Condition Monitoring Algorithms in MATLAB® (Springer Tracts in Mechanical Engineering)

Foreword
Preface
Acknowledgements
Contents
About the Author
Abbreviations
1 Introduction
	Abstract
	1.1 Why Machinery is Measured?
	1.2 What is Signal Processing Method Development?
	1.3 Commercialization of Novel Diagnostic Techniques
		1.3.1 Case-Based Deduction
		1.3.2 Supervised Data Acquisition
		1.3.3 Multidimensional Analysis
	1.4 Supporting CMS with MATLAB®
	1.5 The Scope
	References
2 Principles of Condition Monitoring Systems
	Abstract
	2.1 Overview
	2.2 CMS Tasks
	2.3 CMS Classification
		2.3.1 Tasks-Based Classification
		2.3.2 Discussion on CMS-Related Glossary
		2.3.3 Other Classifications
	2.4 Stationary CMS Architecture
	2.5 CMS Configuration and Implementation
		2.5.1 Implementation Stages
		2.5.2 CMS Selection
		2.5.3 Initial Configuration, Installation, and Commissioning
		2.5.4 Post-Reference Configuration Tuning
		2.5.5 Final System Tuning
	2.6 CMS Operation and Support
	References
3 Vibration Components Generated by Rotary Machinery
	Abstract
	3.1 Hardware Parameters
	3.2 Vibration Signature
	3.3 The Concept of “Characteristic Frequency”
	3.4 The Concept of “Characteristic Order”
	3.5 Basic Mechanical Components
		3.5.1 Shafts
		3.5.2 Blades
			3.5.2.1 Common-Speed Machinery
			3.5.2.2 Fast-Speed Machinery
		3.5.3 Gearboxes
			3.5.3.1 Parallel Gearboxes
			3.5.3.2 Epicyclic Gearboxes and Multi-stage Gearboxes
		3.5.4 Rolling Element Bearings (REBs)
	3.6 Harmonic Components
		3.6.1 Why Harmonic Components Are Generated in Spectrum?
		3.6.2 Why Harmonic Components Are Generated in Envelope Spectrum?
		3.6.3 What Are Harmonics of Harmonics?
	3.7 Note on Additional Modulations
	References
4 Signal Processing Algorithms
	Abstract
	4.1 Basic Preprocessing Algorithms
		4.1.1 Scaling
		4.1.2 Windowing and Compensation
		4.1.3 Trimming and Zero-Padding
			4.1.3.1 Overview
			4.1.3.2 Numerical Example of One-Sided Preprocessing
			4.1.3.3 Influence on a Spectrum
	4.2 Basic Processing Algorithms
		4.2.1 Filtering
			4.2.1.1 Overview
			4.2.1.2 Filtering Paths and Filter Data Structures
			4.2.1.3 Quick Command Line Filtering
			4.2.1.4 Advanced Command Line Filtering
				4.2.1.4.1 Quick Functions (digitalFilter Class)
				Designfilt Function (digitalFilter Class)
				Fdesign and Design Functions (DSP Toolbox™)
				Butter Function (Filter Coefficients)
			4.2.1.5 GUI-Supported Filtering
				Filter Design
				Filter Implementation of GUI-Generated Filters
				Filter Analysis
			4.2.1.6 User Frequency Domain Filtering
				Synthetic Signal Description
				Low-Pass Filtering
				High-Pass Filtering
				Band-Stop Filtering
				Band-Pass Filtering
			4.2.1.7 Function Reference
			4.2.1.8 Beyond MATLAB®—Filter Coefficients in C Language
		4.2.2 Resampling and Order Spectrum Basics
			4.2.2.1 General Concept
			4.2.2.2 Dictionary
			4.2.2.3 List of Operations
			4.2.2.4 Simplified Algorithm
			4.2.2.5 Advanced Algorithm
			4.2.2.6 Example 1—Synthetic Data
			4.2.2.7 Example 2—Real Data
		4.2.3 Integration
			4.2.3.1 Noise-Free Synthetic Signal
			4.2.3.2 Noisy Synthetic Signal
			4.2.3.3 Real Signal
	4.3 Combined Processing Algorithms
		4.3.1 Signal Envelope and Envelope Spectrum
			4.3.1.1 Overview
			4.3.1.2 MATLAB® Documentation and Functions
			4.3.1.3 Step-by-Step Classical Time-Domain Signal Envelope Example
