Mathematical Modelling

Mathematical Modelling

by Pramod Belkhode, Prashant Maheshwary, Kanchan Borkar, J.P. Modak
Released May 2023
Publisher(s): CRC Press
ISBN: 9781000840155

Read it now on the O’Reilly learning platform with a 10-day free trial.

O’Reilly members get unlimited access to books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.

Start your free trial

Book description

This book investigates human-machine systems through the use of case studies such as crankshaft maintenance, liner piston maintenance, and biodiesel blend performance.

Table of contents

  1. Cover Page
  2. Half Title page
  3. Title Page
  4. Copyright Page
  5. Contents
  6. Author Biographies
  7. 1 Evaluation of the System
    1. 1.1 Introduction
    2. 1.2 Causes and Effects Relationships
    3. 1.3 Ergonomics
    4. 1.4 Anthropometry
    5. 1.5 Approach to Formulate the Mathematical Model
  8. 2 Concept of Field Data-Based Modelling
    1. 2.1 Introduction
    2. 2.2 Formulation of Mathematical Model
    3. 2.3 Limitations of Adopting Field Database Model
    4. 2.4 Identification of Causes and Effects of an Activity
    5. 2.5 Dimensional Analysis
    6. 2.6 Dimensional Equation
      1. 2.6.1 Rayleigh’s Method
      2. 2.6.2 Buckingham π Theorem Method
  9. 3 Design of Experimentation
    1. 3.1 Introduction
    2. 3.2 Limitations of Adopting Field Data-Based Model Formulation for Man Machine System
    3. 3.3 The Approach for Formulating a Field or Experimental Data-Based Model
    4. 3.4 Identification of Variables
    5. 3.5 Problems Associated with Crankshaft/Liner Piston Maintenance Activities of Locoshed
      1. 3.5.1 Independent and Dependent Variables of Crankshaft Maintenance Activity
      2. 3.5.2 Dimensional Analysis of Crankshaft Maintenance Operation
      3. 3.5.3 Establishment of Dimensionless Pi Terms for Crankshaft Maintenance Activity
      4. 3.5.4 Formulation of a Field Data-Based Model for Response Variables of Crankshaft Maintenance Activity
      5. 3.5.5 Model Formulation by Identifying the Curve Fitting Constant and Various Indices of Pi Terms of Crankshaft Maintenance Activity
      6. 3.5.6 Independent and Dependent Variables of Liner Piston Maintenance
      7. 3.5.7 Dimensional Analysis of Liner Piston Maintenance
      8. 3.5.8 Establishment of Dimensionless Pi Terms for Liner Piston Maintenance
      9. 3.5.9 Formulation of a Field Data-Based Model for Response Variables of Liner Piston Maintenance
      10. 3.5.10 Model Formulation by Identifying the Curve Fitting Constant and Various Indices of Pi Terms of Liner Piston Maintenance
    6. 3.6 Problem Associated with Fossil Fuels
      1. 3.6.1 Diesel Blending
      2. 3.6.2 Independent and Dependent π Term
      3. 3.6.3 Establishment of Dimensionless Group of π Terms
      4. 3.6.4 Creation of Field Data-Based Model
      5. 3.6.5 Model Formulation by Identifying the Curve Fitting Constant and Various Indices of π Terms
    7. 3.7 Problem Associated with Conventional Power Generation
      1. 3.7.1 Identification of Variables Affecting the Phenomenon
      2. 3.7.2 Formation of Pi (π) Terms for All Dependent and Independent Variables Affecting the Phenomenon
      3. 3.7.3 Formulation of Experimental Data Base Model for Solar Updraft Tower
  10. 4 Experimentation
    1. 4.1 Introduction
    2. 4.2 Instrumentation and Data Collection
      1. 4.2.1 Instrumentation for Crankshaft Maintenance Activity
      2. 4.2.2 Data Collection f rom Field for Crankshaft Maintenance Activity
      3. 4.2.3 Instrumentation Used for Liner Piston Maintenance Activity
      4. 4.2.4 Data Collection from the Field for Liner Piston Maintenance Activity
