Aims

The aims of the course are to:

• Instil an intuitive approach to structural design.
• Introduce advanced concepts related to the design of structures.

Objectives

As specific objectives, by the end of the course students should be able to:

• Design a wide variety of structures which meet both aesthetic and efficiency criteria.
• Describe the relationship between form and force.
• Manipulate structural geometry or forces to improve the structural behaviour.
• Describe Airy stress functions and be able to design structures using them.
• Describe the relationship between states of self-stress and mechanisms.
• Design prestressable structures which contain mechanisms.
• Describe the load path and how to optimise it.
• Use Lagrange multipliers in constrained optimisation problems in structural design.
• Understand the requirements for minimal total structural volume.
• Describe stiffness and stability from a geometrical perspective.
• Design gridshells and nets. Understand the unique behaviour of each.
• Intuitively understand structural behaviour so that visual design can occur.
• Describe the implications a structure’s design has on the stakeholders.

Content

Content and delivery will be largely provided by Prof Bill Baker. Prof Baker is the consulting partner at Skidmore Owings and Merrill in Chicago and Honorary Professor of this department. He is the world's leading structural engineer for the design of buildings and has been responsible for the design of many of the world's more iconic buildings. Prof Baker will teach the skills needed to become a proficient structural designer. The course aims to inform students about powerful new design tools which are growing in popularity throughout industry, many of which have been developed by Prof Baker in collaboration with this department.

Introduction to the course

A short history of structures and architecture. The importance of geometry and design. Discussion of its wide-reaching impacts and implications.

Graphic statics

Relationship between the form and force. How to design structures so that the forces flow where the designer wants them to.

Maxwell load path theorem

What it is and how it relates to the total volume of structural material used.

Force density

How we can use it to solve linear problems to find the geometry.

Virtual work and energy sizing

How it may be used to optimise the structural geometry, using Lagrange multipliers.

Michell trusses

Optimal structures and their behaviour.

Form finding for trusses

Discussion of the tools available to optimise topology, shape and size for structure.

Mechanisms and states of self-stress

The geometric relationship between mechanisms and states of self-stress, and the Maxwell-Calladine and Euler counts to obtain structurally sound trusses.

Geometric stiffness

The stiffness of structures and mechanisms is considered using force density. A short introduction to rigidity theory.

Airy stress functions and their application to truss design

To identify states of self-stress and mechanisms. The use of funiculars to include external loading.

Design of Gridshells and Cable Nets

How to design shells and gridshells using the Airy stress function and force density. The importance of obtaining planar faces and torsion free nodes. We also consider the design of tension structures, using prestress to stabilise mechanisms.

Aims

The aims of the course are to:

• Instil an intuitive approach to structural design.
• Introduce advanced concepts related to the design of structures.

Objectives

As specific objectives, by the end of the course students should be able to:

• Design a wide variety of structures which meet both aesthetic and efficiency criteria.
• Describe the relationship between form and force.
• Manipulate structural geometry or forces to improve the structural behaviour.
• Describe Airy stress functions and be able to design structures using them.
• Describe the relationship between states of self-stress and mechanisms.
• Design prestressable structures which contain mechanisms.
• Describe the load path and how to optimise it.
• Use Lagrange multipliers in constrained optimisation problems in structural design.
• Understand the requirements for minimal total structural volume.
• Describe stiffness and stability from a geometrical perspective.
• Design gridshells and nets. Understand the unique behaviour of each.
• Intuitively understand structural behaviour so that visual design can occur.
• Describe the implications a structure’s design has on the stakeholders.

Content

Content and delivery will be largely provided by Prof Bill Baker. Prof Baker is the consulting partner at Skidmore Owings and Merrill in Chicago and Honorary Professor of this department. He is the world's leading structural engineer for the design of buildings and has been responsible for the design of many of the world's more iconic buildings. Prof Baker will teach the skills needed to become a proficient structural designer. The course aims to inform students about powerful new design tools which are growing in popularity throughout industry, many of which have been developed by Prof Baker in collaboration with this department.

Introduction to the course

A short history of structures and architecture. The importance of geometry and design. Discussion of its wide-reaching impacts and implications.

Graphic statics

Relationship between the form and force. How to design structures so that the forces flow where the designer wants them to.

Maxwell load path theorem

What it is and how it relates to the total volume of structural material used.

Force density

How we can use it to solve linear problems to find the geometry.

Virtual work and energy sizing

How it may be used to optimise the structural geometry, using Lagrange multipliers.

Michell trusses

Optimal structures and their behaviour.

Form finding for trusses

Discussion of the tools available to optimise topology, shape and size for structure.

