Acoustic detection of fan blade faults based on dynamic Cauchy swarm algorithm to optimize support vector machine

2.1. Detection acoustic signal preprocessing

In the initial stage of the wind turbine blade fault acoustic detection system, it is necessary to preprocess the original acoustic signal acquired. The main purpose of this step is to remove noise and interference components from the signal, improve the signal quality, and lay a solid foundation for subsequent feature extraction and frequency-domain analysis. The blades operate in the field for a long time, subject to not only environmental factors such as wind, sand, rain, snow, extreme temperatures, and wind gusts, but also the mechanical forces from the wind turbine. As a result, the collected acoustic signal contains various complex and highly variable strong background noise components, including wind, thunder, rain, and variable pitch noise. When early-stage blade faults occur, the acoustic energy is weak and easily masked by strong background noise. Owing to the limitations of the experimental conditions, the background noise contained in the collected blade acoustic signal is primarily wind noise. Currently, the operational threshold of the wind turbine is generally when the average wind speed exceeds 3.5 m/s, and when the wind speed reaches 12 m/s, the sound pressure level of the wind noise can reach 100 dB. Compared to other background noises, the impact of wind noise is particularly pronounced. Therefore, wind noise must be filtered before extracting the acoustic fault characteristics of the blades.

The spectral energy of wind noise is predominantly concentrated below 200 Hz, whereas fault-induced acoustic signals (e.g., those generated by blade cracking) exhibit a broad frequency range extending to several kHz. Given the rapid attenuation of high-frequency components and the considerable distance between detection microphones and blades, the acquired high-frequency signal energy becomes significantly attenuated in practice, which reduces fault diagnosis reliability. To address this limitation, the present study employed a bandpass filter for preprocessing raw acoustic signals.

To achieve the flattest possible frequency response curve in the wind turbine blade’s passband, a Butterworth bandpass filter is selected in this study, and the blade’s square amplitude-frequency response function is as follows:

Among them:

where $N$ represents the filter order [7], ${\mathrm{\Omega }}_c$ denotes the 3 dB cutoff frequency, ${\mathrm{\Omega }}_u$ specifies the upper cutoff frequency, and ${\mathrm{\Omega }}_l$ indicates the lower cutoff frequency of the fan blade filter. Higher values of $N$ yield flatter passband characteristics and narrower transition bands, resulting in improved filtering performance at the cost of increased computational complexity.

Considering the computational efficiency and real-time processing requirements, the filter order is set to 30-50. To balance between excluding excessive noise (caused by an overly wide passband) and preserving useful signals (which might be filtered out with an excessively narrow passband), the lower cutoff frequency is selected as 50-200 Hz and the upper cutoff frequency as 10-15 kHz.

2.2. Feature extraction of fan blade sound signal

After preprocessing the acoustic signal, feature extraction is performed. This key step in wind turbine blade fault identification involves extracting signal characteristics that reflect blade operational status. Since wind turbines require minimum wind speeds to generate power, blade rotation inevitably occurs with higher wind speeds and consequently greater wind noise. The acquired acoustic signals additionally contain natural background noise and mechanical noise from yaw operations or cooling duct operation. Analysis of field-recorded signals reveals that blade-sweeping wind noise has the most significant impact on fault acoustic signals compared to other noise sources, being both persistent and high-intensity. Given that wind noise primarily occupies the low-frequency band while fault-induced acoustic signals demonstrate broad spectral distributions, this study utilizes a Butterworth bandpass filter for preprocessing. This method effectively suppresses low-frequency wind noise while retaining essential fault features, achieving preliminary audio denoising. Importantly, acoustic signal analysis typically focuses on macroscopic energy distribution patterns rather than precise frequency-point energy measurements.

The human audible frequency range can be systematically divided into sub-bands according to psychoacoustic principles, typically maintaining a constant ratio between upper and lower cutoff frequencies. Within each sub-band, the sound energy is considered uniformly distributed, allowing comprehensive analysis of spectral energy distribution across all frequency ranges [8]. Octave-based signal feature energy extraction involves two main processing stages:

1) The full frequency band of the fan blade is divided into several subbands.

