Introduction to linear and nonlinear programming

[1] Data analysis has been one of the core activities in scientific research, but limited by the availability of analysis methods in the past, data analysis was often relegated to data processing. To accommodate the variety of data generated by nonlinear and nonstationary processes in nature, the analysis method would have to be adaptive. Hilbert-Huang transform, consisting of empirical mode decomposition and Hilbert spectral analysis, is a newly developed adaptive data analysis method, which has been used extensively in geophysical research. In this review, we will briefly introduce the method, list some recent developments, demonstrate the usefulness of the method, summarize some applications in various geophysical research areas, and finally, discuss the outstanding open problems. We hope this review will serve as an introduction of the method for those new to the concepts, as well as a summary of the present frontiers of its applications for experienced research scientists.

https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2007RG000228

A review on Hilbert‐Huang transform: Method and its applications to geophysical studies

A simple and powerful method for simulating ground motions is to combine parametric or functional descriptions of the ground motion’s amplitude spectrum with a random phase spectrum modified such that the motion is distributed over a duration related to the earthquake magnitude and to the distance from the source. This method of simulating ground motions often goes by the name “the stochastic method.” It is particularly useful for simulating the higher-frequency ground motions of most interest to engineers (generally, f > 0.1 Hz), and it is widely used to predict ground motions for regions of the world in which recordings of motion from potentially damaging earthquakes are not available. This simple method has been successful in matching a variety of ground-motion measures for earthquakes with seismic moments spanning more than 12 orders of magnitude and in diverse tectonic environments. One of the essential characteristics of the method is that it distills what is known about the various factors affecting ground motions (source, path, and site) into simple functional forms. This provides a means by which the results of the rigorous studies reported in other papers in this volume can be incorporated into practical predictions of ground motion.

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Simulation of Ground Motion Using the Stochastic Method


 The spectral ratio between horizontal and vertical components (H/V ratio) of microtremors measured at the ground surface has been used to estimate fundamental periods and amplification factors of a site, although this technique lacks theoretical background. The aim of this article is to formulate the H/V technique in terms of the characteristics of Rayleigh and Love waves, and to contribute to improve the technique. The improvement includes use of not only peaks but also troughs in the H/V ratio for reliable estimation of the period and use of a newly proposed smoothing function for better estimation of the amplification factor. The formulation leads to a simple formula for the amplification factor expressed with the H/V ratio. With microtremor data measured at 546 junior high schools in 23 wards of Tokyo, the improved technique is applied to mapping site periods and amplification factors in the area.

Ground Motion Characteristics Estimated from Spectral Ratio between Horizontal and Verticcl Components of Mietremors.

Minimum Design Loads for Buildings and Other Structures provides requirements for general structural design and includes means for determining dead, live, soil, flood, wind, snow, rain, atmospheric ice, and earthquake loads, as well as their combinations, which are suitable for inclusion in building codes and other documents. This Standard, a revision of ASCE/SEI 7-05, offers a complete update and reorganization of the wind load provisions, expanding them from one chapter into six. The Standard contains new ultimate event wind maps with corresponding reductions in load factors, so that the loads are not affected, and updates the seismic loads with new risk-targeted seismic maps. The snow, live, and atmospheric icing provisions are updated as well. In addition, the Standard includes a detailed Commentary with explanatory and supplementary information designed to assist building code committees and regulatory authorities. Standard ASCE/SEI 7 is an integral part of building codes in the United States. Many of the load provisions are substantially adopted by reference in the International Building Code and the NFPA 5000 Building Construction and Safety Code. Structural engineers, architects, and those engaged in preparing and administering local building codes will find this Standard an essential reference in their practice. Note: New orders are fulfilled from the second printing, which incorporates the errata to the first printing.

