Vibration–current multimodal fusion for within-batch recognition of predefined component faults of a high-pressure abrasive waterjet machine tool

1 Introduction

High-pressure abrasive waterjet (AWJ) machining removes material by using a high-pressure water jet to entrain abrasive particles. Owing to its low thermal effects, broad material applicability, and relatively low cutting forces, AWJ machining has been widely applied to the cutting and machining of metals, composites, and other difficult-to-machine materials (Momber and Kovacevic, 1998; Liu et al., 2019; Llanto et al., 2021). An AWJ machine tool consists of multiple functional units, including a high-pressure pump, abrasive delivery system, cutting head and nozzle, motion system, and electrical drive system. Changes in the operating condition of any of these units may affect jet formation and machining stability. Previous studies have shown that dynamic signals such as cutting forces, acoustic emission, and vibration can reflect the operating condition of AWJ systems. Hlaváč et al. (2021) investigated three-axis force monitoring during AWJ cutting and reported that abnormal force signals could be used to identify operating problems such as incomplete penetration, pumping anomalies, and inappropriate machining parameters. Popan et al. (2024) used acoustic emission signals to monitor the AWJ machining of composite materials and demonstrated their sensitivity to equipment abnormalities, including reduced abrasive flow rate, cutting-head blockage, component wear, and water-pressure drops. These studies indicate the effectiveness of process dynamic signals for AWJ condition monitoring. However, existing research has mainly focused on the cutting head, workpiece, or machining region, whereas joint condition monitoring across the multi-component process chain comprising the high-pressure pump, nozzle, motion system, and abrasive delivery system remains relatively limited. Therefore, simultaneously characterizing the local dynamic responses of key components and changes in the overall machine load remains an important challenge for fault diagnosis of AWJ machine tools.

Data-driven methods provide an effective approach to condition identification for complex mechanical equipment. At the methodological level, Welch’s method for power spectral density estimation (Welch, 1967), support vector machines (SVMs) (Cortes and Vapnik, 1995), and random forests (Breiman, 2001) are commonly used for extracting diagnostic information and recognizing operating states. Recent multimodal studies have further addressed missing or non-contact sensing through digital-twin-enabled feature imputation (Yu et al., 2025), structured cross-channel relationships under strongly biased data (Yu et al., 2026a), and multilevel fusion under limited and imbalanced datasets (Yu et al., 2026b). These advances underscore the value of exploiting complementary sensing information while stating the limits of an experimental dataset clearly.

Recent studies provide relevant, but not directly comparable, context for the present small single-batch experiment. Zhang et al. (2020) considered domain discrepancy under varying conditions; Huang et al. (2020) reviewed multi-source sensing fusion; and Wang et al. (2024) summarized image-based deep-learning diagnosis. Li Z. et al., 2025, Zhang J. et al., 2025, Zhou et al. (2025), and Chen L. et al. (2026) respectively investigated deep multimodal representation, missing-data fusion, adaptive mixture-of-experts fusion, and variable-condition multimodal diagnosis. These methods require different data scales, modalities, or validation designs and are therefore cited as methodological context rather than as a numerical superiority benchmark.

Multimodal fusion can improve the representation and discriminative capability of component states; however, high classification performance does not necessarily imply engineering interpretability. Unlike LLM-based fault-diagnosis systems, the post-classification stage in this study has no generative model, external retrieval, prompt-based inference, or free-text generation. It is a deterministic procedure that applies a fixed topology matrix, pre-defined evidence rules, and a fixed report template to a classifier output.

Knowledge-graph, physics-informed, and LLM-based diagnosis systems have also been reported (Cai et al., 2024; Karkadakattil, 2026; Chen J. et al., 2025; Qaid et al., 2024; Tao et al., 2025; Li D. et al., 2025; Zhang Q. et al., 2025). In contrast, the post-classification stage in this study is deterministic and non-generative: it applies a fixed topology matrix, predefined evidence rules, and a fixed report template to classifier outputs. It does not perform prompt-based inference, external retrieval, raw-waveform access, probability modification, or free-text generation.

This work develops and evaluates a heterogeneous vibration–current fusion framework for within-batch recognition of normal operation and predefined component faults in a high-pressure abrasive waterjet machine tool. Its primary contributions are: (1) a four-location triaxial-vibration and whole-machine-current dataset constructed using aligned 2-s windows; (2) a controlled comparison of unimodal, feature-level, and decision-level fusion models together with conventional and neural-network baselines under fivefold contiguous time-block validation; and (3) feature-group and axis-specific ablations that quantify the contribution and orientation sensitivity of the vibration representation. In addition, an auxiliary deterministic post-classification procedure is implemented to check location–state compatibility and organize structured evidence. The present study verifies only its rule-mapping correctness and separation from classifier outputs; it does not evaluate practical report utility or user acceptance.