Where $f_t$, $f_b$, and $f_i$ represent the upper cutoff, lower cutoff, and center frequencies of each sub-band, respectively. Their relationships are defined as:

When $n$ = 1, the division is termed an octave [9]; when $n$ = 1/3, it becomes a 1/3 octave. The parameter $n$ must be properly selected according to specific analysis requirements. For higher frequency resolution that necessitates narrower sub-bands, $n$ should be set to smaller values.

2) The acoustic energy within each fan blade frequency band is computed.

Let $P_j$ denote the energy of the $j$-th frequency band and $F$ represent the spectral amplitude of the acoustic signal. The sub-band acoustic energy is calculated as:

This energy is then converted to sound pressure level using the following transformation:

where $P_{ref}$ is the reference sound pressure (typically 2×10⁻⁵ Pa in atmospheric conditions) [10], and $S_j$ represents the sound pressure level for the corresponding fan blade frequency band.

2.3. Frequency domain analysis of fan blade signal

Based on the extracted features, frequency domain analysis is performed on the wind turbine blade's acoustic signal. This analysis reveals the signal’s spectral distribution characteristics and facilitates identification of frequency variations induced by blade faults. As a primary approach for vibration signal analysis, frequency domain analysis examines the blade signal’s frequency spectrum through Fourier transform to obtain its amplitude and phase spectra. The method extracts the signal’s frequency components, reflecting the vibration signal’s intrinsic frequency structure through each wind turbine component’s natural frequency. According to theoretical mechanics principles, the wind turbine blade constitutes a single-degree-of-freedom first-order elastic system, with its first-order natural frequency $f$ calculated as shown in Eq. (6):

where $k$ represents the wind turbine blade stiffness coefficient, which is determined by the material properties at a specific location [11]. $m$ denotes the mass at that location, and $\pi$ represents the constant of PI, the value is 3.14. This relationship demonstrates that when the local stiffness is high and the mass is low, the natural frequency increases; conversely, with lower stiffness and higher mass, the natural frequency decreases. Modal analysis of the wind turbine blades reveals that their vibration natural frequency ranges from 0.3 Hz to 1.2 Hz.

This study proposes a frequency-domain methodology for analyzing blade natural frequency migration, consisting of two components: (1) comparative analysis of natural frequencies among three blades within the same unit during identical operational periods, and (2) temporal comparison of natural frequency variations for individual blades across different operational periods within the same unit. The three-blade comparative analysis procedure is implemented as follows. First, the Fourier transform (FFT) method is employed to extract the first-order natural frequencies of the blades from the blade pendulum data $y\left(t\right)$ during a specific period, denoted as $F_y$. Second, the blade’s natural frequency factory value N corresponding to its serial number is obtained from the blade factory report. Finally, the relationship between $F_y$ and $F_n$ is compared to evaluate the blade’s natural frequency variation [12].

When ice accumulates on the blade, the blade mass increases. According to the first-order natural frequency formula $f$, when the blade stiffness coefficient remains constant, $F_y<F_n$. Conversely, when the blade stiffness coefficient decreases due to blade cracking, the first-order natural frequency formula $f$ shows that for constant blade mass, $F_y>F_n$.

The comparative analysis method for evaluating natural frequency variations of the same blade across different operational periods involves the following steps. The blade oscillation arrays are defined as $y\left(a\right)$ and $y\left(b\right)$, where $y\left(a\right)$ represents earlier time data than $y\left(b\right)$. First, the Fast Fourier Transform (FFT) method is applied to extract the first-order natural frequencies $F_a$ and $F_b$ from the oscillation data $y\left(t\right)$. Second, the relationship between $F_a$ and $F_b$ is analyzed to assess blade natural frequency changes. When $F_a$ corresponds to normal operation (pre-icing) and $F_b$ to post-icing conditions, the increased blade mass yields $F_b>F_a$ according to the first-order natural frequency formula $f$. Conversely, when $F_a$ represents normal operation (pre-cracking) and $F_b$ post-cracking conditions, the reduced stiffness coefficient results in $F_b<F_a$. For cross-unit comparison within the same wind field, natural frequencies are normalized to dimensionless frequency coefficients using Eq. (7):

where $H$ represents the dimensionless natural frequency coefficient of the blade [13], $F_y$ denotes the natural frequency extracted from real-time blade oscillation data, and $F_n$ corresponds to the nominal natural frequency value from the blade manufacturer's factory report for the specified blade designation.

