Smart Factory - Module 3

What is a simulation environment and give an example

virtual environment created to imitate the operation of a real-world process or system over time to gain knowledge that can be transferred to reality, eg SimUI, this is where we can generate the digital model

motivation for digital twin in production

More frequent transformations of production system needed because demand changes a lot

there are also tech advances to keep up with

also cost pressure to find most efficient way of production

enables detailed analysis

Model vs Simulation vs Digital twiin

model : helps understand, analyse and explain complex systems by simplifying key features

simulation : uses model to replicate system’s behaviour under different conditions

Digital twin: dynamic digital real time replica of physical system (simulation that continuously gets current data

Applications of a simulation

• evaluation of cause and effect relationship in a system

• plannning and operation of production systems

weaknesses of a simulation

• project-based

• Simulation and domain knowledge required

• usually requires extensive manual data preperation

digital twin consists of

digital master, digital shadow, and intelligent connection btw both

Reasons to create a simulation

• system is too complex, expensise or dangerous

• system works too fast (e.g electronic cicruit or molecules)

• Temporal development/progression too chaotic

• System does not yet exist

• System not fully understood yet (e.g big bang)

• Simulations are reproducible (you can try over and over again easily)

Classification of Simulation models

Time aspect

• dynamic

• static (time independant)

Coincidence/randomness

• deterministic (no random variables, given input always has same output)

• Stochatic ( there is some randomness, results vary )

State of space and Change of time

• continuous or discrete state

• continuous or discrete time

Which type of time modelling is most used

Discrete time simulation

Discrete event simulation

State changes occur at discrete points in time triggerend by specific events

• Event List Management: Known upcoming events are ordered chronologically in an event list.

• Time Jump: The simulation clock jumps directly forward to the timestamp of the next immediate event.

• State Update: The state change associated with that event is executed.

• Future Event Generation: The event execution may schedule new future events, which are added back into the chronological list.

Building digital master

• Define problem and analyse real system using data and expert knowledge

• Make conceptual model with acceptable simplifications

• Implement using development environment (computer programming)

• Do iterative testing and troubleshooting

• Prsentation of simulation results and interpretation

Statistical vs empirical distribution of data

empirical data is the raw, observed information collected from real-world tests or experiences, while statistical data is the mathematical organization and analysis of that raw information

Advantage of statistical over empirical data for simulations

• traceability

• predictability (thanks to higher generalisation)

• expenditure (makes simulations easier to modify)

• data quality

• system understanding

How is data collected and then used for simulatiosn

Empirical data is typically collected as discrete measured values (bar graph), which is then fitted into continuous probability distributions for simulation modeling.

Distribution types

• uniform distribution (all values in interval [a,b] have equal probability)

• triangular distribution ( modal value c , minimun a and maximum b)- suited for limited info

• normal distribution (mean value μ, standard deviation σ) - symmetry around μ

• lognormal distribution (mean value μ, standard deviation σ) - asymmetry

• bi-/multimodal distribution (cannot not be described by simple distribution function — difficult to model)

What is seeding

random numbers are often used in simulations, but computers are never truly random

seeding = setting initial value (seed) for random number generator - if same seed is used, same random numbers are generated (ensures that exact simulation can be reproduced)

95% confidence interval

Small interval in distribution that 95% of the time contain the population’s actual parameters (eg mean value) (instead of giving a single point estimate, there is a range of values that the mean has 95% chance of having)

How to calculate confidence interval KI

• x̄ (Mean): The average value calculated from your simulation runs.

• z (z-value): A critical value based on your chosen confidence level.

• s (Standard deviation): The variability/spread of the sample data.

• n (Sample size): The number of simulation runs or observations.

confidence level= 95% — z=1.96

confidence level= 99% — z=2.58

must be estiated with random sample, testing whole population is to tedious

Sensitivity analysis

Analyses how variation of different variables affect the key performance indicators (KPI)

Identifies the most important factors to focus optimization efforts on for greatest improvement of efficiency eg