2 Materials and methods

2.1 Test rig and multimodal data acquisition

The test rig is a self-developed high-pressure abrasive waterjet machine tool consisting mainly of a high-pressure pump, an abrasive delivery system, a cutting head and nozzle assembly, a motion system, and a control unit. Based on the machine structure and fault-monitoring requirements, four triaxial accelerometers were mounted at the high-pressure pump, nozzle end, machine-tool spindle, and abrasive-tank bottom pressure-port region. Machine supply AC current was acquired independently. The acquisition configuration is summarized in Table 1.

TABLE 1. Configuration and key parameters of multimodal data acquisition system.

Based on the measured quantities and their physical meanings, the triaxial acceleration signals from the four measurement locations are defined as the local vibration modality, which characterizes the dynamic responses of different key components. The current sequence from the machine supply circuit is defined as the machine-level load modality, which characterizes the overall load level and its slowly varying fluctuations. The vibration modality comprises the X-, Y-, and Z-axis components. Together, these two modalities constitute the heterogeneous vibration–current multimodal monitoring system used in this study. The experimental setup and vibration measurement locations are shown in Figure 1, and the main configuration of the multimodal data acquisition system is summarized in Table 1.

2.2 Modality definitions, measurement-location mapping, and fault conditions

Table 2 summarizes the channel configuration, measurement-location mapping, and primary physical representations of the vibration and current modalities. The experiments included the normal condition (Normal) and five representative labeled component conditions: pump plunger/seal wear (F01), nozzle blockage (F02), nozzle wear/orifice enlargement (F03), spindle imbalance/eccentricity (F04), and abrasive-tank pressure fluctuation (F05). Because the monitoring locations were predefined and the condition labels were associated with specific component locations, the present task is defined as within-batch recognition among Normal and five predefined fault labels rather than general fault diagnosis or unknown-location identification. Here, within-batch indicates that model performance is evaluated across contiguous time blocks from the same experimental batch, rather than across independent experiments, operating batches, or machines.

TABLE 2. Channel–location mapping and primary physical responses of the vibration and current modalities.

In this study, a component–window sample is used as the basic sample unit. Each fault sample consists of the triaxial vibration signals from the measurement location corresponding to the faulty component and the machine supply current within the same time window. Under the normal condition, the vibration signals from the four measurement locations are separately paired with the same machine supply current record. Consequently, the four normal samples generated from the same time window share the same current observation and represent the local responses of different components during the same normal operating run; they do not represent four independent experiments. Vibration features are referenced to the normal baseline at the same monitoring location, whereas current features are referenced to the within-batch normal machine-current baseline. The component–fault topology is used only for the subsequent topology-consistency check and rule-based evidence organization and is not involved in the training or performance evaluation of the classification models.

2.3 Temporal alignment of heterogeneous modalities and sample construction

The continuous vibration records for the normal condition and the five fault conditions each contained 114,824 samples. All triaxial channels had the same length and were sampled at 1,000 Hz, corresponding to an effective record duration of approximately 114.824 s. The current record for each condition contained 211 samples over an effective duration of approximately 157.105 s, with a median sampling interval of 0.75 s. Because the vibration and current signals were recorded through independent acquisition chains without a shared hardware clock, strict sample-level synchronization was not performed. Instead, the start of each record was defined as the relative time origin, and the two modalities were matched at the window level under the assumption that their operating sequences were temporally consistent.

Using the vibration signals as the temporal reference, each continuous record was divided into 2-s non-overlapping time windows, and the raw current observations within the corresponding time interval were paired with each vibration window. Given the relatively low sampling frequency of the current signal, linear interpolation was used to estimate the slowly varying load trajectory within each window; the interpolated points were not treated as additional independent observations. Accordingly, only low-frequency statistical features describing load level, variability, and temporal trend were extracted from the current modality. The current data were not used to analyze the motor fundamental frequency, harmonics, or other high-frequency electrical characteristics.

Within the shared effective time range of 0–114 s, 57 complete 2-s non-overlapping windows were obtained and the remaining partial record was excluded. For each F01-F05 condition, the triaxial vibration signal at the corresponding component location was paired with the interpolated current trajectory over the same window. For Normal, each of the four locations generated a component-window sample paired with the same within-window current trajectory. This yielded 228 normal and 285 fault component-window samples, for a total of 513 samples (Table 3). To support the subsequent fivefold contiguous time-block cross-validation, the 57 chronologically ordered windows for each operating condition were partitioned into five non-overlapping blocks containing 12, 12, 11, 11, and 11 windows, respectively. Identical block boundaries were applied across operating conditions and to all four normal-condition monitoring locations.

