Unknown Forces Research Articles

Extending the dynamic response of structural input estimation by combining sensors with unmatched bandwidth

The estimation of external loads acting on mechanic structures is of paramount importance for the design, operation, and control of these systems. In many cases, external loads cannot be measured directly due to the intrusive nature or the high costs of adequate sensors. Model-based estimation techniques yield the possibility to estimate external loads in an indirect manner using indirect measurements. These methods usually assume an optimal sensor behaviour over the entire frequency range of the estimator application, which not necessarily has to be the case due to sensor bandwidth limitations. Therefore, model-based sensor fusion is constrained to sensors and applications that share the same bandwidth. This paper proposes a novel non-intrusive approach to estimating external loading in the presence of incongruent measurement regimes of the involved sensors using Kalman filters. The method uses existing model-based estimation techniques to establish a broadly applicable framework for the fusion of multiple sensors with non-coinciding measurement bandwidths. A promising application of this new approach is not only the combination of sensors that measure the same quantity in different frequency regimes but also the combination of sensor types which are not being used together due to different measurement regimes. The newly formulated approach is tested both numerically and with a validation experiment in which accelerometer and gyroscope measurement are combined. In both cases, the new method shows improved behaviour in terms of estimations quality of an unknown force over traditional Kalman filter formulations in the presence of prominent sensor dynamics and over a wide frequency range.

Hierarchical Control and Cooperative Disturbance Estimation for Multiple Drones: Towards Application to Micro-Meteorology Control

This paper deals with formation control and disturbance estimation problem for multiple drones in the presence of unknown disturbance forces. The unknown disturbance forces are assumed to be generated mainly by wind. In view of application to micro-meteorology control, a formation control law involving a cooperative disturbance estimation mechanism is proposed. The estimated disturbance can be used for meteorology control. The proposed control law consists of three parts: a hierarchical optimal feedback control law for translational motion, a cooperative update law for disturbance estimation, and a nonlinear attitude control law.

A switching Gaussian process latent force model for the identification of mechanical systems with a discontinuous nonlinearity

Abstract An approach for the identification of discontinuous and nonsmooth nonlinear forces, as those generated by frictional contacts, in mechanical systems that can be approximated by a single-degree-of-freedom model is presented. To handle the sharp variations and multiple motion regimes introduced by these nonlinearities in the dynamic response, the partially known physics-based model and noisy measurements of the system’s response to a known input force are combined within a switching Gaussian process latent force model (GPLFM). In this grey-box framework, multiple Gaussian processes are used to model the unknown nonlinear force across different motion regimes and a resetting model enables the generation of discontinuities. The states of the system, nonlinear force, and regime transitions are inferred by using filtering and smoothing techniques for switching linear dynamical systems. The proposed switching GPLFM is applied to a simulated dry friction oscillator and an experimental setup consisting of a single-storey frame with a brass-to-steel contact. Excellent results are obtained in terms of the identified nonlinear and discontinuous friction force for varying: (i) normal load amplitudes in the contact; (ii) measurement noise levels, and (iii) number of samples in the datasets. Moreover, the identified states, friction force, and sequence of motion regimes are used for evaluating: (1) uncertain system parameters; (2) the friction force–velocity relationship, and (3) the static friction force. The correct identification of the discontinuous nonlinear force and the quantification of any remaining uncertainty in its prediction enable the implementation of an accurate forward model able to predict the system’s response to different input forces.

Experimental assessment of an unknown-input estimator for a nonlinear wave energy converter

