Construction and Simulation of a Simple Model

In this tutorial, we will simulate a very simple model consisting of a generator and a writer as shown in the block diagram shown below.

Model Simulation

Let us construct the model first. See Model Construction for more detailed information about model construction.

using Causal

# Describe the model
@defmodel model begin
    @nodes begin
        gen = SinewaveGenerator()
        writer = Writer()
    end
    @branches begin
        gen => writer
    end
end

In this simple model, we have a single output sinusoidal wave generator gen and a writer. In the script above, we constructed the components, connected them together and constructed the model.

We can specify simulation settings such as whether a simulation log file is be to constructed, model components are to be saved in a file, etc.

simdir = "/tmp"
logtofile = true
reportsim = true

At this point, the model is ready for simulation.

t0 = 0.     # Start time
dt = 0.01   # Sampling interval
tf = 10.    # Final time
sim = simulate!(model, t0, dt, tf, simdir=simdir, logtofile=logtofile, reportsim=reportsim)

Simulation(state:done, retcode:success, path:/tmp/Simulation-7045afab-edaf-491f-96e3-84fb4ffbfd7b)

Investigation of Simulation

First, let us observe Simulation instance sim. We start with the directory in which all simulation files are saved.

foreach(println, readlines(`ls -al $(sim.path)`))

total 52
drwxr-xr-x  2 runner docker  4096 May 10 16:15 .
drwxrwxrwt 18 root   root    4096 May 10 16:15 ..
-rw-r--r--  1 runner docker 15332 May 10 16:15 6cd9cf38-d22a-4afe-8e39-6c5124df62dd.jld2
-rw-r--r--  1 runner docker 21491 May 10 16:15 report.jld2
-rw-r--r--  1 runner docker  1139 May 10 16:15 simlog.log

The simulation directory includes a log file simlog.log which helps the user monitor simulation steps.

# Print the contents of log file
open(joinpath(sim.path, "simlog.log"), "r") do file
    for line in readlines(file)
        println(line)
    end
end

┌ Info: 2021-05-10T16:15:20.394 Started simulation...
└ @ Causal /home/runner/work/Causal.jl/Causal.jl/src/utilities/utils.jl:5
┌ Info: 2021-05-10T16:15:20.419 Inspecting model...
└ @ Causal /home/runner/work/Causal.jl/Causal.jl/src/utilities/utils.jl:5
┌ Info: 2021-05-10T16:15:20.445 Done.
└ @ Causal /home/runner/work/Causal.jl/Causal.jl/src/utilities/utils.jl:5
┌ Info: 2021-05-10T16:15:20.445 Initializing the model...
└ @ Causal /home/runner/work/Causal.jl/Causal.jl/src/utilities/utils.jl:5
┌ Info: 2021-05-10T16:15:20.662 Done...
└ @ Causal /home/runner/work/Causal.jl/Causal.jl/src/utilities/utils.jl:5
┌ Info: 2021-05-10T16:15:20.662 Running the simulation...
└ @ Causal /home/runner/work/Causal.jl/Causal.jl/src/utilities/utils.jl:5
┌ Info: 2021-05-10T16:15:20.72 Done...
└ @ Causal /home/runner/work/Causal.jl/Causal.jl/src/utilities/utils.jl:5
┌ Info: 2021-05-10T16:15:20.72 Terminating the simulation...
└ @ Causal /home/runner/work/Causal.jl/Causal.jl/src/utilities/utils.jl:5
┌ Info: 2021-05-10T16:15:20.75 Done.
└ @ Causal /home/runner/work/Causal.jl/Causal.jl/src/utilities/utils.jl:5

report.jld2 file, which includes the information about the simulation and model components, can be read back after the simulation.

julia> using FileIO, JLD2

julia> filecontent = load(joinpath(sim.path, "report.jld2"))
Dict{String,Any} with 9 entries:
  "retcode"         => :success
  "name"            => "Simulation-7045afab-edaf-491f-96e3-84fb4ffbfd7b"
  "model/callbacks" => nothing
  "model/name"      => ""
  "clock"           => Clock(gen:0.0:0.01:10.0, paused:false)
  "model/id"        => "a223ea1b-b5bb-4a6f-a5d3-445c28716a31"
  "components/"     => SinewaveGenerator(amp:1.0, freq:1.0, phase:0.0, offset:0…
  "path"            => "/tmp/Simulation-7045afab-edaf-491f-96e3-84fb4ffbfd7b"
  "state"           => :done

julia> clock = filecontent["model/clock"]
ERROR: KeyError: key "model/clock" not found

Analysis of Simulation Data

After the simulation, the data saved in simulation data files, i.e. in the files of writers, can be read back any offline data analysis can be performed.

# Read the simulation data
t, x = read(getnode(model, :writer).component)

# Plot the data
using Plots
plot(t, x, xlabel="t", ylabel="x", label="")

qt.qpa.xcb: could not connect to display
qt.qpa.plugin: Could not load the Qt platform plugin "xcb" in "" even though it was found.
This application failed to start because no Qt platform plugin could be initialized. Reinstalling the application may fix this problem.

Available platform plugins are: linuxfb, minimal, offscreen, vnc, xcb.

Aborted (core dumped)
connect: Connection refused
GKS: can't connect to GKS socket application

GKS: Open failed in routine OPEN_WS
GKS: GKS not in proper state. GKS must be either in the state WSOP or WSAC in routine ACTIVATE_WS

A Larger Model Simulation

Consider a larger model whose block diagram is given below

The script below illustrates the construction and simulation of this model

using Causal 
using Plots

# Construct the model 
@defmodel model begin 
    @nodes begin 
        gen1 = SinewaveGenerator(frequency=2.)
        gain1 = Gain()
        adder1 = Adder(signs=(+,+))
        gen2 = SinewaveGenerator(frequency=3.)
        adder2 = Adder(signs=(+,+,-))
        gain2 = Gain()
        writer = Writer() 
        gain3 = Gain()
    end 
    @branches begin 
        gen1[1]     =>      gain1[1] 
        gain1[1]    =>      adder1[1]
        adder1[1]   =>      adder2[1]
        gen2[1]     =>      adder1[2]
        gen2[1]     =>      adder2[2]
        adder2[1]   =>      gain2[1]
        gain2[1]    =>      writer[1]
        gain2[1]    =>      gain3[1]
        gain3[1]    =>      adder2[3]
    end
end

# Simulation of the model 
simulate!(model, withbar=false)

# Reading and plotting the simulation data
t, x = read(getnode(model, :writer).component)
plot(t, x)
savefig("larger_model_plot.svg"); nothing # hide