TABLE 3. Composition of vibration-current component-window samples across operating conditions.

2.4 Contiguous time-block cross-validation and data splitting

To reduce evaluation bias and the risk of data leakage that could arise from correlations between adjacent time windows under random splitting, we adopted fivefold contiguous time-block cross-validation rather than randomly splitting the window samples. For each operating condition, the 57 time windows were divided chronologically into five contiguous blocks of approximately equal size, using a consistent block-numbering scheme across all conditions. In each cross-validation fold, blocks with the same index were used as the outer test set, while the remaining four blocks formed the outer training set. For the normal condition, the same time-block partitioning scheme was applied to all four monitored components to ensure that component-level samples sharing the same machine supply current observation within a given time window did not appear simultaneously in the training and test sets.

Within each outer fold, the corresponding outer-test block was held out until final evaluation. For the current-only SVM, vibration-only SVM, feature-level fusion models, and feature-ablation models, the classifier configurations were specified a priori and held fixed across all outer folds; therefore, no classifier hyperparameter search was performed within the outer cross-validation procedure. Feature standardization was fitted using only the corresponding outer-training samples, after which each fixed classifier was trained on the same outer-training set.

For adaptive decision-level fusion, one complete time block from the outer-training data was reserved as a time-ordered inner-validation block. During fusion-weight selection, the branch-specific standardizers and classifiers were fitted only on the remaining inner-training samples, and their probability outputs on the inner-validation block were used to select the fusion weights. After the weights were fixed, the branch-specific standardizers and classifiers were refitted using the complete outer-training set, and the selected weights were applied once to the corresponding outer-test set. For the MM-LF-MLP baseline, the inner-validation block was used only for early stopping, as described in Section 2.6.

The outer-test block was not used for feature standardization, classifier fitting, fusion-weight selection, or early stopping. Across the five outer folds, each component-window sample appeared in the outer-test set exactly once. Evaluation metrics were calculated separately for the five outer-test sets and are reported as the mean ± standard deviation. This validation scheme evaluates recognition stability across contiguous time segments within the same experimental batch. Because each operating condition was obtained from only one continuous experimental run, the reported performance does not demonstrate external generalizability across repeated experiments, dates, operating conditions, sensor remounting, or different machines.

On this basis, vibration and current signals are encoded into features for unimodal recognition of predefined operating-condition labels, joint feature-level fusion, and decision-level fusion. Following numerical classification, the component-state topology and structured evidence are used only to check consistency and organize an evidence record; they are excluded from model training, probability adjustment, and performance-metric calculation. Figure 2 presents this workflow.

2.5 Heterogeneous feature encoding and multimodal fusion

For each 2-s vibration window, time-domain statistical features were calculated from the raw triaxial acceleration signals. Before spectral analysis, each axis was linearly detrended and multiplied by a Hann window to suppress low-frequency drift and spectral leakage. The one-sided spectrum was then calculated, and the dominant frequency was defined as the maximum-amplitude spectral peak searched only over 5–500 Hz. This definition avoids interpreting a near-zero drift bin (for example, 0.49 Hz) as a physical vibration frequency. The resultant magnitude of the triaxial acceleration was calculated using Equation 1.where a x t, a y t, and a z t denote the X-, Y-, and Z-axis acceleration components at time t, respectively, and a v t denotes the resultant magnitude of the triaxial acceleration.

a v t = a x 2 t + a y 2 t + a z 2 t (1)

For each vibration axis, eight time-domain features were extracted: RMS, standard deviation, maximum value, minimum value, peak-to-peak value, skewness, kurtosis, and crest factor. Across the X, Y, and Z-axes, these features formed a 24-dimensional time-domain representation. Eight frequency-domain features were also extracted from each axis: dominant frequency, dominant amplitude, spectral centroid, spectral bandwidth, spectral entropy, and the energy ratios in the 0–50 Hz, 50–200 Hz, and 200–500 Hz bands. These features formed a 24-dimensional frequency-domain representation across the three axes. In addition, 13 triaxial coupling features were calculated: five resultant-acceleration features (RMS, peak-to-peak value, crest factor, kurtosis, and dominant frequency), three axis-energy ratios for the X, Y, and Z-axes, three pairwise Pearson correlation coefficients (X–Y, X–Z, and Y–Z), and two composite coupling descriptors, namely, the standard deviation of the three axis-energy ratios and the ratio between the maximum and minimum axis RMS values. Therefore, the local vibration feature vector comprised 61 dimensions, including 24 time-domain, 24 frequency-domain, and 13 triaxial coupling features. The X, Y, and Z-axes are analyzed separately in the local sensor coordinate system; no global alignment across the four mounting locations is assumed. Resultant and energy-ratio features reduce, but do not eliminate, orientation sensitivity.