Minimum Design Loads for Buildings and Other Structures

The motion of a building depends on the excitation, the coupling of the building to the ground, and the mechanical properties of the building. We separate the building response from the excitation and the ground coupling by deconvolving the motion recorded at different levels in the building and apply this to recordings of the motion in the Robert A. Millikan Library in Pasadena, California. This de- convolution allows for the separation of instrinsic attenuation and radiation damping. The waveforms obtained from deconvolution with the motion in the top floor show a superposition of one upgoing and one downgoing wave. The waveforms obtained by deconvolution with the motion in the basement can be formulated either as a sum of upgoing and downgoing waves, or as a sum over normal modes. Because these deconvolved waves for late time have a monochromatic character, they are most easily analyzed with normal-mode theory. For this building we estimate a shear velocity c 322 m/sec and a quality factor Q 20. These values explain both the propagating waves and the normal modes.

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Extracting the Building Response Using Seismic Interferometry: Theory and Application to the Millikan Library in Pasadena, California

This study examines the rationale of Hilbert-Huang transform (HHT) for analyzing dynamic and earthquake motion recordings in studies of seismology and engineering. In particular, this paper first p...

Hilbert-Huang transform analysis of dynamic and earthquake motion recordings

This paper presents a discrete-time wave-propagation method to calculate the seismic response of multistory buildings, founded on layered soil media and subjected to vertically propagating shear waves. Buildings are modeled as an extension of the layered soil media by considering each story as another layer in the wave-propagation path. The seismic response is expressed in terms of wave travel times between the layers and wave reflection and transmission coefficients at layer interfaces. The method accounts for the filtering effects of the concentrated foundation and floor masses. Compared with commonly used vibration formulation, the wave-propagation formulation provides several advantages, including simplicity, improved accuracy, better representation of damping, the ability to incorporate the soil layers under the foundation, and providing better tools for identification and damage detection from seismic records. Examples are presented to show the versatility and the superiority of the method.

Wave-Propagation Formulation of Seismic Response of Multistory Buildings

Dynamic property measurements of the moment-resisting steel-frame University of California, Los Angeles, Factor building are being made to assess how forces are distributed over the building. Fourier amplitude spectra
have been calculated from several intervals of ambient vibrations, a 24-hour period of strong winds, and from the 28 March 2003 Encino, California (M_L =2.9), the 3 September 2002 Yorba Linda, California (M_L=4.7), and the 3
November 2002 Central Alaska (M_w=7.9) earthquakes. Measurements made from the ambient vibration records show that the first-mode frequency of horizontal vibration is between 0.55 and 0.6 Hz. The second horizontal mode
has a frequency between 1.6 and 1.9 Hz. In contrast, the first-mode frequencies measured from earthquake data are about 0.05 to 0.1 Hz lower than those corresponding to ambient vibration recordings indicating softening
of the soil-structure system as amplitudes become larger. The frequencies revert to pre-earthquake levels within five minutes of the Yorba Linda earthquake. Shaking due to strong winds that occurred during the Encino earthquake dominates the frequency decrease, which correlates in time with the duration of the strong winds. The first shear wave recorded from the Encino and Yorba Linda earthquakes takes about 0.4 sec to travel up the 17-story building.

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Earthquake and Ambient Vibration Monitoring of the Steel-Frame UCLA Factor Building:

A concise review of the fheory of adaptive modeling, identification, and control of dynamic structural systems based on discrete‐time recordings is presented. Adaptive methods have four major advantages over the classical methods: (1) Removal of the noise from the signal is done over the whole frequency band; (2) time‐varying characteristics of systems can be tracked; (3) systems with unknown characteristics can be controlled; and (4) a small segment of the data is needed during the computations. Included in the paper are the discrete‐time representation of single‐input single‐output (SISO) systems, models for SISO systems with noise, the concept of stochastic approximation, recursive prediction error method (RPEM) for system identification, and the adaptive control. Guidelines for model selection and model validation and the computational aspects of the method are also discussed in the paper. The present paper is the first of two companion papers. The theory given in the paper is limited to that which is...

Erdal Safak

Papers

Extracting the Building Response Using Seismic Interferometry: Theory and Application to the Millikan Library in Pasadena, California

Hilbert-Huang transform analysis of dynamic and earthquake motion recordings

Wave-Propagation Formulation of Seismic Response of Multistory Buildings

Earthquake and Ambient Vibration Monitoring of the Steel-Frame UCLA Factor Building:

Adaptive Modeling, Identification, and control of dynamic structural Systems. I: Theory