Optimal Sensor Locations for Structural Identification

The optimum sensor location problem, OSLP, may be thought of in terms of the set of systems, S, the class of input time functions, I, and the identification algorithm (estimator) used, E. Thus, for a given time history of input, the technique of determining the OSL requires, in general, the solution of the optimization and the identification problems simultaneously. A technique which uncouples the two problems is introduced. This is done by means of the concept of an efficient estimator for which the covariance of the parameter estimates is inversely proportional to the Fisher Information Matrix

Nonparametric identification of a class of nonlinear close-coupled dynamic systems

A nonparametric identification technique for the identification of close coupled dynamic systems with arbitrary memoryless nonlinearities is presented. The method utilizes noisy recorded data (acceleration, velocity and displacement) to identify the restoring forces in the system. The masses in the system are assumed to be known (or fairly well estimated from the design drawings). The restoring forces are expanded in a series of orthogonal polnomials and the coefficients of these polynomial expansions are obtained by using least square fit method. A particularly simple and computationally efficient method is proposed for dealing with separable restoring forces. The identified results are found to be relatively insensitive to measurement noise. An analysis of the effects of measurement noise on the quality of the estimates is given. The computations are shown to be relatively quick (when compared say to the Wiener identification method) and the core storage required relatively small, making the method suitable for onboard identification of large space structures

Explicit Solution to the Full Nonlinear Problem for Satellite Formation-keeping

peer reviewedThis paper presents simple and exact formation-keeping guidance schemes that use a new method that is rooted in some recent advances in analytical dynamics. As a result of this new approach, explicit control inputs to exactly maintain a given formation configuration are easily determined using continuous thrust propulsion systems. The complete nonlinear problem is addressed, and no linearizations and/or approximations are made. The approach provides a marked improvement over existing results in that the control forces, which cause geometric formation-keeping constraints to be exactly satisfied for arbitrary reference orbits, are found in closed form. For Keplerian reference orbits, a much simpler and explicit expression for the control needed to exactly satisfy formation-keeping constraints than hereto available is obtained. The paper also includes explicit control results when the follower is inserted into orbit with incorrect initial conditions, as usually happens in practice. The Hill reference frame, which is often more intuitive for formation-keeping, is used in the analysis. While this paper takes an example of a projected circular formation, the methodology that is developed can be applied to any desired configuration or orbital requirements. Extensive computational simulations are performed to demonstrate the ease of implementation, and the numerical accuracy provided by the approach developed herein

First Integrals and Solutions of Duffing-Van der Pol Type Equations

A simple transformation is used to obtain the first integrals and the solutions of the Duffing–van der Pol type equation under certain conditions. It is shown that the system can be totally integrable and this total integrability admits new solutions. The new solutions require weaker conditions on the system’s parameters than hereto known

Reproducibilty of partial weight bearing

Objectives: To find out whether partial weight bearing can be reproduced and retained. Design: In vivo experiment in normal subjects. Intervention: Training for partial weight bearing (25% of body weight) using bathroom scales. Main outcome measurement: Reproducibility on force platform immediately after training and after 60 min. Results: Twelve subjects were asked to reproduce 25% of their body weight through either the dominant or non-dominant limb on force platform after three practice attempts on bathroom scales with concurrent visual feedback. No feedback was provided after the measurements on force plate. The process was repeated after 1 h without any practice sessions in the interim period to find out if the weight practised could be retained. The mean 0-min reading was found to be 25.9% of body weight while the mean 60-min reading was found to be 24.4%. The p-value for the difference between the two means was found to be 0.3841. Conclusions: This study indicates that partial weight bearing instructions can be quantified and graded. Simple bathroom scales are sufficient to educate the patients and this can be practised at home after an initial period of supervision

Parkfield, California, earthquake of June 27, 1966: A three-dimensional moving dislocation

Recordings from five strong-motion accelerograph stations have been used to derive a three-dimensional dislocation model for the Parkfield Earthquake. The model consists of a buried fault which extends from a depth of 3 km to a depth of 9 km below the ground surface. It appears from the analysis, which considers various fault lengths, that the zone of significant faulting was the 20-km-long northwestern section of the fault. The rupture velocity has been found to be between 2.4 and 2.5 km/sec and the dislocation amplitudes have been found to be about 120 cm. There have been comparisons made of the model results with geodetic data on static deformations and creep measurements following the event. In contrast with several other source mechanism studies of the Parkfield event, this model yields a picture which appears to be very consistent with both the dynamic strong-motion measurements as well as the available geodetic and creep data

The identification of building structural systems. II. The nonlinear case

This paper models a building structure as a nonlinear feedback system and studies the effects of such a system model on the structural response to strong ground shaking. Nonlinear kernels arising in the identification procedure have been investigated and an error analysis presented. Applications of the Weiner method in studying the response of a reinforced concrete structure to strong ground shaking have been illustrated. The nature of the second order kernels has been displayed and the nonlinear contribution to the response at the roof level, during strong ground shaking, has been determined

Comparison of earthquake and microtremor ground motions in El Centro, California

Strong earthquake ground shaking has been investigated by the study of 15 events recorded in El Centro, California. The strong-motion records analyzed show that no simple features (e.g., local site conditions) govern the details of local ground shaking. Any effects of local subsoil conditions at this site appear to be overshadowed by the source mechanism and the transmission path, there being no distinctly identifiable site periodicities. Microtremor measurements have been taken in the area surrounding the strong-motion site. The objective was an investigation of possible correlations with strong ground motions and the analysis of site-response characteristics. Basic difficulties in ascertaining local site conditions through such low-amplitude ground motions are illustrated. It has been found that in this area microtremor and earthquake processes are widely different in character, there being little to no correlation between the ground's response to earthquakes and to microtremor excitations. Microtremors have been found to be nonstationary over periods of about a day or so, introducing further uncertainties into inferences from such measurements

Characterization of response spectra through the statistics of oscillator response

This paper presents the physical relationships that exist between the response spectra and the Fourier Transform of strong-motion accelerograms through the extreme value statistics of oscillator response. Under the assumption of a stationary response, it has been shown that the spectrum value depends only on two parameters: arms, the root-mean-square-value of the response, and, ɛ, a parameter which measures the distribution of the energy among the various frequencies. The influence of these parameters on the response statistics together with their physical meaning in terms of the oscillator's characteristics have been studied. Comparisons with the Damped Fourier Transform (Udwadia and Trifunac, 1973) computed velocity spectra and the statistically calculated maximum response are presented for three typical accelerograms. The results indicate that response spectra based on statistical computations lead to good first approximations of the actual response to strong ground motion. In addition to characterizing the response spectrum with statistical curves expressing the expected value and the most probable value of the peak response, the 5 and 95 per cent confidence levels are also indicated, thus giving the lower and upper bounds for these statistical spectral estimates. These confidence levels delineate the 90 per cent confidence interval

An extension of Gauss's principle of least constraint

International audienceGauss's principle of least constraint is reformulated to cover cases in which the constraint forces may do positive or negative work on a system in a virtual displacement. This is needed to deal conveniently with cases in which, for example, friction is significant