Thrust Estimation Research Articles

Thrust estimate method of an on-orbit Hall thruster using Hall drift current

In order to realize the thrust estimation of the Hall thruster during its flight mission, this study establishes an estimation method based on measurement of the Hall drift current. In this method, the Hall drift current is calculated from an inverse magnetostatic problem, which is formulated according to its induced magnetic flux density detected by sensors, and then the thrust is estimated by multiplying the Hall drift current with the characteristic magnetic flux density of the thruster itself. In addition, a three-wire torsion pendulum micro-thrust measurement system is utilized to verify the estimate values obtained from the proposed method. The errors were found to be less than 8% when the discharge voltage ranged from 250 V to 350 V and the anode flow rate ranged from 30 sccm to 50 sccm, indicating the possibility that the proposed thrust estimate method could be practically applied. Moreover, the measurement accuracy of the magnetic flux density is suggested to be lower than 0.015 mT and improvement on the inverse problem solution is required in the future.

Dual-Loop μ-Synthesis Direct Thrust Control for Turbofan Engines

As the power unit of an aircraft, the engine’s primary task is to provide the demanded thrust, making research on direct thrust control crucial. However, being a complicated multivariable system, effective multivariable direct thrust control methods are currently lacking. The main content of this paper is threefold. First, it presents a dual-loop multivariable μ-synthesis direct thrust control scheme for mixed-exhaust low-bypass turbofan engines, which is a typical rotationally symmetric machine. The scheme adjusts fuel flow for thrust control and nozzle area to control the turbine pressure ratio, ensuring thrust tracking while maintaining the engine’s key parameters within safe limits. Second, a fast, accurate thrust estimation algorithm based on aerodynamic thermodynamics and component characteristics is introduced. At last, considering the model uncertainties between off-design and design points, a weight function frequency shaping μ-synthesis control design method is proposed to address internal loop coupling and external disturbance suppression. Nonlinear simulations within the flight envelope show that μ-synthesis direct thrust control achieves robust servo tracking and disturbance rejection, with a maximum steady-state thrust error of no more than 0.1%, and the key parameters are not over their safety boundaries.

Thrust online fusion estimation of high-flow dual variable cycle engine

For the aeroengines, thrust is a crucial performance parameter which is closely related to the mission accessibility. Accurate thrust control is conducive to excavate the potential of the variable cycle engine (VCE) in different operation modes, which meets the requirements of future engine control system. However, the thrust is unmeasured in flight. Besides, the traditional thrust estimation method is difficult to meet the wide-area thrust control requirements due to the strong nonlinearity and large flight envelope for a neoconfiguration VCE of the high-flow triple-bypass, named high-flow dual variable cycle engine (HDVCE). This paper proposes a novel online fusion thrust estimation method mainly under single operation mode for the HDVCE. The problem of individual engine differences is also focused, and the combination of model and data-driven is to generate the thrust estimation with fusion strategy. At first, a multi-combustion chamber coupled dynamic model is established for the HDVCE, and an adaptive network is used for model optimization to improve the model accuracy. On this basis, an EKF-based thrust estimator is built. Secondly, a data-driven thrust estimator is pre-trained by a stacked autoencoder (SAE) and then tuned by back propagation (BP) neural network. Subsequently, the thrust integration is incorporated based on estimation results from the EKF-based and data-driven one using Euclidean distance fusion strategy. Simulation results show that the fusion estimation method proposed in this paper, on the one hand, reduces the effect of model instability on EKF. On the other hand, it ensures the estimation accuracy of SAE-BP far from the training point. The comparisons also reveal that the fusion one produces more than 97% in thrust estimation accuracy and is better than the remaining ones, which is promising for thrust control applications.

