Lecture 1 Flashcards
model
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
we need models for…
simulation, control design and testing, performance / behaviour, evaluation, fundamental insight, online controllers, design, assessment / optimization, safety assessment, certification
properties of a system
- inner structure
- system boundary (interfaces)
- interaction with the environment
subsystems
subsystems consist of elements that are systems themselves
systems engineering
development of systems capable of fulfilling a given task accounting for certain requirements
aircraft systems
- flight control systems
- energy supply and distribution systems
- cabin and payload systems
- flight gear and doors
- propulsion and APU (auxiliary power unit)
- avionics
- safety and emergency systems
types of models
visual, conceptual, functional, systems
mathematical, computational, empirical, statistical, etc.
deterministic model vs probabilistic (stochastic) model
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
data-driven model vs first-principles model
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)
statistical model
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
statistical model’s data sets
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)
accuracy and precision
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
model fidelity levels
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
big-O notation
measure of computational complexity
model complexity
- underfitting - too simple, too little features
- overfitting - too complex, too many features, model is too fitted to training dataset and the error from test set is big
solutions to underfitting / overfitting
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
cross-validation error
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
obtaining cross-validation error
- randomly split training data into x equal subsets
- remove first subset and fit model to remaining data
- predict removed subset using model fitted to remaining data
- remove second subset from dataset and fit model to remaining data
- predict removed subset using model fitted to remaining data
- iterate until there are no subsets left
the result will be n predictions, and ftom them we compute cross-validation error
levels of physical insight
- white box
- grey box
- black box
white box modelling
- complete understanding of inner system structure, system boundary and interaction with its environment
- physical law driven
- can be difficult or impossible to obtain
highest level of physical insight
suitable when system:
1. is simple
2. is well understood
grey box modelling
- limited knowledge of inner system structure, system boundary and interaction with its environment
- captures essential system information
- partly data-driven
suitable when system:
1. is partially understood
2. has very complex components
black box modelling
- no knowledge of inner system structure
- only IO-behaviour
- statistic / machine learning used to build model
- can capture complex behaviours that are hard to model physically
- 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
parametric vs non-parametric model
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
continuous vs discrete model
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
dynamic system
system whose states evolve over time
system identification
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
system identification process
data -> model identification -> model -> model validation -> system -> experiments -> data -> model identification -> model -> …
- design and perform experiments
- define model structure
- estimate parameters
- validate model
