The research team, led by Daniel F. Goncalves together with Aldemir A. Cavallini Jr. and Valder Steffen Jr., focused on a class of machines that is notoriously difficult to monitor: horizontal rotors supported by hydrodynamic bearings. Unlike conventional rolling-element bearings, hydrodynamic bearings support the rotating shaft on a thin, pressurized film of oil, and this fluid-film behavior is inherently nonlinear. That nonlinearity distorts vibration signatures in ways that complicate diagnosis, which is precisely why most existing AI-based fault detection studies, which typically concentrate on rolling bearings, do not translate easily to this class of machinery.

The specific faults the team targeted are among the most common and most confounding in rotating equipment: unbalance, misalignment, and shaft cracks. Each of these defects produces vibration symptoms that overlap substantially, meaning that a maintenance engineer looking at raw vibration data may struggle to distinguish a developing crack from a simple misalignment. The stakes of getting this wrong are high, because a crack that goes undetected can propagate until the shaft fails outright, while an incorrect diagnosis can trigger unnecessary and costly maintenance interventions.

To build their diagnostic system, the researchers combined physical experimentation with high-fidelity simulation. They constructed a test rig consisting of a horizontal steel shaft, 19 millimeters in diameter and 950 millimeters long, driven by an electric motor at a fixed speed of 1,200 revolutions per minute and supported by two hydrodynamic bearings lubricated with ISO VG 68 oil. A corresponding finite element model of the rotor, built from 44 Timoshenko beam elements, was carefully calibrated against the experimental rig using a differential evolution optimization procedure, ensuring that the virtual model faithfully reproduced the machine’s dynamic behavior. This calibrated digital model, implemented with the open-source Rotordynamic Software ROSS, then allowed the team to generate large volumes of synthetic training data covering fault conditions that would be impractical or dangerous to create physically.

From the vibration signals, gathered at two measurement planes with orthogonally positioned proximity sensors, the team extracted features spanning three domains: statistical measures such as skewness, kurtosis, and root-mean-square values in the time domain; harmonic amplitudes in the frequency domain; and wavelet packet sub-band energies in the time-frequency domain. The raw feature set was then distilled using a hybrid strategy that pairs the Relief algorithm, an unsupervised feature ranking method, with SHAP, a model-dependent explainability technique rooted in cooperative game theory. This dual ranking produced a remarkably compact set of just 12 features, a reduction that slashed computational cost while actually improving diagnostic performance compared with using the full feature set or principal component analysis.

The architecture itself operates in two tiers. First, an ensemble of three clustering algorithms, hierarchical agglomerative clustering, DBSCAN, and Gaussian mixture models, votes by majority to flag whether a new vibration sample represents a novelty or deviation from healthy behavior. This unsupervised layer is crucial because real industrial machines rarely come with labeled databases covering every possible operating condition. Then, once an anomaly is detected, supervised classifiers, specifically k-nearest neighbors and support vector machines, take over to identify which specific fault is present. Hyperparameters for every model were tuned through grid search with cross-validation, and the feature selection was performed strictly on training data to prevent any information leakage that could inflate the results.

The performance figures are striking. In numerical tests, both classifiers achieved precision, recall, and F1-scores exceeding 98.9 percent, with the support vector machine reaching a recall of 99.64 percent and the k-nearest neighbors model posting a weighted F1-score of 99.13 percent. In experimental validation on the physical test rig, using 400 samples that included healthy, unbalanced, misaligned, and cracked conditions, the support vector machine achieved a weighted F1-score of 99.30 percent, while the crack class alone reached an F1-score of 98.95 percent despite being the smallest category in the dataset. The few misclassifications that did occur almost exclusively involved confusion between misalignment and cracks, the two faults with the most similar vibration signatures, and even these errors were statistically marginal.

Equally important for industrial deployment is speed. The researchers measured the complete computational pipeline for a single data window, including sliding-window processing, feature extraction via the discrete Fourier transform and wavelet decomposition, feature scaling, and final prediction. The full cycle took roughly 0.17 to 0.18 seconds for classification and about 0.34 seconds for the clustering-based detection stage, comfortably fast enough for real-time monitoring of continuously operating machinery without computational bottlenecks.

