Modelling elements and methods. Building a simulation model. Step 1 ) Get acquinted with the system Step 2 ) Define the dynamic problem Step 3) Construct a conceptual modell Step 4 ) Define the causal loops or casual relationships
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Step 1) Get acquinted with the system
Step 2) Define the dynamic problem
Step 3) Construct a conceptual modell
Step 4) Define the causal loops or casual relationships
Step 5) Express the relationships mathematically in equations
Step 6) Get values of parameters
Step 7) Implement the mathematical relationships in a computer program
Step 8) Run the model
Step 9) Judge if the results are reasonable by comparing to callibration data or ”common sence”
Step 10) Sensitivity analysis
Step 11) Repeat 310 to improve the model and parameter estimates
Step 12) Validate the model by independent data
Step 13) Apply the model
Step 1) Get acquinted with the system
Step 2) Define the dynamic problem
Fundamental dynamic patterns
Overshot
Chaos theory
describes complex motion and the dynamics of sensitive systems.
Chaotic systems are mathematically deterministic but nearly impossible to predict: Unpredicted courses of events
Discovered by Edward Lorenz in 1961 (Butterfly Effect):Weather forecast based on previous calculations and giving not equal precision data.
Chaos theory
http://www.mathjmendl.org/chaos/
Step 3) Construct a conceptual modell
stock and flow diagram
Stock
Other elements
Flow
Connector for direction of dependency
Step 3) Construct a conceptual modell
Example bird population
Potential birth rate
Births
Birth rate
Carrying capacity
Bird population
Death rate
Deaths
Step 4) Define the causal loops or casual relationships
Conceptual modelling: causal loops diagrams (CLD)
Negative feedback:

+
x
y
or
x
y
+

The higher value of x
– the higher value of y
The higher value of y
– the lower value of x
The higher value of x
– the lower value of y
The higher value of y
– the higher value of x
Positive feedback:
+

x
y
x
y
+

The higher value of x
– the higher value of y
The higher value of y
– the higher value of x
The lower value of x – the lower value of y
The lower value of y – the lower value of x
An odd number if negative dependcies in a loop means negative feedback
Potential birth rate
+
Births
+
Birth rate
+
(+)
+
()

+
Carrying capacity
Bird population
()
+

Death rate
+
Deaths
Some problems in the conceptual modelling phase:
Step 5) Express the relationships mathematically in equations
Determine what type of model you will make
 functional or mechanistic
Use ”standard” equations if possible
Analyse relationships with a curve fitting tool
Dynamic models: many functions are differential equations equations
Biological systems: most of the differential equations can not be solved to analytical functions
Thanks to computers: numerical approximations
But: Numerical method is an approximation to the true solution
Dynamic equationsmodels
change of state variables with time
Xt : status of X at time t
X/ t : rate of change
Xt+1=Xt + X
Continuous model in time: dt is infinitive small
Discrete model: t is a period of time
Example bird equationspopulation – numerical solution
Potential birth rate (rpot)
Births (B)
Birth rate (rb)
Carrying capacity (CC)
Bird population (P)
Death rate (rd)
Deaths (D)
For each element that has incoming arrows there has to be an equation
Step 6) Get values of parameters equations
Parameter estimation from
Physical laws
Physical based experiments/observations
General description of ecological processes
Best guess of an expert
Your own intuition
From
literature
Level of trust
Step 7) Implement the mathematical relationships in a computer program
Now we have a solution on paper:
Next step is writing the model to a computer program
Computer modelling – programming
’Telling’ a computer what to do
Compiling = ’translating’
Debugging = finding/correcting errors in the code
What you need:
Discipline and attention to detail
Good memory
Abstract thinking
With a good conceptual model and some general structure it is rather ”easy”
Programming and computer implementation computer program
Computer ’languages’ : ’telling a computer what to do’:
Basic
Fortran (1950), Fortran IV (1966), Fortran77, Fortran90,
Visual Fortran (Formula translation)
Pascal, Delphi
C, C++
Java, J, J++
Phyton
Matlab
Stella
Simulink
SIMILE
Excel
SQL
Step 8) Run the model computer program
Step 9) Judge if the results are reasonable by comparing to callibration data or ”common sence”
Reasons for ”poor” results
Bugs in the computer implementation
Wrong understanding of the dynamical problem
Using an application outside the model´s development conditions
Normal need for parameter callibration
Step 10) callibration data or ”common sence”Sensitivity analysis
Varying parameters and/or variables independently
This may highlight the weakness in the model and indicate which parameters or variables need much attention and high accuracy
Book: 3.4.2 – 3.5.3
If needed go back to improve callibration data or ”common sence”the model
Step 1) Get acquinted with the system
Step 2) Define the dynamic problem
Step 3) Construct a conceptual modell
Step 4) Define the causal loops or casual relationships
Step 5) Express the relationships mathematically in equations
Step 6) Get values of parameters
Step 7) Implement the mathematical relationships in a computer program
Step 8) Run the model
Step 9) Judge if the results are reasonable by comparing to callibration data or ”common sence”
Step 10) Sensitivity analysis
Step 11) Repeat 310 to improve the model and parameter estimates
Step 12) Validate the model by independent data
Step 13) Apply the model to new situations
Step callibration data or ”common sence”12) Validate the model by independent data
 to assure that the model is correct
Simulation models are simplifications of the real world. If you leave out (unimportant) factors and only describe the system by capturing the important factors, you have to prove that the model is still usefull
Verification: concerned with building the model right
Validation: concerned with building the right model.
’Validation is the determination as to whether model behavior departs from real system behavior sufficiently farto jeopardize model objectives’
Validation: callibration data or ”common sence”
Compare modelled and measured values by ’goodnessoffit’
Accuracy of measurements callibration data or ”common sence”
Coincidence: Difference between validation and model data
Associotion: Similarity in trends between validation and model data
High coincidence
and association
Low coincidence
high association
High coincidence
low association
Measures of coincidence callibration data or ”common sence”
Student’s t test
Observations (O), Modelled value (P)
Book section 3.3.1
Measures of association callibration data or ”common sence”
Regression analysis
Correlation coefficient, r
Fstatistics
Plotting of residuals
Book section 3.3.1
Accuracy callibration data or ”common sence” is often used as the complement of error:
95% accuracy implies 5% error
But accuracy refers also often to the fidelity (= trohet) with which the model represents the processes and relationsships
Step callibration data or ”common sence”13) Apply the model
to new situations
Interpolation and extrapolation in time and space
Test of new policies, methods etc
Pack the model in a way that is suitable for the end user
Who is the end user
What will the model do?
How can the application guard against input error
How can the application guard agains misinterpretation of the results
What documentation is needed
Steps in modelling callibration data or ”common sence”
Book: chapter 2
Exercise in conceptual model/causual loop construction from 2011’s exam
Think about a house and its heating system. Assume a simple dynamical model that consists of these variables:  Temperature inside the house  Outdoor temperature  Target temperature set at the thermostats of the radiators  Energy content of the house  Heat production from the radiators  Heat loss to the surrounding Put these variables together in a conceptual model diagram and a causal loop diagram and explain what the diagrams tell you.