Yalei Bai
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Yalei Bai has a total of 46 co-authors. Here are the top co-authors by number of shared publications:
- Min Zheng
School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
5 shared publications - Donglei Wu
College of Energy and Electrical Engineering, Hohai University, Nanjing 210098, China
3 shared publications - Kelin Li
College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
3 shared publications - Tong Zhao
College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, No. 29 Yudao Street, Qinhuai District, Nanjing 210016, China
3 shared publications - Gang Feng
College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2 shared publications - Guangzhao Wang
Hangzhou Zhiyuan Research Institute Co., Hangzhou 310012, China
2 shared publications
Latest Publications
- Open Access
Research on Control Laws and Wall Attachment Characteristics of Four-Way Axisymmetric Aerodynamic Vectoring Nozzles Under Low-Speed Jet Conditions
Fluidic thrust vectoring technology has emerged as one of the key research hotspots in next-generation advanced aircraft design, owing to its compact structure, rapid response and low weight penalty. The aerodynamic vectoring nozzle serves as the core component of this technology. Currently, research on four-way axisymmetric fluidic thrust vectoring nozzles remains limited, and corresponding experimental studies suffer from high costs and strict technical requirements. To fill this gap, this paper presents an experimental study on the control laws of an aerodynamic vectoring nozzle prototype under low-speed jet conditions for preliminary design verification. Taking this nozzle type as the research object, the jet deflection characteristics under various wall configurations are investigated at a jet exit velocity of approximately 80 m/s. Among the four evaluated Coanda wall structures, the composite design integrating a smooth curved front section and a beveled rear–middle section is finally determined. Its key performance indicators meet the engineering requirements: a maximum deflection angle of 13.6°, a control linearity of 87.1% for pitch (vertical) control and 89.8% for yaw (lateral) control, a thrust loss of 4%, and a response rate of no less than 200°/s. This work provides a valuable reference for subsequent practical engineering applications.
Open AccessResearch on Control Laws and Wall Attachment Characteristics of Four-Way Axisymmetric Aerodynamic Vectoring Nozzles Under Low-Speed Jet Conditions
Fluidic thrust vectoring technology has emerged as one of the key research hotspots in next-generation advanced aircraft design, owing to its compact structure, rapid response and low weight penalty. The aerodynamic vectoring nozzle serves as the core component of this technology. Currently, research on four-way axisymmetric fluidic thrust vectoring nozzles remains limited, and corresponding experimental studies suffer from high costs and strict technical requirements. To fill this gap, this paper presents an experimental study on the control laws of an aerodynamic vectoring nozzle prototype under low-speed jet conditions for preliminary design verification. Taking this nozzle type as the research object, the jet deflection characteristics under various wall configurations are investigated at a jet exit velocity of approximately 80 m/s. Among the four evaluated Coanda wall structures, the composite design integrating a smooth curved front section and a beveled rear–middle section is finally determined. Its key performance indicators meet the engineering requirements: a maximum deflection angle of 13.6°, a control linearity of 87.1% for pitch (vertical) control and 89.8% for yaw (lateral) control, a thrust loss of 4%, and a response rate of no less than 200°/s. This work provides a valuable reference for subsequent practical engineering applications.
- Open Access
Enhancement Mechanism of Non-Sinusoidal Trajectory on Dual-Flapping-Wing Energy Harvesting Across Three Layouts
Flapping-wing energy harvesting is a promising technology for distributed wind energy utilization, yet the enhancement mechanism of non-sinusoidal motion trajectories across different dual-wing configurations remains insufficiently elucidated. This work investigates the performance characteristics and underlying flow physics of dual-flapping-wing energy harvesting systems under three typical layouts. Numerical simulations are conducted to compare the harvesting performance of staggered, tandem, and parallel arrangements under both sinusoidal and non-sinusoidal trajectories, with wake vortex structures and aerodynamic forces systematically analyzed. Results indicate that the staggered arrangement achieves the highest efficiency of 68% within the present two-dimensional framework under non-sinusoidal motion, followed by the parallel arrangement (63.2%) and the tandem arrangement (58.3%). The aft wing is identified as the decisive factor governing the overall system performance, while a well-ordered wake vortex pattern is identified as a key characteristic associated with high-efficiency operation. The non-sinusoidal trajectory facilitates vortex merging and orderly arrangement, which enlarges the pressure difference across the airfoil and substantially enhances heaving power output. The staggered configuration combined with the non-sinusoidal trajectory, is recommended as a promising design, providing a reference for the design of multi-flapping-wing energy harvesting systems.
