Turbine Operation Research Articles

Ab initio calculations of Nb-based MAX phases as bond coats for thermal barrier coatings

Thermal barrier coatings (TBCs) are essential to the reliable high-temperature operation of gas turbines and engines. They comprise a ceramic top coat (TC), a metallic bond coat (BC), and a superalloy substrate. Metallic BCs are common, but they require a minimal difference in the coefficient of thermal expansion (CTE) between the TC and substrate. Among ceramic materials, MAX phases have high CTE. This study reports our use of ab initio calculations to assess the suitability of MAX phases as TBCs. We model Nb-based MAX phases with 211 and 312 structures that have Al or Si at the A sites and C or N at the X sites. We use the quasi-harmonic approximation to calculate the Young's moduli and CTEs of the materials with respect to temperature. The Nb2SiN MAX phase appears as the most suitable for use as a BC between various ceramic TCs and an Inconel-718 substrate. It is predicted to be effective in relieving thermal stresses due to its high CTE of 10.882 × 10−⁶ K−1 at 1273 K. The results indicate that carbide MAX phases with high Young's modulus and low CTE should be used with caution. They may not accommodate thermal stresses as effectively, potentially leading to material failure or reduced performance. Overall, our study indicates the potential of Nb-based MAX structures for use as BCs.

Development of Detailed and Reduced Chemical Kinetic Models for Ammonia Gas Turbines

Abstract The power generation sector has been recently moving towards decarbonization and there is an increased interest in replacing conventional fossil fuels with fuels that produce reduced/zero carbon emissions. One such fuel is ammonia (NH3). However, ammonia is hard to ignite, has a low flame speed, and produces a significantly large amount of nitrogen oxide (NOx) emissions. Hence, using 100% ammonia as fuel in gas turbines requires significant modifications and the development of novel combustors. Blending hydrogen with ammonia, however, helps in having better control over the combustion properties. Before utilizing hydrogen-blended ammonia in an actual gas turbine combustor, thorough simulation studies are required to evaluate its performance, possible hazards, and emissions. The literature lacks well-validated chemical kinetic models for the combustion of hydrogen-blended ammonia for undiluted mixtures at gas turbine-relevant conditions (~20 bar). Hence, in this work, we develop a detailed chemical kinetic model for hydrogen blended ammonia combustion and validate it with a wide range of experimental data for both dilute and undiluted mixtures relevant to gas turbine operating conditions. The detailed chemical kinetic mechanism was reduced to a smaller version (32 species mechanism) without significant loss in accuracy using the direct relation graph with error propagation (DRGEP) and full species sensitivity analysis. The resultant mechanism can predict a wide range of experimental results with the least cumulative error and will be a valuable tool in CFD simulations that will enable the development of gas turbines for zero-carbon power generation.

A novel local feature fusion architecture for wind turbine pitch fault diagnosis with redundant feature screening

The safe and reliable operation of the pitch system is essential for the stable and efficient operation of a wind turbine (WT). The pitch fault data collected by supervisory control and data acquisition systems (SCADA) often contain a wide variety of variables, leading to redundant features that interfere with the accuracy of final diagnosis results, making it difficult to meet requirements. Also, the problem of extracting only local features while ignoring global information is present in the feature extraction process using the deep Convolutional Neural Network (CNN) model. To address these issues, the global average correlation coefficient is proposed in this article to measure the correlation between multiple variables in SCADA data. By considering the correlation among multiple variables comprehensively, redundant features are effectively eliminated, enhancing the accuracy of fault diagnosis. Furthermore, a new local amplification fusion architecture network (LAFA-Net) based on multi-head attention (MHA) is introduced. An efficient local feature extraction module, designed to enhance the model’s perception of detailed features while maintaining global context information, is first introduced. LAFA-Net integrates the advantages of CNN and MHA, efficiently extracting and fusing valuable features from filtered data for both local and global aspects. Experiments on real pitch fault data demonstrate that the global average correlation coefficient effectively screens out redundant features in the dataset that negatively impact fault diagnosis results, thereby improving diagnosis efficiency and accuracy. The LAFA-Net model, capable of accurately diagnosing multiple types of pitch faults, shows a superior classification effect and accuracy compared to several advanced models, along with a faster convergence speed.