In the wave energy field, one of the main challenges towards commercialisation of wave energy devices is the development of suitable control laws, able to maximise the absorbed energy while guaranteeing effective satisfaction of any required physical constraint. However, one of the main characteristics of this optimal control problem is that the system behaviour is strongly influenced by the external (uncontrollable) input arising from the wave source, i.e. the wave excitation, which is often unmeasurable. As such, computation of optimal control solutions for WEC systems requires availability of instantaneous knowledge of the wave excitation, and hence input-unknown estimators are developed within the control loop. State-of-the-art estimation strategies are based on the knowledge of control-oriented linearized models of the system, often neglecting the influence of nonlinear phenomena within the system description. We propose, in this paper, an approach inspired by disturbance observer-based control, able to accommodate well-known hydrodynamic nonlinear effects in the process of estimating the unknown excitation force acting on the device. This strategy, which in contrast to the usually applied estimators does not require an implicit/explicit model of the wave excitation force, is tested on a hardware-in-the-loop facility in different sea state conditions, to realistically assess its performance in terms of estimation error and delay. The experimental appraisal show satisfactory results in terms of normalized root mean square error and average delay, which, together with the simplicity of the method, positions the proposed strategy as a promising candidate for hardware implementations in real environments.

Modeling a Viscoelastic Support Considering Its Mass-Inertial Characteristics During Non-Stationary Vibrations of the Beam

Non-stationary loading of a mechanical system consisting of a hinged beam and additional support installed in the beam span was studied using a model of the beam deformation based on the Timoshenko hypothesis with considering rotatory inertia and shear. The system of partial differential equations describing the beam deformation was solved by expanding the unknown functions in the Fourier series with subsequent application of the integral Laplace transform. The additional support was assumed to be realistic rather than rigid. Thus it has linearly elastic, viscous, and inertial components. This means that the effect of a part of the support vibrating with the beam was considered such that their displacements coincide. The beam and additional support reaction were replaced by an unknown concentrated external force applied to the beam. This unknown reaction was assumed to be time-dependent. The time law was determined by solving the first kind of Volterra integral equation. The methodology of deriving the integral equation for the unknown reaction was explained. Analytic formulae and results of computations for specific numerical parameters were given. The impact of the mass value on the additional viscoelastic support reaction and the beam deflection at arbitrary points were determined. The research results of this paper can be helpful for engineers in designing multi-span bridges.

Identification of Time-Varying External Force Using Group Sparse Regularization and Redundant Dictionary.

How to accurately identify unknown time-varying external force from measured structural responses is an important engineering problem, which is critical for assessing the safety condition of the structure. In the context of a few available accelerometers, this paper proposes a novel time-varying external force identification method using group sparse regularization based on the prior knowledge in the redundant dictionary. Firstly, the relationship between time-varying external force and acceleration responses is established, and a redundant dictionary is designed to create a sparse expression of external force. Then, the relevance of atoms in the redundant dictionary is revealed, and this prior knowledge is used to determine the group structures of atoms. As a result, a force identification governing equation is formulated, and the group sparse regularization is reasonably introduced to ensure the accuracy of the identified results. The contribution of this paper is that the group structures of atoms are reasonably determined based on prior knowledge, and the complexity in the process for identifying external force from measured acceleration responses is reduced. Finally, the effectiveness of the proposed method is demonstrated by numerical simulations and an experimental structure. The illustrated results show that, compared with the force identification method based on the standard l1-norm regularization, the proposed method can further improve the identified accuracy of unknown external force and greatly enhance the computational efficiency for the force identification problem.

Robust Trajectory Tracking Control of Space Manipulators in Extended Task Space

This study provides a new class of controllers for freeflying space manipulators subject to unknown undesirable disturbing forces exerted on the end-effector. Based on suitably defined taskspace non-singular terminal sliding manifold and the Lyapunov stability theory, we derive a class of estimated extended transposed Jacobian controllers which seem to be effective in counteracting the unstructured disturbing forces. The numerical computations which are carried out for a space manipulator consisting of a spacecraft propelled by eight thrusters and holonomic manipulator of three revolute kinematic pairs, illustrate the performance of the proposed controller.

Radial oscillations of an electron in a Coulomb attracting field

Abstract The radial motion of an electron in a Coulomb attracting field based on a new theory of the interaction of a particle with an electromagnetic field is studied. It is shown that the electron can perform radial oscillations due to a repulsive force that exists in the vicinity of the center and prevents the electron from approaching the center. This concept of a previously unknown repulsive force significantly shifts the paradigm of the interaction of a charge with an electromagnetic field. A laboratory experiment is proposed to test the new phenomenon.

