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Accurate and stable wind speed prediction can alleviate the uncertain impacts of wind power generation caused by nonlinear characteristics of wind speed, and then improve the reliability of wind power. In this paper, a hybrid model for wind speed prediction based on mode decomposition, parameter optimization and basic prediction model is proposed. First, the extreme-point symmetric mode decomposition (ESMD) is employed to adaptively decompose the denoised wind speed time series into sub-sequences with different frequencies. Second, a fractional-order beetle swarm optimization (FO-BSO) for parameter optimization of the Least squares support vector machine (LSSVM) is proposed. Through benchmark functions and non-parametric statistical test, the advantages of the FO-BSO in accuracy, stability and convergence speed are verified. Subsequently, the ESMD-FO-BSO-LSSVM prediction model is established, and three groups of wind speed datasets with different sampling locations and sampling frequencies are selected for simulation experiments. The results show that the coefficient of determination of 1-step prediction of the proposed model in three datasets are 0.9856, 0.9713, 0.9940, which has 2.43%, 3.38%, 3.08% average promotion than that of 7 comparative models. And the accuracy and stability of ESMD-FO-BSO-LSSVM model in multi-step wind speed prediction have also achieved better performance than 7 competitors.

This article investigates quasi-synchronization for a class of fractional-order delayed neural networks. By utilizing the properties of the Laplace transform, the Caputo derivative, and the Mittag–Leffler function, a new fractional-order differential inequality is introduced. Furthermore, an adaptive controller is designed, resulting in the derivation of an effective criterion to ensure the aforementioned synchronization. Finally, a numerical illustration is provided to demonstrate the validity of the presented theoretical findings.

This paper studies the electrical conductivity of a conductive material with structures similar to graphene, which consists of three basic components. The influence of various factors on the electrical conductivity of the fractional order is also analyzed. Moreover, the new fundamentals of the hexagon $\times n$ ${RL}_{\alpha }C_{\beta }$ circuit network in the fractional domain are introduced, and the general laws are summarized. First, we derive three general formulas of the equivalent impedance ( $Z_{AD}(n)$ , $Z_{BC}(n)$ , and $Z_{AA'}(n))$ of the circuit network by using the matrix transform method and the difference equation model in a special case. In addition, taking $Z_{AA'}(n)$ as an example, we systematically investigate the effects of the seven system parameters (frequency $\omega $ , the number of circuit units $n$ , fractional order $\alpha $ for inductance, fractional order $\beta $ for capacitance, inductance $L$ , capacitance $C$ , and resistance $R$ ) on the impedance characteristics of the 3D fractional order circuit network. Specifically, interesting phenomena and laws are shown by visual figures.

Traditional centrifugal pump performance prediction (CPPP) employs the semi-theoretical and semi-empirical approaches; however, it can lead to many prediction errors. Considering the superiority of deep learning when applied to nonlinear systems, in this paper, a method combining hydraulic loss and convolutional neural network (HLCNN) is applied to CPPP. Head and efficiency were selected as two variables for demonstrating the energy performance of the centrifugal pump in order to reflect the prediction ability of the proposed model. The evaluation results indicate that the predicted head and efficiency are accurate, compared with the experimental results. Furthermore, the HLCNN prediction model was compared against machine learning methods and the computational fluid dynamic method. The proposed HLCNN model obtained a better AREmean, root mean square error, sum of squares due to error, and mean absolute error for centrifugal pump energy performance. The research revealed that the HLCNN model achieves accurate energy performance prediction in the design of centrifugal pumps, reducing the development time and costs.

Abstract Transient stability of a multi‐unit hydroelectric generating system significantly influences the safety operation of power stations. The uncertainty of operating parameter is one of the important factors to influence the system stability during the transient process. For this reason, the target of this paper aims to explore the optimised operating parameter in order to enhance the stability of a multi‐unit hydroelectric generating system. To overcome the limitations of existing methods in literature, a new high‐dimensional, complex and non‐linear dynamic model of the multi‐unit hydroelectric generating system that combines the conventional hydro‐turbine governing system and the shaft system is established. Then, the dynamic behaviour of the proposed system targeting the transient process is exhaustingly investigated with the change of the critical parameters. The calm interval of critical parameters is also determined in order to improve the transient stability of the system. The obtained results not only enrich the theoretical knowledge of transient dynamics but also ensure the safety operation of hydropower stations. Meanwhile, the presented research method, high‐dimensional non‐linear dynamic model and the interesting findings in transient process can promote the development of the theory of non‐linear dynamics.