Pitch Actuator Fault-Tolerant Control of Wind Turbines via an L1 Adaptive Sliding Mode Control (SMC) Scheme

Effective fault identification and management are critical for efficient wind turbine operation. This research presents a novel L1 adaptive-SMC system designed to enhance fault tolerance in wind turbines, specifically addressing common issues such as pump wear, hydraulic leakage, and excessive air content in the oil. By combining SMC with L1 adaptive control, the proposed technique effectively controls rotor speed and power, ensuring reliable performance under various conditions. The controller employs an adjustable gain and an integrated sliding surface to maintain robustness. We validate the controller’s performance in the FAST (Fatigue, Aerodynamics, Structures, and Turbulence) simulation environment using a 5-megawatt wind turbine under high wind speeds. Simulation results demonstrate that the proposed L1 adaptive-SMC outperforms traditional adaptive-SMC and adaptive control schemes, particularly in the presence of faults, unknown disturbances, and turbulent wind fields. This research highlights the controller’s potential to significantly improve the reliability and efficiency of wind turbine operations.

Experimental study on Fuel Heating of A Gas Turbine Engine

In order to mitigate the latent hazards caused by fuel retention in the gas turbine and ensure a higher ignition success rate, an investigation was conducted on the impact of fuel heating on the gas turbine. By incorporating a fuel heating device into the gas turbine, experiments were carried out to evaluate its heating performance at different positions within the fuel system. The objective was to elevate the temperature of the main fuel pipe prior to ignition, thereby reducing ignition success speed and guaranteeing successful combustion initiation. The findings revealed that placing the fuel heating device at the outlet of the fuel control device met all requirements; however, positioning it before this device failed to meet expectations. Furthermore, when subjected to heat, this particular heating device did not accurately reflect actual fuel temperature; additionally, relying solely on circulating heat within the existing fuel system proved inadequate. Consequently, based on these test results, an optimal solution involving supplementary heating devices was determined - a decision that holds immense significance for ensuring steady operation of gas turbines.

Hyper-reduced-order model for estimating convection heat transfer coefficients of turbine rotors

Forced convection heat transfer occurs inside the steam turbine, and it is crucial for thermal and strength analysis to accurately estimate the convection heat transfer coefficients of the turbine rotor. This paper presents a hyper-reduced-order model for efficiently estimating the forced convection heat transfer coefficients of a steam turbine rotor. Unlike the full-order finite element method, the hyper-reduced-order model uses the discrete empirical interpolation method to approximate the domain integration of transient heat conduction simulations. This approach greatly reduces the degrees of freedom of numerical integration, thus substantially improving the computational efficiency of forward heat conduction problems. The hyper-reduced-order model and Levenberg–Marquardt algorithm are combined to minimize temperature errors between the numerical simulation results and remote sensor measurements and iteratively estimate the heat transfer coefficients of forced convection in the rotor. The accuracy and efficiency of the proposed model are verified through a transient heat conduction simulation. Moreover, the effects of the initial guess values and measurement errors are investigated to demonstrate the universality and robustness of the proposed approach in determining the convection heat transfer coefficient. Compared with the full-order finite element model, the proposed hyper-reduced-order model can increase the efficiency of forward heat conduction simulations of the turbine rotor by more than 10 times, and it only takes 0.87 s computer runtime in single transient step simulation, and then rapidly estimate the forced convection heat transfer coefficients. Furthermore, the performance of the proposed approach is insensitive to the initial guess values, and it exhibits great robustness under measurement error. The mean errors are 4.78 %, 2.67 % and 10.51 % when the initial values are 0.015 mW·mm−3·°C−1, 0.05 mW·mm−3·°C−1 and 0.15 mW·mm−3·°C−1 respectively. When there is no measurement error, the estimated error of the convection heat transfer coefficients is 2.67 %, and even if the measurement error reaches 5 %, and the accuracy loss is only 5.57 %. Consequently, this approach is highly suitable for estimating convection heat transfer coefficients during the dynamic operation of steam turbines, and this research provides reliable guidance for the optimization design and safe operation of steam turbines.

