A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacoustic

Barbara Cunha; Christophe Droz; Abdelmalek Zine; Stéphane Foulard; Mohamed Ichchou

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A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacoustic

Barbara Cunha, Christophe Droz, Abdelmalek Zine, Stéphane Foulard, Mohamed Ichchou

arXiv:2204.06362v2Apr 13, 2022cs.LGcs.SDeess.AS

TL;DR

Machine learning applications in structural dynamics and vibroacoustics were not previously reviewed systematically despite extensive activity across the field. This survey synthesizes methods across structural health monitoring, active control, and vibroacoustic product design, finding broad capabilities alongside important data, interpretability, physical-consistency, and implementation constraints.

Problem
ML applications in structural dynamics and vibroacoustics had produced many contributions, but their methods, strengths, weaknesses, implementation status, and research gaps had not been comprehensively reviewed.
Method
The paper conducts an extensive review of ML algorithms and applications in structural health monitoring, active control, and vibroacoustic product design, including digital twins and physics-guided ML.
Results
The reviewed literature shows that ML can perform critical SD&V tasks and can be more efficient and accurate than physics-based methods for some applications, with SHM the most developed area.
Takeaways & Limitations
ML supports failure detection and prognosis, active-control modeling and design, and faster product-design simulations, while physics-guided ML offers more interpretable and physically consistent predictions with less training data.
Takeaways & Limitations
ML applications remain constrained by limited interpretability and physical basis, possible failure to generalize to unseen scenarios, and reliance on substantial data.

Abstract

from arXiv · show

The use of Machine Learning (ML) has rapidly spread across several fields, having encountered many applications in Structural Dynamics and Vibroacoustic (SD\&V). The increasing capabilities of ML to unveil insights from data, driven by unprecedented data availability, algorithms advances and computational power, enhance decision making, uncertainty handling, patterns recognition and real-time assessments. Three main applications in SD\&V have taken advantage of these benefits. In Structural Health Monitoring, ML detection and prognosis lead to safe operation and optimized maintenance schedules. System identification and control design are leveraged by ML techniques in Active Noise Control and Active Vibration Control. Finally, the so-called ML-based surrogate models provide fast alternatives to costly simulations, enabling robust and optimized product design. Despite the many works in the area, they have not been reviewed and analyzed. Therefore, to keep track and understand this ongoing integration of fields, this paper presents a survey of ML applications in SD\&V analyses, shedding light on the current state of implementation and emerging opportunities. The main methodologies, advantages, limitations, and recommendations based on scientific knowledge were identified for each of the three applications. Moreover, the paper considers the role of Digital Twins and Physics Guided ML to overcome current challenges and power future research progress. As a result, the survey provides a broad overview of the present landscape of ML applied in SD\&V and guides the reader to an advanced understanding of progress and prospects in the field.

1. Introduction

Machine learning has become important in structural dynamics and vibroacoustics because it extracts patterns from abundant data and supports analysis across three major application areas. This review organizes those applications, evaluates their strengths and limitations, and identifies opportunities involving digital twins and physics-guided learning.

Three application areas: ML is applied in structural health monitoring, active noise and vibration control, and vibroacoustic product design with surrogate models.These areas use ML for failure detection and prognosis, system identification and controller design, and faster simulation-based design, respectively.
Structural health monitoring: Structural health monitoring uses ML to extract features from vibration and noise data, detect and classify failures, and predict remaining useful life.The review connects these capabilities with safer operation and optimized maintenance scheduling.
Active control: Active control uses ML to identify lightweight system models and optimize noise- and vibration-controller designs when mechanistic models are unknown, incomplete, or high-dimensional.The analyzed workflow should account for the characteristics of the vibration or sound signals.
Vibroacoustic product design: ML-based surrogate models provide fast alternatives to costly simulations for robust and optimized vibroacoustic product design.The review discusses their use in noise, harshness, and vibration development.
Challenges and opportunities: The review identifies limited interpretability, weak physical basis, labeled-data demands, real-time simulation costs, and uncertain justification as continuing challenges.It discusses digital twins and physics-guided approaches among possible directions for addressing these issues.

2. Overview of machine learning methods

The review introduces ML representations, evaluation criteria, learning categories, and commonly used SD&V algorithms. It emphasizes selecting methods according to data, resources, and task while balancing flexibility and predictive power against data, interpretability, and scaling constraints.

