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9783540343547

Optimal Design of Complex Mechanical Systems

by ; ;
  • ISBN13:

    9783540343547

  • ISBN10:

    3540343547

  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2006-10-31
  • Publisher: Springer Verlag
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Summary

"Optimal Design of Complex Mechanical Systems" presents the foundations and practical application of multi-objective optimization methods to Vehicle Design Problems with an extensive overview of examples. The first part provides an introduction and a general theoretical information about the optimization of complex mechanical systems and multi-objective optimization methods. Several presented applications such as the global approximation approach are brand new in literature and extensively exposed the first time in this book. The second Part of the book shows some examples of the application of the proposed methods to the solution of real vehicle design problems.

Table of Contents

Part I Theory
1 Introduction to the Optimal Design of Complex Mechanical Systems
3(22)
1.1 On the Optimal Design of Complex Systems
3(9)
1.2 Finding the Pareto-optimal Sets
12(9)
1.2.1 Exhaustive Method
12(2)
1.2.2 Uniformly Distributed Sequences and Random Search
14(1)
1.2.3 Genetic Algorithms
15(1)
1.2.4 Comparison of Broadly Applicable Methods to Solve Optimisation Problems
16(1)
1.2.5 Global Approximation
16(3)
1.2.6 Multi-objective Programming via Non-linear Programming
19(2)
1.2.7 Algorithms to Solve Optimisation Problems in Scalar Form
21(1)
1.3 Understanding Pareto-optimal Solutions
21(4)
2 Engineering Design and Optimal Design of Complex Mechanical Systems: Definitions
25(22)
2.1 Engineering Design
25(3)
2.1.1 Stages of the Design Process
25(2)
2.1.2 Creativity
27(1)
2.2 Optimal Design of Complex Mechanical Systems
28(2)
2.2.1 Fundamental Hypothesis
28(1)
2.2.2 Single– and Multi-criteria Optimisation
28(1)
2.2.3 Multi-criteria Optimisation (MCO)
28(1)
2.2.4 multi-objective Optimisation (MOO)
29(1)
2.2.5 Multi-objective Programming (MOP)
29(1)
2.3 Complex Systems
30(1)
2.4 System Models
31(1)
2.5 System Performances, Criteria, Objective Functions
32(1)
2.6 System Parameters, Design Variables
33(1)
2.7 Constraints
33(1)
2.8 Space of Design Variables, Space of Objective Functions
34(1)
2.9 Feasible Design Variables Domain, Design Solution
34(1)
2.9.1 Conflict
34(1)
2.10 Multi-objective Programming (MOP)
34(10)
2.10.1 Non-linear Programming (NLP) and Constrained Minimisation
34(3)
2.10.2 Multi-objective Programming: Definition
37(1)
2.10.3 Pareto-optimal Solutions and Pareto-optimal Set
38(3)
2.10.4 Ideal and Nadir Design Solutions
41(1)
2.10.5 Related Concepts
42(1)
2.10.6 Basic Problems and Capabilities of Multi-objective Optimisation
43(1)
2.11 Decomposition of Design Problems
44(3)
3 Multi-objective Optimisation
47(52)
3.1 Methods to Solve Multi-objective Programming (MOP) Problems
47(1)
3.2 Pareto-optimal Set Generation Methods
48(2)
3.3 Global Sensitivity Analysis
50(6)
3.3.1 Global Sensitivity Analysis Based on Linear Regression Methods
50(2)
3.3.2 Sobol Method
52(1)
3.3.3 Spearman Rank Correlation Coefficient
53(3)
3.3.4 Global Sensitivity Via Artificial Neural Network
56(1)
3.4 Pareto-optimal Set Computation
56(27)
3.4.1 Exhaustive Method
57(1)
3.4.2 Low Discrepancy Sequences
57(10)
3.4.3 Selection of the Pareto-optimal Set
67(1)
3.4.4 Genetic Algorithms
68(7)
3.4.5 Unconstrained Minimisation
75(1)
3.4.6 Simplex Method
76(1)
3.4.7 Sequential Unconstrained Minimisation Techniques
76(2)
3.4.8 Method of Feasible Directions, Sequential Quadratic Programming
78(1)
3.4.9 Weighted Sum
