In recent years, the rapid adoption of renewable energy systems, particularly photovoltaic (PV) systems, has underscored the critical role of on-grid inverters in ensuring efficient power conversion and grid integration. As a key power electronic device, the on-grid inverter is prone to failures, especially in switching components like insulated gate bipolar transistors (IGBTs), which can lead to operational disruptions and safety hazards. Traditional fault diagnosis methods for on-grid inverters often rely on offline learning approaches, where models are trained on fixed datasets and require complete retraining when new fault types emerge. This poses significant challenges in terms of adaptability, computational cost, and real-time applicability. To address these limitations, we propose a novel fault diagnosis framework that integrates multi-scale morphological filtering (MMF) with incremental learning techniques, enabling the on-grid inverter system to continuously learn and diagnose new fault types without catastrophic forgetting of historical knowledge.
The core of our approach lies in leveraging mathematical morphology for robust signal processing and incremental classifier and representation learning (iCaRL) for adaptive model updates. By processing three-phase current signals from the on-grid inverter using MMF, we extract discriminative features that are resilient to noise and operational variations. These features are then fed into a one-dimensional convolutional neural network (1D-CNN) for initial fault classification. As new fault scenarios, such as diode open-circuit faults, are encountered, our incremental learning strategy dynamically updates the model by incorporating representative samples and distillation loss, ensuring high accuracy across both historical and new fault types. This method not only enhances the flexibility of fault diagnosis systems for on-grid inverters but also demonstrates superior robustness in noisy environments, as validated through extensive simulations.
To understand the significance of our work, it is essential to recognize the growing complexity of on-grid inverter systems in modern power grids. These inverters are tasked with converting DC power from PV arrays into AC power synchronized with the grid, and their reliability directly impacts overall system performance. Common faults in on-grid inverters include open-circuit and short-circuit failures in IGBTs and diodes, which can cause waveform distortions and secondary damage if not promptly detected. While hardware-based protection mechanisms exist for short-circuit faults, open-circuit faults often require sophisticated diagnostic techniques due to their subtle and prolonged effects. Existing methods, such as Fourier transform, wavelet transform, and machine learning models, have shown promise but lack the ability to adapt incrementally to new fault patterns. Our framework overcomes this by embedding incremental learning into the diagnostic pipeline, making the on-grid inverter a more intelligent and self-evolving component in smart grid applications.
In this article, we delve into the mathematical foundations of multi-scale morphological filtering and its application to fault signal denoising for on-grid inverters. We then detail the incremental learning methodology, including the construction of exemplar sets and the integration of knowledge distillation. Through simulation results, we demonstrate that our approach achieves high diagnostic accuracy, maintains robustness under noise, and effectively mitigates catastrophic forgetting. The remainder of this paper is organized as follows: Section 2 provides background on mathematical morphology and incremental learning; Section 3 describes our proposed methodology; Section 4 presents experimental validation; and Section 5 concludes with insights and future directions.
Mathematical Foundations and Incremental Learning Principles
Mathematical morphology is a nonlinear signal processing technique based on set theory, widely used for feature extraction and noise reduction in time-series data. For an on-grid inverter, the three-phase output currents serve as primary signals for fault detection. The basic operations in mathematical morphology include erosion and dilation, defined for a discrete one-dimensional signal $f(n)$ and a structuring element $g(m)$ as follows:
Erosion: $$(f \Theta g)(n) = \min_{m \in G} \{ f(n + m) – g(m) \}$$
Dilation: $$(f \oplus g)(n) = \max_{m \in G} \{ f(n – m) + g(m) \}$$
where $f(n)$ is defined on $F = \{0, 1, 2, \dots, N-1\}$, $g(m)$ on $G = \{0, 1, 2, \dots, M-1\}$, and $N$ and $M$ are the lengths of the signal and structuring element, respectively. From these, opening and closing operations are derived as composites: opening is erosion followed by dilation, while closing is dilation followed by erosion:
Opening: $$(f \circ g)(n) = ((f \Theta g) \oplus g)(n)$$
Closing: $$(f \cdot g)(n) = ((f \oplus g) \Theta g)(n)$$
Single-scale morphological filtering may not fully capture signal characteristics, as small scales are sensitive to noise and large scales blur details. Therefore, we employ multi-scale morphological filtering (MMF) with a set of scales $S = \{S_1, S_2, \dots, S_K\}$. The structuring element at scale $S_k$ is obtained by dilating $g$ repeatedly: $$S_k g = g \oplus g \oplus \cdots \oplus g \quad \text{(\(S_k – 1\) times)}$$. The filtered signal at each scale is computed, and a weighted synthesis yields the final output: $$f_g(n) = \sum_{k=1}^{K} \omega_k f_{g_k}(n)$$, where weights $\omega_k = S_k / \sum_{k=1}^{K} S_k$ prioritize larger scales for noise suppression. For on-grid inverter fault signals, we use opening to extract upper-half wave loss and closing for lower-half wave loss, optimizing feature retention.
