Diagnosis of Pre-Tightening Force Loosening for Top Cover Bolts in Generator Sets

Abstract

Bolt loosening is a common mechanical failure in large-scale generator sets, especially the top cover bolts, which can lead to unstable operation, affecting the safety and efficiency of the unit. Real-time monitoring of bolt pre-tightening force and the early diagnosis of loosening are crucial for ensuring the long-term safe operation of the generator set. This study proposes a novel method for diagnosing faults in large-scale hydraulic units, with a particular focus on thread loosening failures. The proposed approach utilizes stress feature analysis and intelligent algorithms to enhance the diagnostic process. The study involves a detailed analysis of the stress transfer mechanism during bolt loosening, aiming to elucidate the relationship between changes in pre-tightening force and stress distribution in the surrounding bolts. A combined approach of monitoring the pre-tightening force and signal analysis is employed to facilitate the real-time tracking of dynamic changes. Experimental results show that loosening a single bolt causes stress distribution changes in the entire bolt group, particularly in the adjacent bolts. The study also introduces a diagnosis method combining pre-tightening force changes and VMD (Variational Mode Decomposition), which proves to be highly accurate in locating loosened bolts. Engineering applications validate that VMD analysis combined with the Spearman method effectively identifies changes in stress and has high accuracy and potential for diagnosing bolt loosening failures, providing valuable guidance for generator set maintenance.

1. Introduction

With the increasing scale of the motor systems in hydraulic units, their operating environment has become more complex, and the working conditions are changeable. Fault diagnosis has gradually become one of the key technologies to ensure the safe and stable operation of equipment [1,2,3]. The stability of threaded connections, which are important fastening components in the motor system, directly affects the reliability and operating efficiency of the unit. In practical applications, due to long-term mechanical vibrations, temperature changes, load fluctuations, and other factors, the loosening of threaded connections frequently occurs in large-scale hydraulic units, especially in the threaded connection parts between the rotor and the stator of the motor system [2,4]. Thread loosening not only leads to the mechanical failure of the equipment but may also trigger serious safety accidents, affecting the long-term stability and operational safety of the unit. Therefore, early and accurate identification of thread loosening faults has become an important task for improving the reliability of the motor system and extending the service life of the equipment [5,6,7]. However, the existing fault diagnosis methods mostly rely on traditional rule-based diagnostic techniques. These methods usually require the intervention of human experience and have certain limitations when dealing with complex fault modes [8,9].

