By Ka-Veng Yuen
Bayesian equipment are a strong device in lots of parts of technological know-how and engineering, particularly statistical physics, clinical sciences, electric engineering, and data sciences. also they are excellent for civil engineering functions, 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 level. entire wind strain profiles are tricky to degree lower than working stipulations. fabric houses may be tough to figure out to a truly unique point - particularly concrete, rock, and soil. For air caliber prediction, it truly is tricky to degree the hourly/daily pollution generated by means of automobiles and factories in the region of outrage. it's also tricky to procure the up to date air caliber details of the encompassing towns. moreover, the meteorological stipulations of the day for prediction also are doubtful. those are only a few of the civil engineering examples to which Bayesian probabilistic tools are appropriate. Familiarizes readers with the newest advancements within the box comprises identity difficulties for either dynamic and static structures Addresses not easy civil engineering difficulties resembling modal/model updating offers tools appropriate to mechanical and aerospace engineering provides engineers and engineering scholars a concrete experience of implementation Covers real-world case reports in civil engineering and past, corresponding to: structural overall healthiness tracking seismic attenuation finite-element version updating hydraulic bounce synthetic neural networkair caliber prediction comprises different insightful daily-life examples spouse site with MATLAB code downloads for self sustaining 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 records. practising engineers drawn to the appliance of statistical the way to resolve 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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Extra info for Bayesian Methods for Structural Dynamics and Civil Engineering
36) where the error function is given by: 2 erf (x) = √ π x 0 and it can be computed using the function ‘erf’ in MATLAB® . 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 .
If k is a positive integer. 24) which remains to be Gamma distributed for θ with shape parameter k + 1 and scale parameter (x + 1/α)−1 . Therefore, the Gamma distribution is the conjugate prior distribution for the exponential type of likelihood functions. Conjugate prior distributions are popular because the prior and posterior distributions have the same form so it is easy to quantify the contribution of the updating process by the data. The maximum entropy method is a theoretically sound approach, especially for the case if the bounds of the parameters are known.
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.