Hybrid method for full-field response estimation using sparse measurement data based on inverse analysis and static condensation

In structural health monitoring, measuring the accurate and spatially dense response near critical locations of the structure can be advantageous to estimate damage to the structure. Due to several physical restrictions or limitations of the sensing method, it may not always be possible to generate reliable data at critical locations. In this study, a hybrid method is presented that makes use of the measured displacement data and finite element (FE) model of the structure to predict dense full-field response. The presented method can incorporate unknown boundary conditions and unknown body forces by applying correction/fictitious forces to match predicted and measured responses. Using static condensation followed by inverse analysis, these additional forces are found by setting up a least square problem. Due to the problem being ill-posed, L2-penalty is used to control the prediction error. Numerical simulation of a plate subjected to body force showed an accurate prediction of full-field response except for a few boundary locations. To handle this, the proposed method is used in conjunction with linear interpolation near boundary locations. The method is validated in a laboratory experiment for a plate with a notch having displacement measured using Digital Image Correlation (DIC). On comparing strains calculated using predicted displacements, FEM, and DIC, the predicted strains show better agreement with the FEM than DIC. This affirms that the proposed hybrid technique can be used at critical locations where DIC fails to provide reliable strain data.

Unknown equations in the elerctromagnetic fields

With the help of the extremal theory of dimensions, a close relationship between gravity and electromagnetism was proved and unknown differential equations were found in parallel and consecutive electrical circuits. This became possible due to the use of higher derivatives (in the equations of motion), engendering hitherto unknown forces, which actually affect on dynamics and are far from small, but have not been known until now. This fact was most clearly manifested in a mechanical structure called Tolchin’s inertioid, which moves with high acceleration due to internal rotations and does not obey to the known laws of mechanics. Its movement turns out to be quite understandable only from the standpoint of the higher derivatives of its movement. A similar phenomenon takes place also in the electrical circuits and it is demonstrated in relation of problems in which the differential equations are sought by means of the extremal theory of dimensions. In this work, by means of the “extremal theory of dimensions”, we prove the close connection between gravitation and electromagnetism and also we find the generalization of the known differential equations of the electrical engineering.

Primary–auxiliary model scheduling based estimation of the vertical wheel force in a full vehicle system

In this work we study the estimation problem of the vertical wheel force in a vehicle system subject to non-stationary and unknown excitation, which is a common and critical problem in vehicle durability design. The vehicle system can be approximated by a linear time invariant system under each working condition. However, the working conditions are unknown during the estimation process. A primary–auxiliary model scheduling procedure based on time-domain transmissibilities is proposed and performed to identify the unknown working conditions and estimate the unknown vertical wheel force: In addition to constructing a primary transmissibility family from the pseudo-inputs to the output during the offline stage, an auxiliary transmissibility family is constructed by further decomposing the pseudo-input vector into two parts. The auxiliary family enables identifying the unknown working condition under which the system is currently running, and then an appropriate transmissibility from the primary transmissibility family for estimating the unknown output can be selected during the online estimation stage. Moreover, Finite Impulse Response (FIR) models, ridge regression, and Bayes classifiers are applied to realize the model scheduling procedure. A numerical example and a real-world application to the estimation of the vertical wheel force in a full vehicle system are, respectively, conducted to demonstrate the effectiveness of the proposed method. The results show that the estimates are in good agreement with reference measurements.

Regulating the vibration of aerostatic journal spindle based on piezoelectric ceramics

The aerostatic spindle often occur offset and additional vibration under the action of external load due to the low stiffness, thus affecting the rotary accuracy of the spindle. In order to solve the problem of unbalanced vibration of the spindle, a new type of controllable radial aerostatic bearing is designed by combining piezoelectric ceramics. A bearing-rotor-piezoelectric ceramic coupling model was established, and the control method of variable structure sliding mode control was used to reduce the vibration amplitude due to the unbalance. From the results of simulation and experiment, it is found that when the disturbance is taken as a constant value, the vibration amplitude increases with the increase of force; when the disturbance force is an unknown random force, the control effect is slightly worse than that when the disturbance force is known, but the rotary accuracy can be improved by this suppression effect on the aerostatic spindle. Finally, the correctness and effectiveness of this control method are proved through experiments.

