By Ka-Veng Yuen
Bayesian tools are a robust device 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 tricky to degree less than working stipulations. fabric homes might be tough to figure out to a truly exact point - particularly concrete, rock, and soil. For air caliber prediction, it really is tricky to degree the hourly/daily pollution generated via automobiles and factories in the quarter of shock. it's also tricky to acquire the up-to-date air caliber details 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 equipment are acceptable. Familiarizes readers with the newest advancements within the box comprises id difficulties for either dynamic and static structures Addresses difficult civil engineering difficulties reminiscent of modal/model updating provides equipment acceptable to mechanical and aerospace engineering offers engineers and engineering scholars a concrete feel of implementation Covers real-world case reports in civil engineering and past, resembling: structural healthiness tracking seismic attenuation finite-element version updating hydraulic leap man made neural networkair caliber prediction contains different insightful daily-life examples spouse web site with MATLAB code downloads for autonomous perform Written by means of 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 information. practising engineers attracted to the applying of statistical the way to clear up engineering difficulties also will locate this to be a beneficial text.MATLAB code and lecture fabrics for teachers on hand at wiley.com/go/yuen
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Extra resources for Bayesian Methods for Structural Dynamics and Civil Engineering
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.
Assume that observations of N years are available and there are k1 , k2 , . , kN occurrences in each of the years. By assuming that these occurrences in different years are statistically independent, the posterior PDF of the occurrence rate λ is given by: p(λ|k1 , k2 , . . , kN , C) = N κ0 p(λ|C) N n=1 kn ! n=1 λkn e−λ kn ! 61) N = κ0 p(λ|C) exp −Nλ + kn ln λ n=1 Here, a uniform prior distribution for the occurrence rate λ is used in a sufficiently large range so the inference is contributed solely by the likelihood of the measurement.
1 Independent Uniform Prior In the case of a uniform prior PDF of the coefficients, the optimal coefficient vector b can be obtained by minimizing Jg (b; D, C). This can be achieved by solving the linear algebraic equation: ∂Jg (b; D, C)/∂b = 0, and the updated coefficient vector is readily obtained: ⎡ ⎢ ⎢ ⎢ b = A−1 ⎢ ⎢ ⎢ ⎣ 1 N N n=1 x1 (n)y(n) 1 N N n=1 x2 (n)y(n) .. 104) n=1 By using the Cauchy–Schwarz inequality, it can be easily shown that this matrix is invertible if and only if the vectors [xl (1), xl (2), .
Bayesian Methods for Structural Dynamics and Civil Engineering by Ka-Veng Yuen