197 Digital Signal Processing and Data Analysis

For Whom Intended

  1. Testing laboratory personnel who want to expand their analysis capabilities, perhaps in the interest of improving their test designs;
  2. Analysis personnel responsible for the interpretation of data acquired in the laboratory;
  3. Test requesters/designers who want to know what tools are available and what to expect from them.

Objectives  To help participants to understand basic mechanical and structural concepts and terminology. It is not an in-depth mechanical engineering course but rather a course aimed at individuals who require an intensive review of basic principals, without the assumption of any prior knowledge of the topic. The course is fast paced and as non-mathematical as possible.

Brief Course Description  The objective of the course is to provide participants with a working knowledge of the tools available for analysis of data acquired by digital data acquisition systems for a variety of laboratory and field applications. Basic analysis principals and methods are presented and reinforced with practical examples from everyday testing operations. The interaction between test design, data acquisition and analysis is emphasized. The lectures and discussions are designed to promote understanding the concepts involved through "mechanical feel" rather than mathematics.

Participants are encouraged to offer problems from their own activities for discussion and solution by the class.

The course is presented as a series of highly-interactive lecture/discussion sessions. Problems for individual and group solution are interspersed throughout the course to act as training aids and to evaluate class progress. Special-interest discussions are encouraged outside of the regular course sessions.

Demonstration programs written in LabView are used during the course to illustrate the concepts. These demonstrations are available for download, free of charge. Students are encouraged to download the demonstration programs prior to class, and install them on a laptop computer they can bring with them to class and use to follow along with the instructor when the demonstrations are presented.

Diploma Programs  This course is required for TTi’s Data Acquisition and Analysis Specialist (DAS) diplomat program. It is an optional course for any other TTi specialist diploma programs.

Related Courses  In Course 197-5, Digital Signal Processing, Data Acquisition and Analysis, the content of Course 197-3 is combined with Course 196, Digital Data Acquisition.

Prerequisites  Participants should have attended TTi’s course, Digital Data Acquisition, or some equivalent training program. A good understanding of the engineering problem to be analyzed is expected. An understanding of basic computer and data acquisition principles will be useful.

Text  Each student will receive 180 days access to the on-line electronic course workbook. Renewals and printed textbooks are available for an additional fee.

Internet Complete Course 197-3 features over ten hours of video as well as more in-depth reading material. All chapters of course 197.3 are also available as OnDemand Internet Short Topics. See the course outline below for details.

Course Hours, Certificate and CEUs  Class hours/days for on-site courses can vary from 14-35 hours over 2-5 days as requested by our clients. Upon successful course completion, each participant receives a certificate of completion and one Continuing Education Unit (CEU) for every ten class hours.

Click for a printable course outline (pdf).

Course Outline

Chapter 1 - A Brief Data Acquisition Review

  • Sampling Theory

  • Digitizing Rules

  • Assumptions

Chapter 2 - "Static" (Load/Deflection) Test Analysis

  • Examples of Static Tests
  • Data Characterization Parameters
  • Basic curve fitting—Least square techniques
    • Linear regression
    • Polynomial regression
  • Spline fitting
    • Yield point determination

Chapter 3 - Oscillating-Signal Analysis

  • The Data Window
  • Signal Types
    • Transient
    • Continuous
    • Repeating
  • Time-Domain properties
  • AC/DC Coupling
  • Calculating the Average of the Data
    • Overall or Block Average
    • Running or Moving Average
    • Exponential Average/Smoothing
  • Root-Mean-Square (RMS) Amplitude
    • DC- and AC-Coupled RMS
    • Exponential Average RMS
  • Trend Removal
  • Peak Detection
  • Random Data
    • Probability Distribution
    • Gaussian Noise Properties
    • Kurtosis
    • Stationarity
    • Crest Factor
    • Central Limit Theorem
    • Convolution
    • Cross Correlation

