Privacy Preserving Federated Learning for Energy Disaggregation of Smart Homes

Abstract

ABSTRACT

Smart advanced metering infrastructure and edge devices show promising solutions in digitalising distributed energy systems. Energy disaggregation of household load consumption provides a better understanding of consumers’ appliance‐level usage patterns. Machine learning approaches enhance the power system's efficiency but this is contingent upon sufficient training samples for efficient and accurate prediction tasks. In a centralised setup, transferring such a substantially high volume of information to the cloud server has a communication bottleneck. Although high‐computing edge devices seek to address such problems, the data scarcity and heterogeneity among clients remain challenges to be addressed. Federated learning offers a compelling solution in such a scenario by leveraging the ML model training at edge devices and aggregating the client's updates at a cloud server. However, FL still faces significant security issues, including the potential eavesdropping by a malicious actor with the intention of stealing clients' information while communicating with an honest‐but‐curious server. The study aims to secure the sensitive information of energy users participating in the nonintrusive load monitoring (NILM) program by integrating differential privacy with a personalised federated learning approach. The Fisher information method was adapted to extract the global model information based on common features, while personalised updates will not be shared with the server for client‐specific features. Similarly, the authors employed an adaptive differential privacy only on the shared local updates (DP‐PFL) while communicating with the server. Experimental results on the Pecan Street and REFIT datasets depict that DP‐PFL exhibits more favourable performance on both the energy prediction and status classification tasks compared to other state‐of‐the‐art DP approaches in federated NILM.

Introduction

Energy management of the residential sector plays a significant role in reducing the global carbon emission rate, as it accounts for 30%–40% of total end-use consumption [1]. Robust control, monitoring and prediction programs have the potential to enhance the energy efficiency of the residential energy sector, with the capacity to reduce overall power usage by 5%–20% [2]. Smart grid application with advanced metering infrastructure and edge devices offers promising solutions for the digitalisation of energy systems. In home energy systems, ensuring user comfort represents a significant challenge, necessitating the installation of numerous electronic devices at the household level. Nevertheless, the monitoring of energy consumption for each household appliance through the utilisation of digitalised smart metres represents a costly, invasive and challenging process. To empower a robust energy system through effective demand-side management, nonintrusive load monitoring (NILM), also known as energy disaggregation, presents a better analysis of the accurate load prediction programs by disaggregating the net demand into appliance-level information [3] as shown in Figure 1. Deep learning approaches are new methods to disintegrate household energy consumption into appliance-level energy patterns [4]. However, such neural NILM approaches necessitate cloud servers to train the model with many variable energy data samples, which incurs high computational costs. Model pruning and compression techniques alleviate the training and testing burden and facilitate the implementation of DNN prediction models at the edge. Such edge computing approaches leverage the local training and preserve the consumer data for insights from other users, but data sparsity makes the trained model the least accurate. In such a scenario, collaborative machine learning suggests a better solution to train the ML model at the edge client and share the updates with the cloud server to converge the global model.

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In a centralised energy network, a nonintrusive load monitoring (NILM) application is needed to transmit smart metre data along with the energy profile of home appliances to a remote server. The remote server uses the data to train a machine-learning model, which raises privacy concerns. An adversary could extract detailed information about household energy usage habits, daily activities at home, temperature preferences, appliance usage patterns and the number of occupants at different times [5]. The lifestyle of a household can vary depending on various factors, including financial, social, environmental and even psychological influences. These factors also impact energy usage patterns and the choice of appliances in the household. In this context, federated learning addresses privacy concerns and performs better than local model approaches by aggregating peer client training weights at a central server.

Despite addressing the essential privacy concern, FL is still prone to possible privacy leakage by a passive adversary during the parameters exchange between the clients and server. Several techniques, such as differential privacy, homomorphic encryption and secure multiparty computation, have been adopted to mitigate the privacy leakage issue [6–8]. Similarly, malicious clients in the federation extract private information by sending manipulated updates to the central server during the training process, such as poisoning attacks, model inversion attacks, membership inference attacks and backdoor attacks [9]. To secure the client private data in Google GBoard application, McMahan et al. introduced differential privacy mechanism in federated training [10]. Similarly, to protect the client data from inference attack, Shi et al. employed the sharpness-aware minimisation approaches in the SGD optimisation method of federated learning [11]. However, the existing mitigation and defence mechanisms designed to address the privacy and security concerns associated with FL must be examined in the context of NILM. Existing federated NILM-based approaches have not demonstrated the effectiveness of differential privacy in a heterogeneous home energy network comprising diverse household appliances and a heterogeneous feature distribution. Personalised federated learning (PFL) seems to be effective in preserving the privacy, while employing PFL with differential privacy may further enhance the privacy of the client in federated NILM.

To address these issues, using federated learning with personalisation may provide a more effective solution. This personalised approach to federated learning can identify common features across all clients and client-specific features based on individual appliance usage preferences. This study aims to gain a deeper understanding of the potential applications of federated learning in energy disaggregation, with a particular focus on the aspects of personalisation and privacy leakage. The objectives of the current study are as follows:

• To preserve privacy via personalised federated learning, the Fisher's information matrix approach is employed to determine the clients' shared and personalised features.

• To increase privacy budget and provide secure federated training, differential privacy mechanism has been employed in PFL that can prevent potential privacy breaches in federated energy disaggregation.

• It compares the efficacy of adaptive differential privacy and deep learning models in a personalised federated setup by clipping and adding noise to the shared updates during the training process.

• A fair comparison with other privacy-based federated learning algorithms, such as adaptive differential privacy without personalisation (DP-FedAvg) and sharpness aware minimisation optimiser to perturb gradient (DP-FedSAM), has been carried out.

Literature Review

Secure cyber-physical systems, such as smart grids, aim to protect system information and data, which is of paramount importance for maintaining confidentiality, integrity and availability. In such a cyber-physical system, smart metres collect private data from consumers and share it with trusted utilities, thereby facilitating the smooth operation of the grid. If the utility is deemed untrustworthy, there may be a possibility of information sharing with a third-party exploiter, such as advisors or insurance companies. The dissemination of client energy data to adversaries could result in the acquisition of private information about the user, including details such as lifestyle, appliance preferences, the condition of electric devices, incentive mechanisms, number of occupants and more. The application of energy disaggregation techniques, such as NILM, enables the decomposition of smart metre data into appliance-level signatures, thereby facilitating the extraction of high-level data inferences. Edge computing devices facilitate the prediction of household energy consumption, yet utilities require information regarding net energy usage for generation programs. Likewise, the data provided by the energy user is insufficient for capturing the consumption patterns of a household's net energy demand and that of the appliances used. Privacy-preserving distributed learning enables collaborative learning of a global model at client edges, addressing client privacy concerns and model accuracy. Recently, deep learning applications in NILM for appliance-level energy disaggregation have opened avenues for researchers to address energy consumers' privacy concerns through federated learning.