3.1. Dynamic Cauchy swarm algorithm is used to optimize parameters of support vector machine

Following acoustic signal processing and analysis, the dynamic Cauchy bee colony algorithm (DCABC) is employed to optimize support vector machine (SVM) parameters. As a powerful classification tool, SVM plays a crucial role in wind turbine blade fault detection, though its performance significantly depends on parameter selection. The DCABC algorithm identifies optimal SVM parameter combinations within the search space to enhance fault detection accuracy and efficiency. This algorithm simulates actual bee foraging behavior through three distinct roles: employed bees, onlooker bees, and scout bees. During initialization, the number of food sources equals the colony size, with each source’s location representing a potential solution. The algorithm first randomly generates an initial population, then conducts local searches around the top 50 % individuals with superior fitness values through competitive selection. Subsequently, onlooker bees employ a roulette wheel selection strategy to identify promising solutions for intensive neighborhood searches, generating the remaining population members. Finally, scout bees explore new regions when existing food sources are abandoned. The total number of food sources is denoted as $N$. The initial positions randomly generated within the blade's solution space is expressed as:

where $X_{jmax}$ is the upper boundary of the fan-blade colony search range [14]; $X_{jmin}$ is the lower boundary of the search range of a bee colony on a fan blade; $\text{rand}\left(\mathrm{0,1}\right)$ is a random number between 0 and 1.

According to Eq. (9), the employed bees randomly select food sources for crossover search, update the food source positions, and generate new candidate solutions. The fitness value of each new solution is evaluated using the greedy criterion to determine whether it replaces the current optimal solution for wind turbine blade fault detection:

where $k\in \left\{\mathrm{1,2},\cdots ,N/2\right\}$, $j\in \left\{\mathrm{1,2},\cdots ,n\right\}$, and $k\ne i$; ${\phi }_{ij}$ are random numbers between [–1, 1].

The onlooker bee selects a food source for exploitation based on probability $P_i$ through roulette wheel selection [15], computes the corresponding fitness value from its neighborhood search using Eq. (10), and applies the greedy criterion to determine whether to accept the new solution as the optimal solution for wind turbine blade fault detection:

where $f_{iti}$ is the fan blade moderation function value of $X_i$:

where $f_i$ represents the objective function value of the $i$-th solution for the fan blade [16]; $abs\left(f_i\right)$ is the reference absolute value.

If the nectar source $X_i$ remains unchanged after a predetermined number of limit searches, it is abandoned. The corresponding employed bee transitions to a scout bee and randomly generates a new nectar source according to Eq. (11) to replace the original solution for subsequent iterations.

Due to the stochastic nature of search step size determination, conventional onlooker bee neighborhood searches around selected food sources may fail to ensure sufficient global exploration during initial phases while potentially converging to local optima in later stages. To address this limitation, the proposed swarm optimization algorithm dynamically adjusts search ranges by: (1) expanding exploration scope during initial iterations, and (2) progressively intensifying search near identified promising solutions. Although linear adjustment of step size reduces randomness, it may induce premature convergence. This study introduces a dynamic factor $w$ to modify the wind turbine blade objective function as follows:

where $w_{min}$ denotes the minimum inertia weight of the fan blade [17]; $w_{max}$ is the maximum inertial weight of the fan blade; $f_i$ denotes the fitness value of the fan blade solution, and the position update formula for leader and follower bees is given by:

As shown in Eq. (14), during the initial phase when iteration count $t$ is small, the dynamic weighting factor $w$ remains large. This expanded dynamic factor widens the colony’s search range, enabling the algorithm to escape local optima while maintaining solution diversity and preventing oversight of global optima. In later search stages when $t$ increases, the reduced $w$ value enhances employed bees’ local search capability near promising solutions, thereby improving the algorithm’s dynamic search performance.