For this reason, it is necessary to develop more accurate monitoring systems and related algorithms. With the advancement of signal acquisition technology and the development of machine learning algorithms, fault diagnosis methods based on multi-feature analysis have received extensive attention. In order to improve the accuracy of thread state detection, researchers at home and abroad have carried out relevant research using different methods. Generally speaking, these methods can be divided into two categories: direct methods and indirect methods [10,11]. Direct methods mainly use equipment such as strain gauges to directly measure the strain changes at the bolt connection parts and then infer the pre-tightening force of the bolts [12]. However, the accuracy of direct methods is limited, and they cannot meet the high requirements for the bolt-loosening state under complex working conditions. Therefore, indirect detection methods have gradually become the mainstream of bolt loosening detection research. Common indirect detection techniques include ultrasonic testing [13,14,15], impedance testing [16,17,18], visual inspection [19,20], vibration testing [3,7,10], etc. Among many indirect detection techniques, the ultrasonic method is widely used because of its ability to propagate inside materials and its high precision. The ultrasonic guided wave method excites ultrasonic elastic waves in the structure. During the wave propagation process, the wave propagation mode will be affected by the loosened part of the bolt, thus changing the response characteristics of the wave. Specifically, characteristics such as the amplitude, phase, and frequency components of the wave will change. By comparing the wave response signals in the loosened and non-loosened states, the loosening condition, the degree of loosening, and the location of the bolt connection can be determined [21]. In recent years, more and more research has shown that ultrasonic-based loosening detection methods can effectively evaluate the state of bolt connections. The relevant evaluation parameters include energy loss [22], time-of-flight [23], resonance frequency [24], and velocity ratio [25]. Zhang et al. [26] proposed a bolt loosening detection method based on sub-harmonic resonance analysis and verified the effectiveness of this method through numerical simulation and experiments. Although the ultrasonic method has made significant progress in bolt loosening detection, its limitations are also quite obvious. Because it relies on reflection and scattering phenomena, it is difficult to accurately detect bolt loosening in complex structures [27]. In addition, in practical applications, the ultrasonic method often requires expensive equipment for detection, which poses challenges to its industrial application. Another common indirect detection method is the impedance-based detection technology, which is based on the relationship between the system impedance and the dynamic characteristic parameters. Since defects such as bolt loosening can cause changes in the system impedance, the impedance method can judge the degree of loosening and the state of the bolt connection by monitoring the fluctuations of the impedance. Many scholars have made important progress in the theoretical analysis, numerical simulation, simplified models, and design of measurement systems of the impedance method [28,29]. For example, Lee [30] proposed a scheme for monitoring the state of bolt connections using transfer impedance technology; Sun et al. [31] proposed a method for monitoring bolt loosening in steel structures based on the impedance method. In addition, Shao Junhua et al. [32] studied the bolt loosening monitoring method based on the piezoelectric admittance spectrum, explored the relationship between the peak frequency of the admittance spectrum and the bolt pre-tightening force, and proposed a new method for monitoring bolt loosening based on the frequency change of piezoelectric impedance. Although the impedance method has made a lot of progress in theoretical and experimental research, its application still faces high costs and technical difficulties. Because impedance detection requires the installation of sensors on the surface of the monitored structure, this increases the complexity and cost of the system [33]. Apart from that, Wang [34,35,36,37] et al. carried out a study on bearing failure and modeling in the wind power field, and their proposed modeling method can act as a reference for the monitoring of bolt loosening. Shu [38,39] and Wei [40] et al. carried out a study on the condition monitoring of electric vehicle driveline components.

Despite the availability of various methods for detecting bolt loosening, each technique has inherent limitations. Existing technologies often fail to fully and accurately capture the stress transfer dynamics within the bolt group and the subtle changes associated with bolt loosening. Moreover, there is a lack of efficient, accurate, and cost-effective online monitoring solutions. In response to these challenges, this study introduces a multi-dimensional monitoring approach grounded in the analysis of the bolt group’s stress transfer characteristics. The objective is to integrate the strengths of multiple detection technologies to develop a novel bolt loosening diagnosis and early warning system tailored to the operational conditions of large-scale generator sets. This approach aims to enhance both the precision and reliability of the bolt-loosening state monitoring, ultimately offering practical solutions for improved fault detection and predictive maintenance.

2. Materials

Bolt loosening often occurs because during the long-term operation of hydraulic units, the contact surface between the external load and the threaded connection changes, resulting in a decline in the operating performance of the unit. Thread loosening not only increases energy consumption and reduces the unit’s efficiency but may also lead to more serious mechanical damage and even trigger system failures. Therefore, the early diagnosis of thread loosening failures is of great significance for ensuring the safe and stable operation of hydraulic units. In order to study the loosening of the pre-tightening force of top cover bolts in large-scale generator sets and the stress transfer characteristics of the bolt group, this study designed a test method based on pre-tightening force monitoring and stress transfer characteristic analysis based on the actual working conditions of the Wuqiangxi Hydropower Plant (as shown in Figure 1).