Qi Li et al. proposed DFNILM to analyse the application of transfer learning in distributed NILM, which transfers the trained CNN-LSTM model across various dataset domains [12]. A comparative analysis of data-driven deep learning models has been conducted across three distinct datasets, given the recognition that the datasets from geographically disparate countries exhibit notable differences. The study concluded that the transferability of trained models across other domain samples could be enhanced through the acquisition of higher quality training data. Yunchuan Shi et al. investigated the user data leakage concerns in the context of centralised NILM machine learning and proposed federated learning as a potential solution [13]. A convolutional neural network (CNN) model has been adopted to address the sequence-to-point disaggregation problem and classify events in appliance signatures on the UK-Dale dataset, thereby addressing the issue of model vulnerability using a centralised approach. Wang et al. proposed a multi-task learning approach to cluster appliances with similar features for energy decomposition, highlighting the potential risks associated with using deep neural networks for privacy leakage [14]. They utilised the U-Net architecture to perform multi-target quantile regression and multi-label classification on the UK-Dale dataset, measuring performance for respective loss metrics. Wang et al. proposed a FedNILM framework to evaluate the federated approach generalisation capability with both local and centralised learning NILM configurations on two measured residential and industrial datasets [15]. FedNILM implemented a seq2point learning model, demonstrating improved performance relative to the local model with a fast convergence rate and scalability across heterogeneous networks.

Kaspour et al. proposed attention-based aggregation mechanisms in federated NILM (FedAtt) to extract the appliance consumption pattern based on consumer behavioural differences [16]. FedAtt examines short sequence-to-point (S2P) and variational auto-encoder (VAE) models over UK-Dale and REFIT datasets and suggests differential privacy to add noise during the federated training process to address the problem of inversion attacks at the server. The study evaluated FedAvg, centralised learning, and FedAtt on precision, recall, F1 Score and MAE metrics. The FedAtt with the VAE model outperformed others with an F1 score of 0.89, but the study did not provide any insights about the DP adaptation mechanism, noise parameter selection and relevant results. Zhou et al. proposed a federated load forecasting approach of a household while decomposing the net energy demand into appliance-level prediction and aggregating the estimated values of individual consumption to forecast the home's total energy usage [17]. They used CNN-LSTM and BiLSTM models on the nine kinds of appliances of the UK-Dale dataset to forecast the 250-min load data of five households. The CNN-LSTM model has been employed to decompose the energy for appliance level and subsequently forecast the aggregated energy based on the hybrid BiLSTM model. The study evaluated different hybrid deep learning models with the BiLSTM model based on prediction metric, which yielded an index of 0.08141 MAE and 0.16739 RMSE, respectively.

HEMS of smart homes is responsible for data collection and sample labelling of high-frequency input signals to the respective intelligent devices. Incorrect appliance labelling of any input signal can disturb the monitoring and visualisation of home energy systems. Lin et al. investigated the data cleaning process to improve the data quality fed into the vertical federated NILM system [18]. They set up an experimental testbed to analyse the data pollution with different hardware devices, communication protocols and electrical appliances. The SplitNN model has been evaluated as a global model on the classification task of three experimental HEMS clients resulting in an F1 score of 0.94 for training and 0.92 for testing. Giuseppi et al. introduced a decentralised network for federated NILM load decomposition to address the issue concerning the trust and security of the central server [19]. The Decentralised Federated Learning (DecFedAvg) algorithm exhibits a comparable pattern of mean absolute error (MAE) loss to FedAvg for washing machine energy prediction. A comparison between FedAVG and DecFedAvg over the five appliances from the REFIT dataset on the seq2point learning model gives an average MAE error of 0.057 and 0.054, respectively. Similarly, the authors suggested a mutual consensus-based approach in future research to tailor sophisticated decentralised networks.

Zhang et al. introduced a novel approach, termed ‘FedNILM’, for training personalised models for similar clients in a federated multi-task learning framework [20]. They employed sequence-to-point (Seq2Point) modelling techniques to facilitate multi-tasking and decomposed the model into shared and task-specific layers. Convolutional layers are common for all the clients to extract transferable load features, including the status of the appliances. In contrast, fully connected layers are responsible for learning detailed features about the specific appliances. They analysed the efficacy of personalised federated learning through transfer learning approaches on five REFIT and REDD datasets appliances, utilising the MAE, SAE and F1 score as performance metrics. Results showed that transfer learning improves the personalisation task in all devices except the washing machine and dishwasher, which exhibits a reduction of −27.27% in F1-score and −143.52% SAE metrics degradation, respectively. Change et al. proposed a gradient boosting machine method FedGBM to decompose the smart metre data to predict appliance signatures in a collaborative learning setup [21]. GBM has been implemented across the client federation based on a two-stage voting and node-level parallelism approach to address the issue of co-modelling in NILM. Comparative analysis with CNN and GAN on three open source datasets, UK-DALE, REDD and REFIT, demonstrated that FedGBM achieved comparable accuracy among the four appliances to the two baseline models with the least communication and computation cost.

Federated learning utilises the differential privacy mechanism to ensure robust privacy protection for clients in the event of potential malicious attacks on updates. One of the earliest approaches in this field is DP-FedAvg, which employs the Gaussian mechanism to safeguard client data while training a language model for predicting the next word [10]. Shi et al. proposed DP-FedSAM to minimise the impact of random noise and clipping by using a gradient perturbation optimiser on the updates, thereby improving performance [11]. Sharpness-aware minimisation (SAM) is a min-max SGD optimisation approach that addresses the issue of overly parameterised models and enhances their generalisation ability [22]. DP-FedSAM utilises a SAM optimiser to address the impact of differential privacy (DP) noise, which can result in over-parameterisation of client models in federated learning. The objective is to reduce the $${l}_{2}$$ clipping norm to address inconsistency among client updates and to achieve a flatter curve, thereby facilitating better generalisation of the global model. Similarly, Mazhar et al. utilised an adaptive DP-FedAvg, which employs a noise multiplier to adaptively perturb the noise and clipping during federated training for energy prediction [23]. Chen et al. assessed the significance of client data features by determining the diagonal of the Fisher information matrix for approximation [24]. This study applies a similar approach with dynamic personalisation and differential privacy to protect the household client from gradient leakage. The DP-FedAvg method applies differential privacy to all the local models aggregated on the server. Similarly, DP-FedSAM introduces the optimiser that also perturbs all the gradient updates with differential privacy. To mitigate the effect of DP on the global aggregated model, we only apply DP on the shared parameters of client updates, instead of all the weights. To assess the efficacy of personalised training in federated differential privacy, we compare the Fisher information-based DP mechanism with DP-FedAvg and DP-FedSAM in the NILM energy disaggregation application.

