By Ka-Veng Yuen
Bayesian equipment are a strong instrument in lots of parts of technological know-how and engineering, specifically statistical physics, clinical sciences, electric engineering, and knowledge sciences. also they are perfect for civil engineering functions, given the varied forms of modeling and parametric uncertainty in civil engineering difficulties. for instance, earthquake flooring movement can't be predetermined on the structural layout degree. whole wind strain profiles are tough to degree below working stipulations. fabric houses might be tough to figure out to a truly unique point - specifically concrete, rock, and soil. For air caliber prediction, it's tricky to degree the hourly/daily toxins generated via vehicles and factories in the region of shock. it's also tough to procure the up to date air caliber info of the encompassing towns. in addition, the meteorological stipulations of the day for prediction also are doubtful. those are only a number of the civil engineering examples to which Bayesian probabilistic equipment are appropriate. Familiarizes readers with the newest advancements within the box contains identity difficulties for either dynamic and static structures Addresses hard civil engineering difficulties akin to modal/model updating offers tools acceptable to mechanical and aerospace engineering supplies engineers and engineering scholars a concrete experience of implementation Covers real-world case reviews in civil engineering and past, similar to: structural healthiness tracking seismic attenuation finite-element version updating hydraulic bounce synthetic neural networkair caliber prediction contains different insightful daily-life examples significant other web site with MATLAB code downloads for self reliant perform Written through a number one professional within the use of Bayesian equipment for civil engineering difficulties This ebook is perfect for researchers and graduate scholars in civil and mechanical engineering or utilized likelihood and records. training engineers drawn to the applying of statistical how to resolve engineering difficulties also will locate this to be a worthwhile text.MATLAB code and lecture fabrics for teachers on hand at wiley.com/go/yuen
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Additional resources for Bayesian Methods for Structural Dynamics and Civil Engineering
18). 20) The likelihood function p(D|θ, C) represents the contribution of the measured data in establishing the posterior distribution. It reflects how likely the measurements are observed from the model with a particular set of parameters. The likelihood function can be constructed given the class of probabilistic and physical models of the problem and it is the key of Bayesian updating. If a large amount of measurement is available, the likelihood function will be the dominant factor for the Bayesian inference.
By using this value of the prediction-error variance, the conditional optimal for the uncertain coefficients can be updated. By repeating the last two steps, the updated uncertain parameters can be obtained until convergence is achieved. The conditional PDF p(b|D, C, σ 2 ) is Gaussian with mean b (σ 2 ) and covariance matrix (Nσ −2 A + V−1 )−1 . Furthermore, the conditional PDF p(σ 2 |D, C, b) follows the inverse Gamma distribution IG(α, β) with shape parameter α = N/2 + α0 and scale parameter β = NJg (b; D, C)/2 + β0 .
24 Bayesian Methods for Structural Dynamics and Civil Engineering Another useful special case is that the random variable lies within a finite interval [a, b] without knowing the mean, variance or other moments. 26) will be modified to exclude the terms with λ2 and λ3 . 37) and zero otherwise. 6 Examples of Bayesian Inference Example. Gaussian Random Variable Consider a Gaussian random variable X with mean μ and variance σ 2 . These two parameters are unknown and they are the uncertain parameters for identification.
Bayesian Methods for Structural Dynamics and Civil Engineering by Ka-Veng Yuen