Development of Thrust, Torque, and Power Estimation Model, and Prediction Performance of Earth Pressure Balance Tunnel Boring Machine in Mixed-Face Strata

Development of Thrust, Torque, and Power Estimation Model, and Prediction Performance of Earth Pressure Balance Tunnel Boring Machine in Mixed-Face Strata

CFD-Based Lift and Drag Estimations of a Novel Flight-Style AUV with Bow-Wings: Insights from Drag Polar Curves and Thrust Estimations

CFD-Based Lift and Drag Estimations of a Novel Flight-Style AUV with Bow-Wings: Insights from Drag Polar Curves and Thrust Estimations

A Generalized Thrust Estimation and Control Approach for Multirotors Micro Aerial Vehicles

A Generalized Thrust Estimation and Control Approach for Multirotors Micro Aerial Vehicles

Satellite Fast Maneuver Control Technology Based on Parallel System

An on-orbit thrust estimation method of satellite based on parallel system, which can achieve high-efficiency and high-precision thrust estimation, is proposed. A complete satellite maneuvering parallel system framework is constructed. Initially, a real-time artificial model, which is consistent with the actual system, is established. The injection time of maneuvering control is estimated optimally based on the modification of the artificial model with the specific injection time treated as the optimization parameter. The jet time, with the minimum maneuvering error, is obtained. Then, a maneuver strategy is designed and fed back to the actual system. The method based on a parallel system with jet time as the optimal parameter has higher control accuracy than the previous maneuvering control, which only considers the speed increment. Simulation results show that the terminal error of the first maneuver using the parallel system method is less than 100 meters for a maneuvering mission of tens of kilometers.

A causal-temporal graphic convolutional network (CT-GCN) approach for TBM load prediction in tunnel excavation

This research proposes a novel deep learning approach named causal-temporal graphic convolutional network (CT-GCN) which aims to provide accurate predictions on tunnel boring machine’s (TBM) load parameters. The causal associations among the key TBM operational parameters are detected and quantified with causal effects through the Peter and Clark momentary conditional independence plus (PCMCI+) method. The discovered causality can be further integrated with a deep learning model that consists of graph convolutional network (GCN) and long short-term memory (LSTM) layers for accurate prediction of TBM’s torque and thrust. Data collected from a realistic tunnel project in Singapore is utilized to demonstrate the effectiveness of the proposed approach. The load parameters are predicted with their historical values and another 7 key operational parameters. The results indicate that (1) The proposed CT-GCN approach can achieve a low mean absolute error (MAE) and root mean squared error (RMSE) of 40.90kN∙m and 64.53kN∙m for thrust force (y1) and that of 635.76kN and 1168.59kN for cutterhead torque (y2), respectively. (2) The proposed CT-GCN method achieves 12.86 % and 24.38 % average improvements in the coefficient of determination (R2) for y1 and y2, respectively when compared with the long-short term memory (LSTM) method and that of 5.62 % and 8.60 % improvements when compared with the GCN-LSTM method. (3) Compared with correlation-based GCN models, the proposed approach exerts an average improvement of 43.10 %, 41.97 %, and 22.72 % in terms of MAE, RMSE, and R2 for torque and much better performance for thrust estimation. This study contributes to improving the understanding of TBM operation by quantifying the causality among the key operational parameters. It also contributes to developing a novel deep-learning method that estimates TBM’s load parameters with high accuracy.

A revision of blade element/momentum theory for wind turbines in their high-thrust region

Modern horizontal-axis wind turbines produce maximum power at an optimal tip speed ratio, λopt, of around 7. This is also the approximate start of the high-thrust region, which extends to runaway at λR ≈ 2λopt where no power is produced and the thrust is maximized. The runaway thrust coefficient often exceeds unity. It is well known that the conventional axial momentum equation must be modified whenever the thrust coefficient approaches unity, but most past modifications have no sound physical basis. Our main revision is to include the “wake vorticity” term in the axial momentum balance. This term is related to blade element drag and acts to decouple the thrust from the induced axial velocity when it becomes large near the edge of the rotor as the runaway is approached. The wake vorticity term dominates the axial momentum equation in these conditions and leads to estimates of power and thrust that are consistent with the limited amount of high-quality experimental data in the high-thrust region.