Similarly, several studies have been carried out to preserve the privacy of NILM clients using federated learning, in which they have used several deep learning models [2, 13, 15, 20]. We investigate the performance of such federated NILM deep learning models such as GRU, LSTM, CNN-based sequence-to-point and CNN-LSTM hybrid models under differential privacy and client personalisation using FIM. Previous studies in federated NILM only compared local, centralised, and federated setups, no study has been carried out that analyses the impact of differential privacy and client personalisation to guarantee more secure learning. The list of symbols used in this study is given in Table 1.

TABLE 1 List of symbols used in the study.

Symbol	Description
$$P(t)$$	Power consumption by smart metre
$${P}_{a}(t)$$	Power consumption by appliance $$a$$
$$e(t)$$	Measurement error at the smart metre
$$G(d)$$	Deep learning model under Gaussian DP
$$\omega $$	Global model weight
$$M$$	Number of client in the federated learning
$$\left({x}_{i},{y}_{i}\right)$$	Data samples of client $$i$$ participating in training
$$\sigma $$	Noise multiplier to control privacy
$$(v,u)$$	Shared and personalised model weights of client $$i$$
$${\hat{F}}_{i}$$	Fisher information likelihood function for client $$i$$
$${M}_{1i},{M}_{2i}$$	Fisher information matrix for client $$i$$

System Design

Nonintrusive Load Monitoring

NILM is a technique for identifying the energy consumption of individual appliances from aggregated data, such as energy consumption data from a smart metre. The approach requires a single point of measurement, such as a digitalised metre and no additional measuring instruments are required to be installed in the home, as indicated by its name, ‘nonintrusive’. The following equation defines the aggregated power consumption of a household at time $$t$$. 1 $$P(t)=\sum\limits _{a=1}^{n}{P}_{a}(t)+e(t)$$ where $$P(t)$$ is the net power consumption of all the active equipment $${P}_{a}(t)$$ at the respective time $$t$$ and $$e(t)$$ represents the measurement error. The noise $$e(t)$$ is considered small enough to neglect it, and the NILM algorithm approximates a function $$T$$ that performs mapping of the following equation at each time. 2 $$T(P(t))=\left[{P}_{1}(t),\text{\ldots },{P}_{a}(t),\text{\ldots },{P}_{n}(t)\right]$$

Federated Learning

Instead of bringing all the data together in one place, a cloud server, federated learning (FL) enables the training of machine learning models on individual devices. This approach leverages the client's computing resources to train a global model, achieving higher accuracy than the edge client model. Federated averaging (FedAvg) is a common method used to combine updates from all the devices participating in the training process [25]. In FedAvg, a central server averages the client's updates to the global model and improves the generalisation; it then sends back the global model to the devices so they can keep training it based on their information until it converges. For a given loss function $$f$$ of the respective task, the objective of FL can be defined as follows: 3 $$\underset{\omega }{\min }f(\omega ),\quad \text{where}\quad f(\omega )=\frac{1}{n}\sum\limits _{i=1}^{n}{f}_{i}(\omega )$$ where $${f}_{i}(\omega )=l\left({x}_{i},{y}_{i};\omega \right)$$ is the prediction loss on the training sample of individual clients given as $$\left\{{x}_{i},{y}_{i}\right\}$$ to update the global model weight $$\omega $$ and $$n$$ is the number of clients participating in the respective federated training round.

Federated Differential Privacy

The objective behind a man-in-the-middle or poisoning attack in a federated NILM-based system is to gain financial advantages or avoid regulatory compliance issues. An attacker can manipulate the model to give users false information about their appliance health, leading them to purchase new appliances prematurely. Similarly, an attacker may also manipulate data regarding the appliance or net consumption to encourage clients to consume more energy during peak hours and avoid incentives. A promising defence mechanism to secure against such attacks in Federated Learning (FL) is through differential privacy (DP). In the Gaussian noise mechanism for DP in deep learning [26], the noise magnitude is calibrated to the norm of adjacent inputs $$d$$ and $${d}^{\prime }$$, given as follows: 4 $$G(d)=f(d)+N(0,{S}_{f}^{2}{\sigma }^{2})$$ where $${S}_{f}$$ satisfy $$({\epsilon},\delta )$$ differential privacy according to the targeted values or specified setup. In federated learning any model $$G$$ satisfies $$({\epsilon},\delta )-DP$$ for any adjacent input data d and $${d}^{\prime }$$, by adding noise function as given above. Where $${S}_{f}$$ replace to the maximum $${l}_{2}$$-distance norm $$\Vert f(d)-f\left({d}^{\prime }\right){\Vert }_{2}$$ and $${\epsilon}$$ is the privacy loss parameter with the failure probability $$\delta \in [0,1]$$. In the above equation, the G(d) can achieve $$({\epsilon},\delta )-$$DP privacy by adding Gaussian noise $$N\left(0,{S}_{f}^{2}{\sigma }^{2}\right)$$ with $${\epsilon}\le 1$$ and $$\delta \ge 0.8\cdot \mathrm{exp}\left(-{(\sigma {\epsilon})}^{2}/2\right)$$ in the function $$f(d)$$, which is deep learning models in this study. Here, $$\sigma $$ is the noise multiplier or variance that controls the trade-off between privacy and model degradation during the federated training process.

Personalised Federated Learning

To address the heterogeneity across clients' datasets in federated learning, the disintegration of the single federated model into two parts can address the issue. In PFL, the parameter vector of the model $$w$$ is divided into a client-specific local part $$u$$ and a shared global part $$v$$. Let's consider $$M$$ clients, each with a private dataset $${D}_{i}={\left({x}_{i},{y}_{i}\right)}_{i=1}^{{N}_{i}}$$, where $${N}_{i}$$ represents the size of the dataset for client $$i$$. The parameter vector of $$w$$ is now split into two parts for each client, denoted as $${\omega }_{i}=\left(v,{u}_{i}\right)$$ using personalisation techniques. The above optimisation problem is then transformed into the PFL objective function. 5 $$\underset{v,{u}_{1:m}}{\min }\left\{f\left(v,{u}_{1:i}\right)=1/m\sum\limits _{i=1}^{M}{f}_{i}\left(v,{u}_{i}\right)\right\},$$ where $${u}_{1:i}$$ is given by $$\left({u}_{1},\text{\ldots },{u}_{i}\right)$$ and $${f}_{i}\left(v,{u}_{i}\right)$$ is the empirical risk of client $$i=(1,\text{\ldots },M)$$. PFL at iteration uses two steps to solve the expected risk of client $$i$$ by the following:

• Local Update: In each round, the client $$i$$ in $$M$$ federation collects the latest global weights $${v}^{t}$$ while retaining its local parameter $${u}_{i}^{t}$$ from the earlier round to initial the local training with the model parameters $${\omega }_{i}^{t}=\left({v}_{i}^{t},{u}_{i}^{t}\right)$$. After locally training for $${E}_{l}$$ local epoch on respective client data it obtain new model parameters $${\omega }_{i}^{t+1}=\left({v}_{i}^{t+1},{u}_{i}^{t+1}\right)$$. It send the local updates $${\Delta }{v}_{i}^{t+1}$$ by after taking the difference between $${v}_{i}^{t+1}$$ and $${v}_{i}^{t}$$.