Incremental learning addresses the challenge of adapting models to new data without retraining from scratch. The iCaRL framework combines representation learning with classifier updates to handle new fault types in on-grid inverters. Key components include:
- Exemplar Set Construction: Using a herding algorithm, representative samples from historical fault classes are selected to preserve knowledge. For a class with feature vector mean $\mu$, the $b$-th exemplar $p_b$ is chosen as: $$p_b = \arg\min_{x \in X} \left\| \mu – \frac{1}{b} \left( \phi(x) + \sum_{j=1}^{b-1} \phi(p_j) \right) \right\|$$ where $\phi(x)$ is the feature vector from the 1D-CNN.
- Knowledge Distillation: To prevent catastrophic forgetting, a distillation loss is added to the cross-entropy loss during training on new data. The total loss for model parameters $\theta$ is: $$l(\theta) = – \sum_{(x_i, y_i) \in D} \left( \sum_{y=s}^{t} \delta_{y=y_i} \log O_y(x_i) + \delta_{y \neq y_i} \log(1 – O_y(x_i)) + \sum_{y=1}^{s-1} q_y^i \log O_y(x_i) + (1 – q_y^i) \log(1 – O_y(x_i)) \right)$$ Here, $O_y(x_i)$ is the model’s predicted probability, $q_y^i$ is the soft target from the old model, and $D$ combines exemplars and new samples.
- Nearest-Mean-of-Exemplars (NME) Classifier: Instead of a softmax classifier, NME assigns labels based on proximity to class means: $$y^* = \arg\min_{y=1,\dots,t} \| \phi(x) – \mu_y \|$$ This maintains balance between old and new classes.
These principles form the backbone of our fault diagnosis system for on-grid inverters, enabling continuous learning and high diagnostic performance.
Proposed Methodology for On-Grid Inverter Fault Diagnosis
Our methodology integrates MMF-based signal processing with an incremental learning pipeline for on-grid inverter fault diagnosis. The process involves data generation, preprocessing, model training, and incremental updates. We focus on open-circuit faults in IGBTs and diodes, which are common in on-grid inverters and can degrade system efficiency if undetected.
Step 1: Data Generation and Preprocessing. We simulate a three-phase on-grid inverter model in MATLAB/Simulink, capturing three-phase output currents under various fault conditions. Fault types include single IGBT open-circuit, double IGBT open-circuit, and single diode open-circuit faults, totaling 27 scenarios. For initial training, we consider 22 IGBT-related faults (including normal operation), and for incremental learning, we add 6 diode open-circuit faults as new classes. Signals are sampled at 10 kHz for 0.2 seconds (2000 points per fault), then segmented using a sliding window of size 200 with a stride of 30, yielding samples of dimension (200, 3). Data augmentation via varying DC-link voltages and power outputs expands the dataset. Each sample is standardized to zero mean and unit variance, then processed with MMF to denoise and enhance features. The MMF parameters are optimized based on correlation coefficients between noisy and clean signals, ensuring robust feature extraction for the on-grid inverter.
Step 2: Model Architecture and Initial Training. We employ a 1D-CNN for feature learning, with the following structure: two convolutional layers (kernel size 5, channels 6 and 16), two max-pooling layers (window size 2), two fully connected layers (256 and 64 neurons), and an NME classifier. Dropout (rate 0.2) is added between fully connected layers to prevent overfitting. The model is trained on historical fault data using Adam optimizer with cross-entropy loss, batch size 32, and 150 epochs. The performance is evaluated on a test set to ensure high accuracy before incremental updates. This initial model serves as the base for diagnosing faults in the on-grid inverter.
Step 3: Incremental Learning Procedure. When new fault types (e.g., diode faults) are introduced, we load the trained model and compute feature vectors for historical data. Exemplars are selected using the herding algorithm, with a fixed memory budget (e.g., 600 samples total). The loss function is updated to include distillation loss as in Equation (10), and the model is retrained on a combined dataset of exemplars and new fault samples. After training, the NME classifier is updated with new class means. This process allows the on-grid inverter diagnostic system to adapt without forgetting historical faults. The steps are summarized in the table below:
| Step | Action | Description |
|---|---|---|
| 1 | Data Simulation | Generate three-phase current signals for fault types in on-grid inverter. |
| 2 | MMF Processing | Apply multi-scale morphology to denoise and extract features. |
| 3 | Sliding Window Segmentation | Create samples for training and testing. |
| 4 | Initial Model Training | Train 1D-CNN on historical fault data. |
| 5 | Exemplar Construction | Select representative samples using herding algorithm. |
| 6 | Incremental Training | Retrain model with distillation loss on combined data. |
| 7 | Evaluation | Assess accuracy on historical and new fault types. |
This methodology ensures that the on-grid inverter fault diagnosis system remains accurate and adaptable over time, critical for real-world deployments where fault patterns evolve.
