💻 computer science

Domain-Shift Aware Neural Networks for Unbalance Characterization in Rotating Systems

This paper proposes a domain-shift aware neural network utilizing a maximum mean discrepancy strategy to accurately estimate unbalance masses in rotating shafts under varying operating conditions, demonstrating improved prediction accuracy in Structural Health Monitoring scenarios where physical behaviors and domain discrepancies are not fully known.

Original authors: Bernardo Feijó Junqueira, Claudio Kiyoshi Umezu, Bruno Bilhar Karaziack, Tomaz Junior, Daniel Alves Castello

Published 2026-06-19

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Bernardo Feijó Junqueira, Claudio Kiyoshi Umezu, Bruno Bilhar Karaziack, Tomaz Junior, Daniel Alves Castello

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to teach a robot to guess how heavy a backpack is just by listening to the sound of a person walking.

The Problem: The "Different Shoes" Dilemma
Usually, you'd train the robot in a quiet gym with the person wearing smooth sneakers (the Source). You show it thousands of examples: "This sound means a 5kg backpack; this sound means a 10kg backpack." The robot learns the pattern.

But then, you send the robot to a real job site where the person is wearing heavy, clunky boots and walking on gravel (the Target). The sounds are different. The background noise is louder. The robot, trained only on the gym sounds, gets confused. It might think a light backpack is heavy because the boots are loud, or it might fail completely because the "noise" of the boots looks like a different kind of weight to it. In the world of engineering, this is called Domain Shift. The robot's training data doesn't match the real-world conditions.

The Solution: The "Universal Translator"
This paper introduces a special kind of "smart robot" (a neural network) designed to handle this exact problem. Instead of just memorizing the gym sounds, this robot learns to find the core essence of the sound that stays the same, no matter what shoes the person is wearing.

The researchers call this a Domain-Shift Aware Neural Network. Here is how it works, using a simple analogy:

Two Rooms, One Teacher: Imagine two rooms.
- Room A (Source): Has labeled backpacks (you know exactly how heavy they are).
- Room B (Target): Has unlabeled backpacks (you don't know the weight, and the room is noisy).
The Shared Brain: The robot has a "brain" (a neural network) that looks at the sounds from both rooms.
The "MMD" Trick: The robot uses a special mathematical tool called Maximum Mean Discrepancy (MMD). Think of this as a "similarity detector." It constantly checks: "Do the sounds from Room A and Room B look the same to my brain?"
- If the robot sees a sound from Room A and a sound from Room B that feel different, it adjusts its brain to make them feel more similar.
- It forces the robot to ignore the "noise" of the boots and focus only on the "weight" of the backpack.
The Result: The robot learns a universal language of weight. When it hears the clunky boots in Room B, it can still accurately guess the backpack's weight because it learned to ignore the shoe noise and focus on the core vibration.

The Experiment: A Spinning Shaft
The researchers tested this on a real machine: a spinning metal shaft (like a motor or a fan).

The Goal: Guess how much extra weight (unbalance) was stuck to the spinning shaft just by listening to its vibrations.
The Twist: They trained the robot on a "clean" shaft (Source). Then, they tested it on a "messy" shaft where a second motor was running nearby, creating extra vibrations and noise (Target). This mimics a real factory where many machines are running at once.

What They Found

At Low Speed (500 RPM): The machine was spinning so slowly that the vibrations were weak and quiet. The robot struggled to hear the difference between the "weight" and the background noise. Even with the special "Universal Translator" trick, it couldn't guess the weight well. It was like trying to hear a whisper in a library; there just wasn't enough signal.
At Medium Speed (1000 RPM): This was the sweet spot. The vibrations were loud and clear. The robot used the "Universal Translator" to ignore the extra noise from the second motor and guessed the weight with incredible accuracy (almost perfect).
At High Speed (2000 RPM): The machine was spinning very fast. The vibrations were huge, but they also got complicated and chaotic (like a storm). The robot still did a great job, though slightly less perfect than at medium speed, because the chaos made it harder to isolate the specific "weight" signal.

The Big Takeaway
Without this special "Universal Translator" trick, the robot failed miserably in the noisy environment. It would guess wildly wrong numbers. But with the trick, it learned to adapt.

The paper concludes that this method works very well for Structural Health Monitoring (checking if machines are healthy) when the machine you are testing is slightly different from the one you trained on. It proves that you can teach a computer to understand a machine's "heartbeat" even if the machine is in a noisy, different environment, as long as you teach it to ignore the differences and focus on the similarities.

In short: They taught a computer to ignore the "background noise" of a new environment so it could accurately measure a spinning machine's weight, even when it had never seen that specific environment before.

Technical Summary: Domain-Shift Aware Neural Networks for Unbalance Characterization in Rotating Systems

Problem Statement
This work addresses a critical limitation in Structural Health Monitoring (SHM) for rotating machinery: the degradation of supervised machine learning models when deployed under operational conditions that differ from their training data (domain shift). In practical SHM scenarios, obtaining labeled data for all possible structural states and operating conditions is often infeasible. Consequently, models trained on a "source" domain (e.g., a specific machine or operating regime) frequently fail to generalize to a "target" domain (e.g., the same machine under different loads, speeds, or structural configurations) due to distribution mismatches. Specifically, this paper investigates the regression task of estimating unbalance mass levels in rotating shafts when the target domain exhibits domain discrepancies caused by the activation of a secondary, coupled shaft, which introduces complex dynamic interactions and noise not present in the training data.