79(1)
3.4.10 Constraints Method
80(3)
3.5 Design Synthesis — Choosing a Final Design Solution
83(6)
3.5.1 Utility Function
83(1)
3.5.2 Lexicographic Ordering
84(1)
3.5.3 Goal Programming
85(1)
3.5.4 Preference Via Trained Artificial Neural Network
86(1)
3.5.5 Min—Max Methods
86(2)
3.5.6 Hierarchical Optimisation Method
88(1)
3.5.7 Normal–Boundary Intersection Method
88(1)
3.6 Interactive Methods
89(6)
3.6.1 Interactive Computation of the Pareto-optimal Solutions and Pareto-optimal Set Boundaries Through Pareto Sensitivity Analysis
91(4)
3.7 Symbolical Derivation of PO Sets
95(2)
3.7.1 Theorems of Monotonicity (Optimisation Problems with Constraints)
95(1)
3.7.2 Theorems of Monotonicity (Optimisation Problems without Constraints)
96(1)
3.8 Illustrating the Pareto-optimal Set
97(2)
4 Global Approximation
99(22)
4.1 Global Approximation Techniques
100(1)
4.2 Training Data Generation
101(1)
4.2.1 (Fractional) Factorial Designs
101(1)
4.2.2 Uniformly Distributed Sequences and Orthogonal Array
102(1)
4.3 Selection of the Global Approximation Model
102(2)
4.3.1 Polynomial Linear and Quadratic Interpolation
102(2)
4.4 Least Squares Regression Polynomial Approximation
104(2)
4.5 Kriging Interpolating Models
106(1)
4.6 Artificial Neural Networks
106(15)
4.6.1 Multi-layer Perceptron Neural Network
107(5)
4.6.2 Radial Basis Function Neural Network
112(9)
Part II Applications
5 Optimal Ride Comfort and Active Safety of Road Vehicles
121(38)
5.1 System Model of a Passively Suspended Vehicle
122(10)
5.1.1 Equations of Motion and Response to Stochastic Excitation
122(2)
5.1.2 Derivation of Standard Deviations in Analytical Form
124(4)
5.1.3 Parameter Sensitivity Analysis
128(4)
5.2 Passively Suspended Vehicle System Optimisation
132(10)
5.2.1 Problem Formulation
132(1)
5.2.2 Optimal Performances and Suspension Design Variables
132(10)
5.3 System Model of an Actively Suspended Road Vehicle
142(5)
5.3.1 Equations of Motion and Response to Stochastic Excitation
142(1)
5.3.2 Derivation of Standard Deviations in Analytical Form
143(3)
5.3.3 Comparison of 1S-PSD and 2S-PSD Formulae
146(1)
5.3.4 Validation Problems and Usefulness of the Presented Theory
146(1)
5.4 Actively Suspended Vehicle System Optimisation
147(10)
5.4.1 Optimal Performances and Suspension Design Variables
147(10)
5.5 Conclusion
157(1)
5.6 Appendix: Tabulated Values of the Integral Form
158(1)
6 Optimal Handling and Active Safety of Road Vehicles
159(32)
6.1 System Model
160(13)
6.1.1 Vehicle Response to a Steering Step Input: Linear Model
162(3)
6.1.2 Vehicle Response to a Steering Step Input: Non-Linear Model
165(3)
6.1.3 Objective Functions
168(5)
6.2 Results of the Optimisation
173(9)
6.2.1 Analytical Solution (Linear Case)
174(5)
6.2.2 Numerical Solutions (Linear Case)
179(1)
6.2.3 Numerical Solution (Non-Linear Case)
180(2)
6.3 Validation
182(5)
6.3.1 Validation of the Model
182(3)
6.3.2 Validation of the Optimisation Process
185(2)
6.4 Conclusion
187(4)
7 Optimal Design of the Tyre-Suspension System of a Racing Car
191(24)
7.1 System Model
192(2)
7.1.1 Vehicle Model
192(1)
7.1.2 Tyre Model
193(1)
7.1.3 Validation
193(1)
7.2 Design Variables
194(5)
7.2.1 Suspension System
196(2)
7.2.2 Tyre Characteristic
198(1)
7.3 Running Situations and Objective Functions
199(4)
7.3.1 Steady-state Turning
199(2)
7.3.2 J-Turn
201(1)
7.3.3 Power On–Off while Steering
201(1)
7.3.4 Braking into a Bend
202(1)
7.3.5 Passing over a Kerb While Steering
202(1)
7.4 Search Method
203(2)
7.4.1 Reduction of Objective Functions
203(1)
7.4.2 Pareto-optimal Solutions
203(2)
7.5 Results
205(7)
7.5.1 Comparison of the Performances of Global Approximation Methods
206(6)
7.6 Conclusion
212(3)