Simulations of design and high load operation of a model Francis turbine using bridged approach to turbulence modelling

Abstract Off-design operation of hydraulic turbines is contemporarily frequented for balance of variable energy intermittence in the electric grid. Being operationally highly flexible, these turbines allow a quick transition to off-design operation from the design point. However, such operational flexibility, and therefore the grid balancing capability is impeded by generation of flow instabilities like vortex breakdown during off-design operation. Vortex breakdown causes losses in efficiency and pressure recovery, pressure fluctuations and possibly mechanical vibrations in event of resonance between system natural and flow field fluctuation frequencies. While substantial experimental and numerical effort has already been made to study draft tube vortex breakdown, an accurate numerical flow characterization of the phenomenon is still a challenge. To this end, operation of a high head model Francis turbine under design and high load regimes using a bridged turbulence modelling approach is simulated. The approach allows a seamless transition between direct numerical simulation and Reynolds averaged Navier-Stokes equations. The highest attainable accuracy is limited by the mesh size. As such a satisfactory compromise between desired accuracy and invested computational effort is attained. The flow in the draft tube is free of anomalies under design specified operation. However, at high load an axial flow stagnation occurs centrally, and the flow is separated about the stagnated zone. The core of the vortex is enlarged with flow recirculation within it. Shear layers between the central stagnant zone and surrounding outflow kink and roll up transforming it into a spiral structure. In this work, a basic yet accurate numerical flow characterization of the aforementioned flow situations is achieved.

Processos de vulnerabilização de empreendimentos eólicos em comunidade camponesa no Agreste Meridional de Pernambuco

ABSTRACT Amid sustainable agendas, renewable energy sources play a strong role, especially wind energy. However, the implementation of wind farms produces transformations in communities, causing impacts in different areas and vulnerability processes. The study aims to problematize the reports of the peasant population regarding the processes of vulnerability in the area of influence of the implementation of wind farms in a municipality in Pernambuco. This is an observational, descriptive research with a qualitative approach, carried out in a peasant community, located in the municipality of Caetés, Pernambuco, Brazil. Data collection was carried out through semi-structured interviews. Data analysis was based on the content analysis technique in the thematic modality. It was observed that the arrival and operation of the wind turbines coincided with the emergence of signs and symptoms, such as hearing and skin problems, anxiety, dizziness and headache. This situation allows us to consider a probable connection between the impacts caused by wind towers, already described in the literature, and those present in the participants’ reports. Prudence is necessary when planning and building wind farms, since such health problems can be temporary or permanent, leading the local community to constant suffering.

Study of the efficiency of the joint operation of a cogeneration steam turbine with a heat pump installation

Study of the efficiency of the joint operation of a cogeneration steam turbine with a heat pump installation

A numerical study on the effect of spanwise installation of vortex generators on Francis runner blades

Abstract Hydro turbine operation far off from its best efficiency point introduces vortices and swirl that detaches flow from the blade surface. This break-off of flow accounts to loss in hydrodynamic lift accompanied by pressure fluctuations and vibration that leads to poor performance and mechanical failure of the turbine blades. Vortex generators (VGs) are efficient passive devices deployed to enhance aerodynamic lift of wind turbine blades and aircraft wings and can improve hydrodynamic lift on turbine runner blades as well. This study aims to investigate on the possibility of installation of VGs on the runner blade at leading edge, midspan and trailing edge of the runner blade. The study is carried out on a model Francis turbine developed at Waterpower Laboratory, NTNU. The numerical study is mainly focused on improving performance of the turbine at low speed as well as at the best efficiency speed. The operating head selected for the study is 11.94 m and the speed of the turbine is varied from 233 rpm to 433 rpm at an increment of 25 rpm. The turbine is simulated at different positions of guide vanes and hydraulic performance is calculated and the results of the analysis are compared with reference case without VGs. The results at deep-part load show major improvement in runner efficiency with increment in values up to 4%. The core purpose of the research is to develop effective techniques to operate traditional turbine runner at variable speed with cost-efficient minimal modifications in the geometry of the runner blades.

Verification of thermodynamic parameters of a mixture of generator gas on oxygen-hydrogen fuel with an excess of one of the fuel components