Primary frequency regulation (PFR) is a crucial operating condition for PSPs to realise frequency modulation, and the effectiveness of PFR is significant to the stability of power system frequency. Several challenges and risks have been presented in the PFR process for conventional PSPs, especially for those which run in the isolated grid, such as water inertia, negative damping of speed governor and ultra-low frequency oscillation (ULFO). Variable-speed pumped storage plants (VSPSPs) have the potential to overcome the negative impacts on regulation performance caused by hydraulic factors, due to the advantages of rapid power regulation and independent active power control from turbine output. In this paper, the primary task is to conduct a comprehensive assessment for PFR performance of VSPSPs in isolated power systems. Initially, the hydraulic–mechanical–electrical numerical models are established. Secondly, the rotational speed stability of the pump-turbine is quantified and the advantages of VSUs in suppressing ULFO are assessed. Relevant results reveal that the performance of VSUs is better than that of FSUs in the regulation process. Finally, assessments of frequency regulation performance under various scenarios are conducted with four indicators (standard deviation of power differences, power regulation time delay, settling time and overshoot).

Abstract This study focuses on the fault diagnosis of a hydroelectric generation system with hydraulic‐mechanical‐electric structures. To achieve this analysis, a methodology combining Bayesian network approach and fault diagnosis expert system is presented, which enables the time‐based maintenance to transform to the condition‐based maintenance. First, fault types and the associated fault characteristics of the generation system are extensively analyzed to establish a precise Bayesian network. Then, the Noisy‐Or modeling approach is used to implement the fault diagnosis expert system, which not only reduces node computations without severe information loss but also eliminates the data dependency. Some typical applications are proposed to fully show the methodology capability of the fault diagnosis of the hydroelectric generation system.

To address the difficulty of early fault diagnosis of rolling bearings, this paper proposes a rolling bearing diagnosis method by combining the attention entropy and adaptive deep kernel extreme learning machine (ADKELM). Firstly, the wavelet threshold denoising method is employed to eliminate the noise in the vibration signal. Then, the empirical wavelet transform (EWT) is utilized to decompose the denoised signal, and extract the attention entropy of the intrinsic mode function (IMF) as the feature vector. Next, the hyperparameters of the deep kernel extreme learning machine (DKELM) are optimized using the marine predators algorithm (MPA), so as to achieve the adaptive changes in the DKELM parameters. By analyzing the fault diagnosis performances of the ADKELM model with different kernel functions and hidden layers, the optimal ADKELM model is determined. Compared with conventional machine learning models such as extreme learning machine (ELM), back propagation neural network (BPNN) and probabilistic neural network (PNN), the high efficiency of the method proposed in this paper is verified.

Homes in rural China often have access to water wells for domestic and agricultural use. Given the significant difference in height between the well water and the roof of the house, such an arrangement could be used as a solar-powered pumped-hydro energy generation system. These systems could both limit increases in carbon emissions from coal-powered electricity while alleviating energy insecurity, while providing significant savings to households. The potential for these systems in rural regions across Shaanxi province is investigated by assessing eight key environmental and socioeconomic indicators. The find is that positive impacts across almost all indicators with generally rapid investment payback periods of 6.4–8.1 years, annual net income increases of 314.2 CNY −541.6 CNY per year per household. This research laid a theoretical foundation for the promotion of PV-PH system in Shaanxi Province.

In order to accurately diagnose the fault type of power transformer, this paper proposes a transformer fault diagnosis method based on the combination of time-shift multiscale bubble entropy (TSMBE) and stochastic configuration network (SCN). Firstly, bubble entropy is introduced to overcome the shortcomings of traditional entropy models that rely too heavily on hyperparameters. Secondly, on the basis of bubble entropy, a tool for measuring signal complexity, TSMBE, is proposed. Then, the TSMBE of the transformer vibration signal is extracted as a fault feature. Finally, the fault feature is inputted into the stochastic configuration network model to achieve an accurate identification of different transformer state signals. The proposed method was applied to real power transformer fault cases, and the research results showed that TSMBE-SCN achieved 99.01%, 99.1%, 99.11%, 99.11%, 99.14% and 99.02% of the diagnostic rates under different folding numbers, respectively, compared with conventional diagnostic models MBE-SCN, TSMSE-SCN, MSE-SCN, TSMDE-SCN and MDE-SCN. This comparison shows that TSMBE-SCN has a strong competitive advantage, which verifies that the proposed method has a good diagnostic effect. This study provides a new method for power transformer fault diagnosis, which has good reference value.