Supervised learning: Supervised learning maps labeled inputs to outputs for regression or classification and aims to generalize to unseen data rather than merely fit training samples.Its generalization error reflects bias, variance, and irreducible error, creating an underfitting–overfitting trade-off.
Method selection: No learning algorithm is universally best, so SD&V methods should be selected according to data volume and nature, available resources, and task purpose.The review recommends first identifying the learning category and analysis objective.
Common algorithms: Neural networks are the most used SD&V algorithm across the three application fields, while SVMs dominate SHM classification and GPRs dominate surrogate modeling.PCA, autoencoders, K-means, Q-learning, and policy-gradient methods represent other frequently used categories and tasks.
Neural networks: MLPs learn by optimizing weights and biases through supervised error backpropagation, while deeper networks automatically extract increasingly meaningful representations.Deep learning can outperform shallow methods with sufficient data and computational power but often requires large labeled datasets and remains difficult to interpret.
Gaussian process models: GPR is widely used for SD&V surrogate modeling because it supports probabilistic predictions, small datasets, prior domain knowledge, and information-efficient sampling.Its limitations include kernel and hyperparameter sensitivity and poor scaling with large datasets.

2.2. Unsupervised learning

Unsupervised learning extracts representations and patterns from unlabeled SD&V data, chiefly for dimensionality reduction, clustering, anomaly detection, and reduced-order modeling. The methods trade nonlinear feature capacity or scalability against interpretability, computational cost, and modeling assumptions.

Applications: Unsupervised learning is used in SD&V when labeling is expensive or infeasible, especially for dimensionality reduction, clustering, and anomaly detection.Reduced-dimensional representations also support reduced-order modeling of expensive simulations in active control.
Dimensionality reduction: PCA projects high-dimensional data onto a lower-dimensional orthogonal subspace while minimizing reconstruction error and retaining dominant covariance directions.Its principal components can serve as informative features or reduced coordinates.
Dimensionality reduction: Autoencoders compress inputs through a bottleneck and reconstruct them through expanding layers, learning nonlinear representations by minimizing reconstruction error.They can extract richer nonlinear features than PCA when adequate data and computational resources are available.
Clustering: K-means partitions data into a predefined number of centroid-based clusters by minimizing Euclidean distance to cluster centroids.It is efficient for large datasets but sensitive to initialization and outliers and requires the cluster count in advance.

2.3. Reinforcement learning

Reinforcement learning trains an agent through interactions with an environment, using rewards to learn actions that maximize expected long-term return. The review covers value-based, policy-based, and hybrid or advanced learning strategies relevant to SD&V.

Reinforcement learning: Reinforcement learning learns a policy by mapping environment states to actions and maximizing expected cumulative future reward.Each action changes the state and produces a reward that guides subsequent learning.
Q-learning: Q-learning estimates the expected future reward of state–action pairs and iteratively updates its value function toward the Bellman-optimal solution.A partly random action-selection policy supports updates while the optimal policy is learned implicitly.
Policy-based methods: Policy-gradient methods optimize parameterized action policies directly in action space using gradients of expected future reward.They differ from Q-learning by optimizing policy parameters rather than first searching for an optimal value function.
Advanced strategies: Hybrid and advanced strategies such as semi-supervised learning, active learning, and transfer learning can reduce dependence on labeled data.Active learning selects informative samples, while transfer learning reuses knowledge from related source domains.

3. Structural health monitoring

Structural health monitoring uses ML to detect and diagnose damage and predict remaining useful life from structural measurements. This section organizes SHM by increasingly difficult prediction levels and highlights data scarcity and environmental variability as central challenges.

ML-based SHM supports damage detection, diagnosis, and remaining-useful-life prediction, helping manage structural reliability and maintenance.SHM measurements can support safe operation and service-time optimization.
Deep learning automates high-level feature extraction and can improve diagnosis and prognosis, but requires sufficiently large datasets and training time.Traditional ML remains dependent on handcrafted damage-sensitive features.
SHM faces two major challenges: limited labeled abnormal data and environmental or operational variability that also changes structural dynamic responses.These factors complicate reliable damage-related inference.
As Rytter’s hierarchy advances from detection to location, assessment, and prognosis, labeling becomes more costly and datasets become scarcer.Performance at higher levels usually depends on the preceding levels.
The review surveys ML approaches across SHM hierarchy levels, data scarcity strategies, algorithm choices, strengths, weaknesses, and research gaps.It is structured around data processing, Rytter’s levels, emerging trends, and synthesis.