• Global Update: All the clients participating in the federated training send their local updates $${\Delta }{v}_{i}^{t+1}$$ to the central server for collaborative learning. Once the server receives all the local updates, it performs the FedAVG averaging algorithm to update the shared parameters by $${v}^{t+1}={v}^{t}+1/M{\sum }_{i=1}^{M}{\Delta }{v}^{t+1}$$. The server then sends the updated global model back to the client for the next round, and the process continues until convergence.

Methodology

DP for NILM Clients

In PFL, it is essential to develop a differential privacy mechanism to prevent the potential risk of any privacy leakage due to malicious attacks. User-level differential privacy (DP) will provide a privacy budget to the NILM clients that are indistinguishable, thereby preventing the extraction of their features. To safeguard the shared updates from the potential risks associated with information leakage, user-level differential privacy (DP) is achieved through the application of clipping and noise addition techniques. Clipping operation is carried out to control the maximum contribution of a single NILM client to the energy disaggregation model update, ensuring that DP preserves privacy in any outliers. Similarly, noise addition operation from the random Gaussian distribution, renders it challenging for an adversary to infer specific information about the NILM appliance signatures. The combined effect of clipping and noise addition is given by the following: 6 $${\Delta }{\omega }_{c}={\Delta }\omega /\max \left(1,\Vert {\Delta }\omega {\Vert }_{2}/C\right),{\Delta }{\omega }_{c,N}={\Delta }{\omega }_{c}+\mathcal{N}\left(0,{C}^{2}{\sigma }^{2}/\vert {M}_{t}\vert \right)$$ where $${\Delta }{\omega }_{c}$$ is the original local updates of available clients $$\vert {M}_{t}\vert $$ participating in the training round $$t$$. $$C$$ is the clipping threshold to control the client's maximum contribution to the global update represented by $${\Delta }{\omega }_{c}$$. $${\Delta }{\omega }_{c,N}$$ is obtained after the clipping and noise addition, where $$\mathcal{N}$$ is the Gaussian noise for DP, with noise multiplier $$\sigma $$ which is computed by privacy accountant $${\epsilon}$$ and composition parameter $$\delta $$.

PFL via Fisher Information

In traditional PFL based on image classification tasks, the distinction between the shared and specific parts is already made explicit within the model. For example, in the case of a ResNet model, the first few CNN layers are typically regarded as shared layers, given that they extract the common image features. Conversely, the last few fully connected linear layers are client-specific tasks, as they extract features relevant to the client-specific attributes, which may differ from those of other clients. However, our approach to personalised federated NILM employs the Fisher Information matrix to dynamically determine the sharing and personalised parameters of energy users in each global round. The Fisher Information $$F$$ determines the sensitivity of the log-likelihood function $$\log \,L(y\vert x;\omega )$$ to changes in each parameter $$\omega $$. Let $${\omega }_{i}^{t-1}=\left({v}^{t-1},{u}_{i}^{t-1}\right)$$ denote the parameters of the last round and $${D}_{i}$$ be the client dataset, the Fisher value vector for each weight indexed $$j$$ in $${\omega }_{i}^{t-1}$$ is given as follows: 7 $$F\left({\omega }_{ij}\right)={\left(\frac{\partial \,\log \,L\left({\omega }_{i},{D}_{i}\right)}{\partial {\omega }_{ij}}\right)}^{2},$$ where $$\log \,L\left({\omega }_{i},{D}_{i}\right)$$ denotes log-likelihood function of $${\omega }_{i}$$. Similarly, based upon the above Fisher information approach, we compute the layer-wise Fisher value which dynamically select the parameters for both global and personalised model by setting a threshold and element-wise multiplication.

The overall personalised federated learning mechanism with differential privacy is illustrated in Figure 2. The clients participating in federated learning download the global model from the server. For each global round, the clients compute shared and personalised parameters dynamically, based on the Fisher information as detailed in Equation (7) and associated Algorithm 2. Subsequently, after decomposing the clients' model parameters into the two components, clipping and noise is applied to the parameters according to the differential privacy mechanism as given in Equation (6). This is applied solely to the shared parameters, which are uploaded to the server for aggregation. The server sends the aggregated global model for the next round, and the iterative process continues until the global model converges. The overall personalised federated mechanism under differential privacy (DP) is presented in the Algorithm 1 with a detailed account of how client model decomposition occurs in each global round in the Algorithm 2.

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1

Algorithm

Proposed personalised federated NILM under DP.

Initialise: Client $$(M)$$, global round $$\left({E}_{g}\right)$$, local epoch $$\left({E}_{l}\right)$$, noise multiplier $$(\sigma )$$, clipping $$(C)$$, global model weights $$(\omega )$$, client $$i$$ dataset $${D}_{i}=\left({x}_{i},{y}_{i}\right)$$ for each Global Round $${e}_{g}=1,\text{\ldots },{E}_{g}$$ do  Client Updates: $$i=1$$ to $$M$$ client $$(i\in M)$$   Fisher Information Matrix; $$\hat{F}{\leftarrow}\left({D}_{i},{\omega }_{i}^{t-1}\right)$$ ………as in Equation (7)   $${M}_{1i},{M}_{2i}{\leftarrow}\left({\hat{F}}_{i},\tau \right)$$ ………as in Algorithm 2  $${\omega }_{i}^{t}=\left({v}^{t-1},{u}_{i}^{t-1}\right){\leftarrow}{M}_{1i}\odot {\omega }_{i}^{t-1},{M}_{2i}\odot {\omega }^{t-1}$$ …………as in Algorithm 2   for each Local Epoch $${e}_{l}=1,\text{\ldots },{E}_{l}$$ do    $${u}_{i}^{t}{\leftarrow}{u}_{i}^{t-1}-\eta {\nabla }_{u}\left({v}^{t-1},{u}_{i}^{t-1}\right)$$    $${v}_{i}^{t}{\leftarrow}{v}^{t-1}-\eta {\nabla }_{v}\left({v}^{t-1},{u}_{i}^{t}\right)$$   end for   $${\Delta }{\omega }_{i}^{t}{\leftarrow}\left({v}_{i}^{t},{u}_{i}^{t}\right)-\left({v}_{i}^{t-1},{u}_{i}^{t-1}\right)$$   $${\Delta }{\omega }_{i}^{t}{\leftarrow}{\Delta }{\omega }_{i}^{t}/\max \left(1,\Vert {\Delta }{\omega }_{i}^{t}{\Vert }_{2}/C\right)+\mathcal{N}\left(0,{C}^{2}{\sigma }^{2}/\vert M\vert \right)$$   return $${\Delta }{\omega }_{i}^{t}$$ to Server  Serve Update:   FedAVG$$\left(M,{\omega }^{t}\right)$$   $${\omega }^{t}{\leftarrow}{\omega }^{t-1}+\frac{1}{M}{\sum }_{i=1}^{M}{\Delta }{\omega }_{i}^{t}$$   return $${\omega }^{t}$$ to clients end for

2

Algorithm

Client model decomposition based on Fisher Information.