Experimental Validation and Results
We validate our approach through simulations, comparing it with traditional methods and assessing performance under noise. The on-grid inverter model parameters are: DC-link voltage $U_{dc} = 700$ V, grid voltage 220 V (RMS), switching frequency 10 kHz, and filter inductance $L_1 = 5$ mH. Faults are injected at random times during operation.
Performance of Multi-Scale Morphological Filtering. To evaluate MMF, we add Gaussian white noise at signal-to-noise ratios (SNRs) of 40 dB, 30 dB, and 20 dB to fault signals and compute correlation coefficients between filtered and clean signals. We compare MMF with Fast Fourier Transform (FFT) and Discrete Wavelet Transform (DWT). Results show that MMF maintains correlations above 0.99 even at 20 dB SNR, outperforming FFT and DWT, which drop to 0.9501 and 0.9600, respectively. This demonstrates MMF’s robustness for on-grid inverter signal processing. The correlation coefficients are summarized in the table below:
| Method | 40 dB SNR | 30 dB SNR | 20 dB SNR |
|---|---|---|---|
| MMF | 0.9996 | 0.9967 | 0.9901 |
| FFT | 0.9952 | 0.9752 | 0.9501 |
| DWT | 0.9974 | 0.9844 | 0.9600 |
Initial Model Accuracy. The 1D-CNN model achieves 99.36% accuracy on historical fault test data after 150 epochs, with loss converging to 0.03. This high performance confirms the effectiveness of MMF-1D-CNN for initial fault diagnosis in on-grid inverters. We also test robustness by adding noise during training; at 20 dB SNR, accuracy remains at 98.32%, compared to 94.49% for a plain 1D-CNN, 88.52% for MLP, and 93.75% for GRU. This highlights the denoising capability of MMF for reliable on-grid inverter diagnostics.
Incremental Learning Results. For incremental learning, we introduce 6 new diode fault classes. Using iCaRL with 600 exemplars, the model is retrained for 300 epochs. The accuracy on historical faults is 97.79%, and on new faults is 98.75%, showing minimal catastrophic forgetting. We compare with Progressive Neural Networks (PNN) and Elastic Weight Consolidation (EWC). PNN maintains historical accuracy at 97.51% but doubles model parameters, while EWC suffers from forgetting, balancing accuracy at only 74.19%. Our method offers a better trade-off, as shown in the table:
| Incremental Method | Model Parameters | Historical Accuracy (%) | New Accuracy (%) |
|---|---|---|---|
| iCaRL (Proposed) | 211,628 | 97.79 | 98.75 |
| PNN | 423,256 | 97.51 | 99.03 |
| EWC | 211,628 | 74.19 | 74.19 |
The loss curves during incremental training indicate stable convergence, with distillation loss effectively preserving old knowledge. These results validate that our incremental learning approach enables the on-grid inverter diagnostic system to adapt to new faults while maintaining high performance on historical ones.
Real-Time Application Considerations. In practice, the on-grid inverter system can implement our method by continuously monitoring three-phase currents, applying MMF preprocessing, and using the trained 1D-CNN for feature extraction. The NME classifier then identifies fault types in real-time. When new fault patterns are detected, the incremental learning module updates the model offline, ensuring minimal downtime. This adaptability is crucial for on-grid inverters in dynamic environments, such as smart grids with varying load conditions.
Conclusion and Future Work
We have presented an incremental learning-based fault diagnosis framework for on-grid inverters, combining multi-scale morphological filtering with a 1D-CNN and iCaRL strategy. This approach addresses the limitations of traditional offline methods by enabling continuous learning of new fault types without catastrophic forgetting. Through simulations, we demonstrated that MMF effectively denoises fault signals, enhancing feature extraction for the on-grid inverter, while incremental learning maintains high accuracy across historical and new faults. Our method achieves over 97% accuracy on both categories and shows robustness under noisy conditions, making it suitable for real-world deployment.
The key contributions include: (1) a robust signal processing technique using MMF for on-grid inverter fault signals; (2) an incremental learning pipeline that adapts to new fault scenarios; and (3) comprehensive validation against benchmarks. Future work will explore extending this framework to other power electronic devices, integrating online learning for real-time updates, and testing with hardware-in-the-loop setups for on-grid inverters. Additionally, we plan to investigate multi-task learning and transfer learning to further enhance the adaptability of fault diagnosis systems. By advancing incremental learning techniques, we aim to contribute to more resilient and intelligent on-grid inverter networks in the era of renewable energy integration.
In summary, the proposed methodology offers a scalable and efficient solution for fault diagnosis in on-grid inverters, paving the way for self-evolving diagnostic systems that can keep pace with the evolving demands of modern power grids. As on-grid inverters become more pervasive, such adaptive approaches will be essential for ensuring reliability and safety in energy systems worldwide.