When the number of employed bees exploiting a given food source reaches the abandonment limit, these bees transition to scout bees and generate new solutions through random exploration. To enhance the algorithm's perturbation capability beyond this inherent randomness, this study incorporates the Cauchy distribution into the scout bees’ search mechanism. This modification strengthens the algorithm's ability to escape local optima. The Cauchy probability density function for the wind turbine blade optimization is defined as follows:

Eq. (15) demonstrates that when $t=$1, $f\left(x\right)$ follows the standard Cauchy distribution Cauchy(0,1). The corresponding function generated by this Cauchy random variable is $\beta =\tan [\alpha -1/2\pi ]$, where $\alpha$ represents a uniformly distributed random variable in the interval [0, 1] [18].

The fan blade search formula for scout bees is defined as:

The parameter optimization procedure for the support vector machine using the dynamic Cauchy bee colony algorithm (DCABC) is implemented through the following steps:

(1) Algorithm Initialization: Set the abandonment limit lim and maximum iterations $N$. Since both the penalty parameter $C$ and kernel parameter $y$ require optimization, the solution dimension $D=$2. Randomly generate initial solutions, encode $C$ and $\gamma$ values into the SVM model, evaluate classification accuracy on wind turbine blade training samples to determine fitness values using DCABC, and record these initial solutions with their corresponding fitness values.

(2) Employed Bee Phase: Employ Eq. (14) for guided random search of new food sources. If a new solution's fitness surpasses the current solution's fitness, update the solution; otherwise, retain the current solution.

(3) Probability Calculation: Compute selection probabilities for all solutions using Eq. (10).

(4) Onlooker Bee Phase: Onlooker bees select solutions via roulette wheel selection based on probabilities, perform neighborhood searches using Eq. (14), and evaluate fitness. Update the global best solution if improved solutions are found.

(5) Scout Bee Phase: If a solution's fitness shows no improvement after lim iterations, the employed bee becomes a scout bee to discover new solutions via Eq. (16).

(6) Solution Recording: Store the current optimal solution after each iteration.

(7) Termination Check: If reaching maximum iterations $N$ or satisfying error thresholds, output the optimal solution; otherwise, repeat from Step (2).

3.2. Evaluation of impeller speed

Following the determination of optimal SVM parameters, the impeller speed is evaluated as a critical operational parameter for wind turbine performance assessment and blade condition monitoring. The speed calculation employs a smoothing algorithm comprising three stages: (1) selection of a frequency band containing pure blade acoustic signatures, followed by frequency-axis normalization of the summed noise $S_t$ to derive a one-dimensional noise power array; (2) application of moving average and bandpass filtering to smooth the noise power curve, where the moving average eliminates high-frequency fluctuations while preserving long-term trends; (3) implementation of the computational process as follows:

where $m\left(t\right)$ denotes the moving average of the fan impeller, computed as the arithmetic mean of data subsets with length equal to 1/4 of the minimum rotation period along the time axis, $\mu$ represents the arithmetic mean length of the fan blade [19], $g\left(t\right)$ corresponds to the bandpass-filtered smooth noise power spectrum of the fan impeller, $F\left[\cdot \right]$ and $F^{-1}\left[\cdot \right]$ are the discrete Fourier transform and its inverse respectively, $R\left\{ \right\}$ extracts the real component of the fan impeller input signal, and $H\left(t\right)$ is a composite bandpass filter combining low-pass and high-pass filters:

where $H_{LP}\left(f\right)$ and $H_{HP}\left(f\right)$ represent the low-pass and high-pass filters for the fan impeller, respectively; $L$ denotes the length of the fan impeller's equal-duration signal; $f_{sample}$ is the acoustic sampling frequency; ${\omega }_{max}$ and ${\omega }_{min}$ correspond to the maximum and minimum rotational speeds of the fan [20]. The speed-related frequency band was isolated through bandpass filtering, effectively suppressing non-speed components in the frequency domain to stabilize the noise power signal. The impeller speed was subsequently determined by calculating three times the reciprocal of the time interval between local minima in the processed signal:

where $T_k$ denotes the $k$-th minimum time point and $R_k$ represents the $k$-th impeller speed recorded on the fan’s time axis.