Chapter 4 - Spectral Analysis

  • Types of Spectral Analysis
  • Fourier Transforms
    • Forward Fourier Transform
    • "Leakage"
    • FFT - Fast Fourier Transform
      • FFT speed improvement
  • Graphic Presentation of Fourier Transforms/Spectral Plot Formats
  • Making the Spectral Calculation “Meaningful”
    • Power spectral density (PSD)
      • Acoustic power spectrum
    • Transfer function
    • 1/N Octave Analysis

Chapter 5 - Dynamic Analysis Tools—Data Filtering

  • Introduction to Filtering
    • Analog Filtering
    • Digital Filtering
    • A Fundamental Difference Between Analog & Digital Filters
    • Filter Characteristics
  • Filtering in the Frequency Domain
    • "Standard" Waveforms
      • Square
      • Sine Non-Integer Waves/Buffer
      • Filtered Random, Square and Sine waves
    • Real Filter Emulations
  • Filtering in the Time Domain (the More-General Case)
    • “Running or Moving Average”
    • Running “Parabolic Average”
    • Non-Recursive or FIR Filters
      • Convolution Filters
        • Convolution Filter Design Process
        • Advanced Convolution Filter Design

    • Recursive (or IIR) Filtering

    • Impulse Function

Chapter 6 - Dynamic Analysis Tools—Integration and Differentiation

  • Integration and Differentiation .. Operations
  • “Fundamental” Discrete Integration
    • Integrating With Simpson’s Rule
  • “Fundamental” Discrete Differentiation
  • Spectral-Domain Integration & Differentiation
    • High/Low Passed Integration/Differentiation
    • Shock Integration by Time & Spectral Calculation
  • Time- vs. Spectral-Domain Integration & Differentiation
  • Integration of Accelerometer Data
    • Offset, Noise, The "Velocity" Test, "Adjusting" the data
    • AC Coupling

Chapter 7 - Analysis of Transient Tests

  • Definition of "Transient"
  • Transient Test Types
  • Transient Tests—Analysis Options
  • Shock Response Spectra
    • SRS Mechanical Analog
    • SRS Calculation: Spectral Domain
      • The “Smallwood” Algorithm
    • Detection of Acceleration-Offset Errors
    • The “Velocity Criterion” for Data Acceptability
    • Offset Handling in SRS Analysis
    • AC-Coupling Process/Effect
    • Data “Correction” by High-Pass Filtering
    • SRS Analysis Procedure
      • Example
    • Recommended Practices
    • Damage Potential
    • Different Methods of Bandwidth Control
    • Peak-Detection

Chapter 8 - Spectral Analysis of “Continuous” Tests

  • Reasons for Analyzing “Short” Blocks
  • Finite measurement-length effects
  • Windowing: Window types/uses/advantages and disadvantages
    • Triangle (Bartlett) Window
    • 10% Versine
    • Hanning Window
    • Hamming Window
    • Blackman Window
    • Flat-Top Window (HP P301)
    • Window Comparison
  • Selecting the Window to use
    • Sine Testing
    • Random Testing

Chapter 9 - Data Averaging, Noise Reduction, Random Signals

  • Averaging
    • Noise Rejection by Averaging
  • Time Domain block averaging process
  • Auto-Spectral averaging process
    • Effect of windowing
    • Overlapped processing
    • Data Reliability — Degrees of Freedom
  • Calculating Transfer Functions from Random Data
  • Transfer Functions by Cross/Auto Spectra
  • Coherence
    • Hammer Calibration Data
  • Averaging Assumptions and Compromises
  • Making Random Time Histories

Chapter 10 - Special Topics

  • Making Test Results Agree
    • Option 1: Standardize the Hardware
    • Option 2: Use analytical tools to "Normalize" the data

      • Defining a “Standard System Transfer Function

      • The "Standard" filter
  • Data interpolation
    • Averaging and derivative techniques
    • Spectral extension
  • Data Acquisition System Calibration

Chapter 11 - Conclusions and Wrap-up

Appendix A - Glossary of Terms

Appendix B - Buzzwords and Jargon

Appendix C - Review Questions

Award of Certificates for successful completion

Click for a printable course outline (pdf).

revised 210903