3.1. Data processing and features extraction

SHM accuracy depends strongly on acquiring and representing vibration or acoustic data appropriately. Traditional ML relies mainly on handcrafted features, whereas deep learning can automate extraction and dimensionality reduction for sufficiently large datasets.

Proper data acquisition, signal processing, and feature extraction and selection are crucial because ML damage-prediction accuracy depends on input-data quality.Preprocessing can also improve deep-learning accuracy and efficiency when raw data are used.
Frequency-domain representations suit stationary signals, while time-frequency or wavelet representations are convenient for non-stationary signals.These transformations are commonly useful for vibration and acoustic signals in SD&V.
Features may be extracted in time, frequency, and time-frequency domains using statistics, spectral descriptors, compressed sensing, and vibration-image methods.Examples include RMS, skewness, kurtosis, harmonics, and spectral skewness.
Feature-selection choices depend on signal behavior: linear discriminant analysis suits non-stationary cases, PCA stationary signals, and independent component analysis combined faults.Decision trees and LASSO can select relevant features implicitly.
Deep learning can automate feature extraction and selection, while unsupervised models can reduce dimensions before shallow ML prediction.This configuration has been explored with both unlabeled and labeled SHM datasets.

3.2. Damage detection (level 1)

Damage detection is the foundational SHM task and can often use unlabeled data to identify deviations from healthy dynamic responses. ML methods must distinguish damage from environmental variability and noise while supporting increasingly robust detection.

Damage detection identifies whether a signal is healthy or unhealthy and provides the foundation for subsequent SHM diagnosis levels.Because healthy-condition data are more available, unsupervised learning is widely applicable.
Anomaly detection uses unlabeled data but must distinguish damage from environmental or operational variability and noise to avoid false positives.False positives can trigger unnecessary maintenance.
Only-healthy training and representative-sample selection have been used to improve anomaly-detection accuracy while reducing dataset size or computational time.Reported examples include one-class SVM and k-nearest-neighbor methods for time-series and centrifugal-fan data.
Reconstruction-based methods can improve detection by isolating structural changes caused by damage from environmental effects.PCA has modeled both linear and nonlinear environmental effects in long-term bridge vibration data.
Deep autoencoders have been used successfully for anomaly detection in wind turbines and aircraft using reconstruction errors from multi-sensor or raw time-series data.Clustering was additionally used for aircraft-fault disambiguation.
Supervised detection can benefit from environmental and operational inputs, with RF and SVM outperforming several alternatives in natural-frequency prediction.The comparison included MLP, decision tree, and multiple linear regression.

3.3. Damage location (level 2)

Damage location identifies where a fault occurs and generally requires supervised learning for inspection and maintenance planning. Approaches use acoustic emissions, modal features, or non-parametric representations, with sensor placement and data-processing choices shaping applicability.

Damage location enables more targeted inspection and maintenance routines and generally requires supervised learning.It is the second level of SHM diagnosis.
Acoustic-emission localization can use sensor time-of-flight differences, but practical implementations may require multiple sensors near the structure.Gaussian-process regression has mapped artificial damage sources while selecting active sensors.
Damage-location studies commonly use parametric modal features or non-parametric features extracted with PCA or autoregressive models before classification.Natural frequencies and mode shapes support classifiers such as MLP and neuro-fuzzy systems.
Artificial damage is often represented through stiffness reduction, lost connections, or added mass in simulations or experiments.These representations are used to study damaged structural responses in non-rotating structures.
ML has localized damage in aircraft wings and framed structures, including real-time joint-failure detection with compact 1D CNNs.One study also combined sparse-autoencoder features with a dropout neural network for induction-motor damage location.

3.4. Damage assessment (level 3)

Damage assessment in SHM classifies damage severity or mode, but labeled data scarcity and varying operating conditions make robust diagnosis difficult. Reviewed studies apply ML and deep learning to vibration-based fault classification across rotating machinery and civil structures.

Damage assessment remains challenging because labeled data are scarce and measurements vary with system complexity, sensor heterogeneity, noise, and operating conditions.
Raw reshaped vibration signals produced the most accurate gear-crack classification input among tested CNN encodings.
Frequency-domain inputs substantially improved 1D CNN gear-fault classification over raw and time-frequency inputs, while also outperforming MLP, SVM, and RF.
DBN-based approaches supported multisensor fusion and achieved higher bearing-fault classification accuracy than SVM, k-NN, and MLP.
For civil structures, neural networks predicted corrosion severity and I-beam damage location or severity using finite-element or structural-mode data.

