Generation of Fourier amplitude spectra and power spectral density functions compatible with orientation-independent design spectra for bidirectional seismic analyses of nuclear facilities

A spectral description for extreme sea states offshore Denmark Part II: Directional spreading function

The Bridge Engineering Laboratory in Kitami Institute of Technology, Japan has introduced a number of different damage identification techniques to detect structural damage and identify its location utilizing piezoelectric actuators as a localized excitation source. Several spectral functions, such as cross spectral density, power spectral density, phase angle and transfer function estimate, were used to estimate the dynamic response of the structure. Each function’s magnitude, measured in a specified frequency range, is used in the damage identification methods. The change of the spectral function magnitude between the baseline state and the current state is then used to identify the location of possible damage in the structure. It is then necessary to determine which spectral function is best able to estimate the dynamic response and which algorithm is best able to identify the damage. The first part of this paper compares the performance of different spectral functions when their magnitude is used in one damage identification algorithm using experimental data from a railway steel bridge. The second part of this paper compares the performance of different damage identification algorithms using the same data.

Reduction of leakage and increase of resolution in power spectral density and coherence functions

The development of a suitable set of input ground motions is crucial for dynamic time history analyses. The US Nuclear Regulatory Commission (NRC) requires that these motions generate response spectra closely matching the plant’s design spectrum. Additionally, the NRC recommends verifying the motions’ power spectral densities (PSDs) against a target function to ensure sufficient energy across all frequencies. Current NRC guidelines in Standard Review Plan (SRP) provide a general method for creating target PSDs for any design spectrum. However, this method does not explicitly consider the influence of strong motion duration on the relationship between PSD and response spectrum. This article proposes an improved approach that incorporates the expected strong motion duration into the target PSD generation process. The method first constructs a Fourier amplitude spectrum (FAS) compatible with both the design spectrum and the expected strong motion duration. Subsequently, a large set of synthetic motions based on this FAS is used to construct the target PSD function. It is shown that current target PSD functions tabulated in SRP 3.7.1 implicitly infer an expected strong motion duration of approximately 9 s. The proposed method can be used to construct target PSDs tailored to different strong motion durations.

Signal processing of flutter flight test data enables verification of aircraft flutter design, and the signal from a flutter flight test excited by atmospheric turbulence is a particularly important form of the flutter test. Owing to the randomness of atmospheric turbulence excitation, multi-channel analysis of turbulence responses at various positions in the same component can improve the analytical accuracy of flutter signal processing. The relationship between the maximum singular value of the multi-channel turbulence response power spectral density matrix and the system self-power spectral density function is elucidated herein using a frequency domain decomposition method. However, there is a contradiction in the power spectral density function between the spectral line density and the spectral line smoothing calculated based on the periodogram of the frequency domain decomposition. By applying an autoregressive spectral model, the power spectral density function of the turbulence response is calculated to achieve spectral line smoothing and sufficient spectral line density. Additionally, the power spectral density function is then used to construct the power spectral density function matrix of the multi-channel turbulence response, and the maximum singular value curve is calculated based on the singular value decomposition of each spectral pin. Finally, the modal parameters of the turbulence response signal are estimated via multi-modal frequency domain fitting. The developed approach is validated based on simulations and flutter flight test turbulence response signals.

When the structures are subjected to multi-input seismic waves, two methods which are spectral analysis and time history analysis, are considered. In this paper the data which are needed in the analyses are researched. The theoretical correlation functions and spectral density functions between acceleration, velocity and displacement in three cases, are obtained. Those three cases are (a) the same seismic waves, (b) the seismic waves which have the same wave and the time lag and (c) the seismic waves which have only different Fourier amplitude spectra. From mean values of several power spectral density functions in accelerations, one equation is made, and mean square power and cross power spectral density functions are obtained. As the time history analysis, the method (a) by Fourier trans-form and the method (b) that the simulation of the seismogragh is used, are studied. The method (a) is the way that the lower frequency part of the Fourier amplitude spectra is cut off. The relations of the maximum values of the result's acceleration, velocity and displacement, are given with the cut-off frequency ω_c. The best result is given when the cut-off frequency ω_c equals to 1.0. The method (b) is the way that uses the filter which is disital simulation of simple pendulum. The velocity is obtained by the filter of which the period is too long, and the displacement is obtained by the filter of which the period and the damping coefficient are respectively 2.0sec. and 0.8, and the displacement's amplification factor equals to 2.7.

For seismic analysis of nuclear structures, synthetic acceleration time histories are often required and are generated to envelop design response spectra following the U.S. Nuclear Regulatory Commission, Standard Review Plan (SRP) Section 3.7.1. It has been recognized that without an additional check of the power spectral density (PSD) functions, spectral matching alone may not ensure that synthetic acceleration time histories have adequate power over the frequency range of interest. The SRP Section 3.7.1 Appendix A provides a target PSD function for the Regulatory Guide 1.60 horizontal spectral shape. For other spectral shapes, additional guidance on developing the target PSD functions compatible with the design spectra is desired. This paper presents a general procedure for the development of target PSD functions for any practical design response spectral shapes, which has been incorporated into the recent SRP 3.7.1, Revision 4.