A method for direct in-space thrust estimation from low-acceleration orbital maneuvers

This paper presents a method for performing direct in-space thrust estimation for low-acceleration propulsion systems using measurements of the spacecraft’s position taken during an orbital maneuver. The method is based on the ensemble Kalman update which does not require linearization of the spacecraft dynamics nor does it require Gaussian distributions for parameter uncertainties and measurement noise, allowing for a more general approach to thrust estimation. In addition, modeling error, such as that caused by the truncation of a spherical-harmonics representation of the Earth’s gravitational field, can be explicitly accounted for by representing the error with Gaussian processes. Simulated experiments show that uncertainty in the propulsive acceleration magnitude on the order of 0.1 mum/s^2 (1sigma) can be achieved at an orbit altitude of approximately 410 km with temporally-sparse measurements even in the presence of uncertain atmospheric drag, and Monte Carlo analysis demonstrates the consistency of the inference results. Trends in the estimate of the propulsive acceleration with the true acceleration value are explored empirically and theoretically in order to allow for generalization of the results. The outcome of this work is a systematic approach to direct in-space thrust estimation that can support the final steps of development for future in-space electric propulsion systems or the calibration of a thruster during a mission.

Evaluation of generalized k-ω turbulence model in strong separated flow estimation of thrust optimized parabolic nozzle

One of the frequently reported defects of RANS-based turbulence models is overestimation of turbulent kinetic energy production in high speed separated flow problems, which causes significant prediction errors. The correct estimation of such flow in thrust optimized parabolic nozzles extremely depends upon the accurate prediction of the onset of flow separation. In this paper, firstly, the significant error of conventional RANS-based turbulence models is shown to predict the onset of flow separation in this type of nozzles. Then, the prediction accuracy is improved through the modification of the essential parameters of the generalized k-ω (GEKO) turbulence model. It was found that modifying the separation and mixing parameters of the GEKO model to realize the turbulent kinetic energy production resulted in the accurate prediction of onset of flow separation at the extensive range of nozzle pressure ratios. Using this modified model with new coefficients reduced the error of about 30% of the k-ω-sst model in estimating the onset of flow separation. Also, the nozzle pressure value at which the transition from free shock separation (FSS) to restricted shock separation (RSS) occurs is well predicted by this approach. After strengthening the turbulence model, the flow physics has been investigated with increasing and decreasing nozzle chamber pressure. The length of the separation shock and reflected shock waves which impose the presence of FSS or RSS patterns and transitional phenomena are discussed. Our new findings show that unlike the transition from FSS to RSS, the inverse transition from RSS to FSS did not depend on the length of the separation and reflective shocks.

Iodine Electric Propulsion System Thrust Validation: From Numerical Modeling to In-Space Testing

In this paper, we complete a full-thrust audit of an iodine-based gridded ion thruster. Prior results have demonstrated excellent agreement between indirect and direct laboratory thrust estimates. Here, thrust estimates from numerical modeling, indirect laboratory testing from diagnostic probes and propulsion system telemetry, indirect in-space testing from onboard propulsion system telemetry, and direct in-space testing by analyzing orbital maneuvers are compared to demonstrate consistency between the four methods and complete the thrust audit. Results from recent in-space testing of the iodine-based thruster demonstrate that thrust estimates from all four methods agree to within three standard deviations of uncertainty for the 11 maneuvers studied. This thrust audit represents a critical step toward improving the understanding and technological maturity of iodine-based gridded ion thrusters for future mission applications, and it demonstrates the utility of recently developed in-space thrust inference techniques for analyzing low-thrust maneuvers.

Bending moment characteristic analysis of utility-scale onshore wind turbine blades based on monitoring data

Bending moment is an important parameter in structural design of the wind turbine blades. The purpose of the present study is to accurately determine the actual bending moments on the blades of wind turbine in service and study the characteristics. It can be helpful to provide supports for the design load of wind turbine blades. For this purpose, a blade load monitoring system was developed and installed on a 2 MW onshore wind turbine to measure bending moments at the blade root. A simulation model which is consistent with the monitoring wind turbine was used to verify the availability of the system. Based on the monitored bending moments and operational conditions of the wind turbine, the characteristics and fatigue load of blade root bending moments were analyzed. Meanwhile, the relationship between bending moments of blade root and operational parameters was discussed. A thrust estimation method based on monitored bending moments of blade root was presented which will help to assess the loads on the tower and foundation of the wind turbine. At last, a calculation method of equivalent fatigue load based on wind speed-rotor speed joint distribution was established which will contribute to the fatigue design of blades.