Mechanisms and states of self-stress

The geometric relationship between mechanisms and states of self-stress, and the Maxwell-Calladine and Euler counts to obtain structurally sound trusses.

Geometric stiffness

The stiffness of structures and mechanisms is considered using force density. A short introduction to rigidity theory.

Airy stress functions and their application to truss design

To identify states of self-stress and mechanisms. The use of funiculars to include external loading.

Design of Gridshells and Cable Nets

How to design shells and gridshells using the Airy stress function and force density. The importance of obtaining planar faces and torsion free nodes. We also consider the design of tension structures, using prestress to stabilise mechanisms.

Aims

The aims of the course are to:

• Instil an intuitive approach to structural design.
• Introduce advanced concepts related to the design of structures.

Objectives

As specific objectives, by the end of the course students should be able to:

• Design a wide variety of structures which meet both aesthetic and efficiency criteria.
• Describe the relationship between form and force.
• Manipulate structural geometry or forces to improve the structural behaviour.
• Describe Airy stress functions and be able to design structures using them.
• Describe the relationship between states of self-stress and mechanisms.
• Design prestressable structures which contain mechanisms.
• Describe the load path and how to optimise it.
• Use Lagrange multipliers in constrained optimisation problems in structural design.
• Understand the requirements for minimal total structural volume.
• Describe stiffness and stability from a geometrical perspective.
• Design gridshells and nets. Understand the unique behaviour of each.
• Intuitively understand structural behaviour so that visual design can occur.
• Describe the implications a structure’s design has on the stakeholders.

Content

Content and delivery will be largely provided by Prof Bill Baker. Prof Baker is the consulting partner at Skidmore Owings and Merrill in Chicago and Honorary Professor of this department. He is the world's leading structural engineer for the design of buildings and has been responsible for the design of many of the world's more iconic buildings. Prof Baker will teach the skills needed to become a proficient structural designer. The course aims to inform students about powerful new design tools which are growing in popularity throughout industry, many of which have been developed by Prof Baker in collaboration with this department.

Introduction to the course

A short history of structures and architecture. The importance of geometry and design. Discussion of its wide-reaching impacts and implications.

Graphic statics

Relationship between the form and force. How to design structures so that the forces flow where the designer wants them to.

Maxwell load path theorem

What it is and how it relates to the total volume of structural material used.

Force density

How we can use it to solve linear problems to find the geometry.

Virtual work and energy sizing

How it may be used to optimise the structural geometry, using Lagrange multipliers.

Michell trusses

Optimal structures and their behaviour.

Form finding for trusses

Discussion of the tools available to optimise topology, shape and size for structure.

Mechanisms and states of self-stress

The geometric relationship between mechanisms and states of self-stress, and the Maxwell-Calladine and Euler counts to obtain structurally sound trusses.

Geometric stiffness

The stiffness of structures and mechanisms is considered using force density. A short introduction to rigidity theory.

Airy stress functions and their application to truss design

To identify states of self-stress and mechanisms. The use of funiculars to include external loading.

Design of Gridshells and Cable Nets

How to design shells and gridshells using the Airy stress function and force density. The importance of obtaining planar faces and torsion free nodes. We also consider the design of tension structures, using prestress to stabilise mechanisms.

Aims

The aims of the course are to:

• Introduce students to foundational theoretical concepts and methodological tools essential for the successful development, analysis, and application of advanced Machine Learning and Computational Statistical methods.

Objectives

As specific objectives, by the end of the course students should be able to:

• Introduce the students to the required statistical and mathematical concepts that underpin all rigorously designed Machine Learning and Computational Statistical methods that can be used practically across all the contemporary engineering sciences
• Introduce the students to advanced computational statistical inference methods required to design Machine Learning solutions to a range of challenging large scale engineering problems where data and models are synthesised

Content

By successful completion of this course the student will have an appreciation and basic understanding of the mathematical, probabilistic, and statistical foundations of modern Computational Statistical Methods and recent developments in Machine Learning algorithms.

Computational Statistics and Machine Learning

Lecture.1. Monte Carlo Methods - A : Numerically computing integrals, the law of large numbers for Monte Carlo estimators, The Central Limit Theorem for Monte Carlo estimators.

Lecture.2. Monte Carlo Methods - B : Improving MC estimators, Importance Sampling, Control Variates to reduce variance of estimates.

Lecture.3. Lebesgue Integral and Measure - A : Difference between Riemann and Lebesgue Integral, why Lebesgue integral is required for machine learning and engineering, definition of Lebesgue integral.

Lecture.4. Lebesgue Integral and Measure - B : Definition of Lebesgue Measure, Radon-Nikodym derivative and change of measure, Measure theoretic basis of Probability (Kolmogorov), Random Variables.

