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EN
The aim of the paper is to investigate the differences as far as the numerical accuracy is concerned between feedforward layered Artificial Neural Networks (ANN) learned by means of Kalman filtering (KF) and ANN learned by means of the evidence procedure for Bayesian technique. The stress-strain experimental time series for concrete hysteresis loops obtained by the experiment of cyclic loading is presented as considered example.
EN
This paper presents the application of Bayesian Neural Networks (BNN) in the identification of parameters of a load causing partial yielding of a cross-section of a portal frame. As the source of the data in the identification procedure the eigenfrequencies and eigenvectors are used. The applied BNN are either of SSN/MAP (Maximum A Posteriori) or of T-BNN (True Bayesian Neural Networks) type, the results are compared with the results of the identification performed using Standard Neural Networks (SNN).
3
Content available remote Bayesowskie sieci neuronowe w analizie problemów regresji
EN
The lecture entitled "Bayesian Neural Networks in the Analysis of Regression Problems" deals with basics of the Bayesian inference (BI) and its various methods and relations to the Standard Neural Networks (SNNs). In subsequent Sections the following problems are discussed: 1) Bayesian Neural Networks (BNNs) as a fusing of SNN and BI; 2) The regression and Feed-forward Layered Neural Network (FLNN); 3) Principles of BI; 4) Maximum Likelihood (ML) and Maximum APosterior (MAP) methods; 5) Criterion of Maximum EVidence (MEV), 6)Types of BNNs. Special attention is focused on the application of MAP for the controlling the over-fitting of the neural approximation. The MEV is also explored for the design of deterministic networks FLNN/MAP. The more extended application of BI enables to formulate a semi-probabilistic simple network S-BNN and a truly probabilistic Bayesian network T-BNN. A numerical efficiency of the Bayesian methods and networks is discussed in paper [1] presented at the XIII Symposium DYNKON2008.
EN
Standard artificial neural networks and Baycsian neural networks (BNNs) are briefly discussed on example of a simple feed-forward layered neural networks (FLNN). Main ideas of the Baycsian approach and basics of the applied BNNs are presented in short. A study case corresponds to prediction of Displacement Response Spectrum inside buildings at the basement level (DRSb). Data for network training and testing were adopted as DRS corresponding to the preprocessed accelerograms. They were taken from measurements in the Lcgnica-Gtogow Copperfield at monitored 5-storey buildings subjected to paraseismic excitations from explosives in nearby strip mines. Results of neural predictions by three NNs (standard FLNN trained by means of the conjugate gradient learning method, Simple Bayesian SBNN and Full Bayesian FBNN) are presented. The errors of predictions are on average on the level of 4% errors.
5
Content available remote Prediction of concrete fatigue durability using Bayesian neural networks
EN
The utility of Bayesian neural networks to predict concrete fatigue durability as a function of concrete mechanical parameters of a specimen and characteristics of the loading cycle is investigated. Bayesian approach to learning neural networks allows automatic control of the complexity of the non-linear model, calculation of error bars and automatic determination of the relevance of various input variables. Comparative results on experimental data set slow that Bayesian neural networks works well.
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