💻 computer science

Fault Diagnosis for Underwater Vehicles using Moving Horizon Estimation and Gaussian Processes

This paper proposes a robust fault diagnosis framework for underwater vehicles that combines Moving Horizon Estimation with Gaussian Processes to distinguish actuator faults from unmodeled dynamics, enabling accurate detection, isolation, and magnitude estimation validated through laboratory experiments.

Original authors: Fotis Panetsos, Kostas J. Kyriakopoulos

Published 2026-09-16

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Fotis Panetsos, Kostas J. Kyriakopoulos

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

Deep beneath the surface, where sunlight fades and pressure mounts, underwater robots are tasked with some of humanity's most critical missions. From inspecting submerged oil rigs to monitoring fragile marine ecosystems, these machines operate in an environment that is hostile, unpredictable, and unforgiving. A single mechanical failure, such as a thruster losing power, can turn a routine survey into a lost vehicle or a failed mission. Because these robots cannot be easily repaired once deployed, engineers have long sought ways to give them the ability to recognize when something is wrong. The challenge lies in distinguishing a genuine mechanical breakdown from the natural, chaotic noise of the ocean itself. The water pushes and pulls on the vehicle in ways that are difficult to predict perfectly, creating a fog of uncertainty that often masks the early signs of a fault.

To solve this, researchers at New York University Abu Dhabi have developed a new system that allows underwater vehicles to diagnose their own health with remarkable precision, even when the surrounding water behaves in unexpected ways. Their approach combines a mathematical model of how the vehicle should move with a learning system that understands how the vehicle actually moves in the real world. By comparing these two perspectives, the system can isolate the specific signature of a broken thruster from the general chaos of unmodeled water dynamics. In a series of tests inside a large laboratory water tank, the team demonstrated that their method could not only detect when a thruster failed but also pinpoint exactly which one was broken and calculate how much power it had lost, all while the vehicle was moving.

The core of this innovation lies in how the researchers handle the unknown. Traditional methods rely on a perfect mathematical description of the vehicle and its environment. However, in reality, no model is perfect; factors like the shape of the hull, the viscosity of the water, and the presence of debris create small, unpredictable forces that the model cannot account for. These "unmodeled dynamics" often look exactly like a fault to a standard diagnostic system, leading to false alarms or missed detections. The researchers addressed this by using a technique called a Moving Horizon Estimator. Imagine a system that constantly looks back at the last few seconds of the vehicle's movement, comparing its actual path against where the mathematical model predicted it should be. The difference between the two is treated as a "lumped disturbance," a single value that captures everything the model missed, including both the natural noise of the water and any potential mechanical failure.

To separate the noise from the fault, the team introduced a second layer of intelligence using Gaussian Processes. This is a type of machine learning that excels at learning patterns from data while simultaneously measuring how uncertain it is about those patterns. Before any faults occurred, the researchers ran the vehicle through various maneuvers to collect data on how it behaved under normal conditions. They fed this data into the Gaussian Process, which learned to predict the "noise" of the unmodeled dynamics for any given situation. When the vehicle was operating, the system compared the lumped disturbance estimated by the first layer against the Gaussian Process's prediction of what the noise should be. If the difference between the two was small, the vehicle was healthy. If the difference was large and statistically significant, it signaled a problem.

The researchers tested this framework on a small, seven-thruster underwater vehicle known as the VideoRay Defender. They conducted experiments in a water tank measuring 6.3 meters by 3.7 meters, using a camera system to track the vehicle's position with high precision. In the first set of tests, the vehicle was teleoperated, meaning a human pilot controlled its movements via a joystick. The researchers simulated a complete failure in one of the horizontal thrusters by cutting its power. Within two seconds of the failure, the system detected the anomaly, correctly identified the specific broken thruster, and calculated that its effectiveness had dropped to zero. The system achieved this by analyzing the residual signal—the gap between the estimated disturbance and the learned noise prediction—which clearly revealed the fault's signature.

The true test of the system's robustness came during closed-loop experiments, where the vehicle was programmed to follow a specific elliptical path on its own, without human intervention. In these scenarios, the vehicle had to constantly adjust its thrusters to stay on course, creating a complex, dynamic environment. The researchers introduced a partial failure, reducing the power of one thruster to just 25% of its normal capacity. The system successfully identified the fault, isolated the specific thruster, and accurately estimated the remaining power level. Crucially, the team also ran a comparison test where they ignored the unmodeled dynamics and relied only on the raw disturbance estimates. Without the learning component, the system generated false alarms, triggering warnings even when the vehicle was healthy, and failed to accurately measure the severity of the fault. This confirmed that learning the background noise was essential for reliable diagnosis.

The results, validated across multiple scenarios including total thruster failure and partial degradation, show that the proposed framework offers a significant leap forward in underwater robotics safety. By integrating a model-based estimator with a data-driven learning system, the researchers created a diagnostic tool that is both sensitive enough to catch subtle faults and robust enough to ignore the natural turbulence of the ocean. While the current work focuses on single faults and controlled laboratory conditions, the success of this approach suggests a future where underwater vehicles can operate with a higher degree of autonomy and safety, capable of self-diagnosis even in the most challenging and unpredictable environments. The team plans to extend this work to handle multiple simultaneous faults and to adapt the system for use in the open ocean, where environmental disturbances are far more severe.

