conditioning for energy disaggregation.</figcaption></figure>

The intermediate layers are commonly modulated by simple functions such as biasing [24], scaling [6,15] or affine [7,8] transformations. In this regard, Feature-wise Linear Modulation (FiLM) [27] is a general-purpose framework to apply affine transformations for modulating the intermediate feature maps of convolution layers from the conditioning input. The affine transformations are applied by means of ad hoc FiLM layers distributed along the DNN to be modulated. The FiLM layer is defined as follows:

$$ \text{FiLM}(\mathbf{F}_{j,k}^{(i)}) = \gamma_{j,k}^{(i)} \mathbf{F}_{j,k}^{(i)} + \beta_{j,k}^{(i)} \quad (4) $$
where the feature map of the j-th convolutional layer and the k-th channel $F_{j,k}^{(i)}$ computed from i-th input sample is scaled and shifted by means of the parameters $\gamma_{j,k}$ and $\beta_{j,k}$. All $\gamma_j$ and $\beta_j$ corresponding to all FiLM layers are computed from the conditioning input $S_D$ by the functions $f_c$ and $h_c$, respectively:

$$ \gamma_j^{(i)} = f_c(S_D^{(i)}) \qquad \beta_j^{(i)} = h_c(S_D^{(i)}) \qquad (5) $$

In practice, an auxiliary neural network or *FiLM generator* is used to approximate $f_c$ and $h_c$ from the conditioning information $S_D$ —both are computed by the same network with two outputs—. The FiLM framework has been able to meaningfully modulate neural networks in complex tasks, such as visual reasoning [27], by adding only a small amount of extra parameters to the main model. Note that FiLM modulations only need two parameters per channel to be conditioned, so that they are independent from the input size and, more importantly, a complete retraining of the network is not necessary in order to change its outcome according to the user's intentions.

<figure><img src="image_3.png" /><figcaption>Fig. 2. Multi-task FCN-dAE architecture.</figcaption></figure>
## 4 Multi-task Fully-Convolutional Denoising Autoencoder

Following the FiLM framework, we propose the conditioned DNN-based model shown in Fig. 2. The conditioned DNN model is based on the architecture *fully-convolutional denoising autoencoder* (FCN-dAE) proposed in [13] and conditioning information $S_D$ is the target individual load to be disaggregated, indicated by the user, thus addressing the NILM problem as a multi-task problem. In the resulting multi-task FCN-dAE (multi FCN-dAE), the estimation of the N individual loads is no longer performed by a set of functions $\{D_m\}$, but a single conditioned NILM model D is able to compute the whole disaggregations.

The target individual consumption should be indicated in $S_D$ using an interpretable format to the user. In this case, the target consumption is specified as a one-hot encoding vector, but more complex formats of $S_D$, such as attributes related to the individual consumption (e.g., location, type of consumption or any prior knowledge) are also appropriate. Once the $S_D$ is introduced in the model, all the FiLM parameters ($\gamma_j$ and $\beta_j$) are computed by a FiLM generator made of three fully-connected layers and an output fully-connected layer with a number of units equal to the number of affine parameters required.

The computed FiLM parameters are then used for the FiLM layers that modulates all the feature maps of the encoder of the main network. By modulating only the encoder, the latent space representation is conditioned to the target consumption indicated in $S_D$. Then, the decoder is capable of reconstructing each subspace to the corresponding individual consumption.

<table><caption>**Table 1.** Description of the individual nodes measured from the hospital facility.</caption><thead><tr><td>Meter</td><td>Sample rate</td><td>#samples</td><td>Description</td></tr></thead><tbody><tr><td>Total consumption</td><td>1 min</td><td>519278</td><td>Consumptions of whole facility</td></tr><tr><td>CGBT-2.Montante0</td><td>1 min</td><td>507353</td><td>South zone lifts</td></tr><tr><td>Radiologia1</td><td>1 min</td><td>507305</td><td>X-ray room 1</td></tr><tr><td>Radiologia2</td><td>1 min</td><td>507354</td><td>X-ray room 2</td></tr><tr><td>RehabilitacionA</td><td>1 min</td><td>507355</td><td>Rehab facilities A</td></tr><tr><td>RehabilitacionB</td><td>1 min</td><td>507307</td><td>Rehab facilities B</td></tr><tr><td>Subcentral3</td><td>1 min</td><td>507353</td><td>West zone consumption</td></tr><tr><td>CPD</td><td>1 min</td><td>507353</td><td>Server and a data center</td></tr><tr><td>Plantas.2-7</td><td>1 min</td><td>507353</td><td>South zone floor from 2 to 7</td></tr><tr><td>Plantas.8-13</td><td>1 min</td><td>507355</td><td>South zone floor from 8 to 13</td></tr></tbody></table>

