Study on Noise Reduction of Hydrostatic Leveling Signals for Wind Turbine Foundations Based on CEEMDAN-SG Algorithm

Abstract

The hydrostatic leveling monitoring data related to the settlement of the wind turbine foundation display substantial fluctuations along with considerable noise. In this study, based on the characteristic of the hydrostatic level measurement data of wind turbine foundation, a joint denoising method that integrates the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) algorithm with Savitzky–Golay (SG) filtering is proposed. Several commonly used denoising algorithms were presented to verify the effectiveness of the proposed joint algorithm. The denoising performance of each algorithm was evaluated through quantitative analysis, which included calculating the signal-to-noise ratio, mean square error, and coefficient of determination derived from the simulated signal data. The corresponding results affirm the effectiveness and superiority of the proposed algorithms. Furthermore, the proposed algorithm was employed to mitigate the inherent noise present in field measurement data. Subsequently, a qualitative analysis was undertaken to elucidate the correlation between the denoised results and the fundamental stress state of the actual wind turbine foundation. The results demonstrate that the joint noise reduction method exhibits significant advantages compared to the individual CEEMDAN and SG algorithms. Moreover, the refined hydrostatic leveling signal precisely captures the settlement trends within the wind turbine foundation, providing a clearer understanding of its structural stability and performance.

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

1. Introduction

The settlement represents a crucial indicator for evaluating the health status of buildings and holds great significance for numerous important national infrastructure projects [1, 2]. In the domain of wind turbines, offshore wind turbines are constantly exposed to the influences of complex and harsh marine environments, such as sea winds, waves, and tides, over an extended period [3]. Meanwhile, the construction sites for onshore wind turbines are often situated in mountainous regions and plains characterized by challenging conditions. Precise assessment of settlement is crucial for ensuring the long-term safety and reliability of both offshore and onshore wind turbine facilities. This is because excessive settlement in the foundation of a wind turbine can alter its verticality and force state, subsequently leading to a decline in power generation efficiency, accelerated mechanical wear and fatigue, and in severe cases, potentially resulting in the collapse of the turbine. Consequently, such a settlement can lead to significant economic losses and pose severe safety hazards. The accurate measurement of settlement in wind turbine structures facilitates the prompt identification of alterations in foundation stability, furnishing a crucial foundation for the deployment of tailored maintenance and reinforcement initiatives, thereby guaranteeing the seamless operation and sustainable progression of wind turbine projects.

In engineering, common settlement monitoring techniques encompass leveling measurement [4], GPS observation [5], remote sensing monitoring [6], laser ranging [7], and hydrostatic leveling measurement [8]. Among these methods, hydrostatic leveling instruments are preferred in major engineering projects owing to their simplicity, high precision, and excellent stability [9]. Martin [10] investigated the current situation and emerging trends associated with the application of hydrostatic leveling systems (HLSs) in the domain of civil engineering. Fu [11] carried out a study on the accuracy of HLS observation in the monitoring of underground tunnels. Martin [12] explored the application of HLS for the long-term monitoring of European synchrotron radiation equipment and its rapid adaptability in controlled storage. Yin [13] utilized the HLS method to measure settlement during the construction of the upper deep excavation of a shield tunnel, enabling a precise assessment of the safety of the tunnel structure.

However, hydrostatic leveling instruments, by their operational principle, are sensitive to ambient temperature variations. Daily temperature fluctuations, as well as temperature differences and gradients among multiple measuring points, can significantly increase the signal noise within the HLS. Tsvetkov, Yepin, and Shestakov [14] investigated the impact of positioning on HLS and introduced a model to predict the influence of liquid density variations on leveling accuracy across different terrains. Based on the results of numerical simulations, Tsvetkov, Lekomtsev, and Yepin [15] conducted a detailed analysis of temperature dynamics in a streamlined simulation of the mixing process within a long-base HLS.