Open AccessEnhancement Mechanism of Non-Sinusoidal Trajectory on Dual-Flapping-Wing Energy Harvesting Across Three Layouts
Flapping-wing energy harvesting is a promising technology for distributed wind energy utilization, yet the enhancement mechanism of non-sinusoidal motion trajectories across different dual-wing configurations remains insufficiently elucidated. This work investigates the performance characteristics and underlying flow physics of dual-flapping-wing energy harvesting systems under three typical layouts. Numerical simulations are conducted to compare the harvesting performance of staggered, tandem, and parallel arrangements under both sinusoidal and non-sinusoidal trajectories, with wake vortex structures and aerodynamic forces systematically analyzed. Results indicate that the staggered arrangement achieves the highest efficiency of 68% within the present two-dimensional framework under non-sinusoidal motion, followed by the parallel arrangement (63.2%) and the tandem arrangement (58.3%). The aft wing is identified as the decisive factor governing the overall system performance, while a well-ordered wake vortex pattern is identified as a key characteristic associated with high-efficiency operation. The non-sinusoidal trajectory facilitates vortex merging and orderly arrangement, which enlarges the pressure difference across the airfoil and substantially enhances heaving power output. The staggered configuration combined with the non-sinusoidal trajectory, is recommended as a promising design, providing a reference for the design of multi-flapping-wing energy harvesting systems.
- Open Access
- 12 September 2026
- Published by MDPI AG in Applied Sciences
- Vol. 16 (18) , 9051
An Efficient Trajectory Planner for Fixed-Wing UAVs via Improved A*-Guided Initialization
This study proposes an efficient trajectory planning method for fixed-wing unmanned aerial vehicles (UAVs) based on an improved A*-guided initialization strategy for complex obstacle environments. An improved three-dimensional A* method is developed to generate smooth and collision-free global paths with enhanced search efficiency and path quality. The generated paths are then converted into dynamics-informed state and control trajectories, which serve as initial guesses for trajectory optimization. Simulation results under different obstacle complexities show that, compared with conventional linear interpolation initialization, the proposed method significantly improves solution success rate and computational efficiency, while producing more reasonable obstacle-avoidance strategies, smoother state variations, and more coordinated control inputs.
- 12 September 2026
- Published by MDPI AG in Applied Sciences
- Vol. 16 (18) , 9051
Open AccessAn Efficient Trajectory Planner for Fixed-Wing UAVs via Improved A*-Guided Initialization
This study proposes an efficient trajectory planning method for fixed-wing unmanned aerial vehicles (UAVs) based on an improved A*-guided initialization strategy for complex obstacle environments. An improved three-dimensional A* method is developed to generate smooth and collision-free global paths with enhanced search efficiency and path quality. The generated paths are then converted into dynamics-informed state and control trajectories, which serve as initial guesses for trajectory optimization. Simulation results under different obstacle complexities show that, compared with conventional linear interpolation initialization, the proposed method significantly improves solution success rate and computational efficiency, while producing more reasonable obstacle-avoidance strategies, smoother state variations, and more coordinated control inputs.
- 1 September 2026
- Published by AIP Publishing in Physics of Fluids
- Vol. 38 (9)
Effect of circumferential grooving on the performance and flow mechanism of an axial flow fan with a large tip-clearance ratio
This study investigates an industrial axial flow fan with a large tip-clearance ratio of 1%. We use numerical simulations and experimental validation to examine how the number, axial location, and distribution of circumferential casing grooves affect aerodynamic performance under near-stall conditions. The results indicate that a single circumferential groove enlarges the low-velocity separation region within the tip clearance, intensifies turbulence, and aggravates flow blockage, thereby deteriorating fan performance. In contrast, a properly arranged multigroove configuration effectively suppresses tip leakage. The configuration involving a continuous circumferential groove structure significantly reduces blockage of the passage, which is associated with reverse-flow regions. Under near-stall conditions, this configuration increases static pressure by up to 15.7%, improves static pressure efficiency by 12%, and enhances the stall margin by 8.3%. These findings further reveal a zonal control mechanism of casing treatments in industrial axial flow fans with large tip-clearance ratios. Finally, grooves near the leading edge expand the radial clearance and promote the interaction and dissipation between reverse leakage flow and primary leakage flow. Conversely, grooves positioned near the trailing edge generate stable vortex structures that suppress the accumulation of reverse flow.