3.5. Damage prediction (level 4)

Damage prediction uses ML to forecast degradation and remaining useful life, supporting maintenance planning and safer operation. The reviewed studies include recurrent, probabilistic, similarity-based, and neuro-fuzzy approaches, but performance can depend on health-index quality and configuration transferability.

Health prognosis forecasts degradation curves and remaining useful life, potentially supporting maintenance scheduling, reduced downtime, and safe operating conditions.
Run-to-failure data are rare, while RNN-based predictors can avoid degradation-trend assumptions and handle noisy or missing data with multisensor temporal dependencies.
RUL predictions strongly depended on health-index predictions, which differed significantly across relevance vector machine, GPR, and NN approaches.
GPR is appropriate for RUL prediction with small datasets, while neuro-fuzzy models combine engineering knowledge with statistical information from data-driven methods.
A CNN-LSTM brake-squeal method classified noise and predicted squeal timing, but performed poorly when applied to a different brake configuration.
Similarity-based RUL prediction can use degradation patterns from similar structures to monitor incipient damage.

3.6. Current trends in ML-based SHM

Current SHM trends address scarce labeled data and limited transferability through hybrid, semi-supervised, active, population-based, and transfer-learning approaches. These methods incorporate physics, unlabeled data, targeted labeling, or information from related structures.

Hybrid models combine physics-based and ML-based components to reduce data needs, include unseen scenarios, and improve interpretability while learning from measurements.
Semi-supervised learning exploits abundant unlabeled data alongside scarce labeled samples for damage classification and RUL prediction.
Active learning reduces labeling requirements by querying samples expected to maximize information gained during model updates.
Population-based SHM transfers damage information between similar structures when representative labeled data across damaged states and operating conditions are difficult to obtain.
Transfer learning addresses distribution differences between source and target structures, while heterogeneous PBSHM remains less implemented because of substantial discrepancies.

3.7. On the merits of ML-based SHM algorithms

ML algorithm choice in SHM depends on dataset size, feature availability, task complexity, and interpretability needs. Traditional models often suit smaller or feature-engineered datasets, whereas deep models support larger-scale and end-to-end or sequential analyses.

Traditional ML is convenient for small datasets and expert-defined features, whereas deep learning is better suited to large-scale data and end-to-end prediction.
SVM supports data-efficient classification and one-class anomaly detection, but kernel and hyperparameter choices affect suitability, especially for large datasets.
Decision trees, naive Bayes, and k-NN are interpretable for investigating diagnostic rules and physical meaning, while RF improves tree generalization with less interpretability.
CNNs are prominent for vision-based SHM and can process time series when temporal spatial relationships are encoded appropriately.
RNNs suit sequential SHM data and complex damage forecasting, but their computational and implementation costs are higher.
DBNs use unsupervised layer pretraining followed by supervised fine-tuning and have reported improved accuracy or separability over traditional ML and PCA.
PCA commonly performs linear feature reduction, whereas autoencoders extract nonlinear features but require more data and may learn unnecessary information.

4. Active control of noise and vibration

ML supports active noise and vibration control through system identification, reduced-order modeling, and controller design, particularly when conventional techniques struggle with complex or nonlinear systems. The review highlights benefits alongside practical trade-offs, including training demands, computational cost, and slower adaptation.

4.2. ML-driven controller design: Reinforcement learning achieved satisfactory or improved control in acoustic, bending, torsional, rotating-machine, industrial, and flexible-building applications, including performance beyond PD control in one experimental transfer.
4.3. On the merits of ML for active control of noise and vibration: The main limitations are considerable training time and computational expense for reinforcement learning, while some ML control approaches adapt slowly and may not suit transient online applications.
ML is applied in active control for system identification, reduced-order modeling, and controller design, especially when traditional techniques may fail for complex and nonlinear systems.
4.1. Dynamic system modeling with ML: System identification with ML avoids selecting a single classical model order by supporting broader hypothesis spaces through black-box models and extensions of NARX or Kalman filters.
4.1.2. Reduced order models and sensors /actuators placement: Reduced-order ML methods use dimensionality reduction, including PCA, DMD, and ML-enhanced NNM, while potentially reducing sensor and actuator requirements without sacrificing control performance.
4.2. ML-driven controller design: Neural networks determine controller parameters and adapt to changing conditions, while reinforcement learning learns control policies for complex and uncertain dynamics through system interaction.

