The acoustic signature of a wind turbine main shaft is characterized using the EZR (Zhou and Wu, 2022; Wang et al., 2021), which effectively combines frame level energy and zero crossing information to highlight defect related patterns. A dual threshold segmentation algorithm is applied to localize high EZR regions, which are then normalized to form sample matrices for subsequent input into the MSCNN. The complete procedure is as follows.

Let x n denote the acquired acoustic waveform. After windowing and framing with frame length N, the ith frame signal x i n is obtained. The frame energy is calculated as in Equation 1: E i = ∑ n = 1 N x i 2 n (1)

To mitigate the misinterpretation of transient noise as defect onset or offset, an enhanced energy measure introduces a robustness constant (Equation 2): L E i = log 10 1 + E i a (2)

The robustness constant α = 0.003 (range 0.001 , 0.005 ) was determined through pilot experiments on 100 training samples, providing an optimal balance between noise suppression and feature preservation. Values below 0.001 exhibited excessive sensitivity to noise, while values above 0.005 tended to over-smooth critical transient features.

To stabilize the calculation of the zero-crossing rate (ZCR) and eliminate minor zero drift artifacts, a central clipping operation is applied to the framed signal as in Equation 3, x i n : x ∼ i n = x i n , x i n ≥ δ 0 , x i n ≥ δ (3)

The center-cropping threshold δ is a dimensionless scaling parameter. The value δ = 0.7 was selected from the range [0.5, 1.0] based on maximizing drift artifact removal effectiveness (91% effectiveness) while minimizing signal distortion (<3.5% relative error).

Following central clipping, the ZCR of each frame is computed as in Equation 4, where the sign function is defined in Equation 5: Z C R i = ∑ n = 1 N sign x ∼ i n − sign x ∼ i n − 1 (4) sign x ∼ i n = 1 , x ∼ i n ≥ 0 − 1 , x ∼ i n < 0 (5)

The Energy to Zero Ratio (EZR) is then defined as in Equation 6: E Z R i = L E i Z C R i + b (6)

The regularization parameter b = 0.03 (range [0.01, 0.05]) ensures numerical stability when the zero-crossing rate (ZCR) approaches zero (condition number <500), avoiding the overflow errors observed with b ≤ 0.02 while preventing the systematic bias (<0.5%) associated with b ≥ 0.04 .

The dual-threshold segmentation mechanism adopts a two-level decision process to reliably identify defect-related acoustic events. The high threshold T 2 is set to the 95th percentile of the EZR distribution across all training samples, yielding T 2 = 0.035 . This percentile-based rule robustly triggers candidate defect waves while limiting false positives from stochastic noise spikes. The low threshold T 1 is fixed at 0.015 ( ≈ 43 % of T 2 ), determined via receiver operating characteristic (ROC) analysis to balance detection sensitivity and false-alarm rate. Operationally, when an EZR excursion exceeds T 2 , the algorithm searches bidirectionally (backward and forward in time) for the nearest intersections with T 1 , which define the temporal boundaries of the acoustic signature. This hysteresis strategy captures complete defect signatures despite transient EZR fluctuations. Thresholds were validated by a grid search over T 2 ∈ 0.025 , 0.045 and T 1 / T 2 ∈ 0.3 , 0.5 on the validation set; the selected pair ( T 2 = 0.035 , T 1 = 0.015 ) achieved the highest F1-score (0.92), confirming their effectiveness for wind-turbine main-shaft defect detection.

For individual acoustic signature extraction, the ultrasonic signal is processed frame-by-frame to compute energy and EZR, from which a smoothed EZR sequence is obtained. The dual-threshold scheme then delineates segment boundaries: when EZR first exceeds T 2 , a significant event is flagged; the start point is set by backtracking to where EZR falls below T 1 , and the end point is set when EZR again drops below T 1 . This procedure yields stable boundaries and shows strong robustness to noise. To meet the MSCNN input requirements, each extracted segment is resampled to a fixed duration and amplitude-normalized to ensure consistency in temporal length and signal magnitude. In this design, T 2 provides precise event triggering, whereas T 1 supplies hysteresis, suppressing noise while preserving the completeness of defect information.