Lecture.5. Markov Chain Monte Carlo - A : Definition of Markov chain and invariant distributions, presentation of the Metropolis and Hastings method.

Lecture.6. Markov Chain Monte Carlo - B : Metropolis Hastings in multiple dimensions, the Gibbs Sampler.

Lecture.7. Vector, Metric, and Banach Spaces : generalisation of Euclidean space in R^3 to infinite dimensional spaces, Completion of space and definition of Banach space of functions.

Lecture.8. Hilbert Spaces : Inner product space, definition of Hilbert space, Cauchy sequences and function approximation, Reproducing kernel Hilbert Space and function approximation.

Lecture.9. Sobolev Spaces : Definition of weak derivatives, understanding rates of convergence of function approximations based on properties of Sobolev space (smoothness)

Lecture.10. Gaussian Measure in Hilbert Space : Illustrating non-existence of Lebesgue Measure in function space, construction of finite Gaussian measure in Hilbert space, definition of Bayes rule (via Radon-Nikodym derivative) in Hilbert space employing Gaussian measure as reference - GP's.

Lecture.11. MCMC in Hilbert space : defining dimension invariant Markov transition kernel in Hilbert space and how overcomes degeneracy in high dimensions.

Lecture.12. Langevin Dynamics Simulation I - use of Langevin dynamics to simulate from a desired probability measure.

Lecture.13. Langevin Dynamics Simulation II  - use of approximate Langevin dynamics to simulate from a desired probability measure.

Lecture.14. Parallel Tempering - indtroduction to simulation from multi-modal target probability measures. 

Aims

The aims of the course are to:

• Introduce students to foundational theoretical concepts and methodological tools essential for the successful development, analysis, and application of advanced Machine Learning and Computational Statistical methods.

Objectives

As specific objectives, by the end of the course students should be able to:

• Introduce the students to the required statistical and mathematical concepts that underpin all rigorously designed Machine Learning and Computational Statistical methods that can be used practically across all the contemporary engineering sciences
• Introduce the students to advanced computational statistical inference methods required to design Machine Learning solutions to a range of challenging large scale engineering problems where data and models are synthesised

Content

By successful completion of this course the student will have an appreciation and basic understanding of the mathematical, probabilistic, and statistical foundations of modern Computational Statistical Methods and recent developments in Machine Learning algorithms.

Computational Statistics and Machine Learning

Lecture.1. Monte Carlo Methods - A : Numerically computing integrals, the law of large numbers for Monte Carlo estimators, The Central Limit Theorem for Monte Carlo estimators.

Lecture.2. Monte Carlo Methods - B : Improving MC estimators, Importance Sampling, Control Variates to reduce variance of estimates.

Lecture.3. Lebesgue Integral and Measure - A : Difference between Riemann and Lebesgue Integral, why Lebesgue integral is required for machine learning and engineering, definition of Lebesgue integral.

Lecture.4. Lebesgue Integral and Measure - B : Definition of Lebesgue Measure, Radon-Nikodym derivative and change of measure, Measure theoretic basis of Probability (Kolmogorov), Random Variables.

Lecture.5. Markov Chain Monte Carlo - A : Definition of Markov chain and invariant distributions, presentation of the Metropolis and Hastings method.

Lecture.6. Markov Chain Monte Carlo - B : Metropolis Hastings in multiple dimensions, the Gibbs Sampler.

Lecture.7. Vector, Metric, and Banach Spaces : generalisation of Euclidean space in R^3 to infinite dimensional spaces, Completion of space and definition of Banach space of functions.

Lecture.8. Hilbert Spaces : Inner product space, definition of Hilbert space, Cauchy sequences and function approximation, Reproducing kernel Hilbert Space and function approximation.

Lecture.9. Sobolev Spaces : Definition of weak derivatives, understanding rates of convergence of function approximations based on properties of Sobolev space (smoothness)

Lecture.10. Gaussian Measure in Hilbert Space : Illustrating non-existence of Lebesgue Measure in function space, construction of finite Gaussian measure in Hilbert space, definition of Bayes rule (via Radon-Nikodym derivative) in Hilbert space employing Gaussian measure as reference - GP's.

Lecture.11. MCMC in Hilbert space : defining dimension invariant Markov transition kernel in Hilbert space and how overcomes degeneracy in high dimensions.

Lecture.12. Langevin Dynamics Simulation I - use of Langevin dynamics to simulate from a desired probability measure.

Lecture.13. Langevin Dynamics Simulation II  - use of approximate Langevin dynamics to simulate from a desired probability measure.

Lecture.14. Parallel Tempering - indtroduction to simulation from multi-modal target probability measures.