Lecture 1

Question 1

model

Answer 1

simplified description of a real system, process, phenomenon

based on original system

reflects only the relevant selection of the original system properties

usable in place of the original system for some purposes

Question 2

we need models for…

Answer 2

simulation, control design and testing, performance / behaviour, evaluation, fundamental insight, online controllers, design, assessment / optimization, safety assessment, certification

Question 3

properties of a system

Answer 3

1. inner structure
2. system boundary (interfaces)
3. interaction with the environment

Question 4

subsystems

Answer 4

subsystems consist of elements that are systems themselves

Question 5

systems engineering

Answer 5

development of systems capable of fulfilling a given task accounting for certain requirements

Question 6

aircraft systems

Answer 6

1. flight control systems
2. energy supply and distribution systems
3. cabin and payload systems
4. flight gear and doors
5. propulsion and APU (auxiliary power unit)
6. avionics
7. safety and emergency systems

Question 7

types of models

Answer 7

visual, conceptual, functional, systems

mathematical, computational, empirical, statistical, etc.

Question 8

deterministic model vs probabilistic (stochastic) model

Answer 8

deterministic (ideal):
1. outcome is certain given initial values and boundary conditions
2. given input always gives the same output
3. represents ideal system

probabilistic (real):
1. include a random (probabilistic) component
2. outputs are random variables that can take on values in a particular uncertainty range
3. the same input might produce different outputs
4. more realistic representation of the system

Question 9

data-driven model vs first-principles model

Answer 9

data-driven model - set of data for input, set of data for output, but we don’t know what is in between

first-principles model - we know exactly what is going on in between input and output (e.g. physics-wise)

Question 10

statistical model

Answer 10

non-deterministic model

instead or specific values, the variables are random variables with probability distribution

combination of mathematical modelling and statistical assumptions to represent a set of data

based on data from data-generating process

Question 11

statistical model’s data sets

Answer 11

training set (estimation set):
1. 70% of data
2. used to create the model
3. known input and output

test set (validation set):
1. testing the model’s learnt ability to make correct predictions (from the learning process on training dataset)

Question 12

accuracy and precision

Answer 12

accuracy: how close are the model’s results to the actual value of the real system

precision: how close are the model’s results to each other

Question 13

model fidelity levels

Answer 13

the degree of exactness with which something is copied or reproduced

L0: based on empirical knowledge (rough estimation)
L2: simplified physics principles - limited nr of effects considered
L3: physical behaviour represented by more accurate relationships and equations
L4: very high computational costs - only local, distinct effects, high precision, high nr of features captured

Question 14

big-O notation

Answer 14

measure of computational complexity

Question 15

model complexity

Answer 15

1. underfitting - too simple, too little features
2. overfitting - too complex, too many features, model is too fitted to training dataset and the error from test set is big

Question 16

solutions to underfitting / overfitting

Answer 16

underfitting:
1. increase order of polynomial
2. switch to nonlinear model
3. get different dynamics of the system

overfitting:
1. decrease order of polynomial
2. decrease ranges of factors
3. increase number of training sets

Question 17

cross-validation error

Answer 17

provides a more reliable estimate of a model’s performance versus a single train-test split

it evaluates the model on several subsets of the data, resolving the issue of variability in the training and validation data and leading to a more robust performance estimation

Question 18

obtaining cross-validation error

Answer 18

1. randomly split training data into x equal subsets
2. remove first subset and fit model to remaining data
3. predict removed subset using model fitted to remaining data
4. remove second subset from dataset and fit model to remaining data
5. predict removed subset using model fitted to remaining data
6. iterate until there are no subsets left

the result will be n predictions, and ftom them we compute cross-validation error

Question 19

levels of physical insight

Answer 19

1. white box
2. grey box
3. black box

Question 20

white box modelling

Answer 20

1. complete understanding of inner system structure, system boundary and interaction with its environment
2. physical law driven
3. can be difficult or impossible to obtain

highest level of physical insight

suitable when system:
1. is simple
2. is well understood

Question 21

grey box modelling

Answer 21

1. limited knowledge of inner system structure, system boundary and interaction with its environment
2. captures essential system information
3. partly data-driven

suitable when system:
1. is partially understood
2. has very complex components

Question 22

black box modelling

Answer 22

1. no knowledge of inner system structure
2. only IO-behaviour
3. statistic / machine learning used to build model
4. can capture complex behaviours that are hard to model physically
5. fully data-driven

lowest level of physical insight

suitable when system:
1. is highly complex
2. is not well understood
3. can be experimented on

Question 23

parametric vs non-parametric model

Answer 23

parametric model:
1. based on finite set of parameters
2. response is a function of input variables and parameters

non-parametric model:
1. parameter space is infinite-dimensional
2. no assumptions on distribution of the data
3. number of parameters can grow with amount of data considered

Question 24

continuous vs discrete model

Answer 24

continuous model:
1. output changes continuously over time
2. assumed behaviour of many ideal physical models

discrete model:
1. output changes only at discrete point in time
2. computer-based models are discrete

Question 25

dynamic system

Answer 25

system whose states evolve over time

Question 26

system identification

Answer 26

deriving a model of a dynamic system from data, capturing input-output behaviour

can allow for an effective compromise between high accuracy, low complexity and low computational cost

can be applied to model aerodynamics, propulsion, body dynamics or full systems

Question 27

system identification process

Answer 27

data -> model identification -> model -> model validation -> system -> experiments -> data -> model identification -> model -> …

1. design and perform experiments
2. define model structure
3. estimate parameters
4. validate model