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MATLAB代写-CA6110-Assignment 2

时间：2021-04-17

CA6110 Statistical Methods and Data Analytics

Assignment 2

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

0.5 11.7

2.0 9.8

3.5 11.9

5.0 27.8

2

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

Assignment 2

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

0.5 11.7

2.0 9.8

3.5 11.9

5.0 27.8

2

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