Valder Steffen

Damage prognosis for aerospace, civil and mechanical systems

Virginia Polytech Inst & State Univ, Ctr Intelligent Mat Syst & Struct, Blacksburg, VA 24061 USA

Multimodal vibration damping through piezoelectric patches and optimal resonant shunt circuits

Piezoelectric elements connected to shunt circuits and bonded to a mechanical structure form a dissipation device that can be designed to add damping to the mechanical system. Due to the piezoelectric effect, part of the vibration energy is transformed into electrical energy that can be conveniently dissipated. Therefore, by using appropriate electrical circuits, it is possible to dissipate strain energy and, as a consequence, vibration is suppressed through the added passive damping. From the electrical point of view, the piezoelectric element behaves like a capacitor in series with a controlled voltage source and the shunt circuit, commonly formed by an RL network, is tuned to dissipate the electrical energy, more efficiently in a given frequency band. It is important to know that large inductances are frequently required, leading to the necessity of using synthetic inductors (obtained from operational amplifiers). From the mechanical point of view, the vibration energy can be attenuated in a single mode, or in multiple modes, according to the design of the damping device and the frequency band of interest. This work is devoted to the study of passive damping systems for single modes or multiple modes, based on piezoelectric patches and resonant shunt circuits. The present contribution discusses the modeling of piezoelectric patches coupled to shunt circuits, where the basics of resonant shunt circuits (series and parallel topologies) are presented. Following, the devices used in passive control (piezoelectric patch and synthetic inductors) are analyzed from the electrical and experimental viewpoints. The modeling of multi-degree-of-freedom mechanical systems, including the effects of the passive damping devices is revisited, and, then a design methodology for the multi-modal case is defined. Also, it is briefly reviewed the optimization method used for design purposes, namely the LifeCycle Model. Finally, experimental results are reported, illustrating the success of using the methodology presented in passive damping applications applied to mechanical and mechatronic systems.

Modal Active Vibration Control of a Rotor Using Piezoelectric Stack Actuators

This work deals with active vibration control of a rotating machine in both steady state and transient motion. Two stacks of piezoelectric ceramic orthogonally arranged in a plane localized at one of the bearings were used as the control actuators, using a modal control strategy. The optimal controller LQR was used to calculate the control gain, working together with an LQE observer that estimates the modal state. Simulation carried out on FEM model suggested the feasibility of the control strategy, and experimental tests using a physical test rig show good agreement with the numerical results, and confirm the efficiency of the strategy.

Finite Element Modeling of a Plate with Localized Piezoelectric Sensors and Actuators

This paper presents the numerical modeling of a plate structure containing bonded piezoelectric material. Hamiltons principle is employed to derive the finite element equations using the mechanical energy of the structure and the electrical energy of the piezoelectric material. Then, a numerical model is developed based on Kirchhoffs plate theory. A computational program is implemented for analyzing the static and dynamic behavior of composite plates with piezoelectric layers symmetrically bonded to the top and bottom surfaces. A set of numerical simulations is performed and the results are compared with those from analytical formulation available in the literature and with software ANSYS® .

Solution of inverse radiative transfer problems in two-layer participating media with differential evolution

In the present work the differential evolution approach (DE) is used for the estimation of radiative properties in two-layer participating media. This physical phenomenon is modelled by an integro-differential equation known as the Boltzmann equation. A review of the optimization technique used is presented. The direct radiative transfer problem is solved by using the collocation method. Then, case studies are presented aimed at illustrating the efficiency of the methodology used in the treatment of an inverse problem of radiative transfer. The results obtained from the solution of the inverse problem are compared with those obtained from a hybridization of simulated annealing and Levenberg–Marquardt methods. The preliminary results indicate that the proposed approach characterizes a promising methodology for the present type of inverse problem.

A low-cost electromechanical impedance-based SHM architecture for multiplexed piezoceramic actuators