Utilizing the flexibility of hydropower to integrate more intermittent renewable energy into the power grid requires hydro units to expand the operating range; this duty, however, requires a continuous improvement of their stability during part-load conditions. This study focuses on the stability performance of hydropower generation systems (HGS) during flexible operation. First, a dynamic model of HGS that reflects the characteristics of part-load conditions is established by introducing pressure pulsation in the draft tube. Second, the model of HGS is coupled with a shafting system to investigate the vibration property of the unit. Then, the validity of the coupling model is verified by comparing it with a traditional model and actual data. Finally, some possible ways to mitigate the instability caused by part-load operation are explored. The results show that part-load operation of the system is accompanied by significant dynamic response fluctuations (5%). Moreover, the interaction effect of multiple vibration sources and the vibration performance in a part-load condition are investigated. This paper is expected to provide support for improving the stability of HGS part-load operation and offer useful insights for exploiting the flexibility potential of HGS.

The balancing holes in centrifugal pumps with seals mounted in both suction and discharge sides are one of the approaches used by pump manufacturers to reduce the axial thrust. The balance hole diameter directly affects the axial force of the centrifugal pump. The flow characteristics in the balance chamber are closely related to the balance hole diameter. However, research is not very clear on the internal flow of the balanced chamber, due to the small axial and radial sizes and the complicated flow conditions in the chamber. In this paper, we analyzed the influence of the balance hole diameter on the liquid leakage rate, flow velocity, and vortex motion in the balance chamber. The results indicated that when the balance hole diameter was lower than the design value, the volume flow rate of leakage flow was proportional to the diameter. The liquid flow rate and vortex distribution rules in the balance chamber were mainly associated with the coeffect of radial leakage flow in the rear sealing ring interval and the axial balance hole leakage flow. The research has revealed the mechanisms of leakage flow of the balance chamber in the centrifugal pump and that this is of great significance for accurate calculation and balancing of the axial force.

In a sudden load increasing process (SLIP), the hydroelectric generating system (HGS) experiences a severe vibration response due to the sudden change of the hydraulic-mechanical-electric parameters (HMEPs). The instability of HGS limits the ability of sudden load increase, and its flexibility and reliability are reduced. Thus, in this study, a new transient nonlinear coupling model of HGS is proposed, which couples the hydro-turbine governing system (HTGS) and the hydro-turbine generator shafting system (HGSS) with the hydraulic-mechanical-electric coupling force, rotating speed, flow rate, hydro-turbine torque, electromagnetic torque, and guide vane opening. By using numerical simulation, the influences of different HMEPs on the vibration characteristics of HGS in SLIP are analyzed. The result shows that, compared with stable operating conditions, the vibration amplitude of HGS increases sharply in SLIP. The increase of the sudden load increasing amount, blade exit flow angle, mass eccentricity and excitation current, and the decrease in guide bearing stiffness and average air gap between the stator and rotor cause abnormal vibration of different degrees in the HGS. Hydraulic factors have the greatest influence on the nonlinear dynamic behavior of HGS. The maximum vibration amplitude of HGS in SLIP is increased by 70.46%, compared with that under stable operating conditions. This study provides reasonable reference for the analysis of the nonlinear dynamic behavior of HGS in SLIP under the multiple vibration sources.

The use of renewable energy has become a necessity to generate electricity, and is taking the place of conventional coal-fired power, as it has clear economic and environmental benefits. The purpose of this paper is to quantify the comprehensive benefits of hydropower in reducing wind power fluctuation in a hybrid coal-fired/hydro/wind power system. To achieve this, a wind–hydropower generation system must be established, and its complementary characteristic is also illustrated based on the resultant wind speed. Then, based on Institute of Electrical and Electronics Engineers (IEEE) 14 Bus Power System, coal-fired generation is introduced to model a final hybrid integrated power system. The comprehensive benefit evaluation method, including the power consumption profit, the peak load profit, the energy conservation profit, the guide vane fatigue cost, the maintenance cost, and the start-stop cost, is presented to assess the join operation benefits of the wind/hydropower/coal-fired integrated system. The complementary investigation shows that the hydropower system has an excellent effect on suppressing wind power fluctuation, although the fatigue damage of hydraulic guide vanes is a little severe for the time scale of hours, compared with that of seconds. The quantified benefit shows that the increased power consumption profit, the increased guide vane fatigue loss cost, the decreased peak-load profit, and the increased energy conservation profit are RMB 1262.43 million/year, RMB 0.37 million/year, RMB 333.97 million/year and RMB 0.54 million/year, with the wind and hydropower ratio increasing from 16% to 25%, which directly leads to the annual total revenue increasing to RMB 143.2673 million. The implementation of this paper can contribute to making more efficient use of wind-hydro power in conventional electricity production.

