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Random Data: Analysis and Measurement Procedures, Fourth Edition

Book Description

A timely update of the classic book on the theory and application of random data analysis

First published in 1971, Random Data served as an authoritative book on the analysis of experimental physical data for engineering and scientific applications. This Fourth Edition features coverage of new developments in random data management and analysis procedures that are applicable to a broad range of applied fields, from the aerospace and automotive industries to oceanographic and biomedical research.

This new edition continues to maintain a balance of classic theory and novel techniques. The authors expand on the treatment of random data analysis theory, including derivations of key relationships in probability and random process theory. The book remains unique in its practical treatment of nonstationary data analysis and nonlinear system analysis, presenting the latest techniques on modern data acquisition, storage, conversion, and qualification of random data prior to its digital analysis. The Fourth Edition also includes:

  • A new chapter on frequency domain techniques to model and identify nonlinear systems from measured input/output random data

  • New material on the analysis of multiple-input/single-output linear models

  • The latest recommended methods for data acquisition and processing of random data

  • Important mathematical formulas to design experiments and evaluate results of random data analysis and measurement procedures

  • Answers to the problem in each chapter

  • Comprehensive and self-contained, Random Data, Fourth Edition is an indispensible book for courses on random data analysis theory and applications at the upper-undergraduate and graduate level. It is also an insightful reference for engineers and scientists who use statistical methods to investigate and solve problems with dynamic data.