This procedure, illustrated in Figure 1, exemplifies the extraction of individual acoustic features from a wind turbine main shaft using the EZR method. The left panel shows the raw ultrasonic echo signal, which includes the transmitted wave, intrinsic structural wave, and backwall reflection from the shaft. By applying the dual threshold EZR segmentation method, high EZR segments correlated with potential defects are isolated (as highlighted by the middle arrow). The right panel displays the resulting acoustic signature, comprising both the intrinsic structural response and the moderate crack reflection, which serves as the standardized input for subsequent MSCNN based feature learning.

To address the limitations of conventional CNN based crack detection models such as restricted feature expressiveness from fixed size convolution kernels and insufficient multi-dimensional feature extraction this study proposes a MSCNN tailored to the characteristics of acoustic wave signals (Huang and Wang, 2019; Chen et al., 2024; Fu et al., 2020). The MSCNN employs parallel convolutional branches with kernels of varying sizes to extract features at different temporal scales. Small kernels capture fine grained, short term details, whereas large kernels extract broader, long term structural patterns, enabling the network to model the diverse morphology and topology of crack related signals. The framework diagram of the multi - scale convolutional neural network is shown in Figure 2.

A CNN is a deep, feed forward network characterized by convolutional operations, sparse connections, and weight sharing. A one dimensional architecture is adopted because: (i) the EZR feature already encodes time-frequency information; (ii) 1D inputs better preserve temporal structure of transient crack signatures; and (iii) computational efficiency is critical for real-time monitoring. In MSCNN, convolution kernels of different sizes operate in parallel, each followed by a pooling layer, allowing simultaneous extraction of multi scale temporal features. Formally, the convolution operation is expressed as in Equation 7: f e a i , j l = f b i l + ∑ i = 1 d W i l , x t + d − i l − 1 (7) where x t + d − i l − 1 is the input 1D sequence, x t + d − i l − 1 is the weight tensor with F l output channels and F l − 1 input channels, b l ∈ R F l is the bias term, d ⊆ 3 , 5 , 7 is the kernel size for capturing multi-scale patterns, and different strides match the temporal scale of interest. The activation function f · is ReLU, chosen because: (i) its sparsity aligns with the clustered sparse energy distribution of acoustic signals; (ii) it suppresses low amplitude noise leakage compared to Leaky ReLU; and (iii) combined with batch normalization, it achieves faster convergence and smaller generalization gaps on our dataset without observable dying neuron effects.

Following convolution, the max-pooling operation is defined in Equation 8: p m , n h = max n − 1 g < t < n g f e a m , t h , n = 1 , 2 , … (8) where f e a h m , t denotes the activation of the hth neuron in the mth feature map of at layer t, g is the pooling kernel width, and p h m , n is the output of the pooling operation. Max-pooling serves multiple purposes: (i) reducing temporal dimensions by half while retaining salient features, (ii) providing translational invariance to minor temporal shifts in crack signatures, and (iii) acting as an implicit regularizer by reducing feature map complexity. Batch normalization, applied before each activation, stabilizes training by normalizing layer inputs, which is particularly beneficial in data-scarce scenarios where gradient estimates from small batches can be unstable. Together, these techniques reduce overfitting risk and accelerate convergence, as evidenced by our ablation studies. This multi-scale framework enhances temporal feature diversity, enabling the model to robustly identify both common and complex crack patterns in wind turbine main shafts.

Outputs from all branches are concatenated into a unified feature vector, followed by batch normalization (BN) to stabilize training and accelerate convergence. The final representation is expressed as in Equation 9: Y = f g c b short , b midium , b long (9) where b short , b midium , and b long are the short, medium, and long term features, respectively; ⊕ denotes the feature concatenation operation.

To address the limited feature representation capability of conventional fixed-kernel CNNs in capturing multi-scale acoustic characteristics of crack defects, we propose an integrated framework that combines ultrasonic guided wave acquisition, EZR-based signature extraction, and MSCNN classification. The MSCNN employs parallel convolutional branches with varying kernel sizes to extract features across multiple temporal scales, enabling robust identification of diverse crack types in wind turbine main shafts. Notably, the framework can recognize previously unseen compound crack patterns through similarity based decomposition, eliminating the need for exhaustive training data covering all possible defect combinations. The proposed framework comprises four main stages, progressing from raw ultrasonic signal acquisition to classification of previously unseen crack patterns, as illustrated in Figure 3.