## 5 Results

The multi-task FCN-dAE approach is evaluated by comparing its performance with other state-of-the-art NILM architectures, such as *denoising AutoEncoders*
[17], biLSTM [16] and vanilla FCN-dAE [13]. These models are applied to an non-residential NILM dataset from a hospital complex [13], where the total energy consumption was measured together with 9 individual consumptions. Further details about the measurements of the individual nodes are described in Table 1.

All the models were trained using pairs of sequences of total and individual consumptions {$P, p_m$} with length of 1440 minutes ($L = 1440$). For training the proposed multi-task FCN-dAE, the one-hot vectors $S_D$ are also attached to the training sequences. User-defined parameters related to the main architecture (number of layers, number of kernels, initialization, etc.) are the same as the initial FCN-dAE work, except for the latent space dimension which had to be increased to improve the training error. On the other hand, the parameters related to the FiLM generator network were manually adjusted to those that provided the best training error.

After training, the individual consumptions estimated by all the architectures using 1-month test sequence are compared in Table 2, using the MAE and RMSE reconstruction metrics [26].

<table><caption>**Table 2.** Comparison of disaggregation performance between sequence-to-sequence models and multi-task FCN-dAE.</caption><thead><tr><th></th><th></th><th>biLSTM</th><th>dAE</th><th>FCN-dAE</th><th>multi-FCN-dAE</th></tr></thead><tbody><tr><td rowspan="10">MAE</td><td>CGBT-2.Montante0</td><td>2.9095</td><td><strong>2.4863</strong></td><td>2.5609</td><td>3.2711</td></tr><tr><td>Radiologia1</td><td>8.2969</td><td>7.0405</td><td><strong>5.9346</strong></td><td>7.3891</td></tr><tr><td>Radiologia2</td><td>3.3974</td><td>3.1002</td><td><strong>2.7061</strong></td><td>3.2705</td></tr><tr><td>RehabilitacionA</td><td>1.4721</td><td><strong>1.2164</strong></td><td>1.2789</td><td>1.5251</td></tr><tr><td>RehabilitacionB</td><td>3.8967</td><td>3.0455</td><td><strong>2.8464</strong></td><td>3.7287</td></tr><tr><td>Subcentral3</td><td>2.7142</td><td>2.5553</td><td><strong>2.552</strong></td><td>3.3734</td></tr><tr><td>CPD</td><td>4.2315</td><td>4.3056</td><td>3.9156</td><td><strong>2.6909</strong></td></tr><tr><td>Plantas.2-7</td><td>2.4502</td><td>2.4512</td><td><strong>2.109</strong></td><td>3.6736</td></tr><tr><td>Plantas.8-13</td><td>2.3686</td><td>2.5463</td><td><strong>2.0707</strong></td><td>4.5218</td></tr><tr><td rowspan="10">RMSE</td><td>CGBT-2.Montante0</td><td>5.2149</td><td>3.5161</td><td><strong>3.4271</strong></td><td>5.318</td></tr><tr><td>Radiologia1</td><td>11.6352</td><td>9.8098</td><td><strong>8.771</strong></td><td>10.8085</td></tr><tr><td>Radiologia2</td><td>6.0392</td><td>5.6539</td><td><strong>5.3551</strong></td><td>5.7545</td></tr><tr><td>RehabilitacionA</td><td>2.1273</td><td><strong>1.648</strong></td><td>1.6881</td><td>2.0971</td></tr><tr><td>RehabilitacionB</td><td>6.4429</td><td>4.0777</td><td><strong>3.7579</strong></td><td>5.4655</td></tr><tr><td>Subcentral3</td><td>3.5735</td><td>3.2491</td><td><strong>3.2287</strong></td><td>4.195</td></tr><tr><td>CPD</td><td>4.6070</td><td>4.6968</td><td>4.3564</td><td><strong>3.1575</strong></td></tr><tr><td>Plantas.2-7</td><td>3.1213</td><td>3.0926</td><td><strong>2.7183</strong></td><td>4.5093</td></tr><tr><td>Plantas.8-13</td><td>3.0489</td><td>3.1191</td><td><strong>2.6963</strong></td><td>4.9767</td></tr></tbody></table>
Considering that the proposed multi-task FCN-dAE is built using one network, the performance is close to other methods which use several networks (one disaggregator per each node). Although the DNN-based model using the same baseline (FCN-dAE) architecture shows better overall errors, a comparison of graphical representations of individual nodes extracted, shown in Fig. 3, expose competitive results for the disaggregation of the multi-FCN-dAE method.

