# Analytic Continual Learning-Based Non-Intrusive Load Monitoring Adaptive to Diverse New Appliances
## 3 Methodology
### Lightweight Dual-Branch NILM Model  
The proposed model consists of a feature extraction module, a novelty detection branch, and a load identification branch. Its detailed architecture is shown in the lower part of Figure 1. Given the close relevance between novelty detection and load identification, the dual branches share a common feature extraction module for improved computational efficiency. The model takes current and voltage waveforms concatenated along the channel dimension as input. These simple inputs preserve key electrical characteristics and their temporal dependencies. The feature extraction module comprises three stacked submodules followed by a fully connected layer. Each submodule sequentially connects depthwise separable convolution, batch normalization, and a ReLU activation function. Specifically, the depthwise separable convolution decomposes a standard convolution intoa depthwise one-dimensional (1D) convolution within each channel and a pointwise 1D convolution that aggregates information across channels. This design significantly reduces computational costs [21]. Batch normalization standardizes each feature in a training batch using its mean and variance [22]. Its learnable parameters enable the model to adapt to the amplitude distribution of diverse appliance waveforms. Notably, the proposed model is more lightweight in both input and architecture than the existing NILM models based on image-based waveform representations and two-dimensional convolution networks (2D-CNNs) [5; 23]. This lightweight design is motivated by the following reasons: (1) It enables easy deployment on low-resource hardware, especially when continual learning from streaming data is required. (2) Using raw waveforms as input reduces data processing complexity and minimizes the parameter count of the feature extraction module. (3) The lightweight 1D convolution has been proven effective in extracting features from appliance waveforms [4].  
To avoid storing original appliance data, the novelty detection branch adopts the deep support vector data description (SVDD) method [24]. Specifically, two fully connected layers map the discriminative feature \(X^{\text{en}}\), produced by the feature extraction module, to a feature space where learned appliances are tightly clustered. Since only data from learned appliances are available when constructing the mapping \(f(X^{\text{en}}\); \(W^{\text{en}})\), the objective is to enclose these data points as tightly as possible within a hypersphere centered at \(c\) with radius \(r\), as shown in (1). The hypersphere center \(c\) is set to the initial mean of the original appliance data in the feature space. In this space, the 99 th percentile of distances from the center is used as a detection threshold. A feature exceeding this threshold is detected as  
Figure 1: Overview of the proposed NILM framework for adapting to new appliances. SCL stands for supervised contrastive learning, ACL for analytic continual learning, DS-Conv for depthwise separable convolution, 1D-Conv for one-dimensional convolution, BN for batch normalization, and FC for a fully connected layer.  
a new appliance. To prevent trivial minimization of (1) by setting \(W^{n}\) to zero, the fully connected layers in the novelty detection branch are implemented without bias terms.  
\[\underset{W^{n}}{\text{min}}\frac{1}{m}\underset{j=1}{\overset{m}{\sum}}\Big{\|} f(X_{j}^{\text{en}};W^{n})-c\Big{\|}_{2}+\lambda\|W^{n}\|_{2} \tag{1}\]