- 1 September 2026
- Published by AIP Publishing in Physics of Fluids
- Vol. 38 (9)
Effect of circumferential grooving on the performance and flow mechanism of an axial flow fan with a large tip-clearance ratio
This study investigates an industrial axial flow fan with a large tip-clearance ratio of 1%. We use numerical simulations and experimental validation to examine how the number, axial location, and distribution of circumferential casing grooves affect aerodynamic performance under near-stall conditions. The results indicate that a single circumferential groove enlarges the low-velocity separation region within the tip clearance, intensifies turbulence, and aggravates flow blockage, thereby deteriorating fan performance. In contrast, a properly arranged multigroove configuration effectively suppresses tip leakage. The configuration involving a continuous circumferential groove structure significantly reduces blockage of the passage, which is associated with reverse-flow regions. Under near-stall conditions, this configuration increases static pressure by up to 15.7%, improves static pressure efficiency by 12%, and enhances the stall margin by 8.3%. These findings further reveal a zonal control mechanism of casing treatments in industrial axial flow fans with large tip-clearance ratios. Finally, grooves near the leading edge expand the radial clearance and promote the interaction and dissipation between reverse leakage flow and primary leakage flow. Conversely, grooves positioned near the trailing edge generate stable vortex structures that suppress the accumulation of reverse flow.
- Open Access
- 1 September 2025
- Published by IOP Publishing in Journal of Physics: Conference Series
- Vol. 3120 (1)
A hybrid quadrotor UAV control strategy using gray wolf-particle swarm optimization and fuzzy control
Small quadcopter UAVs are highly susceptible to wind disturbances, making it essential to maintain overall stability. An advanced control architecture comprising inner and outer loop mechanisms is presented in this study. The proposed system utilizes the Gray Wolf-Particle Swarm Optimization algorithm (GWOPSO), along with fuzzy control, PID, and LADRC controllers. This approach is compared with traditional PID and PID-LADRC controllers through simulations. It is shown through simulation that the combined control strategy, which combines GWOPSO and fuzzy control, significantly outperforms traditional methods in terms of trajectory tracking and resistance to minor wind disturbances. Additionally, these results indicate that using GWOPSO to optimize the controller parameters is both effective and feasible. This evidence supports the conclusion that the hybrid algorithm exhibits a stronger ability to withstand disturbances and offers enhanced stability.
- 1 September 2025
- Published by IOP Publishing in Journal of Physics: Conference Series
- Vol. 3120 (1)
Open AccessA hybrid quadrotor UAV control strategy using gray wolf-particle swarm optimization and fuzzy control
Small quadcopter UAVs are highly susceptible to wind disturbances, making it essential to maintain overall stability. An advanced control architecture comprising inner and outer loop mechanisms is presented in this study. The proposed system utilizes the Gray Wolf-Particle Swarm Optimization algorithm (GWOPSO), along with fuzzy control, PID, and LADRC controllers. This approach is compared with traditional PID and PID-LADRC controllers through simulations. It is shown through simulation that the combined control strategy, which combines GWOPSO and fuzzy control, significantly outperforms traditional methods in terms of trajectory tracking and resistance to minor wind disturbances. Additionally, these results indicate that using GWOPSO to optimize the controller parameters is both effective and feasible. This evidence supports the conclusion that the hybrid algorithm exhibits a stronger ability to withstand disturbances and offers enhanced stability.