Currently, some scholars have established calibration models of HLS through laboratory experiments, theoretical analysis, on-site tests, and other means, which can take into account the effects of environmental temperature, material expansion, liquid density, and the distance between measuring points on the measurement results [16, 17]. Jin et al. [18] employed a high-precision temperature sensor to continuously monitor ambient temperature fluctuations during the collection of HLS data. By incorporating these temperature records, real-time corrections can be applied to HLS readings, significantly improving the accuracy of measurements. Similarly, Bo, Guo, and Qi [19] quantified the impact of temperature variations on HLS measurements by developing a model that captures the correlation between temperature fluctuations and HLS readings, and subsequently adjusting the readings through the application of a correction factor. However, research suggests that the HLS calibration model is only efficacious in processing data with temperature ramp-up or cool-down rates below 0.1°C/min. When the temperature increase exceeds this rate, the data become distorted, suggesting that the HLS correction model may not be universally applicable to all engineering projects [20]. Therefore, accurately obtaining hydrostatic leveling signals poses a significant challenge in assessing engineering settlement.

Many scholars have conducted extensive research into methods for smoothing data and reducing noise in monitoring systems. Zhao et al. [21] refined the long short-term memory (LSTM) model by incorporating the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), a sophisticated digital signal processing technique employed in engineering. They pointed out that the CEEMDAN algorithm possesses superior performance compared to empirical mode decomposition (EMD) and ensemble empirical mode decomposition (EEMD), thereby making it a more fitting choice for enhancing LSTM predictions. The empirical results demonstrate that the application of noise reduction using the CEEMDAN algorithm can significantly enhance the predictive performance of the LSTM model. Zu et al. [22] observed that the CEEMDAN algorithm exhibits limited resolution in dealing with high-frequency components, prompting them to propose a novel hybrid noise reduction method known as full coefficient empirical modal decomposition combined with adaptive noise boosting wavelet transform. Fábián [23] proposed extending the application of the Savitzky–Golay (SG) filtering to three-dimensional triangular meshes, with the objective of smoothing functions defined on irregular two-dimensional triangular meshes. This proposal underscores the superiority of SG filtering in data smoothing. Zhao et al. [24] further employed the SG filter algorithm for preprocessing spectral data to achieve smoothing. Their results demonstrate that the relative error remains relatively stable after applying the SG preprocessing to the investigated spectral data.

Given that the CEEMDAN algorithm has limitations in processing high-frequency components, while the SG filter has a distinct advantage in data smoothing, an innovative CEEMDAN-SG joint denoising method is proposed and applied to the analysis process of wind turbine base hydrostatic leveling data. The CEEMDAN-SG joint denoising method decomposes the noisy static level measurement signal into several signal components. Subsequently, the high-frequency signal components are filtered and denoised using the SG filtering algorithm to effectively reduce high-frequency noise interference. Thereafter, the integration of low-frequency signal components and trend terms facilitates the reconstruction of denoised signals, accurately restoring the inherent characteristics of the data. This algorithm was initially applied to analyze indoor model test data for wind turbines, rigorously assessing its validity and reliability, thereby establishing a firm groundwork for practical implementations. Subsequently, the method was extended to actual wind turbine foundation monitoring projects, offering reliable data processing support for the stability evaluation and safety oversight of wind turbine foundations within the realm of civil engineering. The work undertaken has similarly facilitated enhancements in the construction quality, operational efficiency, and maintenance benchmarks of the entire wind turbine foundation project.

2. Theoretical Basis

2.1. CEEMDAN Algorithm

EMD is a technique that disassembles a signal by its inherent local characteristics and demonstrates high efficacy in extracting local features during the decomposition of nonstationary signals. Nevertheless, its decomposition outcomes lack stability in the presence of noise [25].

To enhance the performance of EMD, the EEMD method was proposed, integrating the concept of random perturbations. In this methodology, throughout each decomposition iteration, multiple sets of intrinsic mode functions (IMFs) are generated by injecting various random noises into the original signal. Subsequently, these IMFs are averaged to obtain the ultimate decomposition result [26].