			4.3.1.4 Analytical Considerations
			4.3.1.5 General Envelope Calculation Function
			4.3.1.6 PATH 1: Envelope Spectrum from Time-Domain Filtered Signal
			4.3.1.7 PATH 2: Envelope Spectrum from Frequency-Domain Filtered Signal
			4.3.1.8 PATH 3: Envelope Order Spectrum from Angle-Domain Filtered Signal
			4.3.1.9 PATH 4: Envelope Order Spectrum from Order-Domain Filtered Signal
			4.3.1.10 Summary
		4.3.2 Velocity and Displacement Spectrum from Acceleration Signal
			4.3.2.1 Overview
			4.3.2.2 Algorithms in a Nutshell
			4.3.2.3 Signal Processing Blocks
				4.3.2.3.1 HP Filtration
				4.3.2.3.2 Integration
				4.3.2.3.3 Signal Scaling
				4.3.2.3.4 Resampling
				4.3.2.3.5 Calculation of Spectral Amplitudes
				4.3.2.3.6 Calculation of Spectral Resolution
			4.3.2.4 Examples
				4.3.2.4.1 List of Signals
				4.3.2.4.1 Single Sinusoidal Component
				4.3.2.4.3 Variable Speed Component
				4.3.2.4.4 Real Rotary Machinery Signal
			4.3.2.5 Influence of Filtering Domain
			4.3.2.6 Omega Arithmetics
			4.3.2.7 Displacements Spectrum
				4.3.2.7.1 General Concept
				4.3.2.7.2 Single Sinusoidal Component
				4.3.2.7.3 Real Rotary Machinery Signal
		4.3.3 Time Synchronous Averaging (TSA)
			4.3.3.1 Overview
			4.3.3.2 Time-Domain and Angle-Domain Waveforms
				MATLAB® “tsa” Function
				4.3.3.2.2 User Analysis of Rational Transmission Ratios
			4.3.3.3 Resampled Signals Spectral Analysis
			4.3.3.4 TSA Signals Spectral Analysis
	4.4 Instantaneous Speed Calculation and Reconstruction
		4.4.1 Basic Operations on Real Phase Marker (PM) Signal
		4.4.2 Tachorpm Function
		4.4.3 Explanation of Instantaneous Speed Shape Profile
		4.4.4 Extraction of Instantaneous Speed from Tacholess Vibration Signal
			4.4.4.1 Overview
			4.4.4.2 Simple Sinusoidal Signals
				4.4.4.2.1 Findpeaks Function
				4.4.4.2.2 User Pulse Detection Function
				4.4.4.2.3 Signal Phase Demodulation
			4.4.4.3 Complex Real Signals
				4.4.4.3.1 General Concept
				4.4.4.3.2 Limited Speed Fluctuation (Direct Phase Demodulation)
				4.4.4.3.3 Urbanek’s Two-Step Procedure in RPM Track Tool
				4.4.4.3.4 Polygon-Based Reconstruction
		4.4.5 Summarizing Comparison
	4.5 Other SP Algorithms
	References
5 Vibration-Based Condition Assessment Methods
	Abstract
	5.1 Overview
	5.2 MATLAB® Predictive Maintenance Toolbox™
	5.3 Protection Scalar Health Indicators
		5.3.1 Acceleration PP
		5.3.2 Acceleration RMS
		5.3.3 Velocity RMS
			5.3.3.1 Overview
			5.3.3.2 VRMS Calculated in Time-Domain
			5.3.3.3 VRMS Calculated in Frequency-Domain
			5.3.3.4 Practical Considerations
	5.4 Monitoring Scalar Health Indicators as Trend Data
		5.4.1 Classification of Monitoring Health Indicators
		5.4.2 Trend Data
	5.5 Evaluation of Scalar Health Indicators
		5.5.1 General Evaluation Paths
		5.5.2 Extraction of Narrowband Signals
		5.5.3 Evaluation of Spectral Amplitudes of Narrowband Signals
		5.5.4 Evaluation of Spectral Indexes of Narrowband Health Indicators
	5.6 Extended Role of Scalar Indicators in Diagnostic System
	5.7 Diagnostic Figures
		5.7.1 Classification and Selection
		5.7.2 2-D Figures Generated from a Single Continuous Signal
			5.7.2.1 General Concept
			5.7.2.2 Time-Domain Waveform (TD)
			5.7.2.3 Spectrum (S)
			5.7.2.4 Averaged Spectrum (AS)
		5.7.3 3-D Figures Generated from a Single Signal (Colormaps)