- Open Access
- 12 August 2025
- Published by MDPI AG in Applied Sciences
- Vol. 15 (16) , 8882
Multi-Objective ADRC-Based Aircraft Gust Load Control
In this paper, we propose a dual-loop Active Disturbance Rejection Control (ADRC) strategy for gust load alleviation in flexible aircraft. By decoupling the control of modal and normal accelerations and spatially allocating control surfaces, the method effectively resolves signal interference. Simulation results show that compared to the uncontrolled case, the ADRC controller reduces the wing root bending moment peak by 38%, the normal load factor peak by 32%, and the pitch angle fluctuation by 38%. Robustness tests under actuator delays (4 Δt and 8 Δt) and gain perturbations (−50% and +100%) further confirm that the system maintains time-domain stability and effective load mitigation across varying conditions. These results demonstrate that the proposed ADRC scheme not only improves load suppression but also offers strong robustness against parameter uncertainty, providing theoretical and practical support for next-generation active control systems in aeroelastic environments.
- 12 August 2025
- Published by MDPI AG in Applied Sciences
- Vol. 15 (16) , 8882
Open AccessMulti-Objective ADRC-Based Aircraft Gust Load Control
In this paper, we propose a dual-loop Active Disturbance Rejection Control (ADRC) strategy for gust load alleviation in flexible aircraft. By decoupling the control of modal and normal accelerations and spatially allocating control surfaces, the method effectively resolves signal interference. Simulation results show that compared to the uncontrolled case, the ADRC controller reduces the wing root bending moment peak by 38%, the normal load factor peak by 32%, and the pitch angle fluctuation by 38%. Robustness tests under actuator delays (4 Δt and 8 Δt) and gain perturbations (−50% and +100%) further confirm that the system maintains time-domain stability and effective load mitigation across varying conditions. These results demonstrate that the proposed ADRC scheme not only improves load suppression but also offers strong robustness against parameter uncertainty, providing theoretical and practical support for next-generation active control systems in aeroelastic environments.
- Open Access
- 5 August 2025
- Published by MDPI AG in Electronics
- Vol. 14 (15) , 3124
A Second-Order LADRC-Based Control Strategy for Quadrotor UAVs Using a Modified Crayfish Optimization Algorithm and Fuzzy Logic
To enhance the rapid and stable tracking of a specified trajectory by quadcopter drones, while ensuring a degree of resistance to external wind disturbances, this paper proposes an integrated control strategy that combines an optimization algorithm and fuzzy control. In this system, both the position and attitude loops utilize second-order Linear Active Disturbance Rejection Control (LADRC) controllers, supplemented by fuzzy controllers. These controllers have been optimized using a modified crayfish optimization algorithm (MCOA), resulting in a dual-closed-loop control system. In comparisons with both the dual-closed-loop LADRC controller and the dual-closed-loop fuzzy control LADRC controller, the proposed method reduces the rise time by 52.87% in the X-channel under wind-free conditions, reduces the maximum trajectory tracking error by 86.37% under wind-disturbed conditions, and reduces the ITAE exponent by 66.2%, which demonstrates that the newly designed system delivers excellent tracking speed and accuracy along the specified trajectory. Furthermore, it remains effective even in the presence of external disturbances, it can reliably maintain the target position and the attitude angle, demonstrating strong resistance to interference and stability.
- 5 August 2025
- Published by MDPI AG in Electronics
- Vol. 14 (15) , 3124
Open AccessA Second-Order LADRC-Based Control Strategy for Quadrotor UAVs Using a Modified Crayfish Optimization Algorithm and Fuzzy Logic
To enhance the rapid and stable tracking of a specified trajectory by quadcopter drones, while ensuring a degree of resistance to external wind disturbances, this paper proposes an integrated control strategy that combines an optimization algorithm and fuzzy control. In this system, both the position and attitude loops utilize second-order Linear Active Disturbance Rejection Control (LADRC) controllers, supplemented by fuzzy controllers. These controllers have been optimized using a modified crayfish optimization algorithm (MCOA), resulting in a dual-closed-loop control system. In comparisons with both the dual-closed-loop LADRC controller and the dual-closed-loop fuzzy control LADRC controller, the proposed method reduces the rise time by 52.87% in the X-channel under wind-free conditions, reduces the maximum trajectory tracking error by 86.37% under wind-disturbed conditions, and reduces the ITAE exponent by 66.2%, which demonstrates that the newly designed system delivers excellent tracking speed and accuracy along the specified trajectory. Furthermore, it remains effective even in the presence of external disturbances, it can reliably maintain the target position and the attitude angle, demonstrating strong resistance to interference and stability.
