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

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

Investigation of earthquake and microtremor ground motions

The nature of strong earthquake ground shaking has been investigated based on a study of 15 accelerograms recorded at El Centro in southern California. It is concluded that the characteristics of the source mechanism and the transmission path play a dominant role in determining the details of strong ground shaking at the site. No local site periodicities could be clearly identified, which suggests that source and transmission path effects overshadow the influence of local site conditions. The method of using microtremor measurements to determine local site characteristics has been tested by direct comparison with strong motion measurements. Microtremor ground motions were recorded at five sites in the El Centro area and measurements were repeated at three of these sites after a period of 24 hours. These low amplitude ground motions have been found to be widely different from the motions caused by strong earthquake ground shaking. Their nonstationary nature over a period of a day or so makes the interpretation of such data from a single microtremor measurement very unreliable. It has been concluded that these microtremor ground motions are forced oscillations of the ground caused by nearby sources of excitation. The microtremor acceleration spectra do not indicate prominent peaks that could be correlated with local site conditions. At this site the use of microtremor measurements to define local subsoil conditions would evidently not be feasible

Variations of strong earthquake ground shaking in the Los Angeles area

Accelerograms recorded at six stations in the metropolitan Los Angeles area during the Borrego Mountain, 1968, the Lytle Creek, 1970, and the San Fernando, 1971, earthquakes in southern California have been studied. In comparing the ground motions recorded during different earthquakes at each of the six stations and in correlations of these motions recorded at different stations during the same earthquake, those aspects of the analysis which emerge from this study and are relevant for seismic zoning have been emphasized. It has been found that the patterns of strong ground shaking in this area depend predominantly on the mechanism and the distance of an earthquake source from a recording station and that the local soil conditions played only a minor role in modifying the ground motion at this particular area. It has been shown that gross spectral characteristics of ground motion recorded at various stations can be approximately related by the seismic moment at the low-frequency end and by the stress drop at the high-frequency end

The Fourier transform, response spectra and their relationship through the statistics of oscillator response

The concept of the Damped Fourier Transform (D. F. S.) has been developed through an understanding of the nature of the response of a damped oscillator to input ground accelerations. It has been shown that such a transform serves as a lower bound to the corresponding damped velocity spectrum curves. A review of the statistics of the maxima of a random function has been done and its application to the determination of response spectrum estimates has been studied. Such simple statistical estimates have been found to be very useful in improving our physical understanding of response spectra

Damped Fourier spectrum and response spectra

This paper describes the physical relationships that exist between the Fourier transform and the response spectrum of a strong-motion accelerogram. By developing the new concept of the “Damped Fourier Spectrum” (D.F.S.), we show that the velocity and displacement of the damped oscillator can be represented by a linear combination of the real and imaginary parts of the D.F.S. and by the initial conditions. The D.F.S. represents a new way of “smoothing” the classical Fourier Transform by using a physically based filter