why do you wish to classify them in this manner? Should not acoustic emission be a sub-category of elastic wave?

I followed the rules of the Table 1.1 in the linked reference. Yes, it looks like acoustic emission is also a kind of transverse wave. But here the elastic wave based damage identification is specifically the method based on the mechanism  that elastic waves will be reflected and scattered by discontinuities, and evaluation of damage can be achieved by scrutinizing the wave signals scattered by damage. And the AE-based identification is based on presence or growth of damage can be evaluated by capturing damage-emitted acoustic waves. 

https://books.google.ca/books?hl=en&lr=&id=jvzkoGBwBl0C&oi=fnd&pg=PA1&dq=Su+and+Ye+2009+structural+health+monitoring&ots=SNs_3YpoeX&sig=-AcrnY6NFBmDnPHVJL3PYjHf3ys#v=onepage&q=Su%20and%20Ye%202009%20structural%20health%20monitoring&f=false

Several types of damage may be detected by a spatially diffuse static stressing or thermal dtressing, coupled with a sensitive out-of-plane or in-plane full-field displacement (here, deformation) measurement technique. Such techniques are well-known in electronics, car and plane measurement, but also in other fields. Most often used techniques are speckle interferometry and speckle shearography.  They are modern techniques based upon holographic interferometry.

I hope it may provide you with useful information,

Dan

Dear Dr. Borza, thanks a lot for your information. Speckle interferometry is an advanced technique to visualise static and dynamic displacements of components. I am studying the embedded crack identification using the piezoelectric sensors and elastic waves, so I want to focus on the damage identification methods using just mechanical signals. Thanks again. 

Dear Huangchao Yu,

I hope you found my modest contribution useful. you may see more, for example, in:

https://www.researchgate.net/publication/235897610_Full-field_experimental-numerical_study_of_mechanical_static_strain_and_stress_in_piezoelectric_multilayer_compression-type_actuators

https://www.researchgate.net/publication/274958548_Investigations_on_potentially_dangerous_mechanical_deformations

https://www.researchgate.net/publication/274572161_Manufacture_of_smart_composite_panels_for_the_industry_and_verification_of_their_structural_properties_with_holographic_methods

In all these cases, as in other (not visible on research gate) you have embedded crack iidentification in active structures (different piezo structures, or other components) based only on mechanical data.

The (simplified( principle is: a uniform mechanical state of stress should produce a uniform state of strain. Different defects act as stress concentrators, leading to strain concentrations appearing to the researcher as interferometric fringe local modifications visible on the acquired images or anomalies in the curvature foeld.

It is a very "generous" principle, explaining why it may be applied i a great variety of situation.

Article Full-field experimental–numerical study of mechanical static...

Conference Paper Investigations on potentially dangerous mechanical deformations

Conference Paper Manufacture of smart composite panels for the industry and v...

Dear Dr. Borza, thank you very much for your professional answers and help. I will read the papers you recommend recently. I would refer to your articles if I will use the method or compare them. Thanks again. Best Regards.