Figure 1a shows a picture of the hydroelectric power station site, and Figure 1b shows the hydraulic turbine unit. This is to fully consider the impact of bolt-loosening faults on the unit performance of the hydraulic turbine unit under actual working conditions. This study considers the hydroelectric generating units used for experiments in this hydroelectric power station as the research object. In order to better secure the machine equipment, these machines have more fastening bolts—up to 144 bolts. It should be noted that considering the danger of the testing environment of the hydropower generation system, the experiments carried out in this paper were conducted under the guidance of the engineering and technical personnel of the hydroelectric power station, and the safety during the testing process was fully considered. During the testing process, the testing equipment included a bolt pre-tightening force monitoring system, a stress signal acquisition system, a hydraulic torque control system, and a data processing and analysis system. Figure 2 shows the monitoring position relationship between the thread loosening state and the pre-tightening force changes of surrounding bolts during the testing process. In the experiment, 12 bolts were numbered from 1 to 12, respectively. During the testing process, one bolt was gradually loosened by a hydraulic torque wrench, while the other bolts remained in the normal pre-tightened state. The stress changes in all bolts were monitored in real time by strain gauges installed at the threaded connection parts. No sensor was installed on the pre-tightening force of the loosening bolt. Instead, the degree of loosening and its impact on the surrounding bolts were judged by monitoring the stress changes in the surrounding bolts.

The core of the experiment is to simulate the bolt-loosening process and monitor the stress changes in the surrounding bolts. The stress signal acquisition system is a key part of this experimental platform. Strain gauges were installed on the surface of the threaded connectors to monitor the stress changes at the threaded connections. This experiment was carried out under the actual working conditions of the normal operation of the hydraulic turbine unit. The purpose of this study was to detect the looseness of the surrounding bolts by means of a small number of stress–strain sensors. So, we chose 12 bolts to monitor during the test. In terms of the selection of test bolts, we did not make any special regulations or requirements, and the 12 bolts were selected randomly. When the turbine is running, these bolts bear external loads from water pressure and equipment loads; hence, their pre-tightening forces will be affected to varying degrees. The bolts are subject not only to traction (tensile stress) but also to other types of mechanical loads, including shear and torsional forces. These additional stresses can arise due to the dynamic forces acting on the generator set, such as vibration, thermal expansion, and operational torque. However, in this paper, we focus only on the axial stress variation of the bolt. Anyway, we made further clarifications in the revised manuscript. To ensure the accuracy of the experiment, an ultrasonic bolt pre-tightening force monitoring device was used during the experiment. This device can monitor the changes in bolt pre-tightening force in real time and has high precision measurement capabilities. At the same time, a hydraulic torque wrench was used to precisely control the loosening and re-tightening of bolts, ensuring the standardization and reliability of bolt operations. The core of the experimental method is to simulate the complete loosening of one bolt and observe the changes in the pre-tightening force of its adjacent bolts. The specific steps are as follows: First, zero-point calibration is carried out on the 12 bolts through the ultrasonic bolt pre-tightening force monitoring device to ensure that the initial pre-tightening force values of each bolt are accurate. Then, a hydraulic torque wrench is used to gradually loosen the bolt between No. 6 and No. 7, and the changes in the pre-tightening force of adjacent bolts (such as No. 6 and No. 7) are recorded in real time during the loosening process. Immediately after that, the loosened bolt is re-tightened to the predetermined torque using a hydraulic torque wrench, and the changes in the pre-tightening force during the re-tightening process are recorded again through the ultrasonic monitoring device. Through this process, we can obtain the data on the changes in the pre-tightening force of each bolt and its adjacent bolts during the bolt-loosening and re-tightening processes. In particular, during the loosening process, the attenuation of the pre-tightening force of a bolt may cause changes in the pre-tightening force of adjacent bolts. Therefore, a detailed analysis of the pre-tightening force of adjacent bolts is required. The experimental data will help us reveal the impact of bolt loosening on the overall stability of the fastening system, as well as the change rules of the pre-tightening force of surrounding bolts under different degrees of loosening. During the experiment, the testing system utilizes the iBolt USM-1 from iFAst Beijing, China, for the accurate monitoring of bolt loosening. Initially, strain gauges are installed on the bolt surfaces to measure stress changes. These sensors are calibrated using known loads, ensuring linearity and temperature compensation to minimize external influences. Additionally, an ultrasonic pre-tightening force monitoring system is employed; its calibration involves establishing a relationship between the travel time of sound wave and bolt pre-tightening force. This is achieved by applying incremental loads while recording the corresponding time delays. The system also integrates all sensors into a data acquisition system, ensuring synchronization and accurate time alignment of signals from different sensors. Calibration includes adjusting gain settings and filtering noise to enhance signal accuracy. Finally, experimental validation is conducted under varying loosening conditions to assess the reliability and precision of the system, confirming its effectiveness in monitoring stress and pre-tightening force changes during bolt loosening. This comprehensive calibration process ensures the accuracy and stability of the system for fault diagnosis.