Technical Summary: Fault Diagnosis for Underwater Vehicles using Moving Horizon Estimation and Gaussian Processes

Problem Statement
Underwater vehicles (UVs) operate in complex environments where actuator faults, particularly in thrusters due to wear, biofouling, or entanglement, pose significant risks to mission safety and success. While Fault Detection and Diagnosis (FDD) techniques exist, they face a critical challenge: distinguishing between actual actuator faults and "unmodeled dynamics" (e.g., hydrodynamic effects, parameter uncertainties, and simplifying assumptions). Model-based approaches often rely on accurate dynamic models; however, discrepancies between nominal models and true system behavior can lead to false alarms or inaccurate fault magnitude estimation. Conversely, data-driven (model-free) approaches often require extensive fault data for training, which is difficult to obtain, and typically lack the ability to provide quantitative estimates of fault severity. The core problem addressed is the development of a robust FDD framework capable of detecting, isolating, and quantifying single actuator faults in the presence of varying unmodeled dynamics without relying on pre-collected fault data.

Methodology
The authors propose a unified, model-based FDD framework that integrates three primary components:

Moving Horizon Estimator (MHE): An MHE is formulated based on the nominal UV dynamics to estimate a "lumped disturbance" vector ( $d$ ). This vector aggregates both unmodeled dynamics ( $d_n$ ) and fault-induced effects ( $d_f$ ). The disturbance is modeled as a random walk, and the MHE solves a constrained optimization problem over a finite receding horizon to provide dynamics-consistent estimates of the total disturbance.
Gaussian Processes (GP): To separate unmodeled dynamics from faults, the authors employ Gaussian Processes (specifically Stochastic Variational Gaussian Processes, or SVGP, for computational efficiency). The GPs are trained only on data collected during fault-free operation. They learn a nonparametric probabilistic representation of the unmodeled dynamics ( $d_n$ ) across diverse operating conditions, providing both a predicted mean and a predictive uncertainty (variance/covariance).
Generalized Likelihood Ratio Test (GLRT): A residual signal is generated by comparing the MHE's lumped disturbance estimate against the GP's prediction of the unmodeled dynamics. Under normal conditions, this residual follows a zero-mean Gaussian distribution defined by the GP's predictive uncertainty. In the presence of a fault, the residual exhibits a non-zero mean. A GLRT is formulated for each thruster to test the hypothesis of normal operation versus a single fault. The test utilizes a moving window of residual data and adapts its threshold based on the state-dependent GP uncertainty. If a fault is detected, the framework provides a Maximum Likelihood Estimate (MLE) of the fault magnitude ( $\lambda_j$ ), representing the loss of effectiveness.

Key Contributions

Robustness to Unmodeled Dynamics: By explicitly modeling unmodeled dynamics using GPs, the framework achieves robustness against model inaccuracies and varying operating conditions, a common failure point in traditional model-based FDD.
Quantitative Fault Estimation: Unlike many classification-based data-driven methods, this approach provides a quantitative estimate of the fault magnitude (loss of thrust effectiveness), not just the fault type.
Adaptive Thresholding: The use of GP predictive uncertainty allows the GLRT to adapt to changing operating conditions, reducing the need for manually tuned, constant thresholds and minimizing false alarms.
Data Efficiency: The method does not require fault data for training the GP models, as it learns only the nominal unmodeled dynamics. Fault detection relies on statistical deviations from this learned baseline.
Experimental Validation: The methodology was experimentally validated on a VideoRay Defender vehicle in a laboratory water tank under both open-loop (teleoperation) and closed-loop (trajectory tracking) control scenarios.

Experimental Results
The framework was tested in a 6.3m × 3.7m water tank using a VideoRay Defender equipped with seven thrusters.

Teleoperation (Open-Loop): Experiments involving complete failure of Thruster 2 and Thruster 3 demonstrated that the GLRT statistic successfully exceeded the detection threshold approximately 2 seconds after fault injection. The MLE accurately converged to the true fault magnitude ( $\lambda=0$ ).
Closed-Loop Control: The system was tested while tracking an ellipsoidal trajectory. Faults were introduced at $t=65$ s, including complete failure ( $\lambda_0=0$ ), partial failure ( $\lambda_0=0.25$ ), and intermediate loss ( $\lambda_0=0.5$ ). The framework successfully detected and isolated the faults and estimated their magnitudes.
Comparative Analysis: A comparison was performed where unmodeled dynamics were ignored (residuals based solely on MHE). This baseline approach resulted in false alarms prior to fault injection and inaccurate fault magnitude estimation. This confirmed that the GP-based approximation of unmodeled dynamics is essential for reliable performance.
Computation: The MHE optimization and SVGP inference were executed in real-time (approx. 7.8 ms and 20.2 ms, respectively) on a standard workstation with an NVIDIA RTX 4090 GPU.

Significance and Claims
The paper claims that the proposed methodology enables reliable fault detection, isolation, and quantitative severity estimation for underwater vehicles even when the vehicle dynamics are imperfectly modeled. The integration of MHE and GPs allows the system to distinguish between inherent modeling errors and actual actuator failures, thereby reducing false alarms and improving diagnostic accuracy. The authors emphasize that this approach is particularly valuable for safety-critical missions where fault data is scarce and operating conditions are variable.

Future Work
The authors identify three primary directions for future research:

Extending the framework to handle the simultaneous occurrence of multiple faults.
Incorporating significant environmental disturbances by implementing online GP training with a safe update mechanism.
Integrating the FDD framework with an active fault-tolerant control scheme to enhance overall control performance.

Technical Summary: Fault Diagnosis for Underwater Vehicles using Moving Horizon Estimation and Gaussian Processes

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