Wavelet Transform Modulus Maxima ridge and its application on Stratigraphic Profiling STUDENT: R CHUN-HSIANG WANG LECTURER: JIAN-JIUN DING DATE: 2014/11/27 1

Outline  Introduction  Wavelet Transformation  Wavelet Zoom  Wavelet Transform Modulus Maxima  Application-Stratigraphic profiling  SBT of CPT  Demonstration - Simulative case  Demonstration – Real case  Conclusion 2

Outline  Introduction  Wavelet Transformation  Wavelet Zoom  Wavelet Transform Modulus Maxima  Application-Stratigraphic profiling  SBT of CPT  Demonstration - Simulative case  Demonstration – Real case  Conclusion 3

Introduction  Why we need Wavelet Transform? 4 Time Frequency AnalysisWavelet Short-time Fourier TransformWavelet Transform Time & FrequencyTransition & Scaling Characteristic of FrequencyDistinguish local property

Outline  Introduction  Wavelet Transformation  Wavelet Zoom  Wavelet Transform Modulus Maxima  Application-Stratigraphic profiling  SBT of CPT  Demonstration - Simulative case  Demonstration – Real case  Conclusion 5

Continuous Wavelet Transform 6 Wavelet Transform = Dilation + Translation CWT: → Convolution Form Dilation Translation

CWT-cont.  Basis characteristics if is a wavelet basis, then

CWT-cont.  Famous Wavelet Basis Type 8 DerGaussianMexican Hat

CWT-cont.  DerGaussain function as example 9

Wavelet Zoom  Focus on localized signal structures with a zooming procedure that progressively reduces the scale parameter 10

Lipschitz Regularity  A function is pointwise Lipschitz at, if there exists, and a polynomial of degree such that,  The Lipschitz regularity of at or over is the least upper bound of the such that is Lipschitz. 11

Lipschitz Regularity-Example 12 Jump Cusp Lipschitz alpha =0Lipschitz alpha =1

Vanishing moment  A wavelet with a fast decay has n vanishing moments iff there exists with a fast decay such that,  Ψ(t) with n vanishing moments can only “see” a change point with Lipschitz regularity α that is less than n. 13

Wavelet Transform Modulus Maxima(WTMM)  WTMM = ridge   The dip of equation of this ridge is 0.5 definitely. 14

WTMM-cont. 15

Outline  Introduction  Wavelet Transformation  Wavelet Zoom  Wavelet Transform Modulus Maxima  Application-Stratigraphic profiling  SBT of CPT  Demonstration - Simulative case  Demonstration – Real case  Conclusion 16

Geotechnical Engineering 大地工程  Soil mechanics  Rock mechanics, Tunnel Engineering  Soil Dynamics, Geotechnical Earthquake Engineering  Engineering Geology, Fault Detecting  Foundation Engineering, underground Excavation  …… 17

Cone Penetration Test 圓錐貫入試驗  In-situ Test  Main Measurement  Cone Resistance,q c  Friction Sleeve,f s  Pore Water Pressure,u 2  Target  Site investigation 18 P.K. Robertson, 1990

Soil Behavior Type(SBT)  P.K. Robertson, Sensitive, fine grained 2.Organic soils (peats) 3.Clays (clay to silty clay) 4.Silt mixtures (clayey silt to silty clay) 5.Sand mixtures (silty sand to sandy silt) 6.Sands (clean sand to silty sand) 7.Gravelly sand to sand 8.Very stiff sand to clayey sand 9.Very stiff, fine grained

I c imply SBT  P.K. Robertson, SBTDescription Ic < 1.31Gravelly sand to dense sand 1.31< Ic < 2.05Sands: clean sand to silty sand 2.05< Ic < 2.60Sand mixtures: silty sand to sandy silt 2.60< Ic < 2.95Silt mixtures: clayey silt to silty clay 2.95< Ic < 3.60Clays: silty clay to clay Ic > 3.60Organic soil

Insight of Soil Layers  location at which the soil behavior type index changes abruptly 21 SBT 6 SBT 3 But in reality…… There will be some noise definitely!

Transition Zone  Cone can sense a layer boundary up to a distance of 15 cone diameters ahead and behind. 22 That will make us more difficult to identify layers !

Outline  Introduction  Wavelet Transformation  Wavelet Zoom  Wavelet Transform Modulus Maxima  Application-Stratigraphic profiling  SBT of CPT  Demonstration - Simulative case  Demonstration – Real case  Conclusion 23

Simulated Case Demonstration 24

In-situ Case Demonstration-NGES  Taxes A&M University 25 (National Geotechnical Experimentation Site,1993)

NGES-cont. 26

NGES-cont. 27

More difficult case  Oslo Main airport station 28

Oslo in-situ case-cont. 29

Outline  Introduction  Wavelet Transformation  Wavelet Zoom  Wavelet Transform Modulus Maxima  Application-Stratigraphic profiling  SBT of CPT  Demonstration - Simulative case  Demonstration – Real case  Conclusion 30

Conclusion  WTMM is widely applied to detecting discontinuity, like jump or cusp, in nowaday engineering.  Using a series of scale, or narrowing windows, we can grab the characteristic of a signal at some one local position.  It’s used to bore one or several holes at a construction site for investigation the stratigraphic property. If we enforce CPT and WTMM in field investigation, it will be more efficient and economical. 31

Conclusion-cont.  In Taiwan we usually take USCS as main principle of soil classification but not SBT of CPT. However, it must take lots of time and manpower if we still take USCS.  SBT of CPT has a clear and concise image of civil engineering application, because of the clear distinguishing principle of sand and clay. It will help us to realize a better design in engineering. 32

Reference  P.K. Robertson, C.E. Wride, Evaluating cyclic liquefaction potential using the cone penetration test, 1998  P.K. Robertson, Interpretation of cone penetration tests — a unified approach, 2009  B. S. Chen, P.W. Mayne, Profiling the overconsolidation raito of clays by Piezocone tests, 1994  Y. Wang, Probabilistic identification of underground soil stratification using cone penetration tests, 2013  J. Benoît, A. J. Lutenegger, National Geotechnical Experimentation Sites, 1993  Mallat, A Wavelet Tour of Signal Processing,

Thanks for your listening! 34