What is a model?
- Based on Original System
- Reflects Relevant Properties
- Simplification of Reality
What are the uses of Models?(8)
- Simulation
- Control Design and Testing
- Performance / Behavior Eval.
- Fundamental Insight
- Online Controllers
- Design Assessment / Optimiz.
- Safety Assessment
- Certification
What are three diagrams used in modelling and what for?
Block Diagrams: To model the building blocks of a system
Internal Definition Diagrams: To model interactions between blocks
Sequence Diagrams: To model interactions over time
What are some typical properties of a system? (3)
- Inner Structure
- System Boundaries
- Interaction with Environment
What are Subsystems?
Elements within a system that themselves are systems.
What is System Engineering?
Development of systems capable of fulfilling a given task while accounting for certain requirements
What does an Aircraft system consist of? (7)
- Flight Control Systems
- Energy Supply and Distribution
- Cabin and Payload systems
- Flight Gear and Doors
- Propulsion and APU
- Avionics
- Safety and Emergency Systems
What are the three main types of models?
- Visual
- Conceptual
- Mathematical
What is a deterministic model?
- Outcome is certain given initial values and boundary conditions
- Represents an ideal system
What is a Probabilistic / Stochastic model?
- Includes random component
- Outputs are random variables that can take on range of values
- Same input can lead to different outputs
What are data driven and first-principle models?
First principle models are physics based
Data driven models are statistical
What are properties of statistical data driven models?
- Non-deterministic
- Based on data generation process
- Data comes from greater population using sampling (sampling methods used)
- Hypothesis is made about real data generating process in attempt to capture nature of process using statistical tools
(what statistical method represents the process best) - The goal is to infer statements about real world process
What are the purposes of the training and data sets?
Training set is used the train the model.
Predictions need to be made in the data set.
What is the process for creating a data driven statistical model?
Train on training set –
Evaluate on validation set – tweak based on results –
Pick model that does best on validation set –
Confirm results on Test Set–
Repeat –
What is accuracy and what is precision?
Accuracy: Describes how close values are to real value
Precision: Describes how close values are to each other
What is model fiedelity?
- Describes how accurately the model can describe the real system in terms of features captured and accuracy of results
What is Computational or Algorithm sided complexity?
- Assesses computational time requirement
- Assesses memory storage requirement
- Assesses feasibility , duration of simulations
- Assesses applicability of controllers
What is the big O notation from lowest to highest?
O(1) < O(log N) < O(N) < O(N log N) < O(N^2) < O(2^N) < O(N!)
What does problem-sided / model complexity describe?
- How complex is model structure
- Number of parameters / predictors / features used
- Relates to generalization
- Is model not too complex but complex enough
What is overfitting and underfitting in regards to mode Comlexity?
Underfitting:
- Not enough features
- Cannot capture relevant effects
- Important aspects neglected
Overfitting:
- Irrelevant info captured
- Overtrained and cannot generalize from training to dataset
- Model degree to high
What should be done in case of underfitting?
- Increase order of polynomial
- Switch to non-linear model
- Get different dynamics of the system
How do you avoid overfitting?
- Decrease order of polynomial
- Decrease range of factors
- Increase training sets
What is cross-validation error
Indicator of generalization quality
How do you obtain cross-validating error?
- Split training and data set into q equal subsets randomly
- Remove first subset and fit model to remaining data
- Predict removed subset using model fitted to remaining data
- Remove second subset from data and fit to remaining data
- Predict removed subset using model fitted to remaining data
- Iterate till no subsets left
Minimum of 5 sets suggested