Finite‐time control of mobile manipulators subject to unknown/unstructured external disturbances

AbstractA robust finite‐time control law is proposed for mobile manipulators with uncertain both kinematic and dynamic equations. Moreover, the following external disturbances are allowed to act on the system: unstructured forces exerted on the end‐effector, slip reaction forces affecting the platform wheels, unknown friction forces coming from joints directly driven by the actuators and undesirable unstructured forces caused by singular configurations. In order to cope with both parametric uncertainties and unknown/unstructured external disturbances, we first transform the original control problem whose non‐holonomic constraints are violated into a steering one in an extended space of generalized coordinates with extended non‐holonomic constraints of the Pfaffian form and then introduce a task space non‐singular terminal sliding manifold. Based on the Lyapunov stability theory, a new class of estimated extended transposed Jacobian control laws is derived which both effectively counteract the external forces and significantly reduce the slipping phenomena. A second order sliding technique is involved in our control law to eliminate undesirable chattering effect. An illustrative example of a mobile manipulator control demonstrates the advantages of the approach. Moreover, numerical comparisons with other representative controllers well‐known in the literature are also given.

PI velocity control of brushless DC motors using the extended dq transformation

AbstractThis paper is concerned with velocity control in brushless direct current (BLDC) motors. Our control scheme is composed of a classical proportional–integral velocity controller and a proportional electric current controller computed in the extended dq coordinate system. We employ a finite time estimator that has been previously proposed in the literature intended to estimate the unknown back electromotive forces. This estimator has been proven previously to converge locally to the true values. This control strategy is proposed to eliminate torque ripple produced by the fact that back electromotive forces in BLDC motors are nonsinusoidal. We present, for the first time, a formal stability result for this control scheme: (a) the state has an ultimate bound provided that the estimate of the back electromotive forces is close to the true values, and (b) this ultimate bound can be rendered arbitrarily small when the estimate of the back electromotive forces converges to the true values. This result stands when starting from any initial condition such that the finite time estimator is ensured to converge to the true values. We verify our findings through simulations.

Online estimation of unknown aerodynamic forces acting on AWE systems

• An EKF can be used for estimating online unknown aerodynamics forces that act on AWE systems. • The control performance of AWE systems can be improved by considering the estimated aerodynamic forces. • By using the EKF, less sensors are necessary to implement nonlinear control laws. • The EKF use increases the robustness of the AWE system in the presence of different sources of uncertainties. • The EKF allows for getting reliable estimations of the aerodynamic coefficients. Airborne Wind Energy systems (AWE) represent a promising solution to environmental challenges that has revolutionized research in the wind industry. The studied AWE system in this work is equipped with a multicopter drone in order to perform take-off and landing maneuvers and the objective consists in presenting an estimation strategy based on an Extended Kalman Filter (EKF) to obtain accurate estimation of the aerodynamic forces needed to improve the performance of the proposed control law for the considered prototype in this study. The proposed method is implemented and tested in a numerical and experimental environment. The obtained results show the effectiveness of the introduced method at estimating unknown forces that act on the system despite the presence of several sources of uncertainty: neglected nonlinearities, poorly known parameters, physical constraints, etc. Moreover, we show that the knowledge of these forces allows one to improve the robustness of the studied AWE system during its take-off and landing phases.

Extraction of the unknown hydrodynamic pressure from stochastic responses of the train-bridge system under wind and wave actions using iterative least square estimation and Kalman filter model

The high-speed train running along a sea-crossing bridge is simultaneously threatened to wind and wave loads. However, in literature, estimating the hydrodynamic pressure acting on multiple piles standing in tandem is usually empirical and unclear. The hydrodynamic load might not be measured correctly or not be available. This study introduces an iterative least square estimation (ILSE) and Kalman filter (KF) model to identify the unknown hydrodynamic force. The ILSE is introduced to identify the unknown hydrodynamic force, while the KF is used to identify the hydrodynamic parameters and generate the time histories of the hydrodynamic forces. Pingtan Railway Bridge, located in China, is selected for the application. The results show that 200 samples are enough to generate an accurate and time-saving result. Additionally, the ILSE can estimate the added mass coefficients and the intensity of the hydrodynamic forces with a good accuracy score of around 1.78%–3.33%. Based on KF estimation, the maximal absolute errors with the target values are 0.03% and 0.08% for 5%, and 10% levels of white noise. Finally, the time history of the hydrodynamic forces is extracted efficiently and accurately.