The sets of records developed for the SAC Steel Project are classified according to the level of seismic hazard and specific geographic region, and have been used extensively for structural response and seismic hazard analyses. This study presents a parametric analysis of these record data sets for generation of uniform hazard earthquake and near-field records. The record parameters define far-field characteristics such as power spectral density and envelope function, and near-field effects such as acceleration pulse, power spectral density and envelope function. The proposed method for generation of near-field records uses the decomposing capabilities of wavelet transform on earthquake records. A set of uniform hazard earthquake accelerograms and near-field ground motions is generated based on the record parameters. The generated uniform hazard earthquake accelerograms representing a uniform level of seismic hazard for a particular geographic region involves seismic hazard studies, calibrated attenuation relationships, and local site amplification models. In order to assess the reliability and efficiency of the presented method, the statistical response spectra obtained from the generated accelerograms have been compared with those from the actual records. The obtained results showed that there is a good compatibility between the response spectra of the generated and actual records in the most of the frequencies.

The wind-induced vibration of structure is very sensitive to the damping ratio of governing modes of interests. Research to identify the damping ratio from the structural response have been developed for several decades, however is still challenging. A novel estimation technique of damping ratio of a structure is proposed in this research, which is based on the integration of power spectral density (PSD) function. The damping ratio estimation concept is devised on the principle that the integration of PSD have a flattening effect of the external load spectral density so that the integral of spectral density function of decomposed mode can be very closed to the corresponding theoretical integral function. The damping ratio can be identified by comparing the two integral functions. In order to extract the damping ratio, the properties of the integral of theoretical spectral density function is examined, and it is also shown that the estimation technique is applicable to the modal response separated from a non-classically damped system. For the validation of the developed technique in this study, numerical analysis for the mathematical model and application for the site-situ measurement were carried out. From the verification process, it was shown that the technique to estimate the damping ratio is robust and reliable with high stability

Buildings and structures in many regions of the world are exposed to environmental factors that can cause damage or failure, making it essential to model these factors accurately in engineering. Stochastic dynamics are crucial for modelling environmental processes, such as earthquake ground motions and wind loads, which can be characterised by a power spectral density (PSD) function that determines the dominant frequencies and corresponding amplitudes of the process. However, when generating a load model described by a PSD function, uncertainties in the processes must be taken into account, which makes a reliable estimation of the PSD function challenging, especially with only limited data available. This study employs the recently developed imprecise PSD function by using a radial basis function network to optimise data-enclosing bounds that produce an interval-valued PSD function. With this approach, a data set in the frequency domain can be bounded for uncertainty quantification. The method described in this work consists of optimising best-case and worst-case PSD functions within the bounds, which are transformed into a separable evolutionary PSD function. The reliability of structures is determined by an upper and lower failure probability, taking into account the present uncertainties. Advanced interval propagation schemes are linked to the imprecise PSD function to determine the failure probabilities efficiently. The method is illustrated by means of three numerical examples.

The subject of this paper is the simulation of multi-dimensional, homogeneous, Gaussian stochastic fields using the spectral representation method. Following this methodology, sample functions of the stochastic field can be generated using a cosine series formula. These sample functions accurately reflect the prescribed probabilistic characteristics of the stochastic field when the number of terms in the cosine series is large. The ensemble-averaged power spectral density or autocorrelation function approaches the corresponding target function as the sample size increases. In addition, the generated sample functions possess ergodic characteristics in the sense that the spatially-averaged mean value, autocorrelation function and power spectral density function are identical with the corresponding targets, when the averaging takes place over the multi-dimensional domain associated with the fundamental period of the cosine series. Another property of the simulated stochastic field is that it is asymptotically Gaussian as the number of terms in the cosine series approaches infinity. The most important feature of the method is that the cosine series formula can be numerically computed very efficiently using the Fast Fourier Transform technique. The main area of application of this method is the Monte Carlo solution of stochastic problems in structural engineering, engineering mechanics and physics. Specifically, the method has been applied to problems involving random loading (random vibration theory) and random material and geometric properties (response variability due to system stochasticity).

Estimation of an imprecise power spectral density function with optimised bounds from scarce data for epistemic uncertainty quantification

Data-driven and physics-based interval modelling of power spectral density functions from limited data

We introduce a Riemannian metric on the cone of spectral density functions of discrete-time random processes. This is motivated by a problem in prediction theory, and it is analogous to the Fisher information metric on simplices of probability density functions. Interestingly, in either metric, geodesics and geodesic distances can be characterized in closed form. The goal of this paper is to highlight analogies and differences between the proposed differential-geometric structure of spectral density functions and the information geometry of the Fisher metric, and raise the question as to what a natural notion of distance between power spectral density functions is.

We investigate the electron-boson spectral density function, $I^2\chi(\omega,T)$, of CuO$_2$ plane in underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212) and underdoped YBa$_2$Cu$_3$O$_{6.50}$ (Y-123) using the Eliashberg formalism. We apply a new (in-plane) pseudogap model to extract the electron-boson spectral function. For extracting the spectral function we assume that the spectral density function consists of two components: a sharp mode and the broad Millis-Monien-Pines (MMP) mode. We observe that both the resulting spectral density function and the intensity of the pseudogap show strong temperature dependences: the sharp mode takes most spectral weight of the function and the peak position of the sharp mode shifts to lower frequency and the depth of pseudogap, $1-\tilde{N}(0,T)$, is getting deeper as temperature decreases. We observe also that the total spectral weight of the electron-boson density and the mass enhancement coefficient increase as temperature decreases. We estimate fictitious (maximum) superconducting transition temperatures, $T_c(T)$, from the extracted spectral functions at various temperatures using a generalized McMillan formula. The estimated (maximum) $T_c$ also shows a strong temperature dependence; it is higher than the actual $T_c$ at all measured temperatures and decreases with temperature lowering. Since as lowering temperature the pseudogap is getting stronger and the maximum $T_c$ is getting lower we propose that the pseudogap may suppress the superconductivity in cuprates.