New design equations for corrugated steel culverts responding to live loads

The current design provisions for corrugated steel culverts in North America consider thrust at the springline to be the critical mechanism and location, respectively, when checking capacity. However, experiments have shown that, at shallow cover depths under vehicle loading, the response of these culverts involves both bending moments and thrust forces, and the critical location in terms of capacity is not at the springline. To address this, 3D finite element modeling of the culvert was undertaken using orthotropic shell elements for the corrugated steel structure and continuum elements for a discrete volume of the surrounding soil. The results of an extensive parametric study are used to develop equations for the critical thrust and bending moment under three different vehicle loading configurations. The proposed equations are then compared to the current design code equations in terms of how well they capture the behavior of the finite element model results. The proposed equations are then used to estimate the response of physical experiments conducted in the laboratory and the field and compared to the responses from distributed strain measurements. The equations were found to provide better estimates of thrust and allow the bending moments, which are currently not considered in North American design codes, to be estimated accurately. Limitations of the proposed equations are also discussed.

Load identification of a 2.5 MW wind turbine tower using Kalman filtering techniques and BDS data

The rapid increase in the number of wind turbine installations and operations, is increasing the importance of the health monitoring of these wind turbines. To assess the remaining service life of a wind turbine, continuous monitoring of the internal forces acting on the critical locations of fatigue in the structure is required. However, a large number of sensors are usually required for the comprehensive determination of the internal force at a site-specific location; additionally, these sensors cannot be placed in locations with strong stress or strain gradients. Therefore, in this paper, a strategy for estimating the thrust at the tower top and the bending moment at any position of the wind turbine tower is proposed, which only requires a limited number of acceleration sensors and the BeiDou Navigation Satellite System (BDS). The estimated load includes static and dynamic components. The former is calculated by fitting the derived function and the BDS data, and the latter is estimated by the time-domain inverse method using the Kalman filter and with acceleration sensors. The performance of the proposed strategy is validated in two case studies, including simulated data and recorded data from a 2.5 MW onshore wind turbine located in China. The results show that the strategy can produce an estimation of thrust and bending moment, with good accuracy.

Numerical investigation and estimation of active earth thrust on gravity retaining walls under seismic excitation

Earthquakes can create severe damage to retaining structures. A numerical study is carried out to understand the seismically induced active earth pressure force on free-standing gravity retaining walls. Dynamic behavior in terms of acceleration amplification/deamplification, deformation mechanism, and earth pressure force are examined. Further, the influence of input peak ground acceleration (PGA), retaining wall height, Young's modulus of the wall, relative density of soil, and soil-structure interaction on total active earth pressure force (Pae) are investigated. The results show that Pae decreases until PGA value is around 0.55 g and later increases for higher values. The primary cause for this response is the loss of wall-soil interaction due to the overturning effect, which dominates until PGA approaches 0.55 g. Also, the generation of failure wedges causes an increase in Pae after 0.55 g. Sensitivity analysis concludes that Pae is highly sensitive to PGA, wall height, and soil-structure interaction. Based on regression analysis, an equation is proposed for the total active thrust. Later, the accuracy of the equation is confirmed by comparing it with the response of FE analysis and established study. This study contributes to developing an equation that is anticipated to provide total active thrust at the initial design stage under comparable work environment.

Orbit Determination and Thrust Estimation for Noncooperative Target Using Angle-Only Measurement

The classical interactive multimodel (IMM) algorithm has some disadvantages in tracking a noncooperative continuous thrust maneuvering spacecraft, such as poor steady-state accuracy, difficult selection of subfilter parameters, and mismatched model jump. To address the abovementioned problems, a variable-dimensional adaptive IMM strong tracking filtering algorithm (VAIMM-STEKF) is proposed to estimate the spacecraft’s position, velocity, and maneuvering acceleration state. VAIMM-STEKF contains 2 models, model 1 and model 2, which correspond to the tracking of the spacecraft in maneuvering and nonmaneuvering situations. Model 1 estimates the position and velocity of the spacecraft to ensure tracking accuracy when no maneuver occurs. Model 2 is a strong tracking filter with an augmented state. The adaptive IMM algorithm adjusts the fixed Markov transfer matrix in real time according to the model output probability. According to the different states of the spacecraft, the corresponding model interactive fusion method, together with the strong tracking filter, is adopted to ensure fast tracking when the spacecraft state changes. This method can also adapt to continuous thrust maneuvering spacecraft with different orders of magnitude. Simulation results show that the position accuracy of VAIMM-STEKF can be improved by approximately 27% and the speed accuracy can be enhanced by approximately 17% under different levels of maneuvering acceleration compared with those of the IMM algorithm. The convergence speed of VAIMM-STEKF is also better than the IMM algorithm.