      5. 4.2.5 Basis for Arriving at Number of Observations
      6. 4.2.6 Calculation of Field Human Energy Consumed in Maintenance Activity
      7. 4.2.7 Calculation of Human Energy Consumed in Crankshaft Maintenance Activity
      8. 4.2.8 Instrumentation and Collection of Data for Solar Updraft Tower
      9. 4.2.9 Instrumentation and Collection of Data for the Engine Performance by Using the Alternative Fuels
      10. 4.2.10 Establishment of Dimensionless Group of π Terms
      11. 4.2.11 Creation of Field Data-Based Model
      12. 4.2.12 Model Formulation by Identifying the Curve Fitting Constant and Various Indices of π Terms
      13. 4.2.13 Basis for Arriving at Number of Observations
  11. 5 Formulation of Mathematical Model
    1. 5.1 Formulation of Field Data-Based Model for Crankshaft Maintenance Operation
      1. 5.1.1 Model Formulation for πD1, Overhauling Time of Crankshaft Maintenance Activity by Identifying the Curve Fitting Constant and Various Indices of pi Terms
      2. 5.1.2 Model Formulation for πD2, Human Energy Consumed in Crankshaft Maintenance Activity by Identifying the Curve Fitting Constant and Various Indices of Pi Terms
      3. 5.1.3 Model Formulation for πD3, Productivity of Crankshaft Maintenance Activity by Identifying the Curve Fitting Constant and Various Indices of Pi Terms
      4. 5.1.4 Models Developed for the Dependent Variables – Crankshaft Maintenance Activity
    2. 5.2 Formulation of Field Data-Based Model For Liner Piston Maintenance Activity
      1. 5.2.1 Model Formulation for πD1, Overhauling Time of Liner Piston Maintenance Activity by Identifying the Curve Fitting Constant and Various Indices of Pi Terms
      2. 5.2.2 Model Formulation for πD2, Human Energy Consumed in Liner Piston Maintenance Activity by Identifying the Curve Fitting Constant and Various Indices of Pi Terms
      3. 5.2.3 Model Formulation for πD3, Productivity of Liner Piston Maintenance Activity by Identifying the Curve Fitting Constant and Various Indices of Pi Terms
      4. 5.2.4 Models Developed for the Dependent Variables − Liner Piston Maintenance Activity
    3. 5.3 Formulation of Field Data-Based Model for Diesel Blending
      1. 5.3.1 Model Formulation by Identifying the Curve Fitting Constant and Various Indices of π Terms
      2. 5.3.2 Model Formulation for Brake Thermal Efficiency (Z1)
      3. 5.3.3 Model Formulation for Brake-Specific Fuel Consumption (Z2)
    4. 5.4 Formulation of Field Data-Based Model for Solar Updraft Tower
      1. 5.4.1 Model Formulation for Turbine Speed Developed by Identifying the Constant and Various Indices of π Terms
      2. 5.4.2 Model Formulation for Turbine Power Developed by Identifying the Constant and Various Indices of π Terms
  12. 6 Artificial Neural Network Simulation
    1. 6.1 Introduction
    2. 6.2 Procedure for Formulation of ANN Simulation
    3. 6.3 Ann Program for Crankshaft Maintenance Activity
      1. 6.3.1 ANN Program for Overhauling Time of Crankshaft Maintenance Activity (z1C)
      2. 6.3.2 ANN Program For Human Energy Consumed in Crankshaft Maintenance Activity (z2C)
      3. 6.3.3 ANN Program for Productivity of Crankshaft Maintenance Activity (z3C)
    4. 6.4 ANN Program for Liner Piston Maintenance Activity
      1. 6.4.1 ANN Program for Overhauling Time of Liner Piston Maintenance Activity (z1P)
      2. 6.4.2 ANN Program for Human Energy Consumed in Liner Piston Maintenance Activity (z2P)
      3. 6.4.3 ANN Program for Productivity of Liner Piston Maintenance Activity (z3P)
    5. 6.5 ANN Program for Brake Thermal Efficiency and Brake-specific Fuel Consumption
      1. 6.5.1 ANN Program for Brake Thermal Efficiency
