# Ultrasound-based Condition Monitoring of Power Converters with Physics-Informed Compression

Youssof Fassi, Vincent Heiries, J. Boutet, Julien Marianne, Sébastien Martin, Mathilde Chareyron, Clément Chambon, Sébastien Boisseau

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Youssof Fassi, Vincent Heiries, J. Boutet, Julien Marianne, Sébastien Martin, et al. Ultrasound-based Condition Monitoring of Power Converters with Physics-Informed Compression. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0144. hal-05105944

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# Ultrasound-based Condition Monitoring of Power Converters with Physics-Informed Compression

Youssof Fassi¹, Vincent Heiries¹, Jérôme Boutet¹, Julien Marianne², Sébastien Martin¹, Mathilde Chareyron¹, Clément Chambon¹, Sébastien Boisseau¹

¹CEA-Leti, Université Grenoble Alpes

²SERMA INGENIERIE

17, Avenue des Martyrs, F-38000
Grenoble, France

Tel.: +33 4 38 78 64 91

E-Mail: youssof.fassi@cea.fr

URL: http://www.cea.fr

## Acknowledgements

This work is part of the IPCEI Microelectronics and Connectivity and was supported by the French Public Authorities within the frame of France 2030.

<figure><img src="image_2.png" /></figure>

## Keywords

«Condition monitoring»; « AC-DC converter»; «Vibration»; « Multi-objective optimization»; «Physics-Informed Machine Learning».

## Abstract

Condition monitoring of power converters is vital but challenging due to sensor invasiveness and high computational demands. This paper introduces a non-invasive ultrasound-based approach using CNN autoencoders with a physics informed loss function for efficient data compression, outperforming traditional wavelet methods, enhancing data storage needs, and improving diagnostic feature extraction.

## Introduction

Power converters are integral to modern electrical systems, ensuring efficient power conversion and distribution. Their reliable operation is crucial for the stability of various applications, from industrial machinery to renewable energy systems. As such, condition monitoring of power converters is essential for early detection of faults and preventing unscheduled downtimes [1, 2]. Traditional monitoring techniques, however, often involve invasive sensors that can interfere

with normal operations, or are difficult to implement on an existing, on-the-field power converter [3]. Other methods rely on indirect measurements but come at the cost of a computationally heavy estimation process [4, 5]. Furthermore, the sheer volume of data generated, particularly at high sampling rates, poses significant challenges for storage and analysis. These issues are exacerbated when monitoring high-frequency signals like ultrasounds, which are gaining attention for their non-invasive nature and high sensitivity to incipient faults.

Ultrasound-based condition monitoring has been successfully applied in various industries, such as non-destructive evaluation (NDE) and monitoring of rotating machinery [6-10]. Despite its potential, its application to power converters remains relatively unexplored. Ultrasound signals, when properly analyzed, can provide valuable insights into the health of power converters without requiring intrusive sensor installations. Previous work by the authors [11] has demonstrated a strong correlation between ultrasound features and power converter efficiency, highlighting its viability as a non-invasive diagnostic tool.

Advancements in data compression techniques, particularly through deep learning models like Convolutional Neural Networks (CNNs), offer promising solutions to the challenges of large data volumes. CNN-based autoencoders can efficiently compress high-dimensional data while preserving critical features, making them suitable for handling ultrasound signals in condition monitoring applications [12-14].

This paper investigates the use of CNN-based autoencoders for compressing ultrasound signals acquired from power converters. The goals are twofold: to enhance data storage efficiency and to
develop compressed representations that retain essential features for diagnostic and prognostic purposes. We will compare the performance of different compression models, including those trained with a custom loss function that incorporates correlation information, against traditional methods such as wavelet compression. The remaining of this work is organized as follows: Section 2 details the proposed compression model and its implementation. Section 3 describes the experimental setup, including the characterization test bench used for signal acquisition. Section 4 presents the results of our experiments, focusing on reconstruction error and the model's generalization capability. Finally, Section 5 concludes the paper and discusses future research directions.

## Ultrasound for Non-Invasive Condition Monitoring

The high sampling frequency of ultrasound signals results in substantial data volumes, necessitating efficient compression methods. Our approach employs a CNN-based autoencoder leveraging its ability to learn compact, informative representations of the input data.

### Autoencoder Architecture

Autoencoders are a class of neural networks designed for unsupervised learning, aiming to encode input data into a latent representation and then reconstruct the original input from this encoding. They consist of three main components: an encoder, which compresses the input into a lower-dimensional latent space; a latent space representation, which serves as the compressed data; and a decoder, which

reconstructs the input from this latent representation using transposed convolution (deconvolution) layers, mirroring the encoder's architecture [15-17].