What truly sets this work apart, however, is its insistence on transparency. Using SHAP values, the team opened the black box and verified that the classifiers were reasoning in physically meaningful ways. The analysis revealed that the amplitude of the second harmonic of the rotational speed, extracted from measurement plane S1, was the single most influential feature for the support vector machine, contributing a total SHAP value of approximately 0.35, with the largest share attributable to crack conditions. This aligns perfectly with rotor dynamics theory, since misalignment and cracks are known to induce periodic disturbances at twice the rotational frequency. Even more compelling, the skewness of the vibration signal emerged as a critical discriminator for cracks, a result the researchers could explain directly: a propagating crack introduces asymmetry into the rotor system, which skews the distribution of the vibration response. The AI, in other words, had independently rediscovered a genuine physical phenomenon.

The Brazilian team is now developing an application programming interface to bring the methodology into real industrial environments, and they acknowledge that the current results were obtained at a single fixed rotational speed, a deliberate choice that isolated fault signatures from the complications of variable operating conditions. Future work will test the framework across different speeds, imbalanced datasets, and bearing-specific failure modes such as journal ovalization and lubrication problems. Still, the implications are considerable. By pairing robust, lightweight classifiers with explanations that a maintenance engineer can verify against physical intuition, the study offers a template for the kind of trustworthy, interpretable AI that Industry 5.0 demands, where intelligent machines and human experts collaborate rather than compete, and where a computer’s diagnosis of a cracked shaft comes with evidence a seasoned engineer can actually check.

Subject of Research: Explainable AI-based vibration fault diagnosis in rotating machines supported by hydrodynamic bearings

Article Title: Fault recognition approach applied to a rotating machine supported by hydrodynamic bearings using explainable artificial intelligence

Article References: Goncalves, D. F., Cavallini, A. A., Jr., & Steffen, V., Jr. (2026). Fault recognition approach applied to a rotating machine supported by hydrodynamic bearings using explainable artificial intelligence. Applied Intelligence, 56(15), Article 461. https://doi.org/10.1007/s10489-026-07491-9

Image Credits: AI Generated

DOI: 10.1007/s10489-026-07491-9

Keywords: rotating machinery, hydrodynamic bearings, fault diagnosis, explainable artificial intelligence, SHAP, vibration analysis, predictive maintenance, machine learning, support vector machine, k-nearest neighbors, ensemble clustering, rotor dynamics

The core problem, the authors explain, is that traditional single-run clustering methods lack stability, robustness, and generalisability. Stability refers to whether results remain consistent across repeated runs; robustness describes resilience to noise; generalisability concerns whether findings hold in different datasets. All three are chronically weak in conventional approaches. This is not simply a matter of sloppy implementation. Kleinberg’s impossibility theorem shows that no clustering method can simultaneously satisfy all desirable properties, and the optimisation problem underlying clustering has no exact solution. Algorithms therefore rely on assumptions and trade-offs, and their stochastic optimisers mean that minor perturbations of the data, different starting points, or a different choice of algorithm can produce substantially different subgroups from the same dataset.

The downstream consequence is a replication crisis for subgroup research. Identified subtypes often vary dramatically across studies, and when broadly similar patterns do emerge, they frequently reflect arbitrary cut-offs along a single severity dimension rather than genuine heterogeneity. In mental health research, the stakes are particularly high: despite decades of effort, current evidence does not support reproducible, biologically valid, and clinically agreed-upon neuroimaging subtypes for mental illnesses. By contrast, fields such as oncology have made real translational progress with tumour subtyping, largely by adopting ensemble clustering methods that combine solutions from different data distributions, algorithms, and optimisation runs into a single consensus.

Ensemble clustering works much like ensemble methods in supervised machine learning, where predictions from many models are pooled to reduce the weaknesses of any single model. The clustering version follows a two-stage framework. The first stage generates many base clusterings, or BCs, by running different algorithms, random seeds, parameter settings, or resampled subsets of observations and variables. The second stage aggregates these partitions into a consensus, defined not as complete agreement but as the stable grouping pattern that recurs across solutions. The tutorial stresses that good BCs should be both diverse and high quality, a difficult balance because aggressive sub-sampling increases diversity while degrading individual partition quality, and optimising quality tends to drive all BCs toward the same answer.

The consensus stage is where the methodological richness lies. The simplest approach is majority voting, but because clustering algorithms return arbitrary cluster labels, BCs must first be relabelled and aligned, and voting fails entirely when BCs are highly diverse. More sophisticated techniques summarise the BCs before running a second-stage clustering model. Cluster labels can be treated as categorical variables and clustered with finite mixture models or k-modes. They can be binary-encoded into a cluster association matrix for k-means-based consensus clustering, or converted into bipartite graphs for graph partitioning methods such as the hypergraph-partitioning algorithm. Alternatively, a co-association matrix records how often each pair of observations is grouped together across BCs, serving directly as a distance matrix for hierarchical clustering in evidence accumulation clustering, or transformed into weighted graphs for algorithms such as the cluster-based similarity partitioning algorithm. Newer options include the link-based clustering ensemble, the meta-clustering algorithm, adaptive clustering ensemble, and even deep learning approaches.