Liquid gas generators (LGG) are additional firing units in the power system of liquid rocket engines (LPRE). The LGG ensure the operation of the power units of the turbopump unit (TPU) of the engine by feeding combustion products (CP) to the turbine drive. The main criteria for the efficiency of the generator gas is the complex (RT)gg and the thermodynamic properties of the mixture, depending on temperature, pressure, the degree of excess of the oxidizer and the enthalpy of the fuel, attributed to the conditions of supply to the nozzles of the GG. Changing the parameters of the generator gas leads to a change in the turbine power parameters due to its effect on the adiabatic operation of the Lad turbine. Depending on the engine circuit under consideration, CP GG can perform work in other units and elements of the engine, as well as influence many parameters of the LPRE. Among the main ones can be noted: the power of the booster gas turbine of the booster turbopump unit (BTPU) in the case of the selection of the generator gas after the GG or turbogas after the main turbine; the temperature of heating the refrigerant in the heat exchanger introduced in the GG; specific impulse of a liquid rocket propulsion system (LRPS), depending on the quantity and properties of the turbogas entering the exhaust pipe of the engine (for the engine circuit without afterburning the generator gas); mixing in the combustion chamber (CC) due to afterburning of turbogas entering the engine chamber after the turbine (for the engine circuit with afterburning of generator gas); parameters of the firing wall of the engine in the case of using a high-temperature gas curtain by blowing generator gas into the supersonic part of the nozzle. For many pairs of fuel during combustion in GG, the nonequilibrium of combustion products is characteristic (especially in hydrocarbon fuels).Due to the fact that the combustion products (CP) during the combustion of an oxygen-hydrogen mixture, due to the simplicity of the reaction, have time to form while staying in the GG (i.e., the time of chemical equilibrium of the CP is less than or equal to the time of stay in the GG), their thermodynamic parameters can be reliably determined using programs that simulate chemical equilibrium reactions. In this article, the issue of obtaining reliable results of thermodynamic calculations of generator gas at low and high coefficients of oxidant excess is investigated. Verification of parameters obtained in the programs “Astra” and “Rocket Propulsion Analysis” with calculated values was carried out. The most suitable program for performing engineering calculations and modeling the thermodynamics of liquid gas generators has been determined.

Improved control strategy and designed control parameters of pitch system for wind turbine considering blade load reduction

As wind turbines increase in the power, the longer the blade, the more severe the blade load. Traditional control strategies and control parameters do not consider to reduce blade load, which seriously threatens the safe operation of wind turbines. Therefore, this study proposes a pitch control strategy based on blade active damping control and a multistage control parameter design method. Firstly, this study proposes a pitch control strategy based on blade active damping control to reduce the blade load based on the establishment of a mathematical model of the pitch system considering the blade load and a dynamic model of blade active damping control. Secondly, in the control parameter initial values design of Stage Ⅰ, this study proposes a variable forgetting factor recursive least squares to identify a simplified mathematical model of the pitch system and a Low–overshoot Chien–Hrones–Reswisk to solve the proportional integral control parameter initial values. Thirdly, in the control parameter optimal values design of Stage Ⅱ, this study proposes an adaptive genetic algorithm with improved hyperbolic tangent function to optimize control parameter at the equilibrium points and proposes an adaptive control to calculate control parameter at the non–equilibrium points. Finally, based on the Bladed software for 2 MW and 5 MW wind turbines, the superiority of the proposed methods, effectiveness and applicability in improving the control accuracy of the output power and generator speed, and reducing the load situation at the blade root position are verified.

On the power and control of a misaligned rotor – beyond the cosine law

Abstract. We present a new model to estimate the performance of a wind turbine operating in misaligned conditions. The model is based on the classic momentum and lifting-line theories, considering a misaligned rotor as a lifting wing of finite span, and accounts for the combined effects of both yaw and uptilt angles. Improving on the classical empirical cosine law in widespread use, the new model reveals the dependency of power not only on the misalignment angle, but also on some rotor design parameters and – crucially – on the way a rotor is governed when it is yawed out of the wind. We show how the model can be readily integrated with arbitrary control laws below, above, and around the rated wind speed. Additionally, the model also shows that a sheared inflow is responsible for the observed lack of symmetry for positive and negative misalignment angles. Notwithstanding its simplicity and insignificant computational cost, the new proposed approach is in excellent agreement with large eddy simulations (LESs) and wind tunnel experiments. Building on the new model, we derive the optimal control strategy for maximizing power on a misaligned rotor. Additionally, we maximize the total power of a cluster of two turbines by wake steering, improving on the solution based on the cosine law.