In our approach, we use a 1D CNN architecture (Figure 1) for both the encoder and the decoder due to its ability to preserve local features in time-series data. This type of network is well-suited for time-series compression tasks, though we introduce several modifications to optimize it for our specific application.

To ensure high-quality signal compression, we employ convolutional layers with padding and strides instead of pooling layers. While pooling layers – commonly used in traditional CNNs, such as max-pooling and average-pooling – reduce dimensionality by aggregating values within a kernel, they can discard important features from the signal, and they are rather more suited for classification tasks [18]. Strided convolutions, by contrast, achieve dimensionality reduction through the step size with which the convolutional kernel moves across the input feature map. By increasing the stride, the output dimensions are reduced without explicitly discarding information within each kernel. The convolutional operation can be described as:

$$y(t) = \sigma \left( \sum_{k=0}^{K-1} x(t+k) \cdot w(k) + b \right) \quad (1)$$

where $x(t)$ is the input signal, $w(k)$ represents the kernel weights, $K$ is the kernel size, $b$ is the bias term, and $y(t)$ is the output signal after performing the convolution operation and the activation function $\sigma$. The stride determines the step size for the kernel as it moves across the input. The operation can be expressed as (2):

<figure><img src="image_3.png" /><figcaption>Figure 1: Proposed ultrasounds compression architecture</figcaption></figure>
$$y(t) = \sigma \left( \sum_{k=0}^{K-1} x(t.s + k) \cdot w(k) + b \right) \quad (2)$$

The convolution operation described here applies to a single layer. As additional layers are stacked, this operation is repeated, with the outputs of one layer serving as inputs to the next, thus progressively reducing the temporal dimension and extracting low level features from the input signal.

When considering strides, the most commonly used value is 2, since it mimics pooling's effect on dimensionality reduction, without significant information loss. However, to achieve higher compression ratios without excessively increasing the network depth, which is crucial for developing an embeddable solution, we employ a stride of 4. This approach allows us to reduce the size of the temporal dimension by a factor of 4 at each convolutional pass, while maintaining a manageable network depth. The dimension of the latent space influences also the compression factor, contributing to the overall compression ratio achieved by the network. This relationship can be expressed as:

$$CR = \frac{N_{input}}{N_{latent}} \quad (3)$$

where *CR* is the compression ratio, *N* is the number of input data points, and *N latent* is the size of the latent space after encoding. We use a kernel size of 9, functioning as the size of the sliding window, and create different networks by stacking convolutional layers to achieve the desired compression ratios, ranging from 8 to 128. By comparison, the most commonly known audio signal compression ratios range from 6 to 10.

## Loss function optimization

To ensure high-quality signal reconstruction, we use the Mean Squared Error (MSE) as the primary loss function, augmented with a custom component that incorporates correlation information to better preserve the signal characteristics. The combined loss function is defined as in equation (1):

$$\mathcal{L}(x, \hat{x}) = \text{MSE}(x, \hat{x}) + \alpha \times \text{corr}(x, \hat{x}) \quad (4)$$

where *x* is the original signal, *x̂* is the reconstructed signal, and *α* is a hyperparameter that balances the two components. The hyperparameter is tuned using a multi-objective loss balancing strategy [19], ensuring that each component contributes approximately equally to the overall loss during training. This approach is found to ensure minimal information loss during compression and to maintain the integrity of the reconstructed signal.

The MSE component of the loss function is:

$$\text{MSE}(x, \hat{x}) = \frac{1}{N} \sum_{i=1}^{N} (x_i - \hat{x}_i)^2 \quad (5)$$

where *N* is the number of samples, *x*<sub>*i*</sub> is the i-th sample of the original signal, and *x̂*<sub>*i*</sub> is the i-th sample of the reconstructed signal.

The correlation component of the loss function is designed to penalize the deviation from perfect correlation value of 1. This ensures that the reconstructed signal maintains the same trends and patterns as the original signal. The correlation loss function, in the Pearson sense, is computed as:

$$\text{corr}(x, \hat{x}) = \left( 1 - \frac{\sum_{i=1}^{N} (x_i - \mu_x)(\hat{x}_i - \mu_{\hat{x}})}{\sigma_x \sigma_{\hat{x}}} \right)^2 \quad (6)$$

where $\mu_x$ and $\mu_{\hat{x}}$ are the mean of the signals *x* and *x̂* respectively, $\sigma_x$ and $\sigma_{\hat{x}}$ are their standard deviations.