Precision Feedback Control Design of Miniature Microwave Discharge Ion Thruster for Space Gravitational Wave Detection

The space gravitational wave detection mission has put forward multiple performance requirements for micro-newton thrusters, such as “fast response, high resolution, and low noise”. In order to solve the problem that the traditional open-loop propulsion system can hardly meet the high-precision performance, the microwave ion thruster with high accuracy and controllability of thrust estimation is adopted as the research object, and the precision feedback control method combining analog circuit and digital control technology is adopted to achieve a resolution of less than 0.1 μN, fast response of 20 ms, and 10−3~1 Hz frequency band noise less than 0.05 μN/Hz1/2 of the thrust performance. Experimental results show that, compared with open-loop regulation, the feedback control can effectively suppress various noises and disturbances caused by device temperature drift and complex operating characteristics of the thruster, and the anti-aliasing filter scheme adopted in this paper can suppress the folding of high-frequency data in the low- and medium-frequency bands during the digital control process, while it can effectively improve the system performance and reduce the impact of thrust noise. The feedback control strategy proposed in this paper verifies the possibility of a microwave ion thruster as an actuator for super “static and precise” space experiment satellites and provides a feasible solution for the application of a microwave ion thruster in deep space science experiment missions such as gravitational wave detection.

Acoustic Thrust Estimation on Turbofan Engines

An acoustic time of flight sensor is operated across a turbofan exhaust plume and is calibrated to provide nozzle thrust in a ground-test cell. Such a sensor could potentially be used to monitor any degradation of engine performance in an on-wing application. Validation of the technique was performed on an AE3007-A1E turbofan engine. Using a pneumatic horn and a set of microphones, the acoustic time of flight across the exhaust plume was estimated. A correlation-based approach was then used to relate the acoustic time of flight to the thrust produced by the engine. The thrust estimates resulting from this single-receiver approach matched load cell data within a root-mean-square (RMS) error of 1.1% full scale. The same approach was also used to estimate the thrust of a TFE731-2B engine. In that case, the estimated thrust matched load cell data to within an RMS error of 1.5% full scale. The technique is shown to significantly improve on a previous technique that produced errors of 5% RMS full scale or greater. Possible explanations for the comparative inaccuracy of the previous technique are analyzed.

Intelligent direct thrust control for multivariable turbofan engine based on reinforcement and deep learning methods

This paper proposes a novel intelligent direct thrust control (IDTC) architecture for a two-spool turbofan engine, in which the thrust is directly controlled by the IDTC architecture with two control variables instead of transforming thrust command to other commands. To realize thrust control, the unmeasurable thrust should be estimated first. A dynamic thrust model (DTM) is proposed to characterize the strong non-linearity of the engine. With the dynamic characteristic data set generation method, the date diversity increases and the thrust under random engine dynamics can be estimated more accurately. For the multi-variable optimal thrust controller, reinforcement learning (RL) method proximal policy optimization (PPO) algorithm is applied in the intelligent controller (IC) design process. Considering the engine characteristics, the reward system and the controller structure are redesigned to realize thrust optimal control and limit protection. The network used in both the DTM and the IC designing are the long short-term memory (LSTM) recurrent neural network (RNN), which can better process the engine time series and get better performance and accuracy. As the traditional evaluation criteria are too conservative to evaluate the overall ability of the proposed IDTC architecture in the full envelope, new criteria are proposed. Numerical simulations shows the satisfactory thrust estimation and control performance of the proposed IDTC architecture in the full envelope above the idle, and verify the superiority against other methods. Also, the strategy selection of the IC under extreme control tasks also shows the intelligence of the controller and gives new ideas for the engine control law design.