The CEEMDAN represents a significant advancement and expansion of the EEMD method [27]. The CEEMDAN algorithm incorporates an adaptive noise control mechanism, which dynamically modulates the intensity and frequency of the noise to augment the stability and precision of the decomposition outcomes. Figure 1 depicts the decomposition process of CEEMDAN. Once the first-order IMF component is identified, the residual is reintroduced as white noise. Thereafter, the average value of the IMF component is computed, followed by iterative procedures.

[figure(s) omitted; refer to PDF]

2.2. SG Filtering

SG filtering is a digital filtering technique that applies linear least squares to fit a low-degree polynomial to a moving window of adjacent data points, thereby performing the convolution process. The window width can be adjusted as needed to achieve varying levels of smoothing for the same data curve [28]. The SG algorithm offers notable advantages over other methods, especially in filtering high-frequency data. It effectively preserves the shape and key features of the signal. As highlighted in the literature [28], SG filtering preserves the details and peaks of the original signal more effectively by fitting a polynomial to a local subset of the data, rather than merely averaging or truncating, as other filters typically do. In spectral analysis, SG filtering retains important physical information. Kennedy [29] emphasized that the SG filter has minimal impact on phase during smoothing, allowing for better preservation of phase information and preventing signal distortion, particularly at high frequencies. The SG filter is effective in selectively filtering high-frequency noise, distinguishing between noise and valuable high-frequency signal components, as discussed in the literature [30]. In data analysis, SG filtering effectively removes pseudo-noise while minimally affecting the useful high-frequency components of the signal. Boashash [31] demonstrated that the SG filter smooths out noise while preserving crucial high-frequency features, which is vital for accurate diagnosis and analysis. The SG filter offers flexible adjustment in terms of polynomial order and window size, accommodating a diverse array of data, ranging from smooth to fluctuating waveforms. In time series analysis, it can effectively smooth out short-term fluctuations while simultaneously capturing long-term trends [32]. Compared to more advanced iterative methods, SG filtering has relatively low computational complexity. This makes SG filtering particularly valuable in real-time applications, such as industrial automation, where fast and accurate data processing is essential for efficient control and decision-making. These advantages make the SG filter highly effective for processing complex, mixed-frequency signals.

This method not only effectively removes noise but also preserves useful information in the signal, especially in the processing of time series data, which has significant advantages [33]. The process of smoothing data by the SG algorithm can be expressed as follows [34]:$$\begin{array}{}\text{(1)}& {\widehat{y}}_j=\sum _{i=-m}^m{a}_i{x}_{j+i}+a_0/n,\end{array}$$where ${\widehat{y}}_j$ represents the smoothed data set; x_j+i is the original data set; a_i, a₀ are the smoothing coefficients; m is the window width; and n is the number of data points in the sliding window, where n = 2m + 1.

2.3. CEEMDAN-SG Algorithm

To address the issue of excessive noise in hydrostatic leveling signals, a hybrid denoising algorithm combining the CEEMDAN algorithm and the SG filtering method is proposed. This approach classifies the signal components using the t-test method and applies SG filtering to reduce noise in the high-frequency components. The t-test has notable advantages, including sample flexibility, applicability to small sample sizes, and fewer assumptions regarding population distribution. It accurately assesses mean differences by taking into account sample variance. It is widely used in various research designs, such as independent and paired samples, across diverse fields, making it essential for statistical analysis and further studies [35]. The effective signal is then reconstructed, ensuring that its characteristic features are preserved during the denoising process. Figure 2 illustrates the steps involved in the joint denoising process of the CEEMDAN-SG algorithm:

[figure(s) omitted; refer to PDF]

1. Use the CEEMDAN algorithm to decompose the hydrostatic leveling signal into multiple IMF components and the RES.

2. Use the t-test method to classify the decomposed IMF components as high-frequency or low-frequency. The first IMF component (IMF1) is designated as index 1, and the sum of IMF1 and IMF2 is labeled as index 2. Similarly, the sum of the first i IMF components is denoted as the index i. Calculate the mean of each index and apply the t-test to determine whether the mean value differs significantly from zero. If the mean of the IMF component at index i is significantly different from zero, the first i−1 IMF components are classified as high frequency, and the remaining components are categorized as low frequency [36].