A local minimum is identified when a value satisfies the condition:

where, $g_{\mathit{min}ima}\left(t\right)$ corresponds to the local minimum value of the impeller signal, $g(t-1)$ and $g(t+1)$ are the adjacent signal values preceding and following the minimum, respectively.

3.3. Implementation of fault acoustic detection

The impeller speed evaluation significantly enhances the reliability of acoustic fault detection. The wind turbine blade fault detection methodology comprises: (1) acoustic signal acquisition and feature extraction, (2) data normalization, (3) DCABC algorithm initialization, (4) optimization of SVM parameters ($C$ and $\gamma$) via DCABC, (5) SVM model training with optimized parameters, and (6) fault detection using experimental datasets. The complete workflow is presented in Fig. 1.

Fig. 1Flow chart of fault acoustic detection.

This completes the acoustic fault detection system design for wind turbine blades, implementing a dynamic Cauchy bee colony algorithm-optimized support vector machine methodology.

4.1. Preparation for experiment

To validate the effectiveness of the proposed wind turbine blade fault acoustic detection method using dynamic Cauchy bee colony algorithm-optimized support vector machine, the designed approach is compared with methods reported in references [3]-[6].

Acoustic signals are acquired from ground-based measurements of wind turbine operation within the rotational speed range of 7-17 r/min. Below this range, power generation ceases, while speeds exceeding this range trigger protective blade stoppage. Each 10-second sample is designed to capture at least three blade-passing events (one complete rotation cycle). The tested wind turbines (model: UP1500-82) have a rated capacity of 1.5 MW. The acquisition system comprises a YG-201 microphone, MPS-140801 data acquisition card, and LabVIEW-equipped laptop computer.

The experiment collects 1,000 acoustic signal samples encompassing four distinct fault conditions (normal operation, leading-edge cracks, trailing-edge cracks, and surface cracks), with 250 samples per category. The dataset is partitioned into training (70 %, 700 samples) and testing (30 %, 300 samples) subsets. To ensure result reliability, 5-fold cross-validation is implemented on the training set-each iteration utilizes 4 subsets (560 samples) for model training and the remaining subset (140 samples) for validation, with this process repeated until all subsets served as the validation set once.

The experimental configuration comprises 16.0 GB RAM with PyCharm 2021.2.4 as the development environment. The computational procedure executes 8,000 operational steps with a sampling frequency range of 0-2,000 Hz.

The experimental setup configuration is illustrated in Fig. 2.

Fig. 2Experimental environment diagram

The study analyzes acoustic detection data from six wind turbine blades (representative samples selected from the aforementioned 1,000-sample dataset). The original dataset comprises wind speed, wind direction, temperature, voltage, current, active power, and impeller rotational speed for model training. Representative sample data are presented in Table 1.

4.2. Experimental results

To validate the algorithm’s effectiveness, a comparative analysis of fitness values is conducted between the proposed method and existing approaches, with results illustrated in Fig. 3.

Fig. 3 demonstrates that the proposed method achieves convergence at 22 iterations, compared to 30 iterations for conventional approaches. This accelerated convergence results from synergistic enhancements combining the dynamic Cauchy bee colony algorithm’s efficient search strategy with optimized SVM parameters, collectively improving both detection performance and computational efficiency. These advantages significantly enhance the method's practical value for wind turbine blade fault acoustic detection.

A comparative analysis of fault detection times between the proposed algorithm and existing methods is presented in Table 2.

