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3.2.2 Decoder
The decoder adopts a MLP structure. It is designed to reconstruct the input feature vector from the latent
space representation produced by the encoder. This component is critical to the model’s reconstruction
ability, with the primary objective of enhancing the model’s robustness and representational power through
the reconstruction process, thus improving performance in anomaly detection tasks within time series data,
particularly in the context of TSA attacks. The decoder comprises several fully connected layers, which pro-
gressively expand the dimensionality of the latent space, ultimately outputting the reconstructed data ˆ with

the same shape as the original input . The calculation of the latent representation received by the decoder
from the encoder is given by:

ℎ = ( ) (30)

Where represents the latent space of the decode and is the original input data. The decoder extracts the
essential features of the input data and maps it to the latent space using:

ℎ 1 = ReLU ( 1 ℎ + 1 ) (31)

Where is the weight matrix and is the bias term. This ReLU activation function enhances the non-linear
feature extraction capability of the decoder, allowing the latent space to enter the higher-dimensional feature
space through multiple layers. If the capsule is used for TSA detection, the network computes the reconstruc-
tion error using the sigmoid function to ensure the output matches the original input data, defined as:

ˆ = sigmoid ( ℎ −1 + ) (32)

To balance the reconstruction error, the mean squared error (MSE) is used as the loss function , and this
error evaluates the difference between the original input data features and the output of the decoder:

= ∥ − ˆ∥ 2 (33)

Byminimizingtheerror,themodelcanaccuratelyreconstructtheinputdata,ensuringthatthecapsulenetwork
retains the feature extraction and representational power necessary for TSA detection tasks.

4. RESULTS
To simulate the basic equipment and scenarios of a regional energy internet and verify the effectiveness of
the detection model, this paper generates a simulation dataset based on the IEEE 14-bus standard network,
incorporating the fundamental characteristics of a regional energy internet. The IEEE 14-bus network is a
widely used and standardized test system that provides representative operational scenarios for power systems
within energy internet frameworks. The network includes key components such as generators, transformers,
and load nodes, effectively reflecting the complexity of multi-node, multi-device coordinated operation in
a regional energy internet. Using the standard topology and parameter settings provided by the Matpower
toolbox, this paper simulates measurement data samples under real-world conditions. To better represent the
measurement errors found in actual data, the signal-to-noise ratio (SNR) of the simulation dataset is set to 20