Uncertain Damping Research Articles

Drone Swarm Robust Cooperative Formation Pursuit through Relative Positioning in a Location Denial Environment

This paper considers the pursuit problem of a moving target by a swarm of drones through a flexible-configuration formation. The drones are modeled by second-order systems subject to uncertain damping ratios, whereas the moving target follows a polynomial-type trajectory whose coefficient vectors are fully unknown. Due to location denial, drones cannot obtain their absolute positions, but they can obtain their positions relative to other neighboring drones and the target. To achieve a robust formation pursuit, a robust cooperative control protocol is synthesized, which comprises three key components, namely, the pseudo drone position estimator, the pseudo target position estimator, and the local internal model control (IMC) law. The pseudo drone position estimator and the pseudo target position estimator aim to recover for each drone the position of itself and the target, respectively, but are subject to some common unknown constant bias in a distributed manner. By subtracting the pseudo target position from the pseudo drone position, each drone can acquire its position relative to the target, which facilitates the design of a local IMC law to fulfill formation pursuit in the presence of system parametric uncertainties. Both pure numerical simulation and hardware-in-the-loop (HIL) simulation are performed to verify the effectiveness of the proposed control protocol.

Response Spectrum with Uncertain Damping Using Artificial Neural Networks

It is evident that the response of linear structures under dynamic loads depends to two important dynamics parameters of structures, namely, the natural periods and structural damping. These parameters always characterize the oscillation and the energy dissipation of buildings. In fact, the values of these parameters differ significantly, before, during and after an earthquake from values selected during the design phase. This phenomenon, among other, introduces uncertainty into the building simulation process, which remarkably influences the structural response and associated performance of the structure under dynamic loads. This paper develops a new methodology to estimate the maximum absolute response for linear structures with uncertain damping using the Artificial Neural Networks (ANN) and the Monte Carlo method. The proposed method is illustrated using the target design response spectra corresponding to the EC8 for linear structures exposed to seismic loads. The numerical results revealed the practical applicability of the proposed methodology and the crucial influence of accounting the damping uncertainty in structural dynamics. Additionally, the method can be used in practice, mainly for important and special structures where uncertainty could lead to significant changes in structural response.

Energy shaping dynamic tube-MPC for underactuated mechanical systems

This work investigates the tracking control problem for underactuated mechanical systems. To this end, we develop an extension of the dynamic tube Model Predictive Control (MPC) approach by combining an MPC design, an ancillary energy shaping controller constructed with the Interconnection and Damping Assignment Passivity-Based Control methodology, and an analytical expression of the dynamic tube. In addition, we extend the proposed approach by including the adaptive compensation of a class of unknown disturbances. The stability analysis is presented by employing a Lyapunov approach. The effectiveness of the proposed controller is demonstrated with simulations on two underactuated systems: a two-mass-spring-damper system with uncertain damping and either linear or nonlinear spring; an inertia-wheel-pendulum with unmodeled disturbances.

Computer Analysis of Dynamic Reliability of Some Concrete Beam Structure Exhibiting Random Damping

An efficiency of the generalized tenth order stochastic perturbation technique in determination of the basic probabilistic characteristics of up to the fourth order of dynamic response of Euler-Bernoulli beams with Gaussian uncertain damping is verified in this work. This is done on civil engineering application of a two-bay reinforced concrete beam using the Stochastic Finite Element Method implementation and its contrast with traditional Monte-Carlo simulation based Finite Element Method study and also with the semi-analytical probabilistic approach. The special purpose numerical implementation of the entire Stochastic perturbation-based Finite Element Method has been entirely programmed in computer algebra system MAPLE 2019 using Runge-Kutta-Fehlberg method. Further usage of the proposed technique to analyze stochastic reliability of the given structure subjected to dynamic oscillatory excitation is also included and discussed here because of a complete lack of the additional detailed demands in the current European designing codes.