In the coming decades, the proportion of wind–solar energy in power system significantly increases, resulting to uncertainties of power fluctuation in abundant wind–solar energy regions. The flexibility operation of Pumped Storage Power Plants (PSPPs) has already been widely recognized to regulate wind–solar power fluctuations; however, less is known about the regulation reliability of the PSPP affected by them. It is a challenge, since various uncertainties exist during this regulation process. Here, a mathematical model with a solar–wind–hydro hybrid power generation system is adopted to investigate the regulation reliability of PSPP. The uncertainties and limitations of model parameters are considered during this process. Five regulation indexes, i.e., rise time, settling time, peak value, peak time and overshoot of the reactive power generator terminal voltage, guide vane opening and angular velocity, are extracted to evaluate the PSSP’s regulation quality. Finally, the PSPP reliability probability affected by parametric uncertainties is presented. The obtained results show that the inertia coefficient is the most sensitivity parameters for the settling time, peak value and peak time with sensitivity index 33.7%, 72.55% and 71.59%, respectively. The corresponding total contribution rate of the top 10 sensitive parameters are 74.45%, 93.45% and 87.15%, respectively. Despite some types of uncertainties not being considered, the results of this research are important for the regulation reliability evaluation of PSPPs in suppressing power fluctuations of wind and solar generation.

The penetration of multiple integrated renewable energies to the power grid are relevant for decision making in energy policy, environment and business. Such an electricity penetration is affected by the intermittent and volatile characteristics of integrated energies, mostly significantly related to the safe and stable electricity production and supply in real world. Here, this paper focuses on the low frequency oscillation analysis of the hydropower generation response to the wind and solar variability. To enable this analysis, a hybrid model of hydropower system integrating with the wind and solar power system is presented. The Nyquist and root-locus stability methods are used to investigate the sensitivity performance of the hydropower governor to the fluctuation of the integrated renewable energies. Additionally, to quantify the risk of the hybrid system, the low frequency oscillation response of hydropower system to wind/solar/hydropower quota and transmission line distance ratio is extensively investigated in this study. The results show that under the case of the wind, solar and hydropower ratio is 40:1:150, the optimal values for maximally reducing hydropower low frequency oscillation are finally determined as kp = 0.8, ki = 0.25 and kd = 0.5. Regarding a certain wind/solar/hydropower quota, it is a promising strategy to increase the solar-load transmission line in order to achieve the safe and stable operation of the hybrid system and a relatively excellent dynamic regulation capacity of the hydropower governor. The model, methods and results implemented in this study are exploited to markedly improve new knowledge applications, policy management, low carbon emissions and investment competitiveness of future energy systems.

Literature about the importance of renewable energy resources, including wind and solar energy, is becoming increasingly important; however, these energy sources are unstable and volatile in nature, and are usually integrated with conventional energy sources, such as hydropower, forming hybrid power generation systems that maintain a stable grid. Short-term changes in wind speed or solar radiation intensity have a great impact on the stability of hybrid systems, and have been reported in the literature. However, reliable models to manage such systems are lacking, and previous studies have regarded the hour scale as the minimum baseline for systematic change. In this article, hybrid power systems are proposed that are controlled on very short time intervals. The results of a feasibility analysis of the proposed model indicate the viability of complementary hybrid systems in controlling and maintaining the stability, which are subjected to short durations of fluctuations in wind or solar radiation. The simulation results indicate that the influence of the shutdown of the wind turbine, with the regulation effect of the hydro power, is 3–5 times greater than that of the short-term wind turbulence fluctuation. When the hydro turbine is adopted to adjust the short-term fluctuation of solar radiation, the effect on the system was suppressed to 0.02–0.2 times of the former.

