Abstract: Bayesian approach can be used for parameter identification and extraction in state space models and its ability for analyzing sequence of data in dynamical system is proved in different literatures. In this paper, adaptive Kalman filter with Bayesian approach for identification of variances in measurement parameter noise is developed. Next, it is applied for estimation of the dynamical state and measurement data in discrete linear dynamical system. This algorithm at each step time estimates noise variance in measurement noise and state of system with Kalman filter. Next, approximation is designed at each step separately and consequently sufficient statistics of the state and noise variances are computed with a fixed-point iteration of an adaptive Kalman filter. Different simulations are applied for showing the influence of noise variance in measurement data on algorithm. Firstly, the effect of noise variance and its distribution on detection and identification performance is simulated in Kalman filter without Bayesian formulation. Then, simulation is applied to adaptive Kalman filter with the ability of noise variance tracking in measurement data. In these simulations, the influence of noise distribution of measurement data in each step is estimated, and true variance of data is obtained by algorithm and is compared in different scenarios. Afterwards, one typical modeling of nonlinear state space model with inducing noise measurement is simulated by this approach. Finally, the performance and the important limitations of this algorithm in these simulations are explained.
Abstract: High-speed turbomachine can experience significant centrifugal and gas bending loads. As a result, the compressor blades must be able to resist high-frequency oscillations due to surge or stall condition in flow field dynamics. In this paper, vibration characteristics of the 6th stage blade compressor have been examined in detail with, using 3-D finite element (FE) methods. The primary aim of this article is to gain an understanding of nonlinear vibration induced in the blade against different loading conditions. The results indicate the nonlinear behavior of the blade as a result of the amplitude of resonances or material properties. Since one of the leading causes of turbine blade failure is high cycle fatigue, simulations were started by specifying the stress distribution in the blade due to the centrifugal rotation. Next, resonant frequencies and critical speeds of the blade were defined by modal analysis. Finally, the harmonic analysis was simulated on the blades.
Abstract: In fields such as neuroscience and especially in cognition modeling of mental processes, uncertainty processing in temporal zone of signal is vital. In this paper, Bayesian online inferences in estimation of change-points location in signal are constructed. This method separated the observed signal into independent series and studies the change and variation of the regime of data locally with related statistical characteristics. We give conditions on simulations of the method when the data characteristics of signals vary, and provide empirical evidence to show the performance of method. It is verified that correlation between series around the change point location and its characteristics such as Signal to Noise Ratios and mean value of signal has important factor on fluctuating in finding proper location of change point. And one of the main contributions of this study is related to representing of these influences of signal statistical characteristics for finding abrupt variation in signal. There are two different structures for simulations which in first case one abrupt change in temporal section of signal is considered with variable position and secondly multiple variations are considered. Finally, influence of statistical characteristic for changing the location of change point is explained in details in simulation results with different artificial signals.
Abstract: This paper presents a prediction performance of
feedforward Multilayer Perceptron (MLP) and Echo State Networks
(ESN) trained with extended Kalman filter. Feedforward neural
networks and ESN are powerful neural networks which can track and
predict nonlinear signals. However, their tracking performance
depends on the specific signals or data sets, having the risk of
instability accompanied by large error. In this study we explore this
process by applying different network size and leaking rate for
prediction of nonlinear or chaotic signals in MLP neural networks.
Major problems of ESN training such as the problem of initialization
of the network and improvement in the prediction performance are
tackled. The influence of coefficient of activation function in the
hidden layer and other key parameters are investigated by simulation
results. Extended Kalman filter is employed in order to improve the
sequential and regulation learning rate of the feedforward neural
networks. This training approach has vital features in the training of
the network when signals have chaotic or non-stationary sequential
pattern. Minimization of the variance in each step of the computation
and hence smoothing of tracking were obtained by examining the
results, indicating satisfactory tracking characteristics for certain
conditions. In addition, simulation results confirmed satisfactory
performance of both of the two neural networks with modified
parameterization in tracking of the nonlinear signals.
Abstract: Recent research in neural networks science and
neuroscience for modeling complex time series data and statistical
learning has focused mostly on learning from high input space and
signals. Local linear models are a strong choice for modeling local
nonlinearity in data series. Locally weighted projection regression is
a flexible and powerful algorithm for nonlinear approximation in
high dimensional signal spaces. In this paper, different learning
scenario of one and two dimensional data series with different
distributions are investigated for simulation and further noise is
inputted to data distribution for making different disordered
distribution in time series data and for evaluation of algorithm in
locality prediction of nonlinearity. Then, the performance of this
algorithm is simulated and also when the distribution of data is high
or when the number of data is less the sensitivity of this approach to
data distribution and influence of important parameter of local
validity in this algorithm with different data distribution is explained.
Abstract: In this paper a real-time obstacle avoidance approach
for both autonomous and non-autonomous dynamical systems (DS) is
presented. In this approach the original dynamics of the controller
which allow us to determine safety margin can be modulated.
Different common types of DS increase the robot’s reactiveness in
the face of uncertainty in the localization of the obstacle especially
when robot moves very fast in changeable complex environments.
The method is validated by simulation and influence of different
autonomous and non-autonomous DS such as important
characteristics of limit cycles and unstable DS. Furthermore, the
position of different obstacles in complex environment is explained.
Finally, the verification of avoidance trajectories is described through
different parameters such as safety factor.
Abstract: In this paper, Bayesian online inference in models of
data series are constructed by change-points algorithm, which
separated the observed time series into independent series and study
the change and variation of the regime of the data with related
statistical characteristics. variation of statistical characteristics of time
series data often represent separated phenomena in the some
dynamical system, like a change in state of brain dynamical reflected
in EEG signal data measurement or a change in important regime of
data in many dynamical system. In this paper, prediction algorithm
for studying change point location in some time series data is
simulated. It is verified that pattern of proposed distribution of data
has important factor on simpler and smother fluctuation of hazard
rate parameter and also for better identification of change point
locations. Finally, the conditions of how the time series distribution
effect on factors in this approach are explained and validated with
different time series databases for some dynamical system.
Abstract: In this paper, we considered and applied parametric
modeling for some experimental data of dynamical system. In this
study, we investigated the different distribution of output
measurement from some dynamical systems. Also, with variance
processing in experimental data we obtained the region of
nonlinearity in experimental data and then identification of output
section is applied in different situation and data distribution. Finally,
the effect of the spanning the measurement such as variance to
identification and limitation of this approach is explained.
Abstract: In this paper, model order reduction method is used
for approximation in linear and nonlinearity aspects in some
experimental data. This method can be used for obtaining offline
reduced model for approximation of experimental data and can
produce and follow the data and order of system and also it can
match to experimental data in some frequency ratios. In this study,
the method is compared in different experimental data and influence
of choosing of order of the model reduction for obtaining the best and
sufficient matching condition for following the data is investigated in
format of imaginary and reality part of the frequency response curve
and finally the effect and important parameter of number of order
reduction in nonlinear experimental data is explained further.
Abstract: Performance of different filtering approaches depends
on modeling of dynamical system and algorithm structure. For
modeling and smoothing the data the evaluation of posterior
distribution in different filtering approach should be chosen carefully.
In this paper different filtering approaches like filter KALMAN,
EKF, UKF, EKS and smoother RTS is simulated in some trajectory
tracking of path and accuracy and limitation of these approaches are
explained. Then probability of model with different filters is
compered and finally the effect of the noise variance to estimation is
described with simulations results.