For the low-sampling-rate current modality, six features were extracted from the slowly varying load trajectory within each window obtained as described in Section 2.3: mean, RMS, standard deviation, peak-to-peak value, coefficient of variation, and trend slope. These features formed the current feature vector x c. Linear interpolation was used only to characterize the slowly varying load variation within each window and did not introduce additional independent current observations. Therefore, the current features characterize the overall machine load level, variability, and temporal trend and were not used to analyze the motor fundamental frequency, harmonics, or other high-frequency electrical characteristics. Each component–window sample thus consisted of 61 local vibration features and six machine supply current features. The vibration and current feature vectors were concatenated to form the joint feature vector, as shown in Equation 2.

x f = x v , x c ∈ R 67 (2)

In Equation 2, x f denotes the fused joint feature vector, and R 67 denotes the 67-dimensional real-valued feature space to which the vector belongs. The vibration features primarily characterize the local structural dynamic response of the monitored components, whereas the current features mainly characterize the overall machine load condition and its slowly varying fluctuations.

To evaluate the contributions of sensing modality, fusion mechanism, and classifier choice, the following models were evaluated under the same fivefold contiguous time-block protocol: current-only SVM, vibration-only SVM, feature-level fusion SVM, Random Forest, Extra Trees, k-nearest neighbors (kNN), equal-weight decision fusion, and adaptive decision-level fusion. The current-only SVM used six load-trajectory features, the vibration-only SVM used 61 vibration features, and joint feature models used the 67-dimensional concatenated feature vector.

All SVM classifiers used a radial-basis-function kernel with C = 10, gamma = 'scale', balanced class weights, and probability estimation. Random Forest and Extra Trees used 300 trees, balanced class weights, and a fixed random seed of 42; kNN used k = 5 with distance weighting. In each outer fold, standardization was fitted only on the outer training data.

The listed classifier configurations were specified before the outer cross-validation procedure and were held fixed across all folds and feature-ablation comparisons; no grid search or other hyperparameter optimization was performed for the SVM, Random Forest, Extra Trees, or kNN classifiers during the outer cross-validation procedure. Only the adaptive decision-fusion weights and the MM-LF-MLP stopping epoch were determined using inner-validation data. The class probabilities from the three branches were fused according to Equation 3.where w v, w c, and w e denote the fusion weights of the vibration SVM, current SVM, and Extra Trees branches, respectively. All fusion weights are nonnegative and are constrained to sum to 1, as expressed in Equation 4.

p f , k = w v p v , k + w c p c , k + w e p e , k (3)

w v + w c + w e = 1 , w v , w c , w e ≥ 0 (4)

For adaptive decision-level fusion, the chronologically last available complete time block within each outer-training set was reserved as the inner-validation block. The standardizers and the three branch classifiers were first fitted using only the remaining inner-training samples. Their class-probability outputs on the inner-validation block were then used for fusion-weight selection. The weights were searched from 0 to one in increments of 0.1, subject to the constraints in Equation 4. The combination yielding the highest inner-validation macro-F1 was selected. After weight selection, the standardizers and branch classifiers were refitted using the complete outer-training set, while the selected weights remained fixed. The final fused probabilities were then calculated once for the corresponding outer-test set, and the class with the highest fused probability was assigned as the predicted state, as expressed in Equation 5.

y ^ = arg max k ∈ C p f , k (5)

Feature ablation separated the vibration representation into time-domain, frequency-domain, and cross-axis groups; it also evaluated X-, Y-, and Z-axis-specific representations. These ablations use the same SVM configuration and outer folds as the primary comparison, and therefore isolate representation changes rather than test-set changes. The fixed component-state set is C = {Normal, F01, F02, F03, F04, F05}.

2.6 Representative neural multimodal fusion baseline

To provide a representative neural multimodal comparator, a compact two-branch late-fusion multilayer perceptron (MM-LF-MLP) was specified under the same fivefold contiguous time-block cross-validation protocol as the other numerical models. The vibration branch receives the 61-dimensional vibration feature vector and contains fully connected layers of 32 and 16 units. The current branch receives the 6-dimensional current feature vector and contains fully connected layers of 16 and 8 units. The two branch outputs are concatenated into a 24-dimensional representation and passed through a 16-unit fusion layer and a six-class softmax output layer. ReLU activation and dropout of 0.2 are used in the hidden layers.