The oil-free compressor is a key component in fabricating polyethylene terephthalate (PET) bottles for beverages and water. At present, the main compressor type used for blowing PET bottles is the reciprocating compressor. However, compared to screw compressors, reciprocating compressors have shortcomings of high energy consumption and too many consumable parts. Many manufacturers of PET bottles in Asia are seeking to replace reciprocating compressors with screw compressors, as we know. Screw compressors can be classified as single-screw compressors (SSC) and twin-screw compressors. Since the load in a twin-screw compressor is far larger than that in an SSC, SSCs are more suitable for being developed for high-pressure applications such as PET bottle blowing. This paper presents a performance study on an oil-free single-screw compressor as the first stage of the PET compressor unit. A 5.4 m3·min−1 prototype and its test rig were developed. The thermophysical process of the moist air is theoretically analyzed. The pressure loss on the flow path and the influence of the important parameters are experimentally investigated. It is found that water vapor cannot be separated during the adiabatic compression process. The results also show that the pressure loss from the discharging duct to the check valve accounts for the largest percentage of the total pressure loss. The experimental results further show that the discharge capacity and shaft power increase almost linearly with the motor speed. The efficiency declines with increasing injected water temperature. The discharge capacity and shaft power all increase with the injected water flowrate, and an optimum flowrate is found to ensure a highest isentropic efficiency. With the increase in discharge pressure, the discharge capacity decreases, and the shaft power increases. The isentropic efficiency is found to have its maximum value at a certain discharge pressure.

To improve the life of the meshing pair in single screw compressor (SSC), several meshing pair profiles (MPP) were proposed for raising the lubrication properties. Therefore, it is necessary to evaluate the lubrication performance of the MPPs. In this paper, an evaluation method based on micro deflecting motion trajectory (MDMT) is proposed and the theoretical model to realize MDMT is established. The model mainly contains a geometric model, a thermodynamics model, a hydrodynamic lubrication model and corresponding algorithm. With the presented method, three kinds of MPP including single straight line type (SSLT), single column type (SCT) and multi column type (MCT) have been analyzed. Obtained results show that compared to the SSLT and SCT, the MCT generates the greatest peak value of the water film pressure. The total torque applied on the gate-rotor generated by the water films decreases with the increment of the discharge pressure and increases with the machine size. The water film stiffness firstly decreases and then increases with the micro deflecting angle increasing. The water film stiffness at trailing side is always larger than that at leading side. As the discharge pressure increases, the MDMT curves approach the leading flank, and the lubrication properties get worse. With the machine size increasing, the MDMT curves move towards the trailing side and the lubrication performance is improved. Comparing to the other two MPPs, the MCT can achieve floating mesh without contact in relatively larger machines and comparably lower discharge pressure.

Water application uniformity is an important performance parameter when designing and operating an irrigation system. Performance tests of a center pivot irrigation system equipped with fixed and rotated spray plate sprinklers (FSPS and RSPS, respectively) were conducted at five travel speeds. The effects of travel speed, collector size, and setting height on water application uniformity were evaluated using Heermann and Hein’s coefficient of uniformity (CUH). The CUH was 12.7% higher for the RSPS than the FSPS and decreased as the travel speed increased. Collector size and setting height affected CUH, and CUH was higher when the collector had a large opening cross-section compared to the collector with a small opening cross-section. CUH was higher when the collector with a low setting height compared to when it a high setting height for the FSPS. However, collector setting height had no effect on CUH for the RSPS. The weighted average water application depth (Dw) decreased as the travel speed increased. Collector size had no significant effect on Dw, but Dw with a low collector setting height was larger than the values with a high collector setting height. The water application rate increased as distance from the pivot point increased and was higher for the FSPS than the RSPS. The results will improve the selection of travel speed and collector when the water application uniformity of a center pivot irrigation system is evaluated.

A six-dimensional nonlinear hydropower system controlled by a nonlinear predictive control method is presented in this paper. In terms of the nonlinear predictive control method; the performance index with terminal penalty function is selected. A simple method to find an appropriate terminal penalty function is introduced and its effectiveness is proved. The input-to-state-stability of the controlled system is proved by using the Lyapunov function. Subsequently a six-dimensional model of the hydropower system is presented in the paper. Different with other hydropower system models; the above model includes the hydro-turbine system; the penstock system; the generator system; and the hydraulic servo system accurately describing the operational process of a hydropower plant. Furthermore, the numerical experiments show that the six-dimensional nonlinear hydropower system controlled by the method is stable. In addition, the numerical experiment also illustrates that the nonlinear predictive control method enjoys great advantages over a traditional control method in nonlinear systems. Finally, a strategy to combine the nonlinear predictive control method with other methods is proposed to further facilitate the application of the nonlinear predictive control method into practice.