Calibration of flow differential pressure coefficients on pump-turbine by thermodynamic method

On-line monitoring of flow rate is rather important to evaluate the water consumption of the pump-turbine and the overall efficiency of the pumped storage station. Flow rate can be worked out based on the flow differential pressure measured in the flow passage and coefficients determined on model test. But the coefficients must be calibrated to obtain the reliable flow rate. As thermodynamic method is a common way to measure the discharge of prototype pump-turbine, site test is carried out on a vertical pump-turbine with 600 m rated head to calibrated the coefficients in this paper. Measuring devices are designed to satisfy both the turbine and pump operating conditions, and test results of flow rate at both turbine and pump operating conditions are presented and show that the calibrated coefficients are different to the predicted values. The calibrated results indicate the importance of site calibration on prototype turbine to ensure the monitoring validity on real-time flow rate.

Thermal performance analysis of gas turbine power plant using soft computing techniques: a review

Gas turbines are pivotal in electricity generation and industry, prized for their efficiency and flexibility in meeting diverse power needs. Optimizing their thermal efficiency is essential for improving energy output and sustainability. Soft computing methods such as neural networks, genetic algorithms, and fuzzy logic offer potent tools for this optimization due to their ability to handle the turbines' nonlinear and dynamic characteristics. These techniques facilitate a deeper understanding of the intricate interplay among various parameters affecting thermal performance, thereby enabling the development of intelligent and adaptive turbine systems. By leveraging soft computing, researchers can enhance gas turbine designs to align with modern energy and environmental objectives. This review emphasizes the application of soft computing approaches in analysing and improving gas turbine thermal performance. Such advancements are instrumental in achieving higher energy efficiency, reducing greenhouse gas emissions, and promoting a sustainable energy landscape. Ultimately, integrating soft computing into gas turbine operations promises to advance both technical capabilities and environmental stewardship in the detection of a more resilient and efficient energy infrastructure.

Modelling of JP-8 distributed combustion using a HyChem mechanism under gas turbine conditions

The critical advantages of liquid fuels in aviation over alternative energy carriers imply their dominance in the upcoming decades. The Mixture Temperature Controlled (MTC) combustion concept allows spatially homogeneous, efficient burning (distributed combustion) with low pollutant emission. MTC combustion of jet fuel JP-8 was investigated in an atmospheric burner, and the measured pollutant concentrations in the flue gas were reproduced using the Hybrid Chemistry (HyChem) approach employing Perfectly Stirred Reactor simulations. Using this robust approach comes with losing spatiotemporal characteristics if the mixture homogeneity assumption is globally valid. The effect of residence time and pressure under typical gas turbine operating conditions was investigated. Stable combustion was present above 3 ms residence time at pressures up the 60 bar, which was the upper limit of the investigated regime, while the lower residence time limit of stable combustion was 0.3 ms. The residence time interval of stable operation could be extended by applying flue gas recirculation. NO emission can be reduced by increasing the operating pressure, while the N2O production is dominant only up to 20 bar and in the 10–100 ms residence time range. CO emission vanishes above 10 ms residence time. Ultra-low emission operation requires >20 bar pressure and 10 ms residence time with distributed combustion, requiring larger combustion chambers for future jet engines.

Prediction of Steam Turbine Blade Erosion Using Computational Fluid Dynamics Simulation Data and Hierarchical Machine Learning

Abstract The information of the degree of blade erosion is vital for the efficient operation of steam turbines. However, it is nearly impossible to directly measure the degree of blade erosion during operation. Moreover, collecting sufficient data of eroded cases for predictive analysis is challenging. Therefore, this paper proposes a blade erosion prediction method using numerical simulation and machine learning. Pressure data of several blade erosion cases are collected from the numerical turbine simulation. The machine learning approach involves training on collected simulation data to predict the degree of erosion for the first-stage stator (1S) and the first-stage rotor blade (1R) from internal pressure data. The proposed erosion prediction model employs a two-step hierarchical approach. First, the proposed model predicts the 1S erosion degree using the k-nearest neighbor (k-NN) regression. Second, the proposed model estimates the 1R erosion degree with linear regression models. These models are tailored for each of the 1S erosion degrees, utilizing pressure data processed through fast Fourier transform (FFT). The evaluation shows that the proposed method achieves the prediction of the 1S erosion with a mean absolute error (MAE) of 0.000693 mm and the 1R erosion with an MAE of 0.458 mm. The evaluation results indicate that the proposed method can accurately capture the degree of turbine blade erosion from internal pressure data. As a result, the proposed method suggests that the erosion prediction method can be effectively used to determine the optimal timing for maintenance, repair, and overhaul (MRO).