The model uses class-weighted cross-entropy loss and the Adam optimizer with a learning rate of 0.001, a batch size of 16, and a maximum of 200 epochs. In each outer fold, standardization is fitted only on the inner-training partition. The chronologically last available complete time block among the outer-training blocks is reserved as the validation block for early stopping (patience = 20); the outer test block is excluded from scaling, early stopping, and model fitting. A fixed random seed of 42 is used in every outer fold.

The neural-network architecture and optimization settings were likewise specified before outer cross-validation and were kept fixed across folds. Only early stopping was determined within the outer-training data using the chronologically reserved validation block; the outer-test block was not used for model selection or training control.

This compact architecture is deliberately matched to the limited sample size and is included as a model-family and fusion-mechanism comparator, not as an assertion that a large neural network is appropriate for the present single-batch dataset.

2.7 Topology-consistency check and rule-based evidence-constrained report organization

After the classifier outputs the six-class probability vector and its top-1 state, the procedure performs a topology-consistency check based on the mapping between monitored locations and allowable states (Table 4). The allowable state set is a post-classification rule only; it is not used for classifier training, probability adjustment, or metric calculation.

TABLE 4. Equipment-topology constraints between monitoring locations and allowable component states.

Subsequently, the monitored component, class-probability vector, top-1 predicted class, feature deviations from the normal baseline, primary diagnostic evidence, and evidence-completeness information are organized into a structured diagnostic record. A predefined rule-based knowledge base was constructed according to the component–fault–symptom–inspection–action schema. For topology-compatible cases with sufficient evidence, the corresponding rules are matched and the diagnostic information is organized using a fixed template comprising observed facts, conditional mechanistic hypotheses, alternative causes, recommended verification actions, and safety notes.

This post-classification procedure does not invoke a large language model, prompt-based generation, external knowledge retrieval, or free-text generation. It does not access raw waveforms and does not modify the predicted class or its probability vector. Its implementation was verified using the complete location–state rule matrix and prediction-invariance checks. These tests evaluate only the correctness and functional separation of the deterministic procedure. No independent domain-expert or user evaluation was conducted; therefore, the explanatory quality, practical report utility, user acceptance, and field effectiveness of the procedure remain outside the validated scope of this study.

2.8 Evaluation metrics

Because the Normal class contains samples from four monitored components, its sample size is four times that of each individual fault class, resulting in a certain degree of class imbalance in the dataset. To reduce the influence of the majority-class proportion on overall accuracy, this study evaluates the classification models using macro-precision, macro-recall, and macro-F1 score in addition to accuracy. For each macro-averaged metric, precision, recall, and F1-score are first calculated separately for each class and are then averaged with equal weights across all classes, ensuring that each fault class contributes equally to the overall evaluation. The six-class within-batch recognition task considered in this study comprises K = 6 equipment states. For the kth class, precision and recall are denoted by P k and R k, respectively, and are calculated using Equations 6 and 7. Here, T P k, F P k and F N k denote the true positives, false positives, and false negatives for class k, respectively.

P k = T P k T P k + F P k (6)

R k = T P k T P k + F N k (7)

Macro-precision is the arithmetic mean of the class-specific precision values and is calculated using Equation 8.

Macro ‐ Precision = 1 K ∑ k = 1 K P k (8)

Macro-recall is the arithmetic mean of the class-specific recall values and is calculated using Equation 9.

Macro ‐ Recall = 1 K ∑ k = 1 K R k (9)

For the kth class, the F1-score is the harmonic mean of precision and recall. Macro-F1 is the arithmetic mean of the F1-scores across the six classes and is calculated using Equation 10.

Macro ‐ F 1 = 1 K ∑ k = 1 K 2 P k R k P k + R k (10)

Because macro-F1 jointly accounts for the precision and recall of each class while assigning equal weight to all six states, it is used as one of the principal evaluation metrics for comparing the overall six-class within-batch recognition performance of the unimodal and multimodal fusion models. All evaluation metrics are calculated independently on the five outer contiguous time test blocks and are reported as the mean ± standard deviation. By comparing the evaluation results of the current-only model, vibration-only model, feature-level fusion model, and adaptive decision-level fusion model, the effects of different modalities and fusion levels on six-class within-batch recognition performance are assessed. It should be noted that the topology-consistency check and rule-based evidence organization are performed only after numerical classification and are not included in the calculation of the classification-performance metrics.