Neumann accelerations of generalized polynomial chaos expansions for larger dynamic systems

This work proposes a method for accelerating generalized polynomial chaos (gPC) expansions, using Neumann series, for uncertainty quantification of complex structures with uncertain damping and spring parameters. Often, classical Monte Carlo simulations are used for uncertainty quantification, however, for larger systems and frequency sweeps this method becomes very computationally expensive. Neumann series have been used with Monte Carlo simulations to decrease computation times, however, the Neumann series does not always converge. More recently gPC expansions have been used for uncertainty quantification. gPC is a stochastic spectral method that develops a surrogate model, whose coefficients can be used to calculate statistical moments. gPC requires sampling the response at predetermined quadrature points, which may become expensive for large systems. This study proposes a new approach where Neumann series are used to calculate the response at gPC quadrature points, in order to accelerate gPC computation times. The validity of this method is shown using large, viscously damped systems. Damping and stiffening elements fully connect degrees of freedom to each other and to ground. First the damping elements are taken as the uncertain parameter, then stiffening elements are taken as the uncertain parameter, and frequency dependent responses such as power dissipated are calculated.

Global Maximum Response of Linear Systems with Uncertain Damping to Irregular Excitation

AbstractIn the evaluation of the global maximum response of a structure subjected to its design load, damping effects must be included; however, the structure damping is often uncertain. This study...

Nonlinear dynamic analysis method for large-scale single-layer lattice domes with uncertain-but-bounded parameters

Currently, nonlinear dynamic analysis for large-scale single-layer domes is commonly performed using deterministic numerical methods. However, in practical engineering cases, complex large-scale single-layer domes have many uncertain parameters that cannot be considered using deterministic methods. Therefore, there is a growing awareness that classical deterministic methods need to be extended towards the introduction of the uncertain aspects in dynamic analysis, and a non-deterministic analysis method for large-scale spatial structures is required. In this paper, a new method is presented by introducing uncertainties into the nonlinear dynamic analysis for large-scale single-layer lattice domes. The method accounts for uncertainties in material properties, structural imperfections, loads, and damping with bounds. The focus is on the treatment of uncertainty in damping and the adopted geometric shape, which is different from that of conventional approaches. Finite element dynamic analyses for sample structures with multiple sources of uncertainty subjected to dynamic loads are performed. Results show that the variability of the variables with an associated uncertainty imposes significant negative effects on the dynamic properties, dynamic demands, and safety of a dome. Uncertain damping in a structure plays the most important role in determining structural performance. The numerical results reveal the differences between conventional analysis methods with deterministic parameters used in previous practical applications and the uncertain analysis method. Finally, a parametric study is performed, and the impacts of sample size on statistical dynamic demands, single uncertain source on structural failure, and single uncertain source on damping coefficients are discussed.

Stabilization of a Relative Equilibrium for an Underactuated AUV With Disturbances Rejection

This paper addresses the robust stabilization of a relative equilibrium for an underactuated autonomous underwater vehicle (AUV) with disturbances rejection. The AUV’s dynamics is described by the Hamiltonian equation in the presence of unknown external disturbances and uncertain hydrodynamic damping. The disturbances arising from slowly varying currents are assumed to be constant, which consists of matched disturbances and unmatched disturbances, simultaneously. The unmatched disturbances and the uncertain damping that make the realization of the system stabilization become more challenging. To achieve the control objective, first, a new Hamiltonian equation, which is stable around the desired relative equilibrium, is designed to serve as the closed-loop dynamics in which an integral action is added to suppress the disturbances. By matching the closed-loop equation and the open-loop equation, an anti-disturbance stabilizing controller is presented, which requires the knowledge of the uncertain damping. Then, the adaptive control method is employed to propose an improved controller, which enhances the robustness of the uncertain damping. The stability is analyzed by the Lyapunov method. The numerical simulations are conducted to demonstrate the obtained result.

Stochastic finite element method for random harmonic analysis of composite plates with uncertain modal damping parameters

Damping parameters of fiber-reinforced composite possess significant uncertainty due to the structural complexity of such materials. Considering the parameters as random variables, this paper uses the generalized polynomial chaos (gPC) expansion to capture the uncertainty in the damping and frequency response function of composite plate structures. A spectral stochastic finite element formulation for damped vibration analysis of laminate plates is employed. Experimental modal data for samples of plates is used to identify and realize the range and probability distributions of uncertain damping parameters. The constructed gPC expansions for the uncertain parameters are used as inputs to a deterministic finite element model to realize random frequency responses on a few numbers of collocation points generated in random space. The realizations then are employed to estimate the unknown deterministic functions of the gPC expansion approximating the responses. Employing modal superposition method to solve harmonic analysis problem yields an efficient sparse gPC expansion representing the responses. The results show while the responses are influenced by the damping uncertainties at the mid and high frequency ranges, the impact in low frequency modes can be safely ignored. Utilizing a few random collocation points, the method indicates also a very good agreement compared to the sampling-based Monte Carlo simulations with large number of realizations. As the deterministic finite element model serves as black-box solver, the procedure can be efficiently adopted to complex structural systems with uncertain parameters in terms of computational time.