Inputs: Global parameters $$(\omega )$$, client parameters $$\left({\omega }_{i}\right)$$, Fisher threshold $$(\tau )$$, client data $$\left({x}_{i},{y}_{i}\right)$$, Binary masks matrix $$\left({M}_{1i},{M}_{2i}\right)$$ Initialise: Fisher diagonal for each parameter $$\left({\omega }_{ij}\right)$$: $${F}_{\mathrm{diag}}=[0,0,\text{\ldots },0]$$ Compute model prediction $$p\left({x}_{i};{\omega }_{i}\right)$$ for each sample $$\left({x}_{ik},{y}_{ik}\right)$$ do  Extract target $$\left({y}_{ik}\right)$$  Compute log-likelihood over loss function $$F$$ as;   $$logL\left({\omega }_{i}\vert {x}_{ik},{y}_{ik}\right)=F\left(p\left({x}_{ik};{\omega }_{i}\right),{y}_{ik}\right)$$  Compute gradients $$({g}_{ij})$$ of log-likelihood w.r.t $${\omega }_{ij}$$;   $${g}_{ij}=\left(\frac{\partial \hspace*{.5em}\log \hspace*{.5em}L\left({\omega }_{i}\vert {x}_{k},{y}_{k}\right)}{\partial {\omega }_{ij}}\right)$$  Accumulate Fisher diagonal values;   $${F}_{\mathrm{diag}}\left({\omega }_{ij}\right)+={g}_{ij}^{2}$$  Binary masks, $${M}_{1i}$$ and $${M}_{2i}$$ for each parameter $$j$$;   $${M}_{1i}[j]=\left\{\begin{array}{@{}ll@{}}1,\quad \hfill & \text{if}\hspace*{.5em}{F}_{\mathrm{diag}}\left({\omega }_{ij}\right)\ge \tau \hfill \\ 0,\quad \hfill & \text{otherwise}\hfill \end{array}\right.\quad \text{and}\quad {M}_{2i}[j]=\left\{\begin{array}{@{}ll@{}}0,\quad \hfill & \text{if}\hspace*{.5em}{F}_{\mathrm{diag}}\left({\omega }_{ij}\right)\ge \tau \hfill \\ 1,\quad \hfill & \text{otherwise}\hfill \end{array}\right.$$ end for return Global and personalised parameters;   $$v{\leftarrow}{M}_{2i}\odot {\omega }^{t-1},{u}_{i}{\leftarrow}{M}_{1i}\odot {\omega }_{i}^{t-1}$$

Experiments

Datasets

In our research, we utilised two distinct datasets: the Pecan Street¹ and REFIT² datasets. The Pecan Street dataset comprises 15-min interval aggregated energy and household appliance data, obtained from energy-measuring devices. It has the energy consumption of four appliances—an air conditioner, an electric vehicle, a kitchen utensil and a refrigerator—estimated from the energy metre. This publicly available data contains electrical measurements from a variety of households and their respective appliances across different cities in the United States [27]. Similarly, the REFIT dataset incorporates high-frequency load measurement data from 20 households in the United Kingdom [28]. The measurements have been taken at every 6-s interval for household appliances, however, for this study purpose, we averaged the data over the one-minute interval. In this study, we focused on data from 10 households of the REFIT dataset, considering both the aggregated energy and the energy consumed by specific appliances, namely the refrigerator, washing machine, television, and microwave. It is important to note that household energy consumption patterns vary based on several factors, including individual preferences, living standards, occupancy and other factors. Although the datasets do not provide information about the factors influencing user energy consumption signatures, it is evident that energy consumption differs among clients, thus making it a heterogeneous home energy network.

Model Architecture

We have implemented federated learning using the PyTorch framework, simplifying the training of deep learning models [29]. PyTorch facilitates the separation of the model architecture from the training process, rendering it an appropriate choice for personalised federated setups and the integration of differential privacy in our simulation environment. We utilised the Ocapus module for the implementation of an adaptive differential privacy mechanism in DP-FedAvg and DP-PFL, which requires a noise multiplier for the target epsilon and delta values [30]. Our findings suggest that a noise multiplier value of 0.5 represents the optimal choice for privacy and accuracy trade-off. The optimal privacy budget is defined by epsilon 1.0 and delta 0.1, as evidenced by the detailed experiments with different hyperparameters. In the study, we also referenced this privacy budget from DP-FedSAM, in which no noise multiplier hyperparameter is required for adaptive privacy protection. The effect of noise in DP-FedSAM is mitigated through bounding the target clipping bound assumed as $$C=0.2$$ and $${l}_{2}$$ norm of gradient updates given as $$\min \left(1,C/\Vert {\Delta }w{\Vert }_{2}\right)$$. A noise term, denoted by the probability density function of a normal distribution with a mean and variance as $$\mathcal{N}\left(0,{C}^{2}{\sigma }^{2}/\sqrt{\vert {M}_{t}\vert }\right)$$ is added to the clipped weights, where $$\sigma =0.8$$ denotes the noise variance instead of noise multiplier in adaptive approach for targeted epsilon and $${M}_{t}=10$$.

We have developed highly adaptable modules for model architecture. The Gate Recurrent Unit (GRU) utilises recurrent neural network layers for time series-based data, with a ReLU activation function. This adaptability ensures that the model is capable of accommodating the varying energy consumption profiles exhibited by disparate clients. Additionally, sequence-to-point (S2P)-based convolutional neural network (CNN), long short-term memory (LSTM) and hybrid CNN-LSTM models, were also employed in this paper, as they have been used in previous federated NILM studies. In the S2P, two CNN layers and two dense linear layers have been used, whereas in the other models, only a single CNN and LSTM layer has been adopted with two hidden layers. To achieve personalisation, Fisher-based approaches have been employed, whereby the diagonal of the log-likelihood is computed in each round from the respective samples and labels associated with the weights in each layer. Such personalisation enables the derivation of shared and client-specific features on a dynamic basis, which is then employed to clip and noise updates during the differential privacy mechanism, thus addressing security concerns. The optimal Fisher threshold for personalisation in this study is 0.35, which results in fast convergence. The optimum value of different hyperparameters used in our simulation is given in Table 2.