3 Results

3.1 Response characteristics and complementarity of heterogeneous modalities

Figure 3 shows representative raw X-axis acceleration time histories from a selected 2-s window under the normal condition and each fault condition at the corresponding monitoring location. F01 shows a stronger periodic component than its pump baseline. The nozzle-end normal signal is intrinsically more irregular than the pump and spindle signals because of the local flow environment; therefore, the non-uniform appearance of F02 and F03 is not interpreted as fault-specific evidence by itself. F04 shows a larger modulation of the displayed X-axis trace, while F05 exhibits intermittent changes. These time histories are illustrative only; the numerical comparisons below use full-record, triaxial resultant features.

The relatively regular responses of F01 and F04 are consistent with periodic mechanical excitation associated with pump reciprocation and spindle rotation, respectively. In contrast, F02 and F03 were measured at the nozzle end, where turbulent multiphase flow, intermittent abrasive impacts, and changes in the local flow path may produce more nonstationary excitation. Because pressure and abrasive-flow variables were not directly measured, this explanation is treated as a plausible mechanism rather than a verified causal conclusion.

To compare the two modalities without conflating sensor locations, vibration statistics were referenced to the normal baseline at the same location, whereas current statistics were referenced to the within-batch normal current sequence. Table 5 and Figure 4 report full-record resultant vibration RMS, mean current, and detrended 5–500 Hz dominant frequencies on all three axes. The common normal current baseline is 13.897 A, and the normal resultant RMS differs by location.

TABLE 5. Full-record vibration and current changes relative to the appropriate normal-state baseline. Spectral peaks are calculated after linear detrending in the 5–500 Hz band.

Relative changes use unrounded full-record values: (fault - normal)/normal × 100%; displayed RMS/current values are rounded to 2/3 decimal places. Vibration changes use triaxial resultant RMS; F02/F03 share the nozzle-end normal baseline, and all current changes share the within-batch normal-current baseline.

For F01, resultant vibration RMS increased from 106.38 to 124.31 m·s^-2 (+16.86%), while mean current increased from 13.897 to 14.735 A (+6.03%). For F02, the corresponding changes were 79.99–93.56 m·s^-2 (+16.96%) and 13.897–15.568 A (+12.03%). For F03, vibration RMS increased from 79.99 to 86.58 m·s^-2 (+8.24%), whereas mean current decreased to 13.348 A (−3.95%). These patterns support complementarity, not a universal superiority of either modality.

For F04, resultant vibration RMS increased from 139.66 to 148.26 m s^-2 (+6.15%) and the dominant peak on all axes was 25.0 Hz after detrending. The visibly modulated raw X-axis segment in Figure 3d is not directly comparable with Table 5 value, because the figure displays one axis in one window whereas the table summarizes the full record through triaxial resultant RMS. For F05, resultant RMS increased from 150.84 to 161.98 m s^-2 (+7.39%); its mean current was essentially unchanged (13.892 A, −0.04%), but current fluctuation increased markedly (coefficient of variation: 0.85% normal to 5.68% F05).

The vibration and current modalities therefore respond to different physical aspects of these induced conditions. Vibration is locally sensitive to structural and flow-related dynamics, whereas current reflects machine-level load and fluctuation. Sensor location and orientation remain material constraints: the same-location normal reference controls for the fixed experiment but does not demonstrate robustness to remounting or a different machine.

3.2 Comparison of unimodal and multimodal fusion classification performance

Table 6 and Figure 5 compare all classifiers under fivefold contiguous time-block cross-validation. The current-only and vibration-only SVMs achieved Macro-F1 values of 91.21% ± 2.77% and 83.77% ± 11.36%, respectively. Feature-level fusion SVM achieved 98.27% ± 3.88%, a within-batch increase of 7.06 and 14.50 percentage points over the current-only and vibration-only SVMs. The fused representation therefore provides a clear benefit over either SVM modality alone in this experimental batch.

TABLE 6. Numerical classification performance under the same fivefold contiguous time-block cross-validation protocol (mean ± standard deviation across outer test folds).

The additional baselines show that model choice also matters. Random Forest and Extra Trees on the joint features achieved 100.00% ± 0.00% and 99.80% ± 0.44% Macro-F1, respectively, whereas kNN achieved 95.03% ± 3.74% and the two-branch MM-LF-MLP achieved 95.86% ± 3.88%. The neural baseline did not exceed the feature-level SVM or tree-based baselines in this small single-batch dataset. These values are internal time-block results only and should not be interpreted as cross-machine or cross-batch generalization.

Equal-weight decision fusion achieved 99.66% ± 0.75% Macro-F1 and adaptive decision-level fusion achieved 99.64% ± 0.50%. Thus, the adaptive weighting did not show a clear advantage over equal weights in the present batch. The previous claim of a significant adaptive-fusion improvement has been removed.

