Nonlinear System Identification and Fault Diagnosis in Mechanical Systems

Mechanical systems often exhibit complex behaviours arising from material nonlinearities, component interactions and varying operating conditions. Nonlinear system identification seeks to construct mathematical models that capture these behaviours more accurately than linear approximations, enabling improved simulation, control and prediction. Fault diagnosis complements identification by detecting, isolating and characterising deviations from normal operation before catastrophic failure occurs. Contemporary approaches integrate physics-based models with data-driven techniques, employing time-domain analyses, frequency-domain transforms and machine learning. Nonlinear frequency response methods reveal harmonics and intermodulation products that signal emerging faults, while modern regression and neural-network frameworks exploit large datasets for adaptive modelling. Crucially, the interconnection of system identification and fault diagnosis facilitates real-time monitoring, predictive maintenance and enhanced reliability across rotors, bearings, turbines and robotic drives. Global interest has surged in developing robust schemes that accommodate environmental disturbances, limited data and evolving fault signatures, thereby underpinning the industrial transition to zero-downtime and smart maintenance regimes.

Research from Nature Portfolio

A novel diagnostic strategy for closed-loop industrial robot drives employs nonlinear spectra derived from output frequency response functions. By modelling the robot’s permanent magnet synchronous motor in differing health states, high-order spectral distributions are extracted via batch data-driven NOFRF analysis. Comparative evaluation in both simulation and real-world closed-loop settings demonstrates that these nonlinear spectral features surpass conventional signal-based indicators, achieving superior accuracy in detecting torque loss faults and power-train anomalies.

Nonlinear System Identification and Fault Diagnosis in Mechanical Systems publication trend

The graph below shows the total number of articles in nonlinear system identification and fault diagnosis in mechanical systems across all publications each year (not limited to Nature Index journals).

Technical terms

Nonlinear system identification: Construction of mathematical models that capture input–output relationships in systems whose responses deviate from superposition and homogeneity.

Fault diagnosis: Process of detecting, localising and characterising abnormal conditions or component failures within a mechanical system.

Nonlinear output frequency response function (NOFRF): Frequency-domain representation of system output that reveals higher-order harmonics and nonlinear coupling effects under sinusoidal excitation.

Nonlinear autoregressive model with exogenous inputs (NARX): A discrete-time model form using past outputs and external inputs to predict current system behaviour in a nonlinear framework.

Regularization: Incorporation of prior knowledge or penalty terms in model estimation to improve robustness and prevent overfitting, especially under noisy or limited data conditions.

References

1. On-line condition monitoring for rotor systems based on nonlinear data-driven modelling and model frequency analysis. Nonlinear Dynamics (2024).
2. Fault Diagnosis for Abnormal Wear of Rolling Element Bearing Fusing Oil Debris Monitoring. Sensors (2023).
3. The Improved WNOFRFs Feature Extraction Method and Its Application to Quantitative Diagnosis for Cracked Rotor Systems. Sensors (2022).
4. Fault mechanism analysis and diagnosis for closed-loop drive system of industrial robot based on nonlinear spectrum. Scientific Reports (2022).