We chose the Pearson correlation coefficient over other measures because it specifically captures the linear relationship between the original and reconstructed signals. Since our goal is to reconstruct the exact same signal as the input, a linear correlation measure is both sufficient and more constraining. The linear correlation coefficient forces the neural network to focus on preserving the original signal's structure in a linear sense, ensuring that the reconstructed signal is not just correlated, but nearly identical to the input.

Using a non-linear correlation measure, while potentially capturing more complex relationships, could allow the network to reconstruct a signal that is different from the input yet still maintains some form of non-linear correlation. This could result in a reconstruction that, while mathematically related, deviates from the original signal's actual form. By using Pearson's linear correlation, we guide the network more effectively toward accurately reproducing the
input signal, thereby enhancing the fidelity of the reconstruction.

## Experimental Setup

For this study, we employed a flyback topology rectifier as the power converter (UCC24630EVM-636). The ultrasound signals, generated intrinsically by the vibration of the magnetic core components during converter operation, were acquired with a Brüel & Kjær 4138-A-015 probe, positioned at a 9 cm distance from the power converter to maintain the non-invasiveness. The generated ultrasound signals are continuous and typically cover a frequency range of [50-130 kHz]. Sampling is made at a frequency of 500 kHz to capture high-frequency ultrasound signals, without the need for externally injected ultrasounds, unlike other Prognostics and Health Management (PHM) techniques.

This approach is particularly interesting because it leverages the natural ultrasound signature of the power converter itself during operation. This represents a significant leap in the power converter field, as it allows for truly passive and non-invasive condition monitoring. By relying solely on the converter's inherent acoustic emissions, we eliminate the need for active signal injection, thereby reducing the overall power consumption and complexity of the monitoring system. It also enhances the reliability of monitoring, as it captures the authentic operational characteristics of the converter, leading to more accurate diagnostics.

The experimental setup (Figure 2) includes a custom-designed adaptive power load circuit, emulating an RLC type of load, which includes resistive, inductive, and capacitive components. Unlike purely resistive loads, this RLC configuration more accurately represents the types of loads encountered in real-world applications, such as those in automotive systems.

<figure><img src="image_4.png" /><figcaption>Figure 2: Experimental setup, the ultrasound probe goes on top of the device under test that is covered in operation</figcaption></figure>

By incorporating these elements, the setup is able to capture the dynamic responses typical of power converters operating under varying conditions. The power load circuit can also target different power operating levels, capturing the dynamic behavior of the converter as it transitions between them. Specifically, we acquired continuous signals at 80%, 100%, and 120% of the nominal output power. For each power level, the signals were captured over a duration of 5 seconds, as these recordings reflect the power converter's operation as it transitions between the power levels, showcasing the switching patterns and variations.

Figure 3 presents a typical ultrasound signal captured during one of these transitions, as the power converter moves from 80% of nominal output power to a 100%.

<figure><img src="image_5.png" /><figcaption>Figure 3: Time-domain signal of the captured ultrasound, measured in Pascals, illustrating switching dynamics from 80% to 100% of nominal power</figcaption></figure>

The data acquisition is conducted using a Spectrum MX4963 card controlled by a LabVIEW script. This script manages both the command and control operations: it sets the power converter to the desired power levels and simultaneously acquires the ultrasound signals. Before analysis, the acquired signals are linearly conditioned and normalized to maximize the resolution and improve the digitization of the acquired signals.

## Results

We evaluate the performance of the CNN-based autoencoder by comparing it with traditional wavelet compression. For different compression ratios, we evaluate the compression strategies with respect to the reconstruction fidelity, measured by MSE. Additionally, we test the
model's generalization capability by assessing its performance across different power levels. We evaluate the performance of the CNN-based autoencoder by comparing it with traditional wavelet compression. For different compression ratios, we evaluate the compression strategies with respect to the reconstruction fidelity, measured by MSE. Additionally, we test the model's generalization capability by assessing its performance across different power levels.

## Compression factor analysis

In this section, we analyze the performance of the proposed CNN-based autoencoder by varying the compression factor from 8 to 128. For comparison, we also evaluate the compression performance of the classical wavelet method. Wavelet compression, specifically using the Discrete Wavelet Transform (DWT), offers significant advantages due to its ability to perform time-scale analysis, capturing local patterns in the time and frequency domains. This makes it particularly effective for analyzing non-stationary signals like those encountered in condition monitoring.