Methodology
The authors propose a Domain-Shift Aware Neural Network based on a domain adaptation framework utilizing Maximum Mean Discrepancy (MMD). The methodology is structured as follows:

Experimental Setup: Data was collected from a laboratory test rig featuring a primary shaft driven by an electric motor and a secondary shaft coupled via a belt. The primary shaft carried controlled unbalance masses (ranging from 0g to 10.8g) at a fixed radial distance. Domain discrepancy was introduced by activating the secondary shaft, creating a "target" domain with different dynamic characteristics compared to the "source" domain (primary shaft only). Tests were conducted at three rotational speeds: 500, 1000, and 2000 RPM.
Data Processing: Raw triaxial accelerometer signals were segmented into non-overlapping windows. Features were constructed by concatenating time-domain signals with the magnitude of their Fast Fourier Transform (FFT) to capture both temporal and spectral characteristics. Data was normalized using statistics derived exclusively from the source domain to prevent information leakage.
Model Architecture: A shared one-dimensional Convolutional Neural Network (CNN) backbone processes inputs from both source and target domains. The network consists of three convolutional blocks, global average pooling, and fully connected layers, outputting a scalar unbalance estimate.
Training Objective: The model is trained using a composite loss function:
$L(\theta) = L_{data}(\theta) + \lambda L_{MMD}(\theta)$
Where $L_{data}$ is the Mean Squared Error (MSE) computed only on labeled source samples, and $L_{MMD}$ is the Maximum Mean Discrepancy loss computed on the latent feature representations of both source and target domains. The MMD loss, utilizing a Student's t-kernel, minimizes the distance between the source and target feature distributions in a Reproducing Kernel Hilbert Space (RKHS). A progressive weighting scheduler (sigmoid-based) is employed to gradually increase the influence of the MMD loss during training, ensuring stable feature learning before enforcing domain alignment.

Key Contributions

Application to Regression in SHM: While domain adaptation is well-explored for fault classification (e.g., bearing fault diagnosis), this work investigates its application to regression tasks (quantitative unbalance estimation), a comparatively underexplored area in SHM literature.
Experimental Validation of Domain Shift: The study provides a controlled experimental framework where domain shift is induced by a secondary mechanical component, allowing for a rigorous assessment of model generalization under physically realistic discrepancies.
Analysis of Operating Regimes: The paper systematically evaluates model performance across low (500 RPM), medium (1000 RPM), and high (2000 RPM) speeds, revealing how rotational speed and signal-to-noise ratios influence the efficacy of domain adaptation.

Results
The performance of the proposed MMD-based model was compared against a baseline model trained solely on source data (without domain alignment, $\lambda=0$ ).

Low-Speed Regime (500 RPM): The model exhibited limited generalization. The low centrifugal forces resulted in weak dynamic signatures and low signal-to-noise ratios, leading to poor feature separability. Even with MMD alignment, the model struggled to distinguish unbalance levels, with the baseline model failing completely (negative $R^2$ ).
Medium-Speed Regime (1000 RPM): This regime yielded the best performance. The model achieved high predictive accuracy with an $R^2$ of 0.9949 (balanced target) and 0.9914 (unbalanced target). The MMD strategy effectively aligned source and target distributions while preserving discriminative features, significantly outperforming the baseline (which showed large dispersion and negative $R^2$ ).
High-Speed Regime (2000 RPM): The model maintained strong generalization ( $R^2 \approx 0.98$ ), though performance slightly degraded compared to 1000 RPM. The authors attribute this to increased nonlinear dynamic effects and harmonic complexity at higher speeds, which introduced additional variability.
Impact of Domain Discrepancy: In all regimes, the presence of an unbalanced secondary shaft (increasing domain discrepancy) reduced accuracy compared to the balanced target condition. However, the domain-shift aware model consistently outperformed the baseline, demonstrating that explicit distribution alignment is crucial for cross-domain regression.

Significance and Claims
The paper claims that explicitly addressing domain shift through MMD-based regularization significantly improves the robustness of regression models in SHM when target data is unlabeled and operational conditions differ from training data. The study highlights that the success of such models is contingent upon the quality of the dynamic excitation; sufficient signal energy and separability (as seen at 1000 RPM) are prerequisites for effective domain adaptation.

The authors maintain a modest stance, noting that their conclusions are specific to the experimental setup and operating conditions. They emphasize that while the approach demonstrates feasibility, it is not universally generalizable without considering specific noise levels, excitation regimes, and mechanical configurations. The work serves as a proof-of-concept for applying domain-adaptive regression strategies to unbalance characterization, suggesting that future research could explore varying unbalance radii and integrating physics-informed modeling to further enhance robustness.

Technical Summary: Domain-Shift Aware Neural Networks for Unbalance Characterization in Rotating Systems

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