		5.7.4 3-D Figures Generated from Array of Discontinuous Signals
	5.8 A Note on Selected Time–Frequency Representations
		5.8.1 General Relations
		5.8.2 Streaming Data Relations
			5.8.2.1 Time-Domain Relations
			5.8.2.2 Frequency-Domain Relations
		5.8.3 Diagnostic Relations
	References
6 Synthetic Signals Generation Methods
	Abstract
	6.1 Overview
	6.2 Sinusoidal Components
		6.2.1 Sinusoidal Template
		6.2.2 Basic Operations on a Single Sinusoidal Component
			6.2.2.1 Amplitude Modulation (AM)
				6.2.2.1.1 Overview
				6.2.2.1.2 Periodic Amplitude Modulation (P-AM)
				6.2.2.1.3 Non-Periodic Monotonic Amplitude Modulation (NPM-AM)
				6.2.2.1.4 Non-Periodic, Quasi-Monotonic Amplitude Modulation (NPQM-AM)
				6.2.2.1.5 Non-Periodic Generalized Amplitude Modulation (NPG-AM)
			6.2.2.2 Frequency Modulation (FM)
				6.2.2.2.1 Overview
				6.2.2.2.2 Periodic Frequency Modulation (P-FM)
				6.2.2.2.3 Non-Periodic Monotonic Frequency Modulation (NPM-FM)
				6.2.2.2.4 Non-Periodic Generalized Frequency Modulation (NPG-FM)
		6.2.3 Combinations of Basic Operations
			6.2.3.1 Oscillatory Signal (P-AM with P-FM)
			6.2.3.2 Run-Up with Critical Speed (NPM-AM + CS Window with NPM-FM)
			6.2.3.3 Generation of Pseudo-FRF (PFRF) Profile
			6.2.3.4 Generalized AM and FM Modulation
	6.3 Decaying Pulses
		6.3.1 Basic Operations
			6.3.1.1 Determination of Time of Pulses
			6.3.1.2 Simplified Signal with Deterministic Carrier
			6.3.1.3 Pulses with Narrowband Random Carrier Signal
			6.3.1.4 Pulses with Periodically Oscillating Repetition Rate
			6.3.1.5 Pulses with Monotonically Increasing Repetition Rate
			6.3.1.6 Pulses with Generalized Frequency-Modulated Repetition Rate
			6.3.1.7 Additional Phase-Locked AM
		6.3.2 Combinations of Operations
			6.3.2.1 Oscillatory Pulses
			6.3.2.2 Run-Up with Critical Speed
			6.3.2.3 Additional Phase-Locked Non-Periodic AM
			6.3.2.4 Generalized AM and FM Modulation
		6.3.3 Jitter
			6.3.3.1 Overview
			6.3.3.2 Jitter as a Cumulative Variable
			6.3.3.3 Jitter as Independent Variable
			6.3.3.4 Combination of Operations
	References
7 Simulating Operational Signals
	Abstract
	7.1 Concept Description
	7.2 Simulated Object Description
		7.2.1 Mechanical Parameters
		7.2.2 Characteristic Orders and Frequencies
	7.3 Signal Generation Graphical Framework
		7.3.1 Slow Shaft Imbalance
		7.3.2 REB Local Inner Race Fault
	7.4 Code Description
		7.4.1 Data Acquisition Parameters
		7.4.2 Generation of User Profiles
			7.4.2.1 Overview
			7.4.2.2 Profile #1: Operational Speed Profile
			7.4.2.3 Profile #2: Pseudo-FRF Profile
			7.4.2.4 Profile #3: Structural Noise Profile
		7.4.3 Definition of Principal Static Data
	7.5 Signal Components
		7.5.1 Fast Shaft and Slow Shaft
		7.5.2 Gearbox
		7.5.3 Rolling Element Bearing
		7.5.4 Random Noise
	7.6 Finalization
	7.7 Resultant Signal
		7.7.1 Two-Dimensional Plots
		7.7.2 Selected Spectrogram Visualization
	References
8 Simulating Long-Term Machine Fault Development
	Abstract
	8.1 Overview
	8.2 Failure Mode and Failure Development Function (FDF)
	8.3 General Scheme of Long-Term Data Generation
	8.4 Relations Between Profiles
	8.5 Code Description
		8.5.1 STAGE No. 1: Generate Failure Mode Functions
		8.5.2 STAGE No. 2: Define Data Acquisition Parameters