A two-step method for analysis of linear systems with uncertain parameters driven by Gaussian noise

A two-step method is proposed to find state properties for linear dynamic systems driven by Gaussian noise with uncertain parameters modeled as a random vector with known probability distribution. First, equations of linear random vibration are used to find the probability law of the state of a system with uncertain parameters conditional on this vector. Second, stochastic reduced order models (SROMs) are employed to calculate properties of the unconditional system state. Bayesian methods are applied to extend the proposed approach to the case when the probability law of the random vector is not available. Various examples are provided to demonstrate the usefulness of the method, including the random vibration response of a spacecraft with uncertain damping model.

Robust updating of uncertain damping models in structural dynamics for low- and medium-frequency ranges

This paper deals with the robust updating of uncertain computational models in the context of structural dynamics in the low- and medium-frequency ranges of composite sandwich panels for which experimental results are available. The uncertain computational model is constructed using the non-parametric probabilistic approach which takes into account model and data uncertainties. The formulation of the robust updating problem includes the effects of uncertainties and consists in minimizing a cost function with respect to an admissible set of updating parameters. Updating is performed in two steps using several cost functions and experimental results. The results of the robust updating problem show that the method proposed is efficient for updating the uncertain computational model in both low- and medium-frequency ranges.

Robust linear quadratic designs with real parameter uncertainty

This note derives a linear quadratic regulator which is robust to real parametric uncertainty, by using the overbounding method of Petersen and Hollot (1986). The resulting controller is determined from the solution of a single modified Riccati equation. This controller has the same guaranteed robustness properties as standard linear quadratic designs for known systems. It is proven that when applied to a structural system, the controller achieves its robustness by minimizing the potential energy of uncertain stiffness elements, and minimizing the rate of dissipation of energy by the uncertain damping elements.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Stochastic Finite Elements for a Beam on a Random Foundation with Uncertain Damping Under a Moving Force

An infinitely long beam on an elastic foundation is subjected to a constant force which is moving with a constant speed along it. The beam rests on a random foundation the stiffness of which is a random function of the length co-ordinate. The coefficient of viscous damping is also a random variable. The steady state vibration is analyzed. It appears that a stochastic stationary process occurs, viewed by an observer moving together with the moving force. A stochastic finite element analysis by means of the first order perturbation and first order second-moment method provides an evaluation of the variance of the deflection and of the bending moment of the beam. The effects of several parameters and of various types of correlation functions are investigated. It is shown that the randomness of the foundation is of greater importance than the uncertainty in the damping. The dynamic and stochastic effects increase with increasing speed of the movement of the force in the subcritical domain, but decrease in the supercritical domain. The coefficient of variation of the deflection of the beam is larger than that of the bending moment at the point of application of the moving force.

Dynamic response of structures with uncertain damping

The uncertainty associated with damping in structural systems is identified and discussed. A second-order perturbation technique is utilized to examine the effects of damping variability on the transient and steady-state dynamic response of structural systems. The results demonstrate that the uncertainty in damping indeed influences the system response. The effects are more pronounced for higher variability of damping values.

Stochastic FEM analysis of vehicle response spectrum due to multiple random excitations.

The power spectra of the internal forces in a vehicle running on an uneven road are investigated based on finite element modeling. The modeling is two-dimensional to treat the random excitations through the front and rear wheels. The damping of the suspensions and tyres is of a non-proportional type. The equation of motion is uncoupled by use of the complex eigenvalue problem. An attempt is made to apply the filtered Poisson process (FPP) to the simulation of a random road surface. The power spectrum generated by the FPP can simulate well the one published as ISO DP 8608 when the parameters are selected properly. The power spectrum of a spring reaction is evaluated regarding the effect of vehicle speed, the sensitivity of the spring constant and the deviation caused by uncertain damping, together with that of the bending moment in the model beam.