3. Apply the SG filtering technique to reduce noise in the high-frequency IMF components.

4. Reconstruct the hydrostatic leveling signal by combining the denoised high-frequency IMF components with the untouched low-frequency IMF components, resulting in a cleaner signal.

3. Simulation and Discussion

3.1. Construction of Simulation Signal

The settlement monitoring data collected on-site is often affected by various factors, such as measurement technology, operator proficiency, temperature, and other environmental conditions, leading to potential errors and making the actual data unavailable. As a result, the denoising performance of various noise reduction algorithms cannot be effectively evaluated using these data. Considering the inherent advantages of indoor model testing, particularly its enhanced controllability, a customized wind turbine foundation model test was designed and conducted to specifically replicate the on-site conditions of the wind turbine foundation. The data obtained from indoor model testing not only allows for a relatively accurate evaluation of the foundation performance under realistic working conditions but also ensures greater stability and reliability. Using these data, the performance of various algorithms can be rigorously assessed, allowing for the identification and selection of the most suitable and optimized algorithm for comprehensive analysis in the actual project.

An indoor model box with dimensions of 1100 mm (L) × 900 mm (W) × 1200 mm (H) was used as the test device. The main frame of the model box was constructed from steel plate and angle steel and welded together with a thickness of 10 mm to ensure the overall rigidity and strength of the box. The front view of the model box consists primarily of transparent tempered glass with a thickness of ~19 mm, while the right elevation is designed to be semiopen for ease of conducting various test operations. The laboratory test system was built to a scale ratio of 1:40, utilizing a horizontal servo loading device to apply horizontal loads to replicate the field loading conditions experienced by wind turbines. The entire test system comprises the model box, reaction frame, wind turbine foundation, wind turbine tower, loading device, and monitoring devices, as shown in Figure 3.

[figure(s) omitted; refer to PDF]

The loading device support frame is securely fastened to the designated area on the right side of the indoor model box with bolts. This frame serves to support and stabilize the horizontal servo actuator, while simultaneously counteracting the reaction force generated by the movement of the actuator. The right end of the horizontal servo actuator is firmly attached to the loading support frame, whereas the left end is connected to the top of the model tower through a circular ring. The integrated servo actuator system can precisely adjust the horizontal load, facilitating the simulation of wind loads on the model.

The loading controller in the test system is responsible for controlling the operation of the loading equipment, while the monitoring data acquisition system is responsible for collecting the elevation signal from the foundation, which can be further converted into settlement data. In this study, simulated elevation signals were collected using the laboratory test system to evaluate the performance of the proposed algorithm. The load controller was designed to apply a sinusoidal load with a peak value of ±338 N, allowing the loading device to simulate cyclic wind loads on the wind turbine tower. Before initiating formal data acquisition, the sensor underwent rigorous calibration and debugging procedures to minimize measurement errors. The acquisition duration was established as 1 h, employing a sampling frequency of 1 sample per second. To guarantee the stability and uninterrupted flow of data, a professional data acquisition instrument was interfaced with the sensor, as illustrated in Figure 3c. The data acquisition instrument is capable of real-time data storage and preliminary processing, instantly storing collected elevation data on a large-capacity memory card and performing basic filtering to remove obvious abnormal spikes. Throughout the acquisition process, data are instantaneously transmitted to a computer via a wireless transmission module, empowering experimental personnel to oversee the progress and quality of data acquisition in real-time. Prompt actions can be taken in response to any detected data loss, mutations, or other anomalies. The data collected initially, which is presented in Figure 4a, contain minimal noise and cannot simulate the complex field noise typically encountered.