The electromechanical impedance (EMI) method has been regarded as a promising tool for structural health monitoring (SHM) in real time. Usually, massive, high-cost, single-channel impedance analyzers are used to process the time domain data, aiming at obtaining the complex, frequency-dependent, EMI functions, from which features related to the presence, position, and extent of damage can be extracted. However, for large structures, it is desirable to deploy an array of piezoelectric transducers over the area to be monitored and interrogate these transducers successively so as to increase the probability of successful detection of damage in an early phase. In this context, a miniaturized, low-cost, highly expandable SHM architecture for monitoring an array of multiplexed piezoelectric transducers is proposed. Each logical block of the proposed architecture is presented in detail. The proposed architecture does not use costly fast Fourier transform analyzers/algorithms nor requires a digital computer for processing. A personal computer is only necessary for user interfacing. It has been verified that the system can work for frequencies ranging from 0 to 400 kHz with high accuracy and stability. A prototype using inexpensive integrated circuits and a digital signal processor was built and tested for two different types of structures: an aluminum beam and an aircraft aluminum panel. Simulated damages were introduced to each structure and the detection performance of the prototype was tested. The actual prototype uses a universal serial bus connection to communicate with a personal computer; however, a WiFi® connection is also available.

Experiments on optimal vibration control of a flexible beam containing piezoelectric sensors and actuators

In this paper, a digital regulator is designed and experimentally implemented for a flexible beam type structure containing piezoelectric sensors and actuators by using optimal control design techniques. The controller consists of a linear quadratic regulator with a state estimator, namely a Kalman observer. The structure is a cantilever beam containing a set of sensor/actuator PVDF/PZT ceramic piezoelectric patches bonded to the beam surface at the optimal location obtained for the first three vibration modes. The equations of motion of the beam are developed by using the assumed modes technique for flexible structures in infinite-dimensional models. This paper uses a method of minimizing the effect of the removed higher order modes on the low frequency dynamics of the truncated model by adding a zero frequency term to the low order model of the system. A measure of the controllability and observability of the system based on the modal cost function for flexible structures containing piezoelectric elements (intelligent structures) is used. The observability and controllability measures are determined especially to guide the placement of sensors and actuators, respectively. The experimental and numerical transfer functions are adjusted by using an optimization procedure. Experimental results illustrate the optimal control design of a cantilever beam structure.

Trajectory modeling of robot manipulators in the presence of obstacles

This paper presents two different strategies for the problem of the optimal trajectory planning of robot manipulators in the presence of fixed obstacles. The first strategy is related to the situation where the trajectory must pass through a given number of points. The second strategy corresponds to the case where only the initial and final points are given. The optimal traveling time and the minimum mechanical energy of the actuators are considered together to build a multiobjective function. The trajectories are defined using spline functions and are obtained through offline computation for online operation. Sequential unconstrained minimization techniques (SUMT) have been used for the optimization. The obstacles are considered as three-dimensional objects sharing the same workspace performed by the robot. The obstacle avoidance is expressed in terms of the distances between potentially colliding parts. Simulation results are presented and show the efficiency of the general methodology used in this paper.

Optimization of aircraft structural components by using nature-inspired algorithms and multi-fidelity approximations

In this work, a flat pressure bulkhead reinforced by an array of beams is designed using a suite of heuristic optimization methods (Ant Colony Optimization, Genetic Algorithms, Particle Swarm Optimization and LifeCycle Optimization), and the Nelder-Mead simplex direct search method. The compromise between numerical performance and computational cost is addressed, calling for inexpensive, yet accurate analysis procedures. At this point, variable fidelity is proposed as a tradeoff solution. The difference between the low-fidelity and high-fidelity models at several points is used to fit a surrogate that corrects the low-fidelity model at other points. This allows faster linear analyses during the optimization; whilst a reduced set of expensive non-linear analyses are run “off-line,” enhancing the linear results according to the physics of the structure. Numerical results report the success of the proposed methodology when applied to aircraft structural components. The main conclusions of the work are (i) the variable fidelity approach enabled the use of intensive computing heuristic optimization techniques; and (ii) this framework succeeded in exploring the design space, providing good initial designs for classical optimization techniques. The final design is obtained when validating the candidate solutions issued from both heuristic and classical optimization. Then, the best design can be chosen by direct comparison of the high-fidelity responses.

Impedance-based Health Monitoring for Aeronautic Structures using Statistical Meta-modeling

In this work, techniques of impedance-based structural health monitoring are applied to aeronautical structures using statistical meta-modeling methods. First, a procedure is developed to find the best test conditions through factorial designs. Also, Taguchi robustness techniques are used to reduce noise influence in damage detection processes. Further, based on meta-models, a procedure is developed for damage identification and characterization, as applied to a vertical fin of an unmanned aerial vehicle (UAV). Structural changes are obtained by using localized adding masses at several determined points along the structure. Finally, by using two meta-models, namely a probabilistic neural network model and a surface response model, it is possible to identify as well as to characterize damage in the structure.