Step 1: Extraction of individual acoustic signatures based on the EZR

Raw acoustic signals are segmented through windowing and framing operations to produce temporal frames of specified length with partial overlap. For each frame, the energy and zero-crossing count are computed to derive the EZR feature, which effectively captures localized acoustic variations under different structural states. A dual-threshold segmentation algorithm is then applied to isolate salient acoustic signatures, followed by z-score normalization and length standardization. This preprocessing stage enhances crack induced acoustic anomalies while suppressing ambient noise, producing standardized feature matrices suitable for subsequent neural network processing.

Step 2: Multi-scale feature construction using MSCNN

The normalized EZR matrices are fed into the MSCNN as one-dimensional time-series inputs, preserving temporal dependencies crucial for detecting transient defect signatures. The MSCNN employs three parallel convolutional branches with different kernel sizes to capture features across multiple temporal scales. Each branch consists of successive Conv1D–MaxPool1D blocks with progressively increasing channel dimensions. Features extracted from all branches are concatenated into a unified high-dimensional vector, which is further refined by fully connected layers to enhance discriminative capability for crack identification.

Step 3: Detection and classification of unknown conditions

For unknown shaft conditions, the EZR based acoustic signature is extracted following the Step-1 procedure. The signal is subsequently segmented to isolate individual acoustic components, because complex or compound cracks typically manifest as multiple high-amplitude regions in the EZR sequence, each corresponding to a distinct structural anomaly. Empirically, different crack configurations exhibit characteristic EZR patterns: a healthy shaft presents a single peak reflecting the inherent structural response; single-crack states exhibit two peaks; and multi-crack states present three or more peaks. Each segmented component is independently input to the trained MSCNN to obtain a deep feature vector, which is then matched against the reference acoustic-signature library using cosine similarity as defined in Equation 10: sim v q , v r = v q · v r v q , v r (10) v q ∈ R d is the query vector, the deep feature of a segmented acoustic component from an unknown sample, with v q = f x , f · denote the trained MSCNN embedding function. v r ∈ R d is the reference vector, the prototype vector of class in the reference library, computed from training embeddings.

The reference library comprises prototype feature vectors for the elementary crack categories: inherent structure, small crack, medium crack, and significant defect. If the maximum similarity falls below a predefined threshold (as specified in the experimental section), the component is classified as healthy; otherwise, it is assigned to the crack category with the highest similarity. For compound cracks, all constituent components are identified and their similarity scores are reported, yielding a comprehensive diagnosis.

Step 4:Classification output and validation

This decomposition based strategy enables the framework to identify previously unseen compound crack patterns by representing them as combinations of known elementary crack types. Specifically, the method can recognize novel multi-crack states using models trained only on basic single crack categories, thereby significantly improving data efficiency and scalability. The validation design for both known and unknown crack states is detailed in Tables 3, 4, demonstrating the framework’s strong generalization capability to unseen defect patterns.

The experimental investigation was carried out on a megawatt class wind turbine main shaft located at a wind farm in Yunnan Province, China. The physical characteristics of the tested main shaft are summarized in Table 1. The shaft is installed within a semi enclosed compartment characterized by limited space and densely arranged equipment. Due to structural constraints, inspection devices can only access the exposed end face near the blade side, while the remaining sections are enclosed within a protective casing. To enable testing without dismantling the shaft, the exposed end face was selected as the inspection location, and the pulse echo method was adopted for ultrasonic signal acquisition.

Considering the inspection depth, an excitation frequency of 4 MHz and a 34 mm diameter straight probe were selected to achieve an optimal balance between penetration depth and defect resolution, in line with industry standards for wind turbine component inspection. Figure 4 illustrates the experimental setup and ultrasonic signal acquisition process. The data acquisition system comprised high precision ultrasonic sensors, signal conditioners, and a data acquisition card with a 100 MHz sampling frequency to ensure capture of fine signal details.

To simulate realistic and variable crack conditions, artificial cracks of varying sizes (minor, moderate, and major) were introduced across the shaft, with their strategic distribution designed to replicate overlapping and heterogeneous defect conditions.