      2. 6.5.2 ANN Program for Brake-specific Fuel Consumption
    6. 6.6 ANN Program for Solar Updraft Tower
      1. 6.6.1 ANN Program for Turbine Speed
      2. 6.6.2 ANN Program for Turbine Power
  13. 7 Sensitivity Analysis
    1. 7.1 Sensitivity Analysis of Crankshaft Maintenance Activity
      1. 7.1.1 Effect of Introduced Change on the Dependent π Term – Overhauling Time of a Maintenance Activity of Crankshaft Maintenance Activity (z1C)
      2. 7.1.2 Effect of Introduced Change on the Dependent π Term – Human Energy Consumed in Crankshaft Maintenance Activity (z2C)
      3. 7.1.3 Effect of Introduced Change on the Dependent π term – Productivity of Crankshaft Maintenance Activity (z3C)
    2. 7.2 Sensitivity Analysis of Liner Piston Maintenance Activity
      1. 7.2.1 Effect of Introduced Change on the Dependent π Term – Overhauling Time of a of Liner Piston Maintenance Activity (z1P)
      2. 7.2.2 Effect of Introduced Change on the Dependent Pi Terms – Human Energy Consumed in Liner Piston Maintenance Activity (z2P)
      3. 7.2.3 Effect of Introduced Change on the Dependent π Term – Productivity of Liner Piston Maintenance Activity (z3P)
    3. 7.3 Optimization of Models for Crankshaft Maintenance Activity
    4. 7.4 Optimization of the Models for Liner Piston Maintenance Activity
    5. 7.5 Reliability of Models
      1. 7.5.1 Reliability of Crankshaft Maintenance Activity
      2. 7.5.2 Reliability of Liner Piston Maintenance Activity
    6. 7.6 Sensitivity Analysis of Brake Thermal Efficiency and Brake Specific Fuel Consumption
      1. 7.6.1 Effect of Introduced Change on the Dependent π Term: Brake Thermal Efficiency
      2. 7.6.2 Effect of Introduced Change on the Dependent π Term: Brake Thermal Efficiency
    7. 7.7 Sensitivity Analysis of Turbine Speed and Turbine Power
      1. 7.7.1 Effect of Introduced Change on the Dependent π Term: Turbine Speed
      2. 7.7.2 Effect of Introduced Change on the Dependent π Term: Power Developed
  14. 8 Interpretation of Mathematical Models
    1. 8.1 Models Developed for Dependent Variables of Crankshaft Maintenance Activity
      1. 8.1.1 Interpretation of Model of Crankshaft Maintenance Activity
        1. 8.1.1.1 Analysis of the Model for Dependent Pi Term – Overhauling Time of Crankshaft Maintenance Activity (z1C)
        2. 8.1.1.2 Analysis of the Model for Dependent Pi Term – Human Energy Consumed in Crankshaft Maintenance Activity (z2C)
        3. 8.1.1.3 Analysis of the Model for Dependent Pi Term – Productivity in Crankshaft Maintenance Activity (z3C)
      2. 8.1.2 Analysis of Performance of Models by ANN Simulation of Crankshaft Maintenance Activity
    2. 8.2 Models Developed for Dependent Variables of Liner Piston Maintenance Activity
      1. 8.2.1 Interpretation of Models of Liner Piston Maintenance Activity
      2. 8.2.2 Analysis of Performance of Models by ANN Simulation of Liner Piston Maintenance Activity
    3. 8.3 Analysis of The Mathematical Model for The Dependent Pi Term Brake Thermal Efficiency
    4. 8.4 Analysis of the Mathematical Model for the Dependent Pi Term Brake Specific Fuel Consumption
    5. 8.5 Models Developed for Dependent Variables Turbine Speed
      1. 8.5.1 Analysis of the Model for Dependent π Term Z1
    6. 8.6 Analysis of Performance of the Models of Power Developed
      1. 8.6.1 Interpretation of the Model
      2. 8.6.2 Analysis of the Model for Dependent π Term Z2
        1. 8.6.2.1 Analysis of Performance of the Models
  15. Bibliography

Product information

  • Title: Mathematical Modelling
  • Author(s): Pramod Belkhode, Prashant Maheshwary, Kanchan Borkar, J.P. Modak
  • Release date: May 2023
  • Publisher(s): CRC Press
  • ISBN: 9781000840155