TABLE 2 Optimum value of hyperparameters used in the simulation.

Parameter	Value
Specific layer	GRU, CNN, LSTM
Hidden layer	2
Activation function	ReLU, Tanh
Noise multiplier $$(N)$$	0.5
Epsilon $$({\epsilon}-DP)$$	1.0
Delta $$(\delta -DP)$$	0.1
Clipping bound $$(C-DP)$$	0.2
Local epoch $$\left({E}_{l}\right)$$	2
Learning rate $$\left({l}_{r}\right)$$	0.001

Results and Discussion

We conducted a study to evaluate the performance of personalisation (DP-PFL) in the federated DP context. To this end, we have compared DP-PFL with two other approaches, namely DP-FedAvg and DP-FedSAM, in an energy disaggregation application for smart homes. To ensure a fair comparison of the three DP methods, comprehensive experiments have been conducted to determine the optimal values of the hyper-parameters. Once the optimal values had been identified, we carried out federated training process with 300 global rounds and two local epochs. In contrast to classification tasks, the time series prediction tasks elevated based on accuracy metrics for possible malicious attack and security analysis [31, 32]. A fair comparison can be made using the RMSE metric to evaluate the loss during the privacy-preserving federated training in smart grids [33, 34]. Furthermore, we also considered personalised federated learning without DP (PFL) to assess the performance accuracy of the differential privacy mechanism in securing and providing privacy to FL.

Figures 3a and 4a show the loss results of the CNN model over the federated rounds for PFL, DP-PFL, DP-FedAvg and DP-FedSAM using the Pecan Street dataset. Similarly, Figures 3b and 4b show the respective RMSE losses of the CNN and hybrid CNN-LSTM models for PFL, DP-PFL, DP-FedAvg and DP-FedSAM on REFIT. It has been shown from the figures that DP-PFL approaches outperform DP-FedAvg and DP-FedSAM approaches, following the same trends with minimal gap to PFL without differential privacy. We evaluated our approaches on four deep learning model such as CNN, GRU, LSTM and CNN-LSTM models, but only shows a S2P-based CNN and hybrid CNN-LSTM models due to redundancy as all of them show similar trends. In DP-PFL, the DP noise and clipping updates are only included in the parameters that are shared by the clients during the communication with the server. In addition, the adaptive noise and clipping in DP-FedAvg performs better than DP-FedSAM, while all shows declining loss with increasing number of training rounds. The smoother performance of DP-PFL indicates that it experiences minimal and similar adjacent global loss variations to PFL. Since we keep the noise hyper-parameters and dense layers the same in all cases, hyper-parameter optimisation for the GRU model may address such a problem.

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The REFIT dataset comprised 6s interval measurement of appliances, averaged over a minute-based time for the study. The DP-PFL performances on the REFIT dataset in Figures 3b and 4b shows a similar trend to that of Pecan Street. The RMSE loss of CNN-LSTM model in DP-FedSAM is higher than the other approaches on Pecan Street dataset as given in Figure 4a. The comparative performance of DP-PFL shows that it outperforms other differential privacy approaches with a least RMSE of 0.7741 for the S2P-based CNN model. Results of DP-FedAvg and DP-SAM for the REFIT dataset show a lower RMSE than Pecan Street for all the respective deep learning models. Appliance-based prediction give better insides to evaluate the performance of global model. We presented two appliances of respective datasets to demonstrate the forecasting accuracy in differentially private federated NILM setup as show in Figures 5 and 6. CNN-LSTM based model show smoother forecasting trends while CNN tough predict peak-value well but highly fluctuates. Studies show that transformer-based model performs well in prediction and address the issue of catastrophic forgetting. Figures 5 and 6 show that differential privacy mechanism in federated learning (in our case DP-PFL) not much affect the prediction performance and which can be further enhance via transformer-based model, specially for appliances that have nonrecurrent profiles.

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The individual performance of each client in the DP-PFL setup for the two datasets is given in Table 3. The best performance is highlighted in bold. Similary, for comparative analysis the individual clients RMSE loss for other differentially private federated approaches DP-FedAvg and DP-FedSAM are given in Tables 4 and 5. The clients that are performing well on the deep learning models have been shown in bold for all the cases being discussed, which are detailed in Tables 3–5. Client-10 gives the smallest RMSE of 0.3836 for CNN model on REFIT dataset, while it gives the largest RMSE of 0.7949 for LSTM model in DP-FedSAM of Pecan Street dataset. Both the datasets are diverse and collected from two different geographical zone: Pecan Street from Austin, USA, while REFIT collected from households of Loughborough, UK. Moreover, the consumption interval also differs, making the study viable for both 1-min and 15-min analysis in future studies. The datasets are diverse as per frequency of appliances usage; however, the study has limitations over the number or types of appliance across each clients assumed to be same for the respective datasets.

TABLE 3 DP-PFL method: average training loss accuracy of individual clients on the two datasets.

Client	Training loss on Pecan	Training loss on REFIT
GRU	CNN	LSTM	CNN-LSTM	GRU	CNN	LSTM	CNN-LSTM
Client-01	0.7476	0.7293	0.7948	0.7619	0.6024	0.4234	0.5370	0.4767
Client-02	0.7297	0.7716	0.7947	0.7676	0.6257	0.3904	0.5639	0.4769
Client-03	0.7659	0.7575	0.7922	0.7568	0.6040	0.4616	0.5434	0.4443
Client-04	0.7250	0.7764	0.7675	0.8099	0.6301	0.4570	0.5137	0.4652
Client-05	0.7523	0.7867	0.8068	0.7625	0.6605	0.4316	0.5658	0.4526
Client-06	0.7422	0.7592	0.8202	0.7661	0.5277	0.4140	0.5114	0.4429
Client-07	0.7257	0.7832	0.8359	0.7614	0.6296	0.4531	0.5394	0.4680
Client-08	0.7347	0.7964	0.8249	0.7708	0.6299	0.4168	0.5355	0.4234
Client-09	0.7185	0.7953	0.8222	0.7935	0.6039	0.4165	0.5217	0.4415
Client-10	0.7516	0.7784	0.8207	0.7729	0.6108	0.3836	0.5595	0.4209

TABLE 4 DP-FedAvg method: average training loss accuracy of DP-PFL individual clients on the two datasets.