[figure(s) omitted; refer to PDF]

Due to the conditions of signal transmission and acquisition, pure sine wave signals are virtually nonexistent. Various external interference sources introduce noise, and white noise and Gaussian white noise serve as effective tools for modeling these interferences. In communication systems, for example, electromagnetic interference, thermal noise within the equipment, and other factors can superimpose the received signal (such as a sinusoidal carrier signal), thereby introducing noise. By incorporating white noise or Gaussian white noise into the sinusoidal waveform, a band-limited noisy signal is generated that more closely resembles real-world scenarios, enabling the testing of noise reduction algorithms in practical situations. White noise exhibits a uniform power spectral density across the entire frequency domain. When white noise is introduced, the signal spectrum is uniformly blended with noise components across various frequencies, corresponding to the frequency of the sine wave components. This creates a sample with noise disturbances at multiple frequencies, which is invaluable for developing noise reduction algorithms capable of effectively filtering out a diverse range of frequency noises. Gaussian white noise, despite being Gaussian in its statistical distribution, also demonstrates broad spectral characteristics, rendering it useful for assessing the capability of the noise reduction algorithms to suppress noise at various frequencies [37]. Therefore, to verify the effectiveness of the algorithm proposed in this study, a target curve is generated by incorporating Gaussian white noise, producing a simulated elevation signal that is more complex and noisier, as shown in Figure 4b.

3.2. Noise Reduction and Evaluation

The noisy simulated signal is decomposed using CEEMDAN, and the decomposition results are shown in Figure 5, yielding eight modal components (IMF1–IMF8) and RES. Among these components, the data curves of IMF1 and IMF2 exhibit more rapid fluctuations, indicating that they belong to high-frequency data. High-frequency data typically reflect the fast-varying components of the signal, with noticeable fluctuations within a short interval of sampling points. In contrast, the relatively slow fluctuations of the RES curve, which display a more obvious trend only over longer sampling intervals, indicate that the RES corresponds to low-frequency data. Low-frequency data generally reflect the slow trends or long-term characteristics of the signal. By observing the fluctuation frequency of each curve in the graph, high-frequency and low-frequency data can be more clearly distinguished. However, corresponding evaluation indicators are still required for classification.

[figure(s) omitted; refer to PDF]

As presented in Section 2, the t-test method is employed to determine whether the mean values of the eight modal components differ significantly from 0. The corresponding results are shown in Table 1. The p-value at index 7 is less than the significance level α (i.e., α = 0.001), indicating that IMF1–IMF6 are high-frequency components, while IMF7 and IMF8 are low-frequency components.

Table 1

p-Value of each index.

Index	1	2	3	4	5	6	7	8
p-Value	0.4682	0.4579	0.4502	0.4509	0.4805	0.0464	0.0000	0.0000

SG filtering is first applied to IMF1–IMF6 components. Then, the filtered IMF1–IMF6 components, low-frequency IMF components, and trend term components are reconstructed to obtain the jointly filtered signal. To evaluate the superiority of the CEEMDAN-SG algorithm in denoising, EEMD, variational mode decomposition (VMD), CEEMDAN, and SG filtering are also used separately to denoise the noisy signal. The comparison results are presented in Figure 6. The results show that the denoising performance of the CEEMDAN-SG algorithm is most consistent with the original signal when compared to EEMD, VMD, CEEMDAN, and SG filtering. Additionally, there are more fluctuations in the elevation signal after denoising with SG filtering, indicating that SG filtering cannot fully eliminate the Gaussian white noise.

[figure(s) omitted; refer to PDF]

In signal processing, the signal-to-noise ratio (SNR), mean square error (MSE), and coefficient of determination (R²) are key metrics for evaluating the performance of noise reduction algorithms. The SNR refers to the ratio of the average power of the signal to the average power of the noise, typically expressed on a logarithmic scale in decibels (dB). According to [38, 39], a higher SNR indicates less noise in the signal. For instance, in the context of frequency-domain signal noise reduction, enhancing the SNR after noise reduction is applied to high-frequency signals in communication systems can markedly decrease the bit error rate during signal transmission, thereby guaranteeing the quality of communication.