Choosing the right components depends on the data. K-means is the most common BC algorithm because it is computationally cheap, though it assumes spherical clusters and is sensitive to outliers; model-based methods such as latent class analysis may better suit psychological data where subgroups plausibly arise from latent generative processes. The co-association matrix remains the most popular consensus tool because heatmaps of it visually display cluster stability and help select the number of clusters. Ensemble size matters too: performance generally improves with more BCs, but benchmarking studies suggest quality plateaus between roughly 50 and 100 base clusterings. A sampling proportion of about 80 percent is typically recommended, capturing most data characteristics while preserving variation among BCs.

A major practical payoff of the ensemble approach is a principled way to choose the number of clusters. Instead of relying on internal validity indices such as Silhouette, Calinski-Harabasz, Dunn, or Gap statistics, which often disagree with one another, researchers can inspect the consensus matrix. When the chosen number of clusters matches the true structure, the matrix displays clear square-shaped blocks along the antidiagonal, indicating pairs of observations that are consistently grouped together or apart. This visual pattern can be quantified through the cumulative distribution function of consensus indices, the delta area plot, the cophenetic correlation coefficient, and the proportion of ambiguous clustering score, though the authors caution that PAC carries an inherent bias toward larger cluster counts because it ignores null reference distributions.

To make the method concrete, the tutorial walks through a full R implementation using packages such as diceR, ConsensusClusterPlus, and clue, with step-by-step code provided in supplementary materials. Using a simulated dataset of 600 observations with 12 variables generated from three multivariate normal clusters, the authors demonstrate the dice function, combining k-means, Gaussian mixture models, and Ward’s hierarchical clustering with the link-based consensus function across 100 BCs. They also cover pre-registration of analysis plans, data assessment, dimensionality reduction via PCA or alternatives such as UMAP and NMF, imputation for missing data introduced by resampling, trimming and reweighting of poor-quality BCs, permutation tests to confirm solutions did not arise by chance, and cross-validation frameworks for tuning hyper-parameters in the absence of ground truth.

The most striking evidence comes from simulations built on three real-world psychological datasets covering quality of life, alexithymic traits, and cannabis expectancies. The team perturbed each dataset by randomly removing between 0.25 and 20 percent of the data, refilling gaps with multiple imputation, and repeated the process 100 times per condition. Even tiny perturbations of 0.25 percent produced substantially different results under single-run methods; hierarchical clustering in one case performed barely better than random assignment. Ensemble clustering consistently showed the slowest decay in stability, measured by the Rand index, and much narrower variability across perturbed dataset pairs, particularly for higher-dimensional data.

The authors are careful about limits. Ensemble methods inherit the assumptions of their base algorithms, so stable solutions can still miss non-convex or arbitrary cluster shapes; stability and internal validity do not guarantee external validity, and even valid, generalisable solutions may lack practical utility if they merely partition severity. Ordinal Likert-scale items and latent constructs can distort distance matrices, and longitudinal data require specialised Bayesian ensemble pipelines. Computational cost is real, though manageable with binary association matrices and high-performance computing. Still, the tutorial’s message is unambiguous: minor perturbations of psychological data can upend single-run clustering, ensemble methods tame that instability, and with mature R tooling now available, the authors advocate widespread adoption to finally turn heterogeneous psychological data into subgroups researchers can trust.

Subject of Research: Ensemble clustering methods for improving the stability and reproducibility of subgroup identification in psychological and psychiatric research

Article Title: Ensemble clustering: A practical tutorial

Article References: Gao, C. X., Wang, S., Zhu, Y., Ziou, M., Teo, S. M., Smith, C. L., Chiu, D., Talhouk, A., Wang, M., Yu, W., Cotton, S. M., & Dwyer, D. (2026). Ensemble clustering: A practical tutorial. Behavior Research Methods, 58(10), Article 286. https://doi.org/10.3758/s13428-026-03158-y

Image Credits: AI Generated

DOI: 10.3758/s13428-026-03158-y

Keywords: ensemble clustering, cluster analysis, consensus clustering, psychiatry, psychology, machine learning, unsupervised learning, R programming, replication crisis, latent class analysis, stability, Behavior Research Methods