Client	Training loss on Pecan	Training loss on REFIT
GRU	CNN	LSTM	CNN-LSTM	GRU	CNN	LSTM	CNN-LSTM
Client-01	0.7576	0.7773	0.8107	0.7581	0.6108	0.4188	0.5571	0.4834
Client-02	0.7610	0.7777	0.8313	0.7741	0.6192	0.4088	0.5546	0.4734
Client-03	0.7413	0.7655	0.7937	0.7693	0.6478	0.4199	0.5455	0.4423
Client-04	0.7402	0.7556	0.7925	0.7871	0.6493	0.4417	0.5562	0.4043
Client-05	0.7601	0.7999	0.7946	0.7878	0.6258	0.4431	0.5355	0.4860
Client-06	0.7556	0.7747	0.8377	0.7993	0.6286	0.4050	0.5506	0.4757
Client-07	0.7362	0.7869	0.7976	0.7512	0.6516	0.4406	0.5516	0.4815
Client-08	0.7558	0.7707	0.8210	0.7698	0.6178	0.4441	0.5579	0.4839
Client-09	0.7444	0.7627	0.8190	0.8105	0.6471	0.4378	0.5426	0.4092
Client-10	0.7626	0.7836	0.8162	0.7528	0.6569	0.4083	0.5421	0.4453

TABLE 5 DP-FedSAM method: average training loss accuracy of individual clients on the two datasets.

Client	Training loss on Pecan	Training loss on REFIT
GRU	CNN	LSTM	CNN-LSTM	GRU	CNN	LSTM	CNN-LSTM
Client-01	0.7552	0.8010	0.8357	0.7891	0.6066	0.4185	0.5664	0.4834
Client-02	0.7700	0.7977	0.8061	0.8104	0.6883	0.4443	0.6102	0.4201
Client-03	0.7761	0.7603	0.7996	0.8253	0.6029	0.4532	0.5742	0.4977
Client-04	0.7725	0.8088	0.7953	0.7759	0.6459	0.4227	0.6373	0.4658
Client-05	0.7642	0.7847	0.8279	0.8169	0.6924	0.4304	0.6099	0.4949
Client-06	0.7552	0.7674	0.8429	0.7785	0.6805	0.4747	0.5601	0.4276
Client-07	0.7688	0.7653	0.8018	0.8135	0.6491	0.4251	0.5795	0.4610
Client-08	0.7445	0.7430	0.8130	0.8141	0.6122	0.4792	0.6025	0.4830
Client-09	0.7505	0.7742	0.8229	0.7839	0.6427	0.4735	0.6539	0.5142
Client-10	0.7465	0.7813	0.7949	0.8062	0.6054	0.4156	0.6208	0.5084

The study evaluates the model performance based on the regression task to forecast the appliance energy demands. However, the status of the appliances have unique characteristics in most of the energy disaggregation studies. We also analysed the classification scenario in our study to predict the ON/OFF status of the appliances of Pecan Street and REFIT datasets. The detailed test results of the respective appliances of both the datasets is given in Appendix A. It shows the details about the federated differential privacy mechanism and DL models performance on the individual appliances with respect to classification metrices, such as accuracy, precision, recall and F1-score. CNN and CNN-LSTM model seems to be effective in classifying the status of the appliances in all the DP-mechanism. In most of the appliances, the accuracy of the DP-PFL models have slightly better performance than DP-FedSAM and DP-FedAVG. As federated learning involve ML training at edges and parameters communication between the server and edge devices. DP-PFL increases the privacy with the same performance level as that of DP-FedSAM and DP-FedAVG. DP-PFL only communicate the shared global model parameters while preserving the personalised weights of the edge clients from potential leakage.

The study shows insight into the impact of differential privacy on federated NILM tasks. It shows the significance of personalisation in enhancing the performance of energy disaggregation under a better privacy budget. Still, the study has some challenges, the study primarily focused on privacy concerns related to protecting the sensitive information of smart home consumers from potential gradient leakage. Also, the study considered an assumption over the types of appliance to be same, which is in realistic may differ across clients, increasing the heterogeneity of the clients. In future studies, we will try to handle such highly heterogeneous setup, and also aim to implement a transformer-based model to enhance the performance of NILM tasks across various time-series datasets. Additionally, model pruning methods and client personalisation under diverse types of appliance may yield improved results of personalisation and differential privacy, as they involve fewer parameters than traditional Federated Learning (FL) training.

Conclusion

Energy disaggregation of consumer smart metres to individual appliance signatures helps to monitor the status of the smart home appliances. NILM task assists demand response program, which can be helpful for efficient smart home operation. Our paper proposes a federated learning approach for nonintrusive load monitoring energy prediction, addressing privacy concerns in a centralised setup. We employed differential privacy to address the security concerns over the malicious attack on client updates. We introduce the personalisation of NILM clients using the Fisher information matrix to enhance federated learning performance within privacy constraints. We comparatively validate the results with other state-of-the-art DP mechanisms in federated NILM setup. The results show that DP-PFL performs better with the least RMSE loss than DP-FedAvg and DP-FedSAM. Similarly, CNN provide better results on appliance-level status classification for both datasets.

Author Contributions

Mazhar Ali: conceptualization, data curation, formal analysis, investigation, methodology, resources, software, validation, visualization, writing – original draft, writing – review and editing. Ajit Kumar: formal analysis, supervision, visualization, writing – review and editing. Bong Jun Choi: conceptualization, formal analysis, funding acquisition, investigation, methodology, project administration, supervision, validation, visualization, writing – review and editing.

Acknowledgements

This research was supported by the MSIT Korea under the NRF Korea (RS-2025-00557379, 90%) and the Information Technology Research Center (ITRC) support program (IITP-2025-RS-2020-II201602, 10%) supervised by the IITP.

Conflicts of Interest

The authors declare no conflicts of interest.

Data Availability Statement

Datasets used in the study are openly available in a public repository that issues datasets with links; (Pecan), (REFIT).

Appendix

Appendix - A

A.1: Pecan Street

Details of the results are presented below.

See Tables A1–A4.

TABLE A1 Performance metrics of DP methods and DL models on air-conditioner.

Methods	Model	Accuracy	Precision	Recall	F-1
DP-FedSAM	GRU	0.5392	0.5833	0.4580	0.5643
LSTM	0.5508	0.7080	0.6085	0.6960
CNN	0.6768	0.7637	0.6885	0.7104
CNN-LSTM	0.6756	0.7857	0.4167	0.5326
DP-FedAVG	GRU	0.5207	0.5005	0.5012	0.5560
LSTM	0.5468	0.7123	0.5451	0.6929
CNN	0.6544	0.7701	0.6645	0.6953
CNN-LSTM	0.7266	0.7813	0.7662	0.7488
DP-PFL	GRU	0.5964	0.5642	0.5380	0.5541
LSTM	0.6084	0.7718	0.6084	0.6593
CNN	0.8324	0.7587	0.6324	0.6771
CNN-LSTM	0.8029	0.7885	0.8112	0.7949

TABLE A2 Performance metrics of DP methods and DL models on electric vehicle.