The MSE represents the mean squared difference between the actual values of the samples and their recovered values. According to [39], the closer the MSE is to 0, the closer the signal is to the original signal. R² reflects the degree of fit of the noise reduction model to the original signal. The closer R² is to 1, the better the performance of the model. A high R² indicates that the model can accurately restore the trend of the data when processing sensor data.

The specific calculation formulas are as follows:$$\begin{array}{}\text{(2)}& \text{SNR}=10\cdot \log \frac{P_{\text{s}}}{P_{\text{n}}},\end{array}$$where $P_{\mathrm{s}}$ represents the average power of the signal and $P_{\mathrm{n}}$ represents the average power of the noise. The logarithmic scale is used here because the power of the signal and noise is usually expressed in dB.$$\begin{array}{}\text{(3)}& \text{MSE}=\frac{1}{n}\sum _{i=1}^n{y_i-{\widehat{y}}_i}^2,\end{array}$$$$\begin{array}{}\text{(4)}& R^2=1-\frac{{\sum }_{i=1}^n{y_i-{\widehat{y}}_i}^2}{{\sum }_{i=1}^n{y_i-{\bar{\widehat{y}}}_i}^2},\end{array}$$where $n$ is the number of samples; $y_i$ is the sample value; and ${\widehat{y}}_i$ is the restoration value.

The comparisons in Table 2 demonstrate the superiority of the proposed CEEMDAN-SG algorithm in noise reduction. Compared to the CEEMDAN and SG algorithms, the SNR values of the CEEMDAN-SG algorithm improve by 4.7945 and 4.4868 dB, or ~21.40% and 19.75%, respectively. The MSE values decrease by 0.0064 and 0.0057, or about 67.37% and 64.77%, respectively. Additionally, the R² values increase by 0.004, or about 0.5%.

Table 2

Evaluation metric values of five algorithms.

Algorithm	SNR/dB	MSE	R2
EEMD	21.7111	0.0111	0.991
VMD	22.4010	0.0096	0.992
CEEMDAN	22.4057	0.0095	0.992
Savitzky–Golay	22.7134	0.0088	0.992
CEEMDAN-SG	27.2002	0.0031	0.997

Compared to the other algorithms, the maximum increase in SNR is 5.4891 dB, or about 25.28%, the maximum decrease in MSE is 0.0080, or about 72.07%, and the maximum increase in R² is 0.006, or about 0.6%. The comprehensive evaluation indices show that the CEEMDAN-SG algorithm is more effective at screening and filtering noise, resulting in more accurate noise reduction and smoother curves.

4. Application in Wind Turbine Project

4.1. Data Source

This section analyzes a wind turbine project built on a rock foundation using rock bolts. To evaluate the safety of the foundation, two hydrostatic leveling instruments were placed along the prevailing wind direction on the surface of the foundation to monitor its deformation. The locations of the measuring points are shown in Figure 7a. The working principle of the static liquid level gauge is to calculate vertical displacement changes by measuring the height of the liquid level changes at each measuring point. Suppose there are n measuring points, point #1 is the reference point. When the observed object has uneven settlement, the distance between the liquid surface in the container of each measuring point and the installation elevation is set as $h_{k1},\cdots ,h_{ki},\cdots ,h_{kn}$ (i and n are the test point codes; k is the test run code). It can be obtained that $h_{ki}-h_{k1}$ is the displacement of point i in the kth measurement with respect to horizontal point 1, and $h_{ki}-h_{ki-1}$ is the displacement of the liquid level sensor at point i in the kth measurement with respect to the previous time. It is important to note that point #0 serves as the datum point for calculating the relative deformation of the wind turbine foundation.

[figure(s) omitted; refer to PDF]

Consequently, the datum point was connected to the electrical equipment foundation through a stainless steel frame (Figure 7b) and positioned at the side of the wind turbine electrical equipment foundation to create a specified liquid level difference.

