By Ka-Veng Yuen
Bayesian equipment are a strong software in lots of components of technological know-how and engineering, particularly statistical physics, clinical sciences, electric engineering, and data sciences. also they are excellent for civil engineering purposes, given the various forms of modeling and parametric uncertainty in civil engineering difficulties. for instance, earthquake floor movement can't be predetermined on the structural layout degree. whole wind strain profiles are tricky to degree less than working stipulations. fabric houses will be tricky to figure out to a really specified point - in particular concrete, rock, and soil. For air caliber prediction, it truly is tricky to degree the hourly/daily pollution generated via automobiles and factories in the quarter of outrage. it's also tough to acquire the up to date air caliber info of the encircling towns. in addition, the meteorological stipulations of the day for prediction also are doubtful. those are only the various civil engineering examples to which Bayesian probabilistic tools are appropriate. Familiarizes readers with the most recent advancements within the box contains identity difficulties for either dynamic and static structures Addresses tough civil engineering difficulties resembling modal/model updating provides tools appropriate to mechanical and aerospace engineering supplies engineers and engineering scholars a concrete experience of implementation Covers real-world case stories in civil engineering and past, comparable to: structural health and wellbeing tracking seismic attenuation finite-element version updating hydraulic leap synthetic neural networkair caliber prediction contains different insightful daily-life examples spouse web site with MATLAB code downloads for self reliant perform Written through a number one specialist within the use of Bayesian tools for civil engineering difficulties This ebook is perfect for researchers and graduate scholars in civil and mechanical engineering or utilized likelihood and facts. working towards engineers drawn to the applying of statistical how you can clear up engineering difficulties also will locate this to be a necessary text.MATLAB code and lecture fabrics for teachers on hand at wiley.com/go/yuen
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Additional info for Bayesian Methods for Structural Dynamics and Civil Engineering
Example. 81) where θ = [θ1 , θ2 ]T ∈ R2 . 83) Concepts and Bayesian Probabilistic Framework 37 ˜ The eigenvalues can be where λ and φ are the eigenvalue and eigenvector of the matrix A. 84) where √ I2 is the 2 × 2 identity matrix. 382 and T are [1, −( 5/2 + 1/2)] and [1, 5/2 − 1/2]T , respectively. Now, identification of the uncertain parameters in θ is proceeded with different types of eigenvalue–eigenvector measurements. 3615. 0191. 85) n=1 where λ(1) (θ) is the smaller model eigenvalue of the matrix A(θ) and λˆ (1) n , n = 1, 2, .
Example. 92) where the actual values of the uncertain parameters are a˜ = −3 and b˜ = 2. 75, 1, . . 0. 94) n=1 where κ0 is a constant that does not depend on the uncertain parameters. The most probable values of the parameters can be obtained by maximizing the posterior PDF. 95) ⎩ 12 12 12 5 6 4 a n=1 xn + b n=1 xn = n=1 xn yn and these are uncoupled with the one for σ0 . 20 shows a typical result of the problem. The dashed line is the true relationship and the crosses are the measurements. Even though the samples are quite scattered in the low range of x, the Bayesian approach reflects the correct weighting for different measurements.
If R0 , R1 , . , RN−1 are used to estimate the model parameters that govern the stochastic process x, it is necessary to construct the likelihood function p(R0 , R1 , . . , RN−1 |θ, C). Even though the individual probability distribution of a particular Rn can be obtained, deriving the joint PDF of R0 , R1 , . . , RN−1 is another story due to the correlation structure of the Rn s. This explains why parametric identification using the correlation function is well-known to be difficult and usually biased.
Bayesian Methods for Structural Dynamics and Civil Engineering by Ka-Veng Yuen