    Table of Contents

    1. Cover
    2. Series Page 1
    3. Series Page 2
    4. Title Page
    5. Copyright
    6. Dedication
    7. Preface
    8. Preface to the Third Edition
    9. Glossary of Symbols
    10. CHAPTER 1: Basic Descriptions and Properties
      1. 1.1 DETERMINISTIC VERSUS RANDOM DATA
      2. 1.2 CLASSIFICATIONS OF DETERMINISTIC DATA
      3. 1.3 CLASSIFICATIONS OF RANDOM DATA
      4. 1.4 ANALYSIS OF RANDOM DATA
      5. PROBLEMS
    11. CHAPTER 2: Linear Physical Systems
      1. 2.1 CONSTANT-PARAMETER LINEAR SYSTEMS
      2. 2.2 BASIC DYNAMIC CHARACTERISTICS
      3. 2.3 FREQUENCY RESPONSE FUNCTIONS
      4. 2.4 ILLUSTRATIONS OF FREQUENCY RESPONSE FUNCTIONS
      5. 2.5 PRACTICAL CONSIDERATIONS
      6. PROBLEMS
      7. REFERENCES
    12. CHAPTER 3: Probability Fundamentals
      1. 3.1 ONE RANDOM VARIABLE
      2. 3.2 TWO RANDOM VARIABLES
      3. 3.3 GAUSSIAN (NORMAL) DISTRIBUTION
      4. 3.4 RAYLEIGH DISTRIBUTION
      5. 3.5 HIGHER ORDER CHANGES OF VARIABLES
      6. PROBLEMS
      7. REFERENCES
    13. CHAPTER 4: Statistical Principles
      1. 4.1 SAMPLE VALUES AND PARAMETER ESTIMATION
      2. 4.2 IMPORTANT PROBABILITY DISTRIBUTION FUNCTIONS
      3. 4.3 SAMPLING DISTRIBUTIONS AND ILLUSTRATIONS
      4. 4.4 CONFIDENCE INTERVALS
      5. 4.5 HYPOTHESIS TESTS
      6. 4.6 CORRELATION AND REGRESSION PROCEDURES
      7. PROBLEMS
      8. REFERENCES
    14. CHAPTER 5: Stationary Random Processes
      1. 5.1 BASIC CONCEPTS
      2. 5.2 SPECTRAL DENSITY FUNCTIONS
      3. 5.3 ERGODIC AND GAUSSIAN RANDOM PROCESSES
      4. 5.4 DERIVATIVE RANDOM PROCESSES
      5. 5.5 LEVEL CROSSINGS AND PEAK VALUES
      6. PROBLEMS
      7. REFERENCES
    15. CHAPTER 6: Single-Input/Output Relationships
      1. 6.1 SINGLE-INPUT/SINGLE-OUTPUT MODELS
      2. 6.2 SINGLE-INPUT/MULTIPLE-OUTPUT MODELS
      3. PROBLEMS
      4. REFERENCES
    16. CHAPTER 7: Multiple-Input/Output Relationships
      1. 7.1 MULTIPLE-INPUT/SINGLE-OUTPUT MODELS
      2. 7.2 TWO-INPUT/ONE-OUTPUT MODELS
      3. 7.3 GENERAL AND CONDITIONED MULTIPLE-INPUT MODELS
      4. 7.4 MODIFIED PROCEDURE TO SOLVE MULTIPLE-INPUT/ SINGLE-OUTPUT MODELS
      5. 7.5 MATRIX FORMULAS FOR MULTIPLE-INPUT/ MULTIPLE-OUTPUT MODELS
      6. PROBLEMS
      7. REFERENCES
    17. CHAPTER 8: Statistical Errors in Basic Estimates
      1. 8.1 DEFINITION OF ERRORS
      2. 8.2 MEAN AND MEAN SQUARE VALUE ESTIMATES
      3. 8.3 PROBABILITY DENSITY FUNCTION ESTIMATES
      4. 8.4 CORRELATION FUNCTION ESTIMATES
      5. 8.5 AUTOSPECTRAL DENSITY FUNCTION ESTIMATES
      6. 8.6 RECORD LENGTH REQUIREMENTS
      7. PROBLEMS
      8. REFERENCES
    18. CHAPTER 9: Statistical Errors in Advanced Estimates
      1. 9.1 CROSS-SPECTRAL DENSITY FUNCTION ESTIMATES
      2. 9.2 SINGLE-INPUT/OUTPUT MODEL ESTIMATES
      3. 9.3 MULTIPLE-INPUT/OUTPUT MODEL ESTIMATES
      4. PROBLEMS
      5. REFERENCES
    19. CHAPTER 10: Data Acquisition and Processing
      1. 10.1 DATA ACQUISITION
      2. 10.2 DATA CONVERSION
      3. 10.3 DATA QUALIFICATION
      4. 10.4 DATA ANALYSIS PROCEDURES
      5. PROBLEMS
      6. REFERENCES
    20. CHAPTER 11: Data Analysis
      1. 11.1 DATA PREPARATION
      2. 11.2 FOURIER SERIES AND FAST FOURIER TRANSFORMS
      3. 11.3 PROBABILITY DENSITY FUNCTIONS
      4. 11.4 AUTOCORRELATION FUNCTIONS
      5. 11.5 AUTOSPECTRAL DENSITY FUNCTIONS
      6. 11.6 JOINT RECORD FUNCTIONS
      7. 11.7 MULTIPLE-INPUT/OUTPUT FUNCTIONS
      8. PROBLEMS
      9. REFERENCES
    21. CHAPTER 12: Nonstationary Data Analysis
      1. 12.1 CLASSES OF NONSTATIONARY DATA
      2. 12.2 PROBABILITY STRUCTURE OF NONSTATIONARY DATA
      3. 12.3 NONSTATIONARY MEAN VALUES
      4. 12.4 NONSTATIONARY MEAN SQUARE VALUES
      5. 12.5 CORRELATION STRUCTURE OF NONSTATIONARY DATA
      6. 12.6 SPECTRAL STRUCTURE OF NONSTATIONARY DATA
      7. 12.7 INPUT/OUTPUT RELATIONS FOR NONSTATIONARY DATA
      8. PROBLEMS
      9. REFERENCES
    22. CHAPTER 13: The Hilbert Transform
      1. 13.1 HILBERT TRANSFORMS FOR GENERAL RECORDS
      2. 13.2 HILBERT TRANSFORMS FOR CORRELATION FUNCTIONS
      3. 13.3 ENVELOPE DETECTION FOLLOWED BY CORRELATION
      4. PROBLEMS
      5. REFERENCES
    23. CHAPTER 14: Nonlinear System Analysis
      1. 14.1 ZERO-MEMORY AND FINITE-MEMORY NONLINEAR SYSTEMS
      2. 14.2 SQUARE-LAWAND CUBIC NONLINEAR MODELS
      3. 14.3 VOLTERRA NONLINEAR MODELS
      4. 14.4 SI/SO MODELS WITH PARALLEL LINEAR AND NONLINEAR SYSTEMS
      5. 14.5 SI/SO MODELS WITH NONLINEAR FEEDBACK
      6. 14.6 RECOMMENDED NONLINEAR MODELS AND TECHNIQUES
      7. 14.7 DUFFING SDOF NONLINEAR SYSTEM
      8. 14.8 NONLINEAR DRIFT FORCE MODEL
      9. PROBLEMS
      10. REFERENCES
    24. Bibliography
    25. Appendix A: Statistical Tables
    26. Appendix B: Definitions for Random Data Analysis
    27. List of Figures
    28. List of Tables
    29. List of Examples
    30. Answers to Problems in Random Data
      1. CHAPTER 1
      2. CHAPTER 2
      3. CHAPTER 3
      4. CHAPTER 4
      5. CHAPTER 5
      6. CHAPTER 6
      7. CHAPTER 7
      8. CHAPTER 8
      9. CHAPTER 9
      10. CHAPTER 10
      11. CHAPTER 11
      12. CHAPTER 12
      13. CHAPTER 13
      14. CHAPTER 14
    31. Index