Three fabrication techniques were employed. This approach enabled the acquisition of acoustic signature signals representing both isolated and composite crack states. Artificial cracks with precisely controlled dimensions were fabricated using three primary methods. Electric discharge machining was employed for small and medium sized cracks, utilizing a 0.2 mm wire to produce defects with high dimensional accuracy and well defined boundaries, while minimizing alterations to the surrounding material properties. Ultrasonic Impact Treatment was applied at selected locations to induce microcracks resembling fatigue induced natural cracks through high frequency impact loading. Mechanical Notching, performed with specialized 0.5 mm tungsten carbide tools, was used to create large cracks with controlled depth and geometry.

Based on statistical data from actual failure cases in the wind energy industry and the structural characteristics of the main shaft, three representative crack sizes were designed: (1) Minor cracks: length 5–10 mm, width 0.2–0.3 mm, depth 2–3 mm; (2) Moderate cracks: length 15–25 mm, width 0.3–0.4 mm, depth 4–6 mm; (3) Major defects: length 30–50 mm, width 0.5–0.7 mm, depth 8–12 mm. To ensure the representativeness of the artificial cracks, their ultrasonic reflection characteristics were compared with those of naturally occurring cracks in defective main shafts retrieved from in service wind turbines. A high degree of similarity (>90%) in waveform features, reflection amplitude, and spectral distribution confirmed that the fabricated cracks effectively replicated natural defect conditions.

A total of eight operating states of the wind turbine main shaft were recorded, covering the healthy condition, single crack states, and multiple crack states. For each state, 400 acoustic signature samples were collected. The acoustic signature data were labeled according to structural components and crack sizes. Table 2 summarizes the operating states, their identifiers, detailed descriptions, and the corresponding extracted acoustic signatures.

As shown in Table 2, the inherent structure component is present in all eight states, yielding 3,200 samples in total (400 per state). Minor cracks appear in C2, C5, C6, and C8, providing 1,600 samples. Moderate cracks are present in C3, C5, C7, and C8, also totaling 1,600 samples. Major defects occur in C4, C6, C7, and C8, likewise totaling 1,600 samples.

To evaluate the model’s capability in identifying unknown crack types, the eight operating states were divided into two distinct datasets as shown in Table 3.

As shown in Table 3, Dataset A (C1–C4) contains healthy and single-crack states and serves as the known-state dataset. Dataset B (C5–C8) contains multiple-crack states and serves as the unknown-state dataset.

Two validation experiments were designed: (1) Recognition of known crack defect states to verify model accuracy for known defects. (2) Recognition of unknown crack defect states–to evaluate generalization to unseen multiple-crack states.

As shown in Table 4, in Experiment 1, 70% of Dataset A was used for training and 30% for testing, resulting in 1,120 and 480 samples, respectively. In Experiment 2, all samples from Dataset A were used for training, while Dataset B served as the test set, each containing 1,600 samples. This rigorous experimental design ensured that the model was never exposed to composite crack data during training, thereby enabling an objective evaluation of its capability to learn from fundamental crack features and generalize to more complex scenarios. Such a design is crucial for validating the practical applicability of the proposed method, as it directly addresses the challenges encountered in real-world engineering applications.

Table 5 presents the detailed network architecture parameters of the MSCNN, including the kernel sizes, strides, padding, channel configurations for each branch, and the output dimensions at each stage.

Table 5 presents the detailed parameters of the MSCNN architecture. The network employs a three branch design with kernel sizes of 7, 5, and 3 to extract multi-scale temporal features from the 1 × 1024 EZR acoustic signatures. Each branch contains three consecutive Conv1D–MaxPool1D blocks with progressively increasing channels (32, 64, and 128). The outputs from the three branches are concatenated, followed by a global average pooling layer and a two-layer fully connected (FC) classifier for four-class defect recognition.

The collected acoustic signals are first subjected to noise reduction processing, followed by adaptive extraction of acoustic signature features.

As shown in Figure 5, the horizontal axis represents the ultrasonic propagation distance along the wind turbine main shaft. In Figure 5a, the raw ultrasonic signal exhibits substantial random fluctuations and high-frequency noise, which obscure meaningful features and make the waveform appear chaotic. In contrast, Figure 5b presents the denoised signal, where the waveform is noticeably smoother, the main peaks are more distinct, and high-frequency noise is effectively suppressed. This enhancement improves both feature clarity and signal interpretability. Notably, pronounced peaks and discontinuities particularly near 1500 mm and 2000 mm are clearly visible after denoising, indicating potential defect-related features. Overall, the denoising process effectively removes high-frequency interference while preserving critical structural information, thereby producing a cleaner, more analytically useful signal suitable for feature extraction and defect localization.