Since the slight fault feature of incipient fault is usually polluted by heavy background noise, it is difficult to extract the weak feature signal in rotating machine. As an adaptive decomposing technique, empirical mode decomposition (EMD) based denoising methods have a good effect on the feature separation and noise elimination. However, for rotating machine with poor working environment, the components attributed to noise might have higher amplitudes, which restrict the efficiency of noise reduction in current EMD-based denoising methods. Therefore, a probabilistic entropy EMD thresholding algorithm for periodic fault signal enhancement in rotating machine is proposed in this paper. In this method, the entropy threshold of each IMF is constructed instead of the threshold applied to N sampling points of each IMF directly, which overcomes the shortcoming of the denoising effect limited by larger amplitude noise reservation and smaller amplitude feature signal reduction in the current denoising methods. Meanwhile, in order to make the amplitudes of all the IMF reduce in a smooth way, a multiscale thresholding algorithm based on quantile statistics to provide probability indexes is presented. Engineering application demonstrates that the proposed method is effective in the noise reduction and fault feature enhancement in the rotating machine.

Due to the fact that the slight fault signals in early failure of mechanical system are usually submerged in heavy background noise, it is unfeasible to extract the weak fault feature via the traditional vibration analysis. Stochastic resonance (SR), as a method of utilizing noise to amplify weak signals in nonlinear dynamical systems, can detect weak signals overwhelmed in the noise. However, based on the analysis of the impact of noise intensity on SR effect, it is concluded that the detection results are dramatically limited by the noise intensity of measured signals, especially for incipient fault feature of mechanical system with poor working environment. Therefore, this paper proposes a partly Duffing oscillator SR method to extract the fault feature of mechanical system. In this method, to locate the appearance of weak fault feature and decrease noise intensity, the permutation entropy index is constructed to select the measured signals for the input of Duffing oscillator system. Then, according to the regulation of system parameters, a reasonable match between the selected signals and Duffing oscillator model is achieved to produce a SR phenomenon and realize the fault diagnosis of mechanical system. Experiment results demonstrate that the proposed method achieves a better effect on the fault diagnosis of mechanical system.

With the fast development of artificial intelligence techniques, data-driven modeling approaches are becoming hotspots in both academic research and engineering practice. This paper proposes a novel data-driven T-S fuzzy model to precisely describe the complicated dynamic behaviors of pumped storage generator motor (PSGM). In premise fuzzy partition of the proposed T-S fuzzy model, a novel variable-length tree-seed algorithm based competitive agglomeration (VTSA-CA) algorithm is presented to determine the optimal number of clusters automatically and improve the fuzzy clustering performances. Besides, in order to promote modeling accuracy of PSGM, the input and output formats in the T-S fuzzy model are selected by an economical parameter controlled auto-regressive (CAR) model derived from a high-order transfer function of PSGM considering the distributed components in the water diversion system of the power plant. The effectiveness and superiority of the T-S fuzzy model for PSGM under different working conditions are validated by performing comparative studies with both practical data and the conventional mechanistic model.

This paper presents an investigation on the undesirable vibration of an oblique-stud stator frame in a large hydropower generator by means of experimental and finite element (FE) analysis. First, field experimental tests were performed, and the results indicate that the main vibration component comes from electromagnetic factors. Then, a 2D-magnetic and 3D-mechanical FE model was developed to investigate the vibration of the stator frame under the action of electromagnetic forces. A set of contrast models was established to study the effects of different kinds of eccentricity and different structures. Based on the comparative analysis between the results of simulations and experimental tests, it can be inferred that the abnormal vibration is generated because of the lack of stiffness in the upper part of structure and the existence of dynamic eccentricity in the rotor–stator system. In addition, the structural simulation analysis shows that the flexible designed oblique-stud stator frame is relatively vulnerable against the electromagnetic forces.

In this paper, a new methodology is proposed to reduce the vortex-induced vibration (VIV) and improve the performance of the stay vane in a 200-MW Francis turbine. The process can be divided into two parts. Firstly, a diagnosis method for stay vane vibration based on field experiments and a finite element method (FEM) is presented. It is found that the resonance between the Kármán vortex and the stay vane is the main cause for the undesired vibration. Then, we focus on establishing an intelligent optimization model of the stay vane’s trailing edge profile. To this end, an approach combining factorial experiments, extreme learning machine (ELM) and particle swarm optimization (PSO) is implemented. Three kinds of improved profiles of the stay vane are proposed and compared. Finally, the profile with a Donaldson trailing edge is adopted as the best solution for the stay vane, and verifications such as computational fluid dynamics (CFD) simulations, structural analysis and fatigue analysis are performed to validate the optimized geometry.