CA6110 Statistical Methods and Data Analytics
Submission Deadline and Location:
8:00 am, 20 April 2021, submit a single PDF file using Canvas Assignment function
Note: late submission will be subjected to score deduction.
Q1(a). Perform discrete cosine transformation (DCT) on the data in the attached Excle
file (i.e., Q1 data file.xlsx). The data is a one-dimensional data profile with 128 data
points. The complete data profile is provided in the worksheet named “Complete
profile”. A 128 × 128 DCT matrix is also included in in the worksheet named “DCT
matrix”. Please include detail steps of DCT in the submission.
Q1(b). 10 data points are taken from the complete profile and used as measurement
data, as shown in the worksheet named “Sparse measurement”. Please recover the
complete data profile from the sparse measurement using orthogonal matching pursuit
(OMP) algorithm. Please include detail steps of OMP in the submission.
Q2. Geotechnical site investigation is performed to characterize subsurface soil for a
foundation design. A borehole is drilled under the intended foundation, and standard
penetration test (SPT) is performed in the borehole. Table Q2-1 summarizes the
corrected SPT results (i.e., (N1)60 values) obtained from the tests for foundation soil.
A regression model is used to correlate SPT results (i.e., (N1)60 values) with the soil
effective friction angle, φ'fdn, which is a key soil property used in foundation design.
Consider, for example, the regression between (N1)60 and φ'fdn below:
εφ ++′= 724.3161.0)ln( 601 fdnN
where ε represents model uncertainty and follows a normal distribution with a zero
mean and standard deviation 496.0=εσ . Table Q2-2 summarizes the prior
knowledge used for φ'fdn in this example, and a uniform distribution is adopted to
represent the relatively uninformative prior knowledge obtained from geotechnical
literature. Using the information above, perform Bayesian analysis to characterize
statistically φ'fdn, and provide its mean, standard deviation and probability distribution.
Table Q2-1 Summary of SPT test results for foundation soil
Depth (m) Corrected SPT N results, (N1)60
Table Q2-2 Prior knowledge for soil effective friction angle φ'fdn
Random variable φ'fdn (◦)
Statistic Mean Standard Deviation
Min 34 1.70
Max 45 6.75 学霸联盟