To identify the onset and endpoint of high-threshold intervals corresponding to potential defects, a double-threshold segmentation method is applied to the EZR processed acoustic signal. Each individual acoustic signature is defined as a fixed-length segment starting from the onset point determined by the double-threshold method, enabling targeted feature extraction. Following segmentation, each signature is normalized, and a sample matrix is constructed for input into the MSCNN.

As illustrated in Figure 6, the proposed algorithm incorporates two level decision mechanism based on EZR. In the first stage, a high threshold T2 is applied to the short time EZR curve to preliminarily identify candidate structural or defect waves, the segment between points A and B. In the second stage, a lower threshold T1 is introduced. From point A, the algorithm searches leftward, and from point B, rightward, to locate points C and D where the signal intersects T1. These points define the start and end of the acoustic signature. To ensure uniform segment lengths, the waveform beyond T1 is extended to a fixed duration. The segmented acoustic signal is thus divided into fixed length individual signatures, with their start and end positions marked by solid and dashed black lines in the figure. Experimental results demonstrate that this method effectively distinguishes between defect-free and defective signals, providing a robust dataset for subsequent defect identification and classification. The resulting segmented acoustic signatures are shown in Figure 7.

As shown in Figure 7, the four types of acoustic signatures correspond to the inherent structure, minor crack, moderate crack, and major defect. In Figure 7a, a single prominent peak represents the inherent structure, the normal ultrasonic propagation path in a structurally intact shaft indicating no interference from cracks or defects. In Figure 7b, a minor secondary peak near 1700 mm suggests a small defect, such as a shallow crack, with limited structural impact. Figure 7c reveals a more pronounced secondary peak in the same region, indicating a medium-sized crack with higher energy reflection. In Figure 7d, the secondary peak near 1700 mm exhibits significantly greater amplitude than in the small and medium defect cases, indicating a major defect or severe material flaw that may require urgent intervention. Across all cases, the inherent structure is consistently observed, underscoring its role as a fundamental ultrasonic feature of the main shaft. Furthermore, the amplitude of the reflected peak increases with defect severity from small to large defects demonstrating that peak amplitude in ultrasonic signals serves as a reliable indicator for defect sizing and severity assessment. This finding provides a valuable basis for non-destructive evaluation of main shaft integrity in wind turbines.

The experimental results demonstrate that the crack feature maps extracted by the MSCNN model at different scales exhibit strong discriminative ability. Compared with single-scale convolution, the multi-scale convolution approach significantly enhances the accuracy of crack detection.

As shown in Figure 10, the t-distributed Stochastic Neighbor Embedding (t-SNE) method is used to visualize the dimensionally reduced feature distributions obtained through different feature extraction methods applied to acoustic signals from the wind turbine main shaft (van der Maaten and Hinton, 2008). These include the raw input signal, features extracted by a CNN, and features extracted by the MSCNN model trained on either known or unknown defect types. Figure 10a shows that the raw signal lacks discernible structure, with feature points for various defects and inherent structural components appearing scattered and overlapping. This confirms that without feature extraction, differentiating between defect types is difficult, underscoring the necessity for advanced feature extraction methods. Figure 10b presents the feature distribution obtained by the CNN model. Compared with the raw signal, the CNN extracted features exhibit preliminary clustering for inherent structure, minor defects, moderate defects, and major defects. However, overlap remains—particularly between minor and moderate defects—indicating that while CNN improves separability, it still struggles with complex defect distinctions. In Figure 10c, the MSCNN model trained on known defect types yields distinctly separated clusters for each class. Feature points corresponding to inherent structure, minor, moderate, and major defects are tightly grouped, with minimal overlap. Notably, the boundary between minor and moderate defects is significantly clearer, demonstrating the superior feature extraction and classification performance of MSCNN when guided by known defect labels. Figure 10d shows the feature distribution generated by the MSCNN model without prior knowledge of defect types. While separability remains superior to that achieved by CNN, it is less distinct than in the known-defect scenario. Some overlap between defect classes persists, particularly between minor and moderate defects. This suggests that although MSCNN can extract discriminative features in unsupervised contexts, the guidance of known labels markedly improves classification performance.