The DWT works by decomposing the signal into different frequency bands using a mother wavelet, allowing for multi-resolution analysis. The most significant levels of decomposition are selected based on the desired compression ratio, and then the compressed signal is reconstructed by applying the inverse transform. In our study, we used the Daubechies wavelet family, which showed lower reconstruction error compared to other wavelet families. Specifically, the Daubechies 4 (db4) wavelet with 8 levels of decomposition was chosen for its superiority in capturing signal characteristics while minimizing distortion during reconstruction.

We compare the reconstruction error, measured using the root mean squared error (RMSE), the mean absolute error (MAE), and the coefficient of determination R², for models trained with the standard MSE loss, the custom loss function that incorporates correlation information, and the wavelet compression method with the db4 wavelet.

<table><caption>Table 1: Performance Metrics for MSE, Proposed, and Wavelet Methods</caption><thead><tr><th rowspan="2">CR</th><th colspan="3">MSE Loss</th><th colspan="3">Proposed Loss</th><th colspan="3">Wavelet</th></tr><tr><th>RMSE (x10<sup>-4</sup>)</th><th>MAE (x10<sup>-4</sup>)</th><th>R<sup>2</sup></th><th>RMSE (x10<sup>-4</sup>)</th><th>MAE (x10<sup>-4</sup>)</th><th>R<sup>2</sup></th><th>RMSE (x10<sup>-4</sup>)</th><th>MAE (x10<sup>-4</sup>)</th><th>R<sup>2</sup></th></tr></thead><tbody><tr><td>8</td><td>0.78</td><td>0.58</td><td>0.987</td><td>0.77</td><td>0.56</td><td>0.987</td><td>5.4</td><td>4.4</td><td>0.491</td></tr><tr><td>16</td><td>0.84</td><td>0.65</td><td>0.985</td><td>0.82</td><td>0.63</td><td>0.985</td><td>6.4</td><td>5.3</td><td>0.304</td></tr><tr><td>32</td><td>0.88</td><td>0.67</td><td>0.983</td><td>0.86</td><td>0.64</td><td>0.984</td><td>7</td><td>6</td><td>0.169</td></tr><tr><td>64</td><td>1.3</td><td>1</td><td>0.961</td><td>1.1</td><td>0.83</td><td>0.976</td><td>7.3</td><td>6.3</td><td>0.083</td></tr><tr><td>128</td><td>3</td><td>2.3</td><td>0.806</td><td>2.4</td><td>1.8</td><td>0.876</td><td>7.5</td><td>6.7</td><td>0.033</td></tr></tbody></table>

Table 1 shows that at lower compression factors (8 to 32), both the standard loss and the custom loss perform similarly and significantly better than the wavelet compression method. However, at higher compression factors (128), the custom loss function provides a noticeable improvement, with a reduction in both RMSE and MAE of 20% compared to the standard loss, indicating that the correlation information becomes increasingly beneficial at higher compression rates. The wavelet compression method, while deterministic with no training needs, does not offer the same level of feature extraction or adaptability to varying compression ratios and exhibits higher errors, highlighting the advantage of the deep learning-based approach.

## Generalization capability

We evaluate the model's robustness to imbalance in the training data by testing its ability to generalize from predominantly one power level. Specifically, using a network with a compression ratio of 64, the model is trained primarily on the 80% power level data, with small percentages of the 120% power level data varying between 5% and 30%. It is then tested exclusively on 120% power data.

We assess the model's ability to generalize by evaluating its robustness to imbalanced training data, where the training and testing datasets correspond to two distinct power domains. These domains are defined by the central frequencies of the power levels: the 80% power level, with a
central frequency of 120 kHz, and the 120% power level, with a central frequency of 124 kHz. Using a network with a compression ratio of 64, the model is predominantly trained on the 80% power level data, with small percentages of 120% power level data varying between 5% and 30%. The model is then tested exclusively on data from the 120% power domain.

This setup is particularly challenging for neural networks [20-21], as the imbalance in the training data makes it more challenging for the model to learn representations of the underrepresented power domain.