When performing formal experimental tests, all operations were carried out strictly in accordance with the predetermined procedures to ensure the accuracy and repeatability of data collection. The ultrasonic bolt pre-tightening force monitoring device used has a multi-channel function and can monitor the changes in the pre-tightening force of multiple bolts simultaneously, which provides strong support for analyzing the complex situations during the loosening process.

3. Methods

To ensure the accuracy of the experiment and the reliability of the data, the Variational Mode Decomposition (VMD) method was used to decompose the collected stress signals and extract modal components with different frequency and time characteristics. The VMD method optimally solves a set of Intrinsic Mode Functions (IMFs) so that the signal can be decomposed into several modes with different frequency bandwidths, and each mode represents a component in the signal. The core idea of the VMD method is to decompose the signal through a variational optimization method to obtain a set of sparsely represented modes, which can effectively remove noise and extract the essential features of the signal. In the application process, it first performs a Hilbert transform on each component to obtain a single-sided spectrum. By mixing an exponential tuned to its respective estimated center frequency, the spectrum of each component is shifted to the baseband region. The VMD of the output signal can be expressed by the following formula:

$$\left\{\begin{array}{c}min\left\{{{\displaystyle \sum _{k=1}^K}‖{\partial }_t\left(\left(\delta \left(t\right)+{\displaystyle \frac{j}{\pi t}}\right){°u}_k(t)\right)\exp (-j{\omega }_{k}t)‖}_2^2\right\}\\ s.t.{\displaystyle \sum _{k=1}^K}{u}_k=f(t)\end{array}\right.$$

(1)

where, ${\partial }_t$ represents taking the partial derivative; $\delta \left(t\right)$ is the Dirac distribution function; “$°$”represents the convolution operation; K is the total number of components; and $f\left(t\right)$ is the original photovoltaic power output signal. The above constrained extremum problem is transformed into an unconstrained problem through the Lagrange multiplier $\lambda$ and the quadratic penalty term $\alpha$, as shown in Equation (2).

$$\begin{gathered} L\left(\left\{u_k\right\},\left\{{\omega }_k\right\},\lambda \right)=\alpha {\sum _{k=1}^K‖{\partial }_t\left(\left(\delta \left(t\right)+{\displaystyle \frac{j}{\pi t}}\right){°u}_k\left(t\right)\right)\exp \left(-j{\omega }_{k}t\right)‖}_2^2 \\ +{‖f\left(t\right)-\sum _{k=1}^K{u}_k\left(t\right)‖}_2^2+\langle \lambda \left(t\right),f\left(t\right)-\sum _{k=1}^K{u}_k\left(t\right)\rangle \end{gathered}$$

(2)

The components and the corresponding central frequencies can be optimized and solved by the Alternating Direction Method of Multipliers, and the updated method is as follows:

$$\begin{array}{c}{\widehat{u}}_k^{\left(n+1\right)}\left(\omega \right)={\displaystyle \frac{\widehat{f}\left(w\right)-{\sum }_{i\ne k}{\widehat{u}}_k^{\left(n\right)}\left(\omega \right)+\frac{{\widehat{\lambda }}^{\left(n\right)}(w)}{2}}{1+{2\alpha (w-w_k^{\left(n\right)})}^2}}\end{array}$$