Regarding the computational efficiency, the trainable weights of the DNN-based models are shown in Fig. 4a, where the proposed multi-FCN-dAE model needs significantly fewer trainable weights than the rest of architectures. Note that the values shown for the rest of models correspond to the total trainable weights of the set of networks {$D_m$} needed to compute all the individual nodes.

The inference time of predicting the output individual consumption sequence is shown in Fig. 4b, where the proposed model is faster than biLSTM but it is slightly slower than the vanilla FCN-dAE and dAE models. However, it is fast enough (around 20 milliseconds) to consider a change in $S_D$ as a fluid mechanism of interaction [10].

<figure><img src="image_4.png" /><figcaption>**Fig. 3.** Several disaggregated individual consumption (blue line) from the hospital complex computed using different DNN-based models compared to ground truth consumptions (gray line). (Color figure online)</figcaption></figure>

## 5.1 Interpretation of Conditioning Mechanisms

The FiLM conditioning mechanism included in our multi-task FCN-dAE approach is able to adaptively modulate the encoder feature maps according to the
target individual consumption, by focusing its attention on those feature maps more related to the target consumption. This modulation is not discrete, but in $S_D^{(i)}$, one can set *continuous transitions* by drawing trajectories between individual nodes. Figure 5a shows several examples of continuous transitions obtained after introducing the same window $P^{(i)}$ to the model and several points of a trajectory between two target one-hot encodings in $S_D$. These transitions insightfully reveal to the user which changes should be applied to the starting individual node to turn it into the end node. This idea is tightly connected to the field of *explainable machine learning*, specially with counterfactual examples [30], since the proposed model is able to reveal which learned features make two sequences from individual nodes different.

The FiLM layer in the encoder also modulates the latent space representation $z$ on the FCN-dAE latent space — see Fig. 2. In Fig. 5b, $z$ representation of 300 sequences of main consumptions (each of them conditioned for all available individual nodes) are displayed after being processed by the *Uniform Manifold Approximation and Projection* (UMAP) [23] to visualize a 2D map of the latent space. The UMAP view reveals that the FiLM conditioning divides the latent space into node-specific subspaces, from which the decoder reconstructs the target individual consumption. The location of node-specific clusters in the view also seems to be meaningful, as similar nodes are projected together, and those nodes that are different between each other are mapped aside —see CPD node.

<figure><img src="image_5.png" /><figcaption>**Fig. 4.** Comparison of computational efficiency between suggested multi-task FCN-dAE and sequence-to-sequence DNN-based models.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Fig. 5.** Interpretability of multi-task FCN-dAE model. (a) Examples of transitions between two individual nodes. (b) UMAP projections of the latent space representation.</figcaption></figure>

# 6 Conclusions

A conditioned fully convolutional neural network is proposed including an auxiliary input to introduce the condition for the extraction of one specific consumption through *Feature-wise Linear Modulation* technique. This reduces complexity with respect to previous models because of the use of a single conditioned NILM model modulated by determined conditions instead of a network per individual consumption.
Performance is compared between several DNN-based NILM methods using data from a non-residential facility like a hospital complex. The results of the multi-task method are competitive with respect to the rest of models using different specific networks. Moreover, computational efficiency is compared through the number of trainable weights and inference time, showing admissible times to process the output. This reduction of the complexity and computational costs allow the model to be used interactively in an eventual interactive application in order to integrate the user into the analysis loop and thus enhance feedback.

Future work includes the consideration of different types of inputs in auxiliary network for the modulation, the integration into an interactive interface, the effect of the conditioning on the number of training data required for proper training and the study of the generalization capabilities between facilities.

**Acknowledgement.** This work was supported by the Ministerio de Ciencia e Inno-
vación/Agencia Estatal de Investigación (MCIN/AEI/ 10.13039/501100011033) under
grants PID2020-115401GB-I00 and PID2020-117890RB-I00. Data were provided by
Hospital of León and SUPPRESS Research Group of University of León within the
project DPI2015-69891-C2-1/2-R.

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