		8.5.3 STAGE No. 3: Generate Common-Pseudo PFRF
		8.5.4 STAGE No. 4: Generate (and Store) Common Structural Noise Base
		8.5.5 STAGE No. 5: Generate and Save Signals
			8.5.5.1 General Information
			8.5.5.2 Function Description
			8.5.5.3 Making Data Folders
			8.5.5.4 Creating General Variables
			8.5.5.5 Main Loop
			8.5.5.6 Finalization
	8.6 Generated Data
	8.7 A Note on the Role of Random Numbers
9 Analysis of Long-Term Fault Development
	Abstract
	9.1 How Large Industrial Data Sets Are Analyzed?
	9.2 Statistical Data Analysis
	9.3 Narrowband Spectral Analysis
		9.3.1 General Information
		9.3.2 Selected Results
	9.4 Two-Dimensional (Spectral) Comparison
		9.4.1 General Information
		9.4.2 Selected Results
			9.4.2.1 No Fault Case
			9.4.2.2 Imbalance Detection and Identification
			9.4.2.3 Gearbox Fault Detection and Identification
			9.4.2.4 REB Fault Detection and Identification
			9.4.2.5 Combined Faults
	9.5 Three-Dimensional Visualization
		9.5.1 General Information
		9.5.2 Selected Results
			9.5.2.1 Imbalance Detection and Identification
			9.5.2.2 Gearbox Fault Detection and Identification
			9.5.2.3 REB Fault Detection and Identification
			9.5.2.4 Multi-fault Detection
		9.5.3 MATLAB® Code for 3-D Analysis of Multiple Discontinuous Signals
			9.5.3.1 Code Framework
			9.5.3.2 Step_1_Select_Data_Folder
			9.5.3.3 Step_2_Select_Spectrum_Type_and_Parameters
			9.5.3.4 STEP_3_CONSTRUCT_ARRAY—Algorithm
			9.5.3.5 STEP_3_CONSTRUCT_ARRAY—Code
			9.5.3.6 Step_4_Generate_Abscissa
			9.5.3.7 Step_5_Select_Display_Options
			9.5.3.8 Step_6_Plot
			9.5.3.9 A Note on Selection of Plotting Function
	9.6 Comparison of Methods
	Reference
10 Connecting MATLAB® to CMS
	Abstract
	10.1 The Role of a PC Computer
	10.2 Data Flow Directions
	10.3 Data Type-Based Roles of MATLAB®
	10.4 Data Type Conversion
	10.5 Array Data and Metadata
	10.6 Exporting Data from MATLAB®
		10.6.1 Overview of Methods
		10.6.2 Manual Data Export
		10.6.3 Programmable Data Conversion
			10.6.3.1 Before Exporting the Data
			10.6.3.2 Exporting via fprintf Function
			10.6.3.3 Exporting via Other Functions
			10.6.3.4 Summary
		10.6.4 Numerical Data Precision
			10.6.4.1 Basic Concept
			10.6.4.2 Full Precision
			10.6.4.3 Data Compression and Placement of the Phase Marker (PM) Bit
			10.6.4.4 Loop Design
	10.7 Importing Data into MATLAB®
		10.7.1 Overview of Methods
		10.7.2 Interactive Data Import
		10.7.3 Programmable Data Import
		10.7.4 Direct Access to CMS Replicated Data Using CMS Libraries
	References
11 Development of Interface for Direct Data Access (DDA)
	Abstract
	11.1 Basic Concept
	11.2 Step-by-Step Procedure
	11.3 CMS Configuration Handling
	11.4 Additional Concerns
		11.4.1 File Versus Database Data Source
		11.4.2 Permission Levels
	References
12 Prototype Tools
	Abstract
	12.1 Overview
	12.2 Script-Based Testing of Health Indicators
		12.2.1 MATLAB® Code for Direct Data Access
		12.2.2 Shaft Imbalance Example
	12.3 GUI-Based Spectral Analysis of Large Data Sets
		12.3.1 MATLAB® Code for Direct Data Access
		12.3.2 Shaft Imbalance Example
		12.3.3 Pump Cavitation
	12.4 Other Concepts
		12.4.1 CMS Performance Display
		12.4.2 Threshold Configuration
	12.5 Summary of Prototype Tools
Index