A Personal History of Random Data Analysis

Sound and Vibration, Jan 2007 by Bendat, Julius S

My interest in Applied Mathematics started during the second World War when I was an undergraduate student at the University of California in Berkeley. In my last two years there, I worked as a Physics Research assistant on the Manhattan Project where I learned a little about nuclear energy, the first major development from this war. Upon graduation in 1944, with the war still on in both Europe and the Pacific, I enlisted in the U.S. Navy to become a radar officer where I learned a little about radar, the second important development from this war. Thus, I was always motivated in my later graduate studies and in my following technical work in the field of random data analysis to investigate how to apply theoretical mathematical ideas to solve practical engineering and scientific problems. The books that I have written both alone and with Allan Piersol have been well received throughout the world, leading to pioneering work on many projects during the past 50 years and the presentations of short courses and seminars in 25 countries.

At the International Modal Analysis Conference IMAC XXIII in Orlando, FL, I gave an invited talk on February 1, 2005 where I spoke about some of my work in the field of random data analysis over the past 50 years. Prof. Al Wicks from Virginia Polytechnic Institute, the Conference Chairman, attended this session and asked me to write a paper to benefit people in the field. Prof. Rune Brincker from Aalborg University in Denmark, the Chairman of the first IOMAC International Operational Modal Analysis Conference, to be held in Copenhagen on April 26-27, 2005, was also present. He invited me to write an introductory paper for the IOMAC Proceedings where I might use a historical perspective. This article was my response to Al Wicks and Rune Brincker.

The IOMAC organizing committee also asked me to give the "Lecture of Honor" at the IOMAC conference dinner in Copenhagen on April 26, 2005. I greatly appreciated this special recognition for the contributions I was able to make with the help of people mentioned in this article.

In particular, I want to acknowledge the close association with Allan Piersol, a mechanical engineer whom I met in 1960 when we did some pioneering research work for the Flight Dynamics Laboratory at WrightPatterson Air Force Base in Dayton, OH. Allan is the coauthor with me of six textbooks on Random Data Analysis and Engineering Applications, that were published by Wiley, New York, from 1966 to 2000.

I also want to thank Paul PaIo, an ocean engineer, who sponsored 10 years of research work from 1985 to 1995 that I did for the U.S. Naval Civil Engineering Laboratory and the Office of Naval Research. This work developed new practical ways to identify and analyze nonlinear system dynamic properties, and to two books on Nonlinear System Techniques and Applications published in 1990 and 1998.

Random Noise Theory Book (1958)

In the late 1950s, time series analysis had not yet matured. The mathematical foundation existed but was available primarily only in research papers. Data had to be collected in analog form, and with the limited memory and speed of computers, digitization and subsequent analysis were awkward and expensive. It was in this period that I wrote my first book in 1958 after working in Los Angeles for five years at Northrop Aircraft Company and the RamoWooldridge Corporation (now TRW Systems) on problems dealing with statistical communication theory and control systems. This book, Principles and Applications of Random Noise Theory, was published by Wiley, New York.1 My objective in writing this book was to explain fundamental concepts from random noise theory in understandable engineering language, with emphasis on physical meanings and mathematical restrictions. I tried to bridge the gap between theoretical research work and the engineering applications that followed. This early 1958 Random Noise Theory book contained ideas on how to define and analyze basic amplitude, time and frequency properties of random data by using probability density functions, correlation functions and spectral density functions. I was influenced by the work of two men: (1) Stephen Rice of the Bell Telephone Labs, author of a monumental paper on "The Mathematical Analysis of Random Noise," published in the Bell System Technical Journal in 1944 and 1945; and (2) Norbert Wiener, author of the hard-to-read book, The Interpolation, Extrapolation and Smoothing of Stationary Time Series, published by Wiley, New York in 1949.

During this first five-year period, I learned to appreciate the differences between theoretical work based on ideal assumptions about random data and linear systems and practical engineering work based on actual measured data and real physical systems. I found that there are no sine waves in nature, that measured data can never be truly Gaussian, and physical systems are not ideal. Also, one can never compute the true properties of random data or linear systems with finite amounts of data. One can only obtain estimates with statistical bias and random errors.