3.3 Feature and axis ablation and functional verification of the deterministic post-classification procedure

Table 7 and Figure 6 quantify the contribution of vibration feature groups and sensor axes. The full 61-dimensional vibration representation achieved 83.77% ± 11.36% Macro-F1. Time-domain, frequency-domain, and cross-axis-only representations achieved 77.50% ± 11.33%, 73.79% ± 7.49%, and 76.87% ± 6.00%, respectively. Adding the six current features to the full vibration representation increased Macro-F1 to 98.27% ± 3.88%. Among axis-specific representations, Y-axis features were highest (81.12% ± 6.10%) in this fixed mounting configuration, but their performance does not establish a globally preferred physical direction because sensor orientations differ by location.

TABLE 7. Feature-group and axis-specific ablation using the vibration SVM configuration and the same five outer time-block folds.

To examine the functional contribution of the deterministic post-classification procedure, three configurations were compared: the numerical classifier alone, the classifier with topology-consistency checking, and the complete procedure with both topology checking and rule-based evidence organization. Because the post-classification procedure is designed not to modify the classifier output, conventional Accuracy or Macro-F1 ablation is not applicable. Instead, the comparison evaluates the availability of topology flags and structured evidence records, the correctness of the predefined location–state mapping, and the invariance of the original class labels and probability vectors. The results are summarized in Table 8.

TABLE 8. Functional verification and component-removal analysis of the deterministic post-classification procedure.

As shown in Table 8, removing the post-classification stages did not change any of the 513 predicted labels or probability vectors. Activating the topology-consistency check generated compatibility results for the classifier outputs, and all 24 predefined location–state combinations were processed consistently with the rule matrix. Adding the evidence-organization stage further produced fixed-template records containing observed feature deviations, conditional hypotheses, alternative causes, recommended verification actions, and safety notes. Thus, the component-removal analysis verifies the functional separation and implementation behavior of the two post-classification stages. It does not demonstrate that the generated reports improve diagnostic accuracy, human decision-making, or field maintenance effectiveness.

3.4 Multimodal evidence-driven cases and rule-based report organization

To improve the verifiability of the rule-based evidence-organization results, the normal condition at the same monitoring location was used as the reference baseline, and feature effect sizes were calculated between the fault and normal windows. For the jth feature, Cohen’s d was used to quantify the standardized mean difference between the fault and normal conditions, as defined in Equation 11:where μ f , j and μ n , j denote the mean values of the feature under the fault condition and the normal condition at the same measurement location, respectively, and s p , j is the pooled standard deviation of the two groups of samples. The absolute effect size, d j , was used to characterize the relative prominence of differences among features, while the sign of the effect size was retained to indicate the direction of change relative to the normal baseline. Importantly, Cohen’s d was used only to construct structured diagnostic evidence and did not participate in classification, class determination, or model-performance evaluation. To demonstrate how structured evidence constrains the rule-based evidence-organization process, two cases with different modality-dominant characteristics, nozzle blockage and spindle imbalance or eccentricity, were selected for analysis. Their observed evidence, constrained mechanistic hypotheses, and recommended on-site verification actions are described below.

d j = μ f , j − μ n , j s p , j (11)

Under nozzle blockage, resultant vibration RMS increased by 16.96% relative to the same-location normal baseline and mean current increased by 12.03% relative to the within-batch normal current baseline. The report record therefore presents both observed changes, while retaining the alternative possibility that nozzle-end flow conditions contribute to local waveform irregularity. It does not infer causality from the waveform appearance alone.

Under spindle imbalance/eccentricity, the detrended dominant peak was 25.0 Hz on X, Y, and Z-axes, and the resultant vibration RMS increased by 6.15%. The structured record identifies the spindle location, retains the quantitative deviations, and proposes inspection of balance and coupling conditions as verification actions. Because the rule stage does not alter classifier probabilities, it cannot compensate for a sensor remounting effect or an unseen operating condition.

These cases illustrate deterministic evidence organization rather than autonomous causal reasoning. The module separates observed facts, conditional hypotheses, alternative causes, verification actions, and safety notes using a fixed template. Predictions with insufficient or topology-incompatible evidence are flagged for manual review.

These two cases are illustrative implementation examples rather than independent validation of report effectiveness. They demonstrate how predefined evidence fields are organized but do not establish that the resulting reports improve human diagnostic decisions or maintenance actions.

4 Discussion

The findings demonstrate the recognition potential of heterogeneous vibration-current fusion within the present experimental batch, but they are bounded by the dataset size, acquisition scheme, and label construction. Every condition was obtained from one continuous experimental run, and the 2-s windows are correlated segments rather than independent whole-machine tests. The reported cross-validation metrics therefore describe recognition across time blocks of this batch, not generalization across independent machines, batches, dates, restarts, or sensor installations.