(3)

$$\begin{array}{c}{\omega }_k^{(n+1)}={\displaystyle \frac{{\int }_0^{\infty }{w\left|{\widehat{u}}_k^{\left(n+1\right)}\left(\omega \right)\right|}^{2}dw}{{\int }_0^{\infty }{\left|{\widehat{u}}_k^{\left(n+1\right)}\left(\omega \right)\right|}^{2}dw}}\end{array}$$

(4)

where, $\widehat{f}\left(w\right)$, ${\widehat{u}}_k\left(\omega \right)$, and $\widehat{\lambda }(w)$ are the Fourier transforms of $f\left(t\right),u\left(t\right),\mathrm{and}\lambda \left(t\right)$, respectively; $\omega$ is the frequency; and $n$ is the number of iterations.

This method enables the decomposition of complex signals into simpler components, each containing specific frequency information. This significantly reduces the complexity of the original signal and facilitates further analysis. By employing the VMD method, complex signals can be broken down into several components with distinct frequency and time characteristics. Analyzing these components reveals hidden information in the signal, providing a solid foundation for diagnosis. During the signal analysis, the VMD method was first used to decompose the stress signals of different threads, resulting in multiple intrinsic mode function (IMF) components. The Hilbert transform was then applied to these IMF components to extract the instantaneous frequency and amplitude variation patterns. These characteristic features can effectively reflect the changes in the thread-loosening state. Notably, under varying degrees of loosening, the spectral characteristics of the IMF components change significantly. By comparing the IMF components across different states, early diagnosis and early warning of thread-loosening faults can be achieved.

The experimental process was conducted in the following steps: First, the vibration and stress signals of the hydraulic turbine are collected under normal operating conditions, and reference data are recorded. Next, during the turbine’s operation, stress and vibration signals are recorded at various stages of loosening by incrementally adjusting the loosening of the threaded connections. Finally, the collected signals are analyzed using VMD, and the frequency-domain characteristics of the IMF components are extracted and compared to identify the signal feature variations under different loosening states. By comparing these signal features across various conditions, the impact of thread loosening on the operation of the hydraulic turbine can be evaluated, providing essential insights for diagnosing thread-loosening faults.

4. Results and Discussions

According to the testing method mentioned in the previous section, we detected the pre-tightening force of the top cover bolts of the hydroelectric generating unit; we selected 12 bolts as the test objects and installed the corresponding sensors on them, as shown in Figure 3. The test started at 16:20 p.m. on 4 May 2024, with the sampling frequency of the equipment being 3 Hz. After 30 min (at the 5298th sampling point), the loosening operation of the experimental bolts was started until the pre-tightening stress was completely lost. Then, pre-tightening was carried out, and the bolts were completely tightened after 1 h of the experimental test (at the 10,892nd sampling point). The stress curves of each bolt of the hydro-turbine unit are shown in Figure 4.

