2. The second recommendation is that an investigation be undertaken to 

 develop new techniques to determine from measured input/output data 

 specific linear and nonlinear system properties between input wave 

 spectra and output response spectra. Practical digital computer pro- 

 cedures are desired where the analysis is conducted in the frequency 

 domain rather than in the time domain. 



(a) Linear systems should be found based on analysis of autospectral 

 and cross-spectral density functions using current known procedures. 



(b) Nonlinear systems should be found based on analysis of appropriate 

 bispectral and cross-bispectral density functions by developing 

 new methods that can provide useful engineering interpretations. 



(c) Special nonlinear coherence functions should be defined to deter- 

 mine the validity of proposed nonlinear models, 



(d) Output spectra should be decomposed into linear components, non- 

 linear components., and remaining uncorrelated noise. (These results 

 will provide the basis for future evaluations and comparisons of 

 measured results with predicted results from CEL models.) 



3. This participant believes it is now feasible to carry out the above work 

 to identify nonlinear system properties and their effects from measured 

 input/output data, where the practical procedures to be developed can 



be direct extensions of current methods used to obtain optimum linear 

 systems from such data. Recommended tasks are as follows: 



1. Study of past published work on bi spectra analysis. 



2. Development of new detailed analytical procedures. 



3. Writing of digital computer programs. 



4. Verification by computer simulation studies, 



J. S. Bendat 



u- 



170 



