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Dynamical systems approach of modelling
Published in A. W. Jayawardena, Environmental and Hydrological Systems Modelling, 2013
‘Surrogate data’ refers to a data set similar to the observed one and consistent with the null hypothesis. Surrogate data have the same properties as the original data but the non-linear phase relations are destroyed. Application of the method of surrogate data involves a null hypothesis against which observations are tested, and a discriminating statistic. If the discriminating statistic for the observed data is different from what is expected under the null hypothesis, then the null hypothesis can be rejected. In the method of surrogate data, the distribution of the discriminating statistic is estimated by generating (Monte Carlo simulation) an ensemble of surrogate data sets that will have the same statistical properties (e.g., mean, variance, autocorrelation, etc.) as those of the observed data. For each surrogate data set, the discriminating statistic from which the distribution can be approximated is computed. The method of surrogate data is an application of the ‘bootstrap’ method.
Estimating the primary crack spacing of reinforced concrete structures: Predictions by neural network versus the innovative strain compliance approach
Published in Mechanics of Advanced Materials and Structures, 2022
Regimantas Ramanauskas, Gintaris Kaklauskas, Aleksandr Sokolov
Employing surrogate data sets, that mimic the statistical behavior of the original real data, provides an additional layer of quality checks on the neural network performance. It was demonstrated that in cases of noisy and limited data sets, even surrogate data sets can provide well performing neural networks [41]. Hence, the best performing neural network trained on surrogate data sets act as a benchmark for real data trained ANNs that must outperform the fake ones. In case the data set input parameters are strongly correlated, contain intricate relationships, there should be a large gap between the coefficients of correlation between the real data set trained ANNs and the surrogate data ones, where the latter should approach R→0. In the context of the present study, it is expected the gap to be significant due to the well-established knowledge of influence of selected input physical and mechanical parameters on the crack spacing. The surrogate data set was generated by employing the Kolmogorov-Smirnov test and random small perturbations to the data.
Identification of flame transfer functions in the presence of intrinsic thermoacoustic feedback and noise
Published in Combustion Theory and Modelling, 2018
Stefan Jaensch, Malte Merk, Thomas Emmert, Wolfgang Polifke
In order to investigate the influence of these reflections on the LES/SI approach, the network model shown in Figure 2 was modified. Instead of the non-reflective inflow and outflow BCs, used for the studies discussed in the previous sections, a low-pass filter according to Equation (33) was applied. In Figure 10, the dependency of the results of the LES/SI approach on the cut-off frequency fc of this filter is shown. A high cut-off frequency corresponds to a large value of the relaxation parameter. Up to a cut-off frequency of 750 Hz, only a small influence of the relaxation parameter on the model identified is observed. For a cut-off frequency of 750 Hz and above (not shown here) the error suddenly increases. For these values the thermoacoustic network model is linearly unstable. This means that the amplitude of the instability grows infinitely in the generated time series as amplitude saturation is governed by nonlinear mechanisms, which are not captured by the linear surrogate data model. The linear unstable mode here can be attributed to the ITA mode of the BRS burner [36,37], which is independent of the duct length used and is thus not suppressed by using compact duct sections in the surrogate data model. An accurate identification from the surrogate data model is not possible any more.
A neuronal population model based on cellular automata to simulate the electrical waves of the brain
Published in Waves in Random and Complex Media, 2021
Ali Khaleghi, Mohammad Reza Mohammadi, Kian Shahi, Ali Motie Nasrabadi
In addition to visual inspection, we performed various quantitative linear and nonlinear analyzes to more accurately compare the time series generated by the network and the real data. Therefore, we ran the CA network 40 times with the above parameters and saved the generated time series for further analysis. The method of surrogate data is used in subsequent analyzes to distinguish between nonlinearity and linearity as well as between pure stochasticity and chaoticity. This method was utilized because a linear stochastic time series can imitate a nonlinear chaotic process following a static nonlinear distortion [30]. Surrogate data are created based on [31] to mimic the original data, relating to their amplitude distribution and autocorrelation.