- Open Access
Numerical Study of the Use of a Flapping Foil in Energy Harvesting with Suction- and Blower-Based Control
The method of extracting energy from a fluid environment using flapping foils offers advantages such as structural simplicity and environmental friendliness. However, its low energy harvesting efficiency remains a significant factor limiting its development. This study employs suction and blower-based control (SBC) to enhance the energy harvesting efficiency of flapping foils. Using an orthogonal experimental design and numerical methods, 49 representative combinations of SBC geometries were selected for numerical simulation. The effects and priority rankings of geometric parameters on foil performance were statistically analyzed. It was found that under the optimal geometry (the suction slot position is 0.54c, the injection slot position is 0.79c, the width of the slot is 0.015c, the angle of the suction slot is −3°, and the angle of the injection slot is −9°), the energy harvesting efficiency can reach 40.7%. Furthermore, under laminar flow conditions, the benefit of SBC increases with higher Reynolds numbers (Re). At Re = 2200, SBC maximized the improvement in energy harvesting efficiency by 76%. No significant correlation was observed between the flapping amplitude and the SBC effect. However, the reduced frequency significantly influences the efficiency improvement generated by SBC. The SBC method shifts the foil’s optimal operating region towards lower reduced frequencies, which benefits energy harvesting efficiency. The research presented herein may have potential applications in the development of marine energy systems and bio-inspired propulsion.
Open AccessNumerical Study of the Use of a Flapping Foil in Energy Harvesting with Suction- and Blower-Based Control
The method of extracting energy from a fluid environment using flapping foils offers advantages such as structural simplicity and environmental friendliness. However, its low energy harvesting efficiency remains a significant factor limiting its development. This study employs suction and blower-based control (SBC) to enhance the energy harvesting efficiency of flapping foils. Using an orthogonal experimental design and numerical methods, 49 representative combinations of SBC geometries were selected for numerical simulation. The effects and priority rankings of geometric parameters on foil performance were statistically analyzed. It was found that under the optimal geometry (the suction slot position is 0.54c, the injection slot position is 0.79c, the width of the slot is 0.015c, the angle of the suction slot is −3°, and the angle of the injection slot is −9°), the energy harvesting efficiency can reach 40.7%. Furthermore, under laminar flow conditions, the benefit of SBC increases with higher Reynolds numbers (Re). At Re = 2200, SBC maximized the improvement in energy harvesting efficiency by 76%. No significant correlation was observed between the flapping amplitude and the SBC effect. However, the reduced frequency significantly influences the efficiency improvement generated by SBC. The SBC method shifts the foil’s optimal operating region towards lower reduced frequencies, which benefits energy harvesting efficiency. The research presented herein may have potential applications in the development of marine energy systems and bio-inspired propulsion.
- Open Access
- 22 May 2025
- Published by MDPI AG in Electronics
- Vol. 14 (11) , 2112
A Hybrid Quadrotor Unmanned Aerial Vehicle Control Strategy Using Self-Adaptive Bald Eagle Search and Fuzzy Logic
In this study, we propose an innovative inner–outer loop control framework for a quadcopter unmanned aerial vehicle (UAV) that significantly enhances the trajectory-tracking speed and accuracy while enhancing robustness against external disturbances. The inner loop employs a Linear Active Disturbance Rejection Controller (LADRC) and the outer loop a proportion integral differential (PID) controller, unified within a fuzzy control scheme. We introduce a Self-Adaptive Bald Eagle Search Optimization algorithm to optimize the initial controller settings, thereby accelerating convergence and improving parameter-tuning precision. Simulation results show that our proposed controller outperforms the conventional two-loop cascade PID configuration, as well as alternative strategies combining an outer-loop PID with a second-order inner-loop LADRC or a fuzzy-enhanced PID-LADRC approach. Moreover, the system maintains the desired position and attitude under external perturbations, underscoring its superior disturbance-rejection capability and stability.