The monitoring data were retrieved and analyzed in depth using the jointed CEEMDAN-SG denoising method. As shown in Figure 8, data were collected from March 12 to April 1, 2023, at 5-min intervals at each measuring point, resulting in a total of 5610 data sets. The data revealed that the fluctuation range of the water level at datum 0 was ~2–3 mm, while datums 1 and 2 exhibited fluctuations as large as 20 mm, indicating a significant anomaly. Some literature [20] mention that this anomalous fluctuation is caused by temperature differences, temperature gradients, and sensor spacing. When the temperature change rate exceeds 0.1°C/min, the data are prone to distortion, and the traditional HLS calibration model is unable to process the data accurately. Therefore, the CEEMDAN-SG joint denoising method was applied to process the hydrostatic level measurement signals, enhancing data quality and analytical accuracy, and providing a reliable data foundation for subsequent related studies.

[figure(s) omitted; refer to PDF]

4.2. Processing of Data and Analysis

Figure 9 outlines the processing of hydrostatic leveling signal data, with Step 2 involving the application of the CEEMDAN-SG algorithm, as shown in Figure 2. To validate the effectiveness of the CEEMDAN-SG joint denoising method, the denoised hydrostatic leveling signal is transformed into the relative elevation signal of the foundation (Step 4). The analysis is then conducted in conjunction with the direction of the wind turbine blades.

[figure(s) omitted; refer to PDF]

The relative elevation signals for measuring points #1 and #2 are shown in Figure 10, clearly indicating that the elevation data of the two points are negatively correlated. For ease of analysis, the initial value is subtracted from the relative elevation signal to calculate the cumulative deformation of the foundation, as shown in Figure 11. At the same time, the correlation analysis of the points on both sides of different stages is plotted according to the steering stage of the wind turbine blades, as shown in Figure 12.

[figure(s) omitted; refer to PDF]

As shown in Figure 12, the cumulative deformations on both sides of the foundation show a clear negative correlation, with correlation coefficients as high as −1 between the two sides of the measuring points within the corresponding phase. Corresponding to Figure 11, it can be observed that the fluctuation ranges from 1 to −3 mm. This observation is consistent with the expected foundation deformation pattern. Since the cumulative deformation of the foundation is influenced by the orientation of the wind turbine blades, the data were analyzed in six different cases. Specifically, conditions 1, 3, and 5 represent the case where the wind turbine blades are aligned with the prevailing north wind direction, while conditions 2 and 4 correspond to the case where the blades are oriented toward the prevailing south wind direction.

For conditions 1, 3, and 5, measuring point #1 exhibits an upward trend, while measuring point #2 shows a downward trend. This is because under these operating conditions, the blades are oriented toward the north, with measuring points #1 and #2 positioned on the windward and leeward sides, respectively. Consequently, the aerodynamic forces acting on the turbine structure cause the two measuring points to experience opposite pressures and stresses. The correlation analysis results in Figure 12 indicate that the correlation coefficient between the trends of the two measuring points is as high as −1, further confirming a strong negative correlation between the two measuring points. The CEEMDAN-SG algorithm accurately captures and isolates these deformation signals through effective noise suppression and precise signal decomposition, eliminating any spurious noise that may mask or distort the true deformation trend. On the contrary, under conditions 2 and 4, measuring point #1 on the leeward side settles while measuring point #2 on the windward side lifts, and the correlation coefficient remains −1. Again, the CEEMDAN-SG algorithm demonstrated its effectiveness by providing clean and reliable deformation data that reflect the physical mechanisms at play. The complex interaction between wind forces and the structural response of turbine is accurately captured in the processed data, enabling a deeper understanding of the foundation performance.