As shown in Figure 4, during the actual detection process, it was observed that the pre-tightening force of the bolts remained within a certain range, with the pre-tightening force of the top cover bolts fluctuating between 10 kN and 20 kN under static working conditions. During the bolt-loosening experiment, as the hydraulic torque wrench gradually loosened the bolts, the pre-tightening force began to change. It was found that when the experimental bolts loosened, the pre-tightening force of the surrounding bolts fluctuated. The stress curve of bolts further from the loosening point exhibited less fluctuation. For example, the stress of bolt No. 7, adjacent to the experimental bolt, was approximately 10 kN before loosening at the 5298th sampling point and decreased to around 9 kN after loosening, with a fluctuation range of 1 kN. However, the stress of bolt No. 1, which was the farthest from the experimental bolt, was hardly affected. After the bolts were loosened, the loosened bolts were re-tightened using a hydraulic torque wrench, and the recovery of the pre-tightening force during the re-tightening process was observed. It was found that after re-tightening, the pre-tightening force of the bolts mostly recovered to a level close to the original pre-tightening force, and the difference between the pre-tightening force of the loosened bolts and the surrounding bolts was minimal. However, it is important to note that although the pre-tightening force of the bolts largely recovered, some bolts did not fully return to the original pre-tightening force. This phenomenon may be attributed to wear on the contact surfaces or other localized damage caused by prolonged loosening, with recovery varying between different bolts. Additionally, due to significant external interference and the operational conditions of the hydro-turbine unit in the real environment, the collected bolt stress signals exhibited large-scale fluctuations, which hindered accurate positioning and analysis of the actual loosened bolt conditions. To address the issue of noise and signal spikes in the environmental sensor data, filtering techniques, such as low-pass filters, can be used to attenuate high-frequency noise, while median filtering can remove spikes by replacing extreme values with the median of neighboring values. Additionally, Kalman filtering can be applied to estimate signal states and reduce noise, particularly in dynamic systems. However, these methods may filter out the official bolt-loosening signals along with them. To further study the characteristic changes in the stress of bolts after loosening, we used the VMD method to analyze the changes in the stress signals from bolt No. 6 and No. 7 adjacent to the loosened bolt. At the same time, for comparison, we analyzed the stress signals from bolt No. 1 and No. 12, which are farthest from the loosened bolt. The obtained results are shown in Figure 5.

As can be seen from Figure 5, the first intrinsic mode function (IMF1) is the most sensitive to the bolt-loosening state, and its waveform characteristics exhibit significant dynamic change features. Specifically, when bolts are in different tightening states, the amplitude, frequency, and phase of IMF1 all show obvious differences. During the gradual process of bolt loosening, the fluctuation amplitude of IMF1 shows a non-linear growth trend, and this change pattern can be regarded as an early warning signal of bolt loosening. The IMF1 signal fluctuations of the adjacent bolts have a significant correlation, indicating the potential interaction mechanism among the bolt group.

For example, in the bolt-loosening test starting at the 5300th sampling point, bolts sp6 and sp7 showed the most significant pre-tightening force response, with the pre-tightening force of these bolts fluctuating by about 10 kN. It is worth noting that the IMF2-IMF10 signals have been fluctuating at different degrees throughout the cycle, but they are not sensitive to the bolt-loosening and tightening processes. Through the synchronous analysis of the upstream and downstream water level data, we observed that the water level difference showed a downward trend during the test, and the changes in data from the 12 monitoring channels showed a high degree of consistency. To further explore the potential interaction mechanism and change rules among the top cover bolts of the hydro-power generating unit during the bolt-loosening and tightening processes throughout the entire test, we conducted VMD analysis on the stress curves of the 12 monitored bolts and extracted the IMF1 information. The corresponding results are shown in Figure 6.

According to Figure 6, throughout the entire test, the information of the IMF1 of each bolt has been fluctuating continuously around 10 KN. This may be caused by the vibration of the hydroelectric generating unit during operation and environmental radiation. When the test was carried out for 30 min (i.e., at the 5300th sampling point), the test bolt was loosened, and it could be clearly observed that the stress of the adjacent bolt No. 7 changed significantly, with its amplitude jumping from -10 to 16. After that, as the test time continued, bolt No. 6 also showed obvious fluctuations, and the fluctuations were transmitted to bolt No. 5. During this process, almost no obvious changes occurred in other bolts. This indicates that when the top cover bolts of the hydroelectric generating unit are loosened, the adjacent bolts of the loosened bolt will generate obvious stress fluctuations and gradually transmit these fluctuations to the other adjacent bolts.

To further explore the correlation of the stress changes in each bolt during the bolt-loosening process, we conducted a correlation analysis on the stress changes in each bolt using Pearson and Spearman, respectively. The results are shown in Figure 7.