8 Integrated Controls for the Improvement of Ride, Comfort, Handling and Active Safety of Road Vehicles
215(30)
8.1 System Models and Reference Driving Situations
216(7)
8.1.1 System Models
216(1)
8.1.2 Reference Driving Situations
216(7)
8.2 Numerical Application
223(20)
8.2.1 First Iteration
223(9)
8.2.2 Second (and Final) Iteration
232(11)
8.3 Conclusions
243(2)
9 Optimal Design of a Double-Cone Synchroniser
245(18)
9.1 Synchroniser System Model
246(3)
9.1.1 Physical Model
246(3)
9.2 Formulation of the Design Problem for the Optimisation of a Synchroniser
249(4)
9.2.1 Design Variables
249(1)
9.2.2 Objective Functions
249(2)
9.2.3 Constraints
251(2)
9.3 Method for the Optimal Design of a Synchroniser
253(5)
9.3.1 Feasible Design Variables Domain
253(1)
9.3.2 Global Sensitivity Analysis
253(2)
9.3.3 Global Approximation
255(1)
9.3.4 Quasi-Monte Carlo Search
256(1)
9.3.5 Multi-Objective Optimisation
257(1)
9.3.6 Robust Design and Synthesis of Optimal Design Solutions
257(1)
9.4 Optimal Design of a Synchroniser
258(2)
9.5 Conclusion
260(3)
10 Optimal Design of the Suspension System of Railway Vehicles
263(22)
10.1 System Model
263(11)
10.1.1 Equations of Motion and Responses to Stochastic Excitation
263(4)
10.1.2 Derivation of Standard Deviations in Analytical Form
267(2)
10.1.3 Complete Formulae Using the 1S-PSD (Eq. (10.7))
269(1)
10.1.4 Formulae for Vanishing Primary Damping Using the 1S-PSD (Eq. (10.7))
270(1)
10.1.5 Simplified Formulae Using the 1S-PSD (Eq. (10.7))
271(1)
10.1.6 Complete Formulae Using the 2S-PSD (Eq. (10.8))
272(1)
10.1.7 Formulae for Vanishing Primary Damping Using the 2S-PSD (Eq. (10.8))
272(1)
10.1.8 Simplified Formulae Using the 2S-PSD (Eq. (10.8))
273(1)
10.2 Validation
274(2)
10.2.1 Primary Stiffness
274(1)
10.2.2 Natural Frequency
275(1)
10.2.3 Damping Ratio
275(1)
10.3 Parameter Sensitivity Analysis
276(7)
10.3.1 Standard Deviation of Force on Axle-box
276(1)
10.3.2 Standard Deviation of Body Acceleration
277(1)
10.3.3 Standard Deviation of Secondary Stroke
278(1)
10.3.4 Optimal Secondary Suspension Design Variables
279(4)
10.4 Conclusion
283(2)
11 Optimal Design of the Layout of Railway Passenger Vehicles
285(18)
11.1 Design Aims and Related Objective Functions
286(2)
11.2 Design Variables to Be Tuned
288(1)
11.3 Constraints
288(2)
11.4 Objective Functions
290(6)
11.4.1 Unloaded Vehicle Mass/Fully Loaded Vehicle Mass
290(3)
11.4.2 Vehicle Length/Payload
293(1)
11.4.3 Ride Comfort
293(1)
11.4.4 Vehicle/Track Dynamic Interaction
293(1)
11.4.5 Three Degrees of Freedom Model
294(2)
11.4.6 Other Indices
296(1)
11.5 Analysis and Choice of Preferred Optimal Solutions
296(5)
11.5.1 Inter-city Cars
298(1)
11.5.2 Sub-urban Cars
298(1)
11.5.3 Urban Cars
299(2)
11.6 Conclusion
301(2)
12 Optimal Design of Helical Spring
303(28)
12.1 Fundamentals of. Optimal Design of Springs
304(4)
12.2 Composite Tubular Spring Models
308(10)
12.2.1 Stress, Strain and Spring Stiffness
309(4)
12.2.2 Global Stability
313(1)
12.2.3 Local Stability
313(3)
12.2.4 Vibrations
316(1)
12.2.5 Spring Material Strength
317(1)
12.3 Model Validation
318(3)
12.4 Numerical Application
321(7)
12.4.1 Design Aims and Related Objective Functions
321(1)
12.4.2 Design Variables to Be Tuned
322(1)
12.4.3 Constraints
323(1)
12.4.4 Finding Optimal Solutions
324(1)
12.4.5 Analysis of the Optimal Solutions
324(4)
12.5 Conclusions
328(1)
12.6 Appendix: Analytical Expression of Critical Load
329(2)
13 Interactive Optimisation of a Flywheel
331(12)
13.1 System Model
332(2)
13.2 Objective Functions
334(1)
13.3 Design Variables
335(1)
13.4 Results
336(7)
References 343(12)
Index 355

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