Patrick Guillaume

Crest-factor minimization using nonlinear Chebyshev approximation methods

Low crest-factor of excitation and response signals is desirable in transfer function measurements, since this allows the maximization of the signal-to-noise ratios (SNRs) for given allowable amplitude ranges of the signals. The authors present a new crest-factor minimization algorithm for periodic signals with prescribed power spectrum. The algorithm is based on approximation of the nondifferentiable Chebyshev (minimax) norm by l/sub p/-norms with increasing values of p, and the calculations are accelerated by using FFTs. Several signals related by linear systems can also be compressed simultaneously. The resulting crest-factors are significantly better than those provided by earlier methods. It is shown that the peak value of a signal can be further decreased by allowing some extra energy at additional frequencies. >

Frequency-domain system identification using non-parametric noise models estimated from a small number of data sets

Abstract This paper discusses the problem of identifying a linear system from the frequency data when the measurements of the input and the output signals are both disturbed with noise. A typical example of such a problem is the identification of a system in a feedback loop. It is known that this problem can be solved using errors-in-varaibles methods if the covariance matrices of the disturbing noise (on input and output measurements) are a priori known. It is shown that the exact covariance matrices can be replaced by the sample covariance matrices: the system can be identified from the sample means and sample covariance matrices calculated from a (small) number M of independently repeated experiments. It is shown that under these conditions the estimates are still strongly consistent for an increasing number of data points N in each experiment ( N → ∞) if M ≥ 4. The loss in efficiency is quantified ( M ≥ 6), and the expected value of the cost function ( M ≥ 4) and its variance ( M ≥ 6) are calculated.

Operational Modal Analysis for Estimating the Dynamic Properties of a Stadium Structure during a Football Game

During a football game, the ambient vibrations at the roof of a football stadium were recorded. A very large data set consisting of 4 hours of data, sampled at 80 Hz, is available. By a data reduction procedure, the complete data set could be analysed at once in a very short time. The data set was also split in shorter segments corresponding to certain events before, during and after the game to investigate the influence of varying operational conditions on the dynamic properties.

ON-LINE MONITORING OF FATIGUE CRACKS USING ULTRASONIC SURFACE WAVES

During the last decade many techniques were developed to detect fatigue cracks, and estimate their location and size. Unfortunately, most of the currently available nondestructive testing methods are off-line: the operational (or fatigue) loading and the inspection are considered as two distinct stages. Mostly, the loading should be released before inspection can take place, and sometimes the device under test even has to be disassembled. In this article, an experimental methodology based on ultrasonic surface waves will be developed to continuously inspect a structure during its operation. The proposed method uses spectral information of transmitted surface waves at several working points of the operational load. Simple statistical indicators of the transmitted wave energy during loading are introduced in order to be able to monitor the structural health on-line. As a validation experiment, a propagating fatigue crack in a sinusoidally loaded beam will be considered. In addition, a comparison with an off-line method is made, showing that the on-line method is also much more sensitive.

Operational modal parameter estimation of MIMO systems using transmissibility functions

Operational modal parameter estimation (OMA) techniques perform system identification without or with only limited knowledge of the operational inputs acting on the system. However, most of the current operational identification techniques impose multiple conditions on the spectral content of the unknown inputs. As a consequence, modeling errors occur if these assumptions are not met. Therefore, there is a general interest in operational identification techniques that can operate independent of the unknown input spectra. This paper introduces poly-reference Transmissibility based Operational Modal Analysis (pTOMA). pTOMA uses parametrically estimated transmissibility functions associated with different loading conditions to obtain the system eigenvalues and eigenvectors using output-only data. Unlike most OMA techniques no strong assumptions are necessary considering the input spectrum. The method is therefore able to correctly identify the system parameters while the excitation may contain (varying) harmonics or strong coloration. A framework to use pTOMA is formulated, the algorithm is introduced and the claimed properties are illustrated by means of a numerical experiment.