As can be seen from Figure 7, during the bolt-loosening period, the Pearson and Spearman correlation coefficients of Bolt No. 6 and Bolt No. 7 are the highest, being 0.814 and 0.741, respectively, while the correlation parameters of other bolts hardly change significantly. This further proves that when a bolt loosens, it will cause stress changes in the adjacent bolts, and this change is generally positively correlated. The stress of bolts farther away from the loosened bolt is hardly affected. In addition, as found from Figure 7, after loosening, the correlation coefficients of some bolts show changes in magnitude. For example, the Spearman correlation coefficient between Bolt No. 7 and Bolt No. 8 is −0.431, and the Spearman correlation coefficient between Bolt No. 6 and Bolt No. 8 is 0.428. This may be because after the bolt loosens, factors such as the structure or working conditions cause a transfer of force. Overall, the Spearman and Pearson correlation heatmaps during the bolt-loosening process well demonstrate the stress-conduction mechanism during the bolt-loosening process.

From the perspective of practical engineering applications, the proposed method—monitoring the stress signals of bolts adjacent to the loosened one, combined with EMD decomposition and Pearson correlation for fault detection—presents several advantages over traditional bolt-loosening detection techniques. Compared to the mechanical methods, such as torque measurement, which require direct physical intervention, this approach enables continuous, non-invasive, and real-time monitoring of bolt conditions without disrupting operations. The use of stress signals from the surrounding bolts enhances the sensitivity to early-stage loosening, making it more responsive to subtle changes that might be overlooked by other methods. Additionally, the combination of EMD and Pearson correlation provides a reliable means of pinpointing the location of loosening by analyzing the relationship between the adjacent bolts. However, there are some practical limitations to this approach. Unlike ultrasonic testing, which can detect material degradation, such as corrosion or fatigue, the proposed method focuses primarily on the stress transfer due to loosening, which may not account for other forms of bolt failure. The effectiveness of the method also depends on proper sensor placement and is susceptible to environmental noise, such as vibration and temperature fluctuations, which could interfere with accurate signal acquisition. Furthermore, the computational demands of EMD for real-time monitoring could pose challenges in large-scale systems with many bolts. Overall, while the proposed method offers an advanced and efficient solution for the detection of bolt-loosening in large-scale generator units, it requires further optimization to improve robustness against environmental interference and computational efficiency for broader industrial applications.

5. Conclusions

This study focuses on diagnosing pre-tightening force loosening faults and stress transfer characteristics in the top cover bolts of large-scale hydropower generating units. It examines the relationship between changes in the pre-tightening force and stress distribution within the bolt group. A multi-dimensional monitoring approach combining pre-tightening force monitoring and signal analysis is proposed. The main conclusions of the study are as follows:

• Bolt loosening causes fluctuations in the pre-tightening force of local bolts and alters the stress transfer characteristics of the entire bolt group. These changes are most noticeable in the surrounding bolts, with sensitivity decreasing with distance from the loosened bolt;
• The VMD method effectively decomposes stress signals during the loosening process, revealing that the first modal is highly sensitive to bolt loosening. This modal can reliably monitor the bolt-tightening state, providing a foundation for fault diagnosis and early warning;
• The results of the Pearson and Spearman correlation analyses of each bolt show that after a bolt loosens, the correlation parameters of the adjacent bolts increase significantly, showing a positive correlation, while the correlation parameters of other bolts hardly change significantly. This further proves that when a bolt loosens, it will cause an increase in the stress of adjacent bolts.

In conclusion, this study provides a new technical solution for the monitoring and diagnosis of bolt-loosening faults in large-scale generating units, reveals the internal laws of stress transfer characteristics during the bolt-loosening process, and has important theoretical value and practical application prospects. Future research can optimize the diagnostic model, improve the detection accuracy, and explore more efficient, long-term operating conditions and low-cost monitoring technologies for wider application in engineering.