## 3 LSTM and FSST-Based Fault Diagnosis Algorithm  
The machine learning-based fault diagnosis algorithm proposed in this paper utilizes waveform segmentation to analyze system status and environmental conditions in time-series data, particularly within the context of smart agriculture. Waveform segmentation involves dividing time-series data into temporally contiguous segments, helping to identify specific periods or operational states. This segmentation is especially valuable for understanding periodic changes in agricultural environments, such as soil moisture variations, temperature fluctuations, and humidity levels. By extracting meaningful semantic segments from the data, the algorithm provides crucial insights into each phase, enhancing the accuracy of fault diagnosis for devices like soil moisture sensors, temperature sensors, and irrigation controllers.  
Algorithm 1 summarizes the main steps of the **machine learning-based fault diagnosis algorithm**. The algorithm consists of three structured stages: data preprocessing, time-frequency feature extraction using the Fourier synchrosqueezed transform (FSST), and waveform segmentation and classification with LSTM. Each stage is designed to improve the analysis and diagnostic accuracy of time-series data collected from agricultural sensors.  
```
0: Time-series data \(X\)
0: Fault diagnosis labels
1: Data Preprocessing:
2: Normalize time-series data: \[X_{\text{rescaled}}=a+\left(\frac{X-\min(X)}{\max(X)-\min(X)}\right)\cdot(b-a)\] (1)
3: Apply bandpass filter: \[\text{Filtered\_X}=\text{BandpassFilter}(X_{\text{rescaled}})\] (2)
4: Time-Frequency Feature Extraction:
5: Apply Fourier synchrosqueezed transform (FSST): \[S_{x}(\omega,t)=\int_{-\infty}^{\infty}x(t)\cdot\frac{1}{\sqrt{2\pi}}e^{-i \omega t}\phi^{*}(t,\omega)dt\] (3)
6: Waveform Segmentation Using LSTM:
7: Split data into training and testing datasets
8: Initialize LSTM neural network:
9: Define input layer
10: Define LSTM layers with hidden nodes
11: Define output layer with softmax activation
12: Train LSTM neural network:
13:for each epoch do
14: Forward pass through LSTM layers
15: Compute loss
16: Backpropagate error
17: Update weights
18:endfor
19: Monitor training accuracy, validation accuracy, loss function, and overfitting
20: Perform waveform segmentation:
21: Predict labels for test data
22: Post-processing:
23: Combine segmented labels for the entire input sequence
24: Output the fault diagnosis labels
```  
**Algorithm 1** Machine learning-based fault diagnosis algorithm.  
Figure 2 illustrates the **semantic segmentation process** as applied to time-series data. This segmentation process, enhanced by the Fourier synchrosqueezed transform (FSST), serves as a key analytical tool for examining dynamic frequency components within each data segment. Using the FSST allows for precise interpretation of time-frequency relationships, allowing the system to effectively detect anomalies and monitor sensor performance. The FSST's ability to capture changes in frequency modes over time is especially beneficial for sensor data analysis in smart agriculture, as it enhances the ability to diagnose and predict equipment performance accurately. In Figure 2, each segment represents a specific operational state that facilitates accurate fault classification. This visualization is particularly useful for understanding the structured approach applied to the fault diagnosis process.