[EQ] Fourier transform

In the previous article, I introduced the Fourier series which describes a periodic signal using an infinite sum of weighted sinusoid functions. However, since most of the signals we care about in practice are not periodic, the application of the Fourier series to an engineering problem is limited. When dealing with aperiodic (non-periodic) signals, FourierContinue

[EQ] Fourier series of rectangular pulse

In the previous article, the introduction of the Fourier series is described. To further understand the Fourier series, a simple example is presented in this article. The example is a pulse signal whose period is 2pi (angular frequency is 1) and its graphical representation is shown in Figure 1. Figure 1. Rectangular pulse signal FigureContinue

[EQ] Fourier series

Fourier series is a way of describing a periodic function as an infinite sum of weighted sine and cosine functions which is analogous to a Taylor series. Note that a series roughly represents a description of the operation of adding infinitely many quantities. Every periodic continuous-time signal can be written as a sum of sinusoidal, whichContinue

[EQ] Introduction to the Z-transform

It is widely known that Fourier transform plays a critical role in many engineering problems, especially deals with signals. Similar to the fact that the Laplace transform is the generalized version of the continuous Fourier transform, Z-transform can be seen as a generalization of discrete time Fourier transform (DTFT). It should be noted that DTFTContinue

[Reliability] Reliability of deterioration system

Since deterioration can lead to degradation of structural systems’ performance and eventually result in structural failure, it is important to assess the reliability of deteriorating structural systems. Assessment of structural deterioration is an instance of time-variant reliability analysis problems, which can be represented as a first-passage problem. Due to intrinsic difficulties stemming from chaotic behaviorsContinue

[Reliability] System reliability analysis using FORM

Since structural systems are usually comprised of a large number of components having different roles in the system, the performance limit subjected to external loads cannot be justified by a single limit-state function. Thus, in general, the structural performance is characterized by multiple limit-state functions, and investigation of the most important random variables or estimationContinue

[Reliability] Functions of Random Variables

With the advent of computational power and the development of various machine learning algorithms, onerous and complicated structural and dynamic analyses are replaced by simple regression or classification functions. Deep learning-based seismic responses prediction of nonlinear structural systems is one of the successful machine learning application examples in the earthquake engineering field (Kim et al.,Continue

[EQ] Seismic Field Test

The in-plane shear and compression wave velocity profiles of soil and rock along with depth contain their dynamic properties under earthquakes such as Poisson’s ratio and shear moduli. Such information may play a critical role in evaluating the seismic capacity of structural systems, assessing liquefaction potential of the site, and designing geotechnical structures. Various methodsContinue

[EQ] Newmark Sliding Block Analysis

Newmark sliding block analysis is one of the popular approaches that estimates the amount of deformation that will occur in soil slope (also embankments and dams) during seismic excitation. The method hinges on the assumption that a failed slope is a rigid block on an inclined plane. As shown in Figure 1, the stability ofContinue

[EQ] Derive Transfer Function from the State-Space Model

Transfer function or frequency response function is defined as the ratio of the output of a system to its input in the Laplace and frequency domain, respectively. When we have the input and output functions of a system as U(s) and Y(s), respectively, the transfer function is defined as In this article, I want toContinue