Methods	Model	Accuracy	Precision	Recall	F-1
DP-FedSAM	GRU	0.5165	0.3960	0.4965	0.4456
LSTM	0.5956	0.581	0.5946	0.5823
CNN	0.6899	0.6845	0.6899	0.682
CNN-LSTM	0.6098	0.6117	0.6098	0.6107
DP-FedAVG	GRU	0.5336	0.3893	0.5146	0.4424
LSTM	0.5966	0.7593	0.4696	0.4458
CNN	0.5783	0.5697	0.5316	0.5724
CNN-LSTM	0.5998	0.5990	0.4598	0.4645
DP-PFL	GRU	0.5424	0.5184	0.5041	0.5234
LSTM	0.6751	0.6706	0.5711	0.6715
CNN	0.6042	0.5831	0.5028	0.5692
CNN-LSTM	0.6985	0.7103	0.5915	0.6713

TABLE A3 Performance metrics of DP methods and DL models on oven.

Methods	Model	Accuracy	Precision	Recall	F-1
DP-FedSAM	GRU	0.5596	0.3696	0.5091	0.4146
LSTM	0.5710	0.755	0.5031	0.4151
CNN	0.5946	0.5846	0.5214	0.5533
CNN-LSTM	0.5731	0.7236	0.5563	0.4202
DP-FedAVG	GRU	0.5603	0.3206	0.4502	0.4138
LSTM	0.5986	0.5884	0.5026	0.5789
CNN	0.6259	0.6231	0.6188	0.5993
CNN-LSTM	0.5819	0.7172	0.5981	0.4415
DP-PFL	GRU	0.5491	0.5074	0.5149	0.4801
LSTM	0.5644	0.3811	0.5154	0.4141
CNN	0.6149	0.613	0.5601	0.5776
CNN-LSTM	0.5712	0.6325	0.5217	0.4157

TABLE A4 Performance metrics of DP methods and DL models on refrigerator.

Methods	Model	Accuracy	Precision	Recall	F-1
DP-FedSAM	GRU	0.4528	0.3707	0.3502	0.4190
LSTM	0.6767	0.6871	0.5576	0.6505
CNN	0.6102	0.5994	0.6008	0.5791
CNN-LSTM	0.5979	0.6502	0.5817	0.4804
DP-FedAVG	GRU	0.4709	0.3553	0.3975	0.4255
LSTM	0.5553	0.6535	0.5465	0.4347
CNN	0.6059	0.5945	0.5829	0.5674
CNN-LSTM	0.5803	0.5528	0.5608	0.4320
DP-PFL	GRU	0.5524	0.5004	0.4525	0.4831
LSTM	0.5801	0.7564	0.4581	0.4260
CNN	0.6193	0.6102	0.5190	0.5940
CNN-LSTM	0.5803	0.5606	0.4839	0.4278

A.2: REFIT

See Tables A5–A8.

TABLE A5 Performance metrics of DP methods and DL models on fridge.

Methods	Model	Accuracy	Precision	Recall	F-1
DP-FedSAM	GRU	0.7804	0.7529	0.7065	0.7246
LSTM	0.8295	0.8422	0.8393	0.8401
CNN	0.9047	0.9050	0.9037	0.9040
CNN-LSTM	0.9035	0.9039	0.9035	0.9036
DP-FedAVG	GRU	0.7954	0.7609	0.7104	0.7406
LSTM	0.8474	0.8565	0.8434	0.8488
CNN	0.9065	0.9069	0.9051	0.9066
CNN-LSTM	0.9051	0.9049	0.9021	0.9050
DP-PFL	GRU	0.8035	0.8742	0.8014	0.8208
LSTM	0.8612	0.8643	0.8562	0.8620
CNN	0.9091	0.9096	0.9094	0.9092
CNN-LSTM	0.9102	0.9098	0.9108	0.9077

TABLE A6 Performance metrics of DP methods and DL models on washing machine.

Methods	Model	Accuracy	Precision	Recall	F-1
DP-FedSAM	GRU	0.7987	0.7509	0.5954	0.8041
LSTM	0.8236	0.5497	0.8254	0.8255
CNN	0.9099	0.9103	0.9059	0.9101
CNN-LSTM	0.9104	0.9101	0.9104	0.9101
DP-FedAVG	GRU	0.8054	0.7609	0.7945	0.8241
LSTM	0.8337	0.8450	0.8337	0.8353
CNN	0.9106	0.9118	0.9103	0.9109
CNN-LSTM	0.9056	0.9087	0.9015	0.9088
DP-PFL	GRU	0.8684	0.8765	0.8548	0.8695
LSTM	0.8498	0.8579	0.8455	0.8511
CNN	0.8935	0.8948	0.8921	0.8939
CNN-LSTM	0.9125	0.9126	0.9005	0.9061

TABLE A7 Performance metrics of DP methods and DL models on television.

Methods	Model	Accuracy	Precision	Recall	F-1
DP-FedSAM	GRU	0.4025	0.7609	0.5204	0.3625
LSTM	0.6844	0.6534	0.5444	0.5454
CNN	0.9059	0.9068	0.9051	0.9062
CNN-LSTM	0.9091	0.9088	0.9065	0.9088
DP-FedAVG	GRU	0.5703	0.6677	0.5630	0.5561
LSTM	0.5858	0.7720	0.4588	0.5951
CNN	0.9129	0.9134	0.9107	0.9130
CNN-LSTM	0.9104	0.9126	0.9106	0.9106
DP-PFL	GRU	0.5956	0.7103	0.4639	0.5722
LSTM	0.6413	0.6573	0.5634	0.5429
CNN	0.9161	0.9164	0.9105	0.9162
CNN-LSTM	0.9174	0.9179	0.9014	0.9176

TABLE A8 Performance metrics of DP methods and DL models on microwave.

Methods	Model	Accuracy	Precision	Recall	F-1
DP-FedSAM	GRU	0.7971	0.7612	0.6907	0.7206
LSTM	0.8417	0.8540	0.8375	0.8433
CNN	0.9062	0.9066	0.9012	0.9064
CNN-LSTM	0.9110	0.9108	0.8910	0.9109
DP-FedAVG	GRU	0.8539	0.7609	0.7946	0.8142
LSTM	0.8353	0.8532	0.8312	0.8371
CNN	0.9077	0.9081	0.9047	0.9078
CNN-LSTM	0.8962	0.8962	0.8902	0.8962
DP-PFL	GRU	0.8208	0.8785	0.8106	0.8219
LSTM	0.8523	0.8644	0.8463	0.8538
CNN	0.9081	0.9067	0.9015	0.9053
CNN-LSTM	0.9065	0.9057	0.8905	0.9066

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