Random Data (eBook)

JULIUS S. BENDAT, PHD, is President of the J. S. Bendat Company, an independent mathematical consulting firm in Los Angeles, California. An internationally recognized authority in the field, Dr. Bendat has over fifty years of consulting experience in the formulation of mathematical models, the development of statistical error analysis criteria, and the interpretation of engineering results. He is the author of Nonlinear System Techniques and Applications and coauthor of Engineering Applications of Correlation and Spectral Analysis, Second Edition, both published by Wiley. The late ALLAN G. PIERSOL, PE, was president of Piersol Engineering Company. His consulting career spanned over fifty years and focused on a wide range of topics including the development of machinery condition monitoring techniques and the statistical analysis of all types of mechanical shock, vibration, and acoustic data. A Fellow of the Acoustical Society of America and the Institute of Environmental Sciences and Technology, Piersol is the coauthor of Engineering Applications of Correlation and Spectral Analysis, Second Edition.

Preface

Preface to the Third Edition.

Glossary of Symbols.

1 Basic Descriptions and Properties.

1.1 Deterministic Versus Random Data.

1.2 Classifications of Deterministic Data.

1.3 Classifications of Random Data.

1.4 Analysis of Random Data.

2 Linear Physical Systems.

2.1 Constant-Parameter Linear Systems.

2.2 Basic Dynamic Characteristics.

2.3 Frequency Response Functions.

2.4 Illustrations of Frequency Response Functions.

2.5 Practical Considerations.

3 Probability Fundamentals.

3.1 One Random Variable.

3.2 Two Random Variables.

3.3 Gaussian (Normal) Distribution.

3.4 Rayleigh Distribution.

3.5 Higher Order Changes of Variables.

4 Statistical Principles.

4.1 Sample Values and Parameter Estimation.

4.2 Important Probability Distribution Functions.

4.3 Sampling Distributions and Illustrations.

4.4 Confidence Intervals.

4.5 Hypothesis Tests.

4.6 Correlation and Regression Procedures.

5 Stationary Random Processes.

5.1 Basic Concepts.

5.2 Spectral Density Functions.

5.3 Ergodic and Gaussian Random Processes.

5.4 Derivative Random Processes.

5.5 Level Crossings and Peak Values.

6 Single-Input/Output Relationships.

6.1 Single-Input/Single-Output Models.

6.2 Single-Input/Multiple-Output Models.

7 Multiple-Input/Output Relationships.

7.1 Multiple-Input/Single-Output Models.

7.2 Two-Input/One-Output Models.

7.3 General and Conditioned Multiple-Input Models.

7.4 Modified Procedure to Solve Multiple-Input/Single-Output Models.

7.5 Matrix Formulas for Multiple-Input/Multiple-Output Models.

8 Statistical Errors in Basic Estimates.

8.1 Definition of Errors.

8.2 Mean and Mean Square Value Estimates.

8.3 Probability Density Function Estimates.

8.4 Correlation Function Estimates.

8.5 Autospectral Density Function Estimates.

8.6 Record Length Requirements.

9 Statistical Errors in Advanced Estimates.

9.1 Cross-Spectral Density Function Estimates.

9.2 Single-Input/Output Model Estimates.

9.3 Multiple-Input/Output Model Estimates.

10 Data Acquisition and Processing.

10.1 Data Acquisition.

10.2 Data Conversion.

10.3 Data Qualification.

10.4 Data Analysis Procedures.

11 Data Analysis.

11.1 Data Preparation.

11.2 Fourier Series and Fast Fourier Transforms.

11.3 Probability Density Functions.

11.4 Autocorrelation Functions.

11.5 Autospectral Density Functions.

11.6 Joint Record Functions.

11.7 Multiple-Input/Output Functions.

12 Nonstationary Data Analysis.

12.1 Classes of Nonstationary Data.

12.2 Probability Structure of Nonstationary Data.

12.3 Nonstationary Mean Values.

12.4 Nonstationary Mean Square Values.

12.5 Correlation Structure of Nonstationary Data.

12.6 Spectral Structure of Nonstationary Data.

12.7 Input/Output Relations for Nonstationary Data.

13 The Hilbert Transform.

13.1 Hilbert Transforms for General Records.

13.2 Hilbert Transforms for Correlation Functions.

13.3 Envelope Detection Followed by Correlation.

14 Nonlinear System Analysis.

14.1 Zero-Memory and Finite-Memory Nonlinear Systems.

14.2 Square-Law and Cubic Nonlinear Models.

14.3 Volterra Nonlinear Models.

14.4 SI/SO Models with Parallel Linear and Nonlinear Systems.

14.5 SI/SO Models with Nonlinear Feedback.

14.6 Recommended Nonlinear Models and Techniques.

14.7 Duffing SDOF Nonlinear System.

14.8 Nonlinear Drift Force Model.

Bibliography.

Appendix A: Statistical Tables.

Appendix B: Definitions for Random Data Analysis.

List of Figures.

List of Tables.

List of Examples.

Answers to Problems in Random Data.

Index.