As shown in Table 2, for all fault types (normal, leading-edge cracking, trailing-edge cracking, and skin cracking), the detection time of the proposed method is generally shorter than that of the other methods. For instance, under normal conditions, the detection time of the proposed method is 6.8 seconds, whereas the method in [3] requires 11.9 seconds, and the method in [4] takes 11.5 seconds. This demonstrates that the proposed method has a significant advantage in detection efficiency. The improvement is attributed to the dynamic Cauchy swarm algorithm, which efficiently identifies the optimal support vector machine (SVM) parameters through its high-performance search strategy and dynamic adjustment capability. This optimization not only enhances the SVM’s classification accuracy but also reduces the model’s training and prediction time.

Fig. 3Comparison curves of fitness values of different methods

To further demonstrate the advantages of the proposed method, the impeller speed is analyzed, and the vibration amplitudes of different methods are compared. The results are presented in Fig. 4.

Fig. 4Evaluation results of impeller speed with different methods

As evident from Fig. 4, the impeller speed amplitude of the conventional method exhibits significant fluctuations, failing to satisfy the requirements for acoustic detection of fan blade faults. In contrast, the proposed method demonstrates smoother impeller speed amplitude with reduced fluctuations. This improvement stems from the method's enhanced classification performance, robustness, and fault feature extraction capability for SVM, along with its ability to maintain stable impeller speed control. These advantages ensure greater stability and reliability in acoustic detection of fan blade faults.

The acoustic detection results for fan blade faults obtained by the proposed and conventional methods are compared in Fig. 5.

Fig. 5Comparison of fault acoustic detection results of different methods.

Fig. 5 clearly illustrates distinct three-dimensional distribution patterns between fault and normal samples. The overlapping ranges between both sample types indicate similarities in blade operating conditions across different states, demonstrating that relying exclusively on environmental variables or operational parameters is insufficient for accurate ice detection on wind turbine blades. In the conventional method, the two sample types exhibit cross-distribution patterns with overlapping data groups, revealing significant coupling between normal and faulty samples. This suggests redundant characteristics in the original data that introduce noise into the sample set. In contrast, the proposed method forms well-separated clusters in the feature space, preserving raw data historicity while effectively suppressing noise interference from the original dataset. In summary, the SVM-optimized acoustic detection method incorporating the dynamic Cauchy bee colony algorithm demonstrates significant advantages, including enhanced SVM classification capability, improved optimization through the dynamic Cauchy algorithm, reduced noise effects, and higher recognition rates. These advantages indicate strong potential for wind turbine blade fault detection applications.

4.3. Classification performance evaluation

To thoroughly assess the classification performance of the proposed method, evaluation metrics including the confusion matrix, accuracy, recall rate, and F1-score are computed. The confusion matrix provides visual representation of the model's predictions for each category, whereas accuracy, recall, and F1 score quantitatively measure the model's performance from different aspects.

(1) Confusion matrix.

The confusion matrix of the proposed method on the test set is presented in Table 3. The results demonstrate accurate predictions for both normal samples and various fault types (leading-edge cracking, trailing-edge cracking, and skin cracking), with minimal misclassification cases observed.

(2) Accuracy, recall, and F1-score.

Based on the confusion matrix analysis, the accuracy, recall, and F1-score for each category are calculated, with the results presented in Table 4.

The data in Tables 3 and 4 demonstrate the excellent classification performance of the proposed method. the confusion matrix reveals accurate predictions across all sample types with minimal false positives: 210 normal samples are correctly classified, with only 5, 3, and 2 misclassified as other faults; 195 leading-edge cracking samples are accurately identified, with a maximum of 8 misclassifications; while trailing-edge cracking and skin cracking samples achieve 205 and 210 correct predictions respectively, with similarly low misclassification rates. Quantitative metrics further confirm this performance, with normal samples achieving 0.95 accuracy, 0.96 recall, and 0.95 F1-score. Leading-edge cracking samples show 0.92 accuracy, 0.89 recall, and 0.91 F1-score, while trailing-edge cracking and skin cracking samples maintain high metric values between 0.93-0.96. These results indicate that the proposed method delivers outstanding classification performance, demonstrating both high accuracy and stability for normal and all fault sample types, confirming its reliability for practical classification tasks.