Experimental Research on a Hybrid Algorithm for Localisation and Reconstruction of the Impact Force Applied to a Rectangular Steel Plate Structure.

Impact force is the most common form of load which acts on engineering structures and presents a great hidden risk to the healthy operation of machinery. Therefore, the identification or monitoring of impact forces is a significant issue in structural health monitoring. The conventional optimisation scheme based on inversion techniques requires a significant amount of time to identify random impact forces (impact force localisation and time history reconstruction) and is not suitable for engineering applications. Recently, a pattern recognition method combined with the similarity metric, PRMCSM, has been proposed, which exhibits rapidity in practical engineering applications. This study proposes a novel scheme for identifying unknown random impact forces which hybridises two existing methods and combines the advantages of both. The experimental results indicate that the localisation accuracy of the proposed algorithm (100%) is higher than that of PRMCSM (92%), and the calculation time of the hybrid algorithm (179 s) for 25 validation cases is approximately one nineteenth of the traditional optimisation strategy (3446 s).

An output‐only structural condition assessment method for civil structures by the stochastic gradient descent method

The interesting to assess the condition of a structure with structural health monitoring data has gained many attentions. Most of the existing methods require the measurement at the force location. This paper presents a novel output-only condition assessment method that does not require measurement at the force location. The unknown structural damage indices and input force can be identified with the stochastic gradient descent method. The dynamic acceleration response sensitivities with respect to the unknown structural damage indices and input force are derived analytically. Both unknown damage indices and unknown input force can be identified by minimizing the discrepancy between the measured and calculated vibration data. Numerical studies on a two-dimensional truss and seven-floor frame and experimental studies on a steel frame structure are presented to verify the accuracy and efficiency of the proposed method. Results demonstrate that the damage severity, location, and unknown input force can be identified. Also, the measurement at the force location is not required. Furthermore, when 20% measurement noise is considered, the identified error is less than 5%.

Initial studies into camera-based modal force reconstruction

Much work has been done toward the reconstruction of an unknown force using measured response. Modal Force Reconstruction (MFR) attempts a solution by using measured modes and vibrations at some number of degrees of freedom. While developed by way of traditional sensors (e.g., accelerometers), the full-field nature of cameras may be exploited for such tasks. In particular, the spatial density of an image can re-establish the traditionally underdetermined problem into one that is overdetermined. Not only does this make the reconstruction well-posed, but the modal matrix being that which needs inversion establishes a niche solution in certain force reconstruction scenarios. This talk will explore the proposed theory behind camera-based MFR and present proofs of concept using analytical models. Limitations and points of error will also be discussed, helping to further establish credibility and understanding. Initial results suggest camera-based MFR to be a viable reconstruction technique with high spatial and temporal accuracy.

High-precision multiparameter estimation of mechanical force by quantum optomechanics.

A nanomechanical oscillator can be used as a sensitive probe of a small linearized mechanical force. We propose a simple quantum optomechanical scheme using a coherent light mode in the cavity and weak short-pulsed light-matter interactions. Our main result is that if we transfer some displacement to the mechanical mode in an initialization phase, then a much weaker optomechanical interaction is enough to obtain a high-precision multiparameter estimation of the unknown force. This approach includes not only estimating the displacement caused by the force but also simultaneously observing the phase shift and squeezing of the mechanical mode. We show that the proposed scheme is robust against typical experimental imperfections and demonstrate the feasibility of our scheme using orders of magnitude weaker optomechanical interactions than in previous related works. Thus, we present a simple, robust estimation scheme requiring only very weak light-matter interactions, which could open the way to new nanomechanical sensors.