<table><caption>**Table 2: Performance Metrics for MSE, Proposed, across imbalanced training data**</caption><thead><tr><th rowspan="2">Imbalance</th><th colspan="3">MSE Loss</th><th colspan="3">Proposed Loss</th></tr><tr><th>RMSE (x10<sup>-4</sup>)</th><th>MAE (x10<sup>-4</sup>)</th><th>R<sup>2</sup></th><th>RMSE (x10<sup>-4</sup>)</th><th>MAE (x10<sup>-4</sup>)</th><th>R<sup>2</sup></th></tr></thead><tbody><tr><td>5%</td><td>6,89</td><td>5,57</td><td>0,387</td><td>4,12</td><td>3,2</td><td>0,773</td></tr><tr><td>10%</td><td>5,74</td><td>4,61</td><td>0,551</td><td>1,87</td><td>1,39</td><td>0,949</td></tr><tr><td>20%</td><td>4,74</td><td>3,55</td><td>0,673</td><td>1,62</td><td>1,25</td><td>0,96</td></tr><tr><td>30%</td><td>1,73</td><td>1,34</td><td>0,948</td><td>1,41</td><td>1,1</td><td>0,969</td></tr></tbody></table>

The results in Table 2 show that the autoencoder trained with the custom loss function exhibits better generalization capability, maintaining lower reconstruction errors even with a significant imbalance in the training data. Specifically, the model does not require extensive data from each power level to perform well.

Figure 4 illustrates that as the proportion of 120% power data in the training set increases, the model's ability to reconstruct 120% power data improves. Notably, with as low as 10% of the 120% power data included in training, the network trained with the custom loss function achieves a significant improvement in reconstruction performance, as indicated by the R² metric.

<figure><img src="image_6.png" /><figcaption>**Figure 4: R² comparison of the two methods across the imbalance percentages of the 120% power level data**</figcaption></figure>

Looking at the frequency content of the reconstructions, the proposed model demonstrates its ability to maintain the frequency content of the signal under imbalanced power conditions, as highlighted in Figure 5. The spectrograms reveal that the custom loss function not only enhances overall reconstruction performance but also preserves frequency-domain features at 120% power. Interestingly, the network is not explicitly constrained during training by any frequency-domain information—it is entirely agnostic to frequency. However, by introducing a time-domain correlation constraint in the proposed loss, the network implicitly learns the frequency representation of a different power level with close but nonetheless distinct frequency characteristics. Not only was the frequency content preserved, but the signal amplitudes were also retained. In contrast, the network trained solely with the standard MSE loss failed to maintain both the spectral content and the signal amplitudes, leading to significant distortions in the reconstructed signal, with amplitudes reduced by several orders of magnitude. This shows the effectiveness of the correlation term in aligning the latent space features with both time and spectral domain characteristics of the signal across power levels. By doing so, the custom loss function also enables the model to bridge gaps between distinct power levels with varying frequency content.

This characteristic is particularly valuable in scenarios where acquiring extensive data at each power level is expensive, and time-consuming, and practically challenging.
Power converters often face such challenges, making it valuable for models to generalize from limited and uneven datasets. The proposed loss

function addresses this issue, ensuring reliable performance under significant data imbalances.

<figure><img src="image_7.png" /><figcaption>Figure 5: Comparative analysis of power spectral density (Pa²/Hz) at 120% of nominal power load for target and model outputs, trained under 10% of imbalance</figcaption></figure>

In practical implementation, our CNN-based autoencoder not only has merits in data compression and feature extraction, it also maintains a lightweight architecture. The largest model, which achieves the highest compression ratio of 128 is just at 32 KB in size. The model is light enough to fit on commercial DSPs like the NUCLEO-G474RE and the LAUNCHXL-F28379D which are standard commercial DSPs. The compact nature of the model also ensures efficient deployment across various hardware platforms, mitigating portability issues and making it highly adaptable to diverse industrial settings.

In addition to its compact size, the CNN architecture inherently reduces both training and inference times, offering a clear advantage over

using other sequential units like LSTMs or GRUs, without compromising performance.

Moreover, due to the hierarchical nature of CNNs, which allows for automatic learning of temporal features from raw data, our approach is well-suited for extracting patterns in high-dimensional data. This structured feature extraction contrasts with traditional machine learning techniques like Support Vector Machines (SVMs), which typically rely on manually crafted features. This way, our CNN-based approach is capable of achieving high compression ratios while maintaining the reconstruction accuracy.
Conclusion

Efficient compression of ultrasound signals using
CNN-based autoencoders offers a viable solution
for non-invasive condition monitoring of power
converters. This approach addresses key
challenges in data storage and processing,
providing a foundation for advanced diagnostic
and prognostic tools.

To enhance the model's generalization capability,
we employed a custom loss function that balances
the network's performance across different
operating conditions. This approach helps prevent
overfitting, particularly in cases of limited or
imbalanced training data, and ensures robust
reconstruction accuracy.

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