5. Vibroacoustic product design with surrogate modeling

Surrogate models provide fast alternatives to high-fidelity SD&V simulations for uncertainty quantification, sensitivity analysis, reliability assessment, and vibroacoustic optimization. The review finds that adaptive sampling, algorithm selection, and physics-informed features help address accuracy, efficiency, and physical-consistency challenges.

ML surrogates accelerate costly SD&V simulations and support uncertainty quantification, sensitivity analysis, reliability assessment, and optimized product design.They are used to explore domains, propagate uncertainties, evaluate sensitivities, and optimize designs with fewer expensive model evaluations.
5.4. On the merits of ML for vibroacoustic product design: Surrogates still struggle with non-smooth resonance behavior, extrapolation, interpretability, and physical consistency, although adaptive refinement and physics-guided features offer mitigation.Models may smooth sharp peaks and valleys, while feature engineering and physics-guided ML can improve accuracy and consistency.
5.1. Surrogate workflow and related methods: NNs outperformed GPR, random forests, and gradient-boosting trees for increasingly complex, non-smooth sound-transmission-loss problems, while tree-based methods were faster.Feature engineering embedded domain knowledge and produced more accurate and physically consistent surrogate results.
5.2. Uncertainty quantification with surrogates: GPR with adaptive sampling reduced true function evaluations for uncertainty and reliability analyses, but higher-dimensional problems remained challenging.Adaptive sampling selected informative points using surrogate predictions and uncertainty, improving computational efficiency for several SD&V analyses.
5.3. Optimization with surrogate models: NN surrogates enabled vehicle-noise optimization while saving time and accommodating higher problem dimensionality than polynomial and response-surface surrogates.Applications included suspension hardpoint optimization and sound-pressure minimization under mass, intrusion, and modal constraints.
5.3. Optimization with surrogate models: Bayesian optimization improves sample efficiency for expensive black-box design by balancing exploration of uncertain regions with exploitation of promising ones.Its acquisition function uses predicted surrogate means and uncertainties to select informative new samples.

6. On future trends and perspectives

Future progress in ML for SD&V centers on integrating lifecycle data, high-fidelity simulations, and physical knowledge while addressing interpretability, data, and modeling challenges.

6.1. Digital twin: Digital twins integrate lifecycle data with data-driven and high-fidelity simulations, but complete implementations remain decades away.They are intended to support evolving system representations, forecasting, mitigation planning, and uncertainty management.
6.2. Physics-guided machine learning: Physics-guided ML combines physical models and data-driven methods to improve consistency, interpretability, robustness, and data efficiency.Reported examples include superior generalizability with scarce noisy data and improved performance over purely physical or data-driven approaches.
6.3. Research gaps and emerging opportunities: ML-based research opportunities include discovering governing equations, creating lifecycle-aware digital twins, and improving interpretability through sensitivity analysis.These directions connect model development with physical insight and product lifecycle information.
6.3. Research gaps and emerging opportunities: Future work should address limited labeled data in SHM and nonsmooth surrogate functions through transfer learning, adaptive sampling, local refinement, and domain decomposition.These methods target data scarcity and the tendency of surrogates to smooth irregular SD&V responses.
6.3. Research gaps and emerging opportunities: Robust active control remains an open direction, including adversarial reward learning, provable guarantees, and related controller-design approaches.

7. Conclusion and discussion

The review finds that ML supports major SD&V tasks across health monitoring, active control, and vibroacoustic design, while future progress depends on addressing interpretability and irregular-response challenges.

7. Conclusion and discussion: ML in SD&V supports structural health monitoring, active noise and vibration control, and vibroacoustic product design.The review identifies these as the three major application areas.
7. Conclusion and discussion: SHM is the most developed application, using time- and frequency-domain measurements for fault detection and remaining useful life prediction.These capabilities support preventive maintenance and component-lifetime utilization.
7. Conclusion and discussion: ML enhances active control through system identification, reduced-order modeling, sensor and actuator placement, and offline or online controller design.
7. Conclusion and discussion: Surrogate models replace costly high-fidelity simulations for design exploration, uncertainty quantification, and optimization, but can perform poorly on highly irregular functions.Adaptive sampling, local refinements, and domain subdivision can improve accuracy near regions of interest.
7. Conclusion and discussion: Digital twins and physics-guided ML offer future directions by integrating lifecycle information and physical knowledge into SD&V workflows.Physics-guided models are associated with greater interpretability, lower training-data needs, and more physically consistent predictions.