- 22 May 2025
- Published by MDPI AG in Electronics
- Vol. 14 (11) , 2112
Open AccessA Hybrid Quadrotor Unmanned Aerial Vehicle Control Strategy Using Self-Adaptive Bald Eagle Search and Fuzzy Logic
In this study, we propose an innovative inner–outer loop control framework for a quadcopter unmanned aerial vehicle (UAV) that significantly enhances the trajectory-tracking speed and accuracy while enhancing robustness against external disturbances. The inner loop employs a Linear Active Disturbance Rejection Controller (LADRC) and the outer loop a proportion integral differential (PID) controller, unified within a fuzzy control scheme. We introduce a Self-Adaptive Bald Eagle Search Optimization algorithm to optimize the initial controller settings, thereby accelerating convergence and improving parameter-tuning precision. Simulation results show that our proposed controller outperforms the conventional two-loop cascade PID configuration, as well as alternative strategies combining an outer-loop PID with a second-order inner-loop LADRC or a fuzzy-enhanced PID-LADRC approach. Moreover, the system maintains the desired position and attitude under external perturbations, underscoring its superior disturbance-rejection capability and stability.
- Open Access
The Lift Enhancement Effect of a New Fluidic Oscillator on High-Lift Wings
Fluidic oscillators have emerged as a prominent topic of research in the field of flow control, owing to their broad sweep range and enhanced control efficiency. However, the underlying mechanisms governing the operation of fluidic oscillators remain poorly understood, and the effect of oscillation frequency on flow control performance has yet to be conclusively determined. In this study, a novel fluidic oscillator is proposed that achieves frequency decoupling by replacing the conventional feedback channel with synthetic jets, thereby enabling modulation of oscillation frequency at a constant momentum coefficient. When applied to a high-lift airfoil, results show that at a momentum coefficient of 14.1%, the lift coefficient increase achieved under F+ = 1 control outperforms that under F+ = 10 by more than 0.3. This finding suggests the presence of an optimal frequency for fluidic oscillators, which maximizes their flow control effectiveness. Notably, this optimal frequency is unaffected by variations in the momentum coefficient. A deeper analysis of the fluidic oscillator’s working principle reveals that periodic oscillations dominate the turbulent kinetic energy and Reynolds shear stress, driving enhanced chordwise momentum exchange. This increased energy transfer strengthens the boundary layer’s resistance to separation, effectively mitigating flow detachment and improving lift enhancement. Finally, the periodic flow field on the surface of the high-lift airfoil under fluidic oscillator control was examined. It was observed that, at low frequencies, the fluidic oscillator effectively controls the shedding of separation vortices, ensuring that the frequency of vortex shedding aligns with the oscillation frequency of the fluidic oscillator. This alignment likely contributes to the superior lift enhancement observed under low-frequency conditions.
Open AccessThe Lift Enhancement Effect of a New Fluidic Oscillator on High-Lift Wings
Fluidic oscillators have emerged as a prominent topic of research in the field of flow control, owing to their broad sweep range and enhanced control efficiency. However, the underlying mechanisms governing the operation of fluidic oscillators remain poorly understood, and the effect of oscillation frequency on flow control performance has yet to be conclusively determined. In this study, a novel fluidic oscillator is proposed that achieves frequency decoupling by replacing the conventional feedback channel with synthetic jets, thereby enabling modulation of oscillation frequency at a constant momentum coefficient. When applied to a high-lift airfoil, results show that at a momentum coefficient of 14.1%, the lift coefficient increase achieved under F+ = 1 control outperforms that under F+ = 10 by more than 0.3. This finding suggests the presence of an optimal frequency for fluidic oscillators, which maximizes their flow control effectiveness. Notably, this optimal frequency is unaffected by variations in the momentum coefficient. A deeper analysis of the fluidic oscillator’s working principle reveals that periodic oscillations dominate the turbulent kinetic energy and Reynolds shear stress, driving enhanced chordwise momentum exchange. This increased energy transfer strengthens the boundary layer’s resistance to separation, effectively mitigating flow detachment and improving lift enhancement. Finally, the periodic flow field on the surface of the high-lift airfoil under fluidic oscillator control was examined. It was observed that, at low frequencies, the fluidic oscillator effectively controls the shedding of separation vortices, ensuring that the frequency of vortex shedding aligns with the oscillation frequency of the fluidic oscillator. This alignment likely contributes to the superior lift enhancement observed under low-frequency conditions.