MS5.1 - Computational methods for stochastic dynamics

In this paper a novel approach is developed for the estimation of evolutionary cross-spectral density functions of bivariate nonstationary random processes that can be used as models of earthquake accelerograms. Specifically, the spectra are estimated by determining the statistical moments of an energy-like quantity of lightly damped single degree-of-freedom (SDOF) linear systems (filters) excited by the stochastic seismic processes [1]. This sequence of SDOF filters is characterized by a varying natural frequency, thus providing a resolution of the bivariate processes along the frequency domain [2]. Notably, an appropriate smoothing procedure is also incorporated, relying on the use of the so-called Savitzky-Golay moving average filter [3]. This is done for obtaining reliable spectra based on a relatively small number of available records. Further, an appropriate model is introduced to capture the shape of the energy-like quantities associated with the output of the filters, leading to enhanced accuracy in the estimated spectra. Finally, several examples involving both simulated and measured data are used to assess the usefulness and reliability of the proposed approach. References [1] Spanos, P.D., 1980, Probabilistic Earthquake Energy Spectra Equations. Journal of the Engineering Mechanics Division, 106: 147-159. [2] Spanos, P.D., Tein, W.Y., Ghanem, R.G., 1996, Heuristic Spectral Estimation of Bivariate nonstationary processes. Meccanica, 31: 207-218. [3] Savitzky, A., and Golay, M.J.E., 1964, Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Analytical Chemistry, 36: 1627–1639.

ORAL presentation is preferred A NOVEL STOCHASTIC METHODOLOGY FOR THE GENERATION OF ARTIFICIAL SEISMIC ACCELEROGRAMS H. Yanni1, M. Fragiadakis1, and I. P. Mitseas1,2 1 School of Civil Engineering, National Technical University of Athens, Greece 2 School of Civil Engineering, University of Leeds, United Kingdom heragian@mail.ntua.gr; mfrag@mail.ntua.gr; Imitseas@mail.ntua.gr Keywords: artificial accelerograms, non-stationary stochastic processes, spectrum compatible, dispersion, ground motion model Abstract. Dynamic structural analysis requires the use of suites of accelerograms that represent the input ground motion. Hazard consistency may be achieved by matching these records either to a design spectrum or to a ground motion model (GMM). The latter approach is more accurate and provides additional detailed hazard information for the site of interest. Besides, the accelerograms adopted for the seismic simulations can be either recorded, or artificially generated. In this setting, seismic codes (e.g. Eurocode 8) recommend the use of artificial accelerograms; however, they do not propose any specific method allowing engineers to resort in a number of pertinent models proposed in the relevant literature. The herein study proposes a novel methodology for the stochastic generation of fully non-stationary artificial accelerograms that are compatible with a target spectral mean and a target variability. Due to the random nature of seismic actions, artificial ground motion time histories can be represented as stochastic processes using spectral representation techniques [1]. Existing spectrum-based models [2,3] are extended in order to introduce controlled variability which is consistent with the seismic hazard defined by a GMM. Therefore, given the seismic scenario (Mw, R) and the soil conditions, the target spectral mean and variability for each period is obtained from the GMM. Based on those data, multiple target response spectra are generated from a random vector that follows the normal distribution. Artificial accelerograms whose response spectra individually match the produced spectra are subsequently generated. The basis for generating spectrum-compatible accelerograms relies on the relationship between the values of the power spectral density (PSD) function of the ground motion and the response spectral values for a given damping ratio [4,5]. Corrective iterations in the frequency domain are performed in order to achieve enhanced matching and to improve the control of variability. Lastly, the proposed methodology provides with suites of fully nonstationary artificial ground motion time histories whose response spectral mean and variability match those of the assigned GMM. [1] M. Shinozuka, G. Deodatis, Simulation of Stochastic Processes by Spectral Representation, Applied Mechanics Reviews 44(4):191-204, 1994. [2] A. Preumont, The generation of non-separable artificial earthquake accelerograms for the design of nuclear power plants, Nuclear Engineering and Design 88(1):59-67, 1985. [3] P. Cacciola, A stochastic approach for generating spectrum compatible fully nonstationary earthquakes, Computers & Structures, 88(15-16):889-901, 2010. [4] E.H. Vanmarcke, D.A. Gasparini, Simulated earthquake ground motions. In: Proceedings of the 4th international conference on structural mechanics in reactor technology, K1/9, San Francisco, CA, USA, 1977. [5] P. Cacciola, P. Colajanni, G. Muscolino, Combination of Modal Responses Consistent with Seismic Input Representation, Journal of Structural Engineering 130(1):47-55, 2004.

This paper is dedicated to identifying the damage of simple structures by the Hamiltonian Monte Carlo(HMC) method. The data studied in this paper comes from the response of numerically simulated simple structures with a randomly distributed damage area. The uncertainties innated in the randomly generated damage distribution and structural material distribution are quantified by a set of random variables which is derived from the well-known spectral decomposition method Karhunen-Loéve expansion method. The fundamental assumption for this approach is that the structural damage is manifested in the changes in the low to mid-frequency vibration response of the structure. Hence point-to-point frequency response functions at a distributed set of locations are adopted to identify structural degradation parameters with Bayesian inference. Thus, a mature Bayesian algorithm is applied to parameterize the whole inverse identification process, and then the HMC method is utilized to identify the random variables in a high dimensional space. Some good results have been observed after applying this identification algorithm on a simply supported beam and a two-sided pinned plate, which proves the validity and accuracy of the derived algorithm.

In numerous regions of the world, buildings and structures are exposed to environmental influences and are thus prone to damage or failure. To design safe structures or assess the reliability of existing structures, the modelling of environmental processes is crucial in engineering, particularly in stochastic dynamics. Examples of such environmental processes that can be described by stochastic processes include earthquake ground motions and wind loads. The power spectral density (PSD) function characterises such processes in the frequency domain and thus determines the signal's dominant frequencies and corresponding amplitudes. When generating a load model described by a PSD function, the uncertainties present in the time signals must be taken into account, which complicates the reliable estimation of such a PSD function. Particularly when only a limited amount of data is available, it is not possible to obtain accurate statistics from this data to derive probabilistic models. In such a case, the specification of bounds representing the limited data set will be practical. In this work, a radial basis function network is utilised to produce basis functions with corresponding weights that are optimised to produce data-enclosing bounds, thus an interval-valued PSD function results. Instead of relying on a discrete or probabilistic representation, the spectral densities at each frequency are described by means of optimised intervals. The proposed method utilises real data records and involves optimising such bounds for the evolutionary PSD function to provide a more realistic description of an environmental process in frequency domain. Advanced interval propagation schemes are linked to the imprecise PSD in a realistic simulation to efficiently determine the reliability of buildings and structures. Thus, the response behaviour and failure probabilities of the structure can be evaluated under consideration of present uncertainties.