The current signal was recorded through an independent acquisition chain with a median sampling interval of approximately 0.75 s. Linear interpolation was used only to align slowly varying load trajectories to vibration-window time; it cannot create high-frequency current information. Current features should therefore be interpreted as level, fluctuation, and trend descriptors rather than as a synchronous dynamic measurement.

Triaxial accelerometers were magnetically mounted, and local orientation, mounting force, contact-surface condition, and remounting may change amplitude-related features. The same-location normal reference and resultant/energy features reduce this confounding in the present data, but do not remove it. The axis ablation is correspondingly local to the current sensor mounting and should not be read as a universal ranking of X, Y, and Z directions.

For a practical deployment, each sensor should be installed at a registered location with a documented local-axis convention and a repeatable mounting procedure. A same-location normal reference should be reacquired after remounting, replacement, or a material change in the contact surface; if this reference cannot be established, the system should retain the numerical output only as a screening result and flag it for manual review. This is an operational control policy, not a validation of remounting robustness in the present dataset.

The fault labels are also coupled to predefined monitoring locations: the pump is associated with F01, the nozzle with F02/F03, the spindle with F04, and the abrasive tank with F05. Model performance may therefore exploit a combined monitoring-location and condition signature. A deployment setting in which a fault can occur at an unknown location, or where location must first be inferred, requires a different experimental design and validation protocol.

Future work should use independent operating batches as the experimental unit and include shutdown-restart cycles, repeated sensor mounting, cross-date tests, varied pressure/feed conditions, and more than one machine. Cross-batch, cross-condition, and leave-one-location-out evaluation should be reported before claiming robust fault diagnosis. Digital-twin-based feature support, graph-guided multichannel fusion, and multilevel fusion under limited data are relevant directions for this expansion (Yu et al., 2025; Yu et al., 2026a; Yu et al., 2026b). A more rigorous physical analysis of vibration-current complementarity requires synchronized measurements of hydraulic, flow, and rotational variables, including pump pressure, nozzle pressure, abrasive-flow rate, water-flow rate, and spindle speed. These variables were not directly recorded in the present experiment. Future work will therefore combine repeated controlled fault experiments with synchronized multi-physics measurements to distinguish local structural excitation from whole-machine load responses and to evaluate their class-specific diagnostic contributions under varied operating conditions.

The empirical support for the post-classification procedure is limited to the 24-pair rule-matrix implementation test, prediction-invariance checks, and two illustrative cases. No independent domain-expert or user evaluation was conducted. Accordingly, this study does not claim that the generated reports improve human decision-making, user acceptance, or field maintenance effectiveness. These outcomes require blinded multi-expert evaluation and prospective deployment studies.

5 Conclusion

This study developed a heterogeneous vibration-current framework for within-batch recognition of Normal and five predefined component faults of a high-pressure abrasive waterjet machine tool at predefined monitoring locations. The framework combines local triaxial vibration features with slowly varying machine-current features and adds a deterministic topology-and-evidence organization step after classification.

• The two modalities provided complementary within-batch observations. Relative to same-location normal baselines, resultant vibration RMS increased by 16.86% for F01, 16.96% for F02, 8.24% for F03, 6.15% for F04, and 7.39% for F05. Mean current increased most for F02 (+12.03%), while F05 was characterized mainly by a rise in current fluctuation rather than a mean - current shift.
• Under fivefold contiguous time-block validation of 513 component-window samples, feature-level fusion SVM achieved 98.27% ± 3.88% Macro-F1 versus 91.21% ± 2.77% for current-only SVM and 83.77% ± 11.36% for vibration-only SVM. Adaptive decision fusion (99.64% ± 0.50%) was comparable to equal-weight fusion (99.66% ± 0.75%), not demonstrably superior. Joint-feature Random Forest and Extra Trees results are reported as additional internal baselines.
• The auxiliary post-classification procedure deterministically checks location–state compatibility and organizes structured evidence without altering classifier outputs. The complete rule matrix was implemented correctly, and all 513 predictions remained unchanged after post-processing. These results verify implementation behavior only; report utility, user acceptance, and field effectiveness remain to be evaluated independently.

These findings are limited to recognition across contiguous time segments within the present single experimental batch. They do not establish generalization across independent machines, operating batches, dates, operating conditions, shutdown/restart cycles, sensor remounting, or unknown fault locations.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

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Footnotes

Edited by: Nand Jee Kanu, Jayawant Shikshan Prasarak Mandal (JSPM), India

Reviewed by: Musaab Zarog, Sultan Qaboos University, Oman

Xin Liu, Tsinghua University, China

Guangsheng Zhou, Wuhan University of Technology, China