In condition 6, in which the wind turbine blades are oriented to the west, perpendicular to the prevailing wind direction, both measuring points show a flat trend without significant fluctuations, and the negative correlation coefficient is significantly reduced. The CEEMDAN-SG algorithm successfully distinguishes this relatively stable state from the dynamic deformation patterns observed in other conditions, further demonstrating its sensitivity and accuracy. By effectively managing the various frequency components and noise in the original monitoring data, it enabled a more precise analysis of the relationship between the cumulative deformation of the measuring points and the orientation of the wind turbine blades.

The analysis of cumulative deformation data at the measuring points, combined with the orientation of the wind turbine blades, clearly shows that the denoised deformation data of the wind turbine foundations are closely related to the basic deformation patterns under various loading conditions. This validates the effectiveness of the CEEMDAN-SG algorithm in extracting authentic deformation signals. The processed data provide a solid foundation for further engineering analysis and decision-making regarding the safety and performance of wind turbine foundations.

Despite the relatively limited data sources and the narrow scope of the investigation into the wind turbine foundation environment, this does not diminish the significant potential of the CEEMDAN-SG algorithm in future engineering applications. As the number of wind turbine projects continues to increase, the availability of engineering data will become increasingly abundant. The CEEMDAN-SG algorithm is expected to be widely applied to monitor wind turbine foundations under diverse environmental conditions. It will provide robust data processing support for stability assessments, safety monitoring, and subsequent maintenance decisions for wind turbine foundations. As a result, it will contribute to enhancing construction quality, optimizing the operation and maintenance levels of the wind turbine industry, and ensuring the safer, more efficient, and sustainable operation of wind turbine projects.

5. Conclusions

In this study, a noise reduction method for hydrostatic leveling measurement signals in wind turbine foundation monitoring data is proposed, utilizing the CEEMDAN-SG algorithm. The effectiveness and superiority of the method are experimentally verified, with field monitoring data analysis demonstrating its ability to address the issue of excessive noise caused by temperature fluctuations and other environmental factors. A t-test is employed to distinguish high- and low-frequency IMF components from the CEEMDAN decomposition, while SG filtering is applied to reduce noise in the high-frequency IMFs, followed by signal reconstruction. Through the analysis of both simulated signal data and engineering examples, the following main conclusions are drawn:

1. The proposed CEEMDAN-SG algorithm outperforms other noise reduction methods, as evidenced by the improved evaluation indices. Notably, compared to the traditional single CEEMDAN algorithm and SG filtering, the CEEMDAN-SG algorithm produces noise reduction results that are closer to the original signal. Specifically, the SNR is maximally improved by 21.40%, the MSE is reduced by 67.37%, and the R² value increases by 0.5%. The inclusion of SG filtering in the CEEMDAN-SG algorithm enables it to preserve more of the original signal features, improving overall denoising performance.

2. The CEEMDAN-SG algorithm successfully mitigates the impact of high-frequency noise induced by temperature variations. An in-depth analysis of field monitoring data reveals that the settlement trend after noise reduction is smoother, facilitating a more accurate understanding of the settlement behavior of wind turbine foundations. Furthermore, the reconstructed signal more precisely reflects the foundation settlement in response to the changing orientation of the wind turbine blades.

Despite the promising results, it is important to note that the current field data sources are limited, and the environment of the wind turbine foundation is relatively simple. As such, more diverse and extensive engineering data are needed to further validate the applicability and robustness of the CEEMDAN-SG algorithm in different real-world scenarios.

Author Contributions

Renjie Li: conceptualization, funding acquisition, project administration. Xiangxing Lu: data curation, resources, validation. Zhixin Song: software, methodology, formal analysis, writing–original draft. Huanwei Wei: conceptualization, supervision, project administration. Fang Tan: conceptualization, funding acquisition, supervision, writing–review and editing, project administration. Zhonghua Liu: investigation, formal analysis, writing–review and editing.

Acknowledgments

The authors would like to express their gratitude to the graduate students of the research group, particularly Shuli Lei and Zhongshuo Li, for their valuable contributions to the monitoring and experimental aspects of this study. Their efforts were instrumental in the successful completion of this research.

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