Maximum likelihood identification of non-stationary operational data

Abstract In-operation modal analysis has become a valid alternative for structures where a classic input–output test would be difficult if not impossible to conduct. Due to practical considerations, measurements are sometimes performed in patches (roving sensor setups) instead of covering the entire structure at once. In practice, one is often confronted with non-stationary ambient excitation sources (e.g., wind, traffic, waves, etc.). Since the scaling of operational mode shape estimates depends on the unknown level of the ambient excitation, an extra effort is required in order to correctly merge the different parts of the mode shapes. In this contribution, two different approaches, for merging operational mode shapes from non-stationary data, are proposed. Both methods are based upon a single maximum likelihood estimation procedure. For comparison and validation, both techniques were applied to non-stationary data sets obtained by scanning laser vibrometry as well as the Z24 bridge bench mark data.

Development of an adaptive response surface method for optimization of computation-intensive models

In general, optimization techniques involve numerous repeated objective function evaluations. As a consequence, optimization times can become very large depending on the complexity of the model to be optimized. This manuscript describes the development of an adaptive response surface method for optimization of computation-intensive models, capable of reducing optimization times. The response model to be optimized is not built from a pre-defined number of design experiments but is adapted and refined during the optimization routine. Different approximation models are applicable in combination with the developed optimization technique. The proposed optimization technique is evaluated on a standard test problem as well as a finite element model design optimization with multiple parameters.

Optimized Excitation Signals for MIMO Frequency Response Function Measurements

Many different excitation signals can be chosen for the nonparametric frequency response function measurements of a linear multiple-input-multiple-output (MIMO) system. In the presence of output noise they will result in different signal-to-noise ratios (SNRs) of the frequency response function measurements. In this paper, these effects are analyzed and compared for three classes of multisine excitations: random multisines, approximately orthogonal random multisines, and orthogonal random multisines, taking also into account the crest-factor minimization. It is shown that the orthogonalization of the inputs yields an essential increase in the measured SNR

Box–Jenkins identification revisited—Part III: Multivariable systems☆

Abstract Part I of this series of three papers handles the identification of single input single output Box–Jenkins models on arbitrary frequency grids in an open and closed loop setting. Part II discusses the computational aspects and illustrates the theory on simulations and a real life problem. This paper extends the results of Parts I and II to multiple input multiple output systems. Contrary to the classical time domain approach, the presented technique does not require symbolic calculus for multiple output polynomial Box–Jenkins models.

Trajectory Planning for the Walking Biped Lucy

A real-time joint trajectory generator for planar walking bipeds is proposed. In the near future this trajectory planner will be implemented on the robot “Lucy”, which is actuated by pleated pneumatic artificial muscles. The trajectory planner generates dynamically stable motion patterns by using a set of objective locomotion parameters as its input, and by tuning and exploiting the natural upper body dynamics. The latter can be determined and manipulated by using the angular momentum equation. Basically, trajectories for hip and swing foot motion are generated, which guarantee that the objective locomotion parameters attain certain prescribed values. Additionally, the hip trajectories are slightly modified such that the upper body motion is steered naturally, meaning that it requires practically no actuation. This has the advantage that the upper body actuation hardly influences the position of the Zero Moment Point. The effectiveness of the strategy developed is demonstrated by simulation results. A first simulation is performed under the assumption of perfect tracking by the controllers of the different actuators. This allows one to verify the effectiveness of the trajectory planner and to evaluate the postural stability. A second simulation is performed while taking the control architecture of the real robot into account. In order to have a more realistic simulation the proposed control architecture is evaluated with a full hybrid dynamic simulation model of the biped “Lucy”. This simulator combines the dynamical behaviour of the robot with the thermodynamical effects that take place in the muscle-valves actuation system. The observed hardware limitations of the real robot and expected model errors are taken into account in order to give a realistic qualitative evaluation of the control performance and to test the robustness.