Robust and intelligent power control for three-bladed horizontal axis wind turbine system using a real wind profile of the northern Morocco

In this work, a robust and intelligent control approach is developed for three-bladed horizontal axis variable-speed wind turbine (VSWT) operating under real climatic conditions (whether the WT is onshore or offshore). Below the rated power, the main purpose of the controller is to optimize the extraction of energy from wind and ensure the full exploitation of the installation, all while minimizing mechanical stress in the system in the presence of uncertainties and external disturbances. In order to achieve optimized wind energy capture without chattering problems or oscillatory phenomena, this study proposes combining the Integral Sliding Mode Control (ISMC) with an artificial neural network technique such as the Radial Basis Function (RBF) to enhance controller performances. Additionally, the RBF neural network (RBFNN) approach is implemented to estimate the wind turbine (WT) model uncertain part, allowing the use of a lower switching gain to achieve faster convergence and avoid steady-state error. Thus, by means of Lyapunov theory, the stability of the system with this controller can be demonstrated. Simulation results of the proposed Neural Network Integral Sliding Mode Control (NN-ISMC) controller are compared with the usual SMC and the standard ISMC. The comparative analysis indicate a superior efficiency of the developed control strategy in terms of decreasing tracking error and eliminating chattering behavior. Moreover, this approach provides a faster transient system response and higher robustness in presence of uncertainties compared to the other controllers.

A Dynamic Testing Approach for Particulate Erosion–Corrosion for Gas Turbine Coatings

Abstract Particle interactions in engines can be complex phenomena leading to degradation of thermal (TBCs) and environmental barrier coatings (EBCs) meant to protect engine components. Ingestion of particles into the engine can lead to recession of coatings due to particle erosion. Similarly, these particles can become molten, adhere to coatings, and result in thermochemical corrosion of coating materials. Erosion testing is often carried out where particles are injected into a gas stream, accelerated within a nozzle, and impinge on samples. Conversely, most molten particle corrosion testing is often done in static furnaces, which does not capture the dynamic nature of deposition. Nevertheless, these damage mechanisms are often tested separately, and no standard exists to test both erosive/corrosive particle interactions with coating materials under relevant turbine operating conditions. Understanding the synergies of particle interactions is crucial in determining operating lifetimes of potential coating materials. Such considerations emphasize the need for realistic approaches in standardizing particle interaction testing in combustion environments. This study outlines efforts at NASA Glenn's Erosion Burner Rig Facility in improving dynamic erosion/corrosion testing methods by assessing the durability of state-of-the-art (SOA) TBC 7 wt % yttria-stabilized zirconia (7YSZ) as a function of particle deposition rate, burner temperature, and particle size. Calibration data to determine particle deposition rate will be presented, and mass and optical profilometry measurements were utilized to estimate mass/volume loss versus deposition per increment of particulate used. Electron microscopy analyses were then carried out to assess coating damage after testing.

A statistic-based tracking method of equivalent constraint position for monopile supported offshore wind turbine

Bearing capacity of pile foundation is one of the important factors affecting the safe operation of the offshore wind turbines. However, due to the influence of different geological conditions, pile types and other factors, it is difficult for the existing monitoring methods to obtain the change of real constraints of the pile foundation. A statistic-based equivalent constraint position prediction method for offshore wind turbines is proposed. The method is based on the first-order displacement and first-order frequency extracting from the measured acceleration signals obtained by the accelerometers installed above the water surface, and statistical method is adopted to eliminate the influence of noise and reduce the error caused by single prediction. The most achievement of the proposed method is that the constraint of pile foundation related to bearing capacity is obtained and quantified by equivalent constraint position, and more accurate assessment of safety state of the offshore wind turbine can be achieved. To verify the reliability of proposed method, numerical model of a 4-MW monopile supported offshore wind turbine considering the pile–soil interaction is carried out. The results show that the proposed method can accurately obtain the equivalent constraint position by a combination of first-order frequency and first-order displacement. Further, the field measurement of an offshore wind turbine located in Rudong County, Jiangsu Province of China is performed. A stable prediction of equivalent constraint range from -30.86 m to -30.15 m is obtained over 43 days of the test. Therefore, the proposed method can be used to predict the change of pile foundation constraint, and is of great significance to the safety assessment of offshore wind turbines.