Differentiation orders in MSO

New functionality has been added to compute, using structural methods, orders of derivatives of known signals, equations, and faults in an ARR based on an MSO. The new method is named MSOdifferentialOrder and is available in both Matlab and Python.

A small example. Consider the MSO

  x1' = -x1 + x2
  x2' = -x2 + x3
  x3 = u
  y = x1 + f

Generating an ARR from this model would result in

y'' + 2 y' + y - u = 0

meaning that the known signal y is differentiated twice and u not differentiated. This can be relevant information when implementing residual generators.

In the toolbox, this can be modeled as

x1, x2, x3, dx1, dx2, u, y, f = sym.symbols(["x1", "x2", "x3", "dx1", "dx2", "u", "y", "f"])
model_def = {"type": "Symbolic", "x": ["x1", "x2", "x3", "dx1", "dx2"], "f": ["f"], "z": ["y", "u"]}
model_def["rels"] = [
    -dx1 + -x1 + x2,  # e1
    -dx2 + -x2 + x3,  # e2
    -x3 + u,  # e3
    -y + x1 + f,  #e4
    fdt.DiffConstraint("dx1", "x1"),  # e5
    fdt.DiffConstraint("dx2", "x2"),  # e6
]

model = fdt.DiagnosisModel(model_def, name="Small model")

and the calls

    mso = model.MSO()[0]  # Take the first MSO
    eqorder, zidx, zorder, fidx, forder = model.MSOdifferentialOrder(mso)

computes

>> print(zorder)
[2 0]

which represents that the first known signal, y, is differentiated twice and the second, u, zero times as expected. You also get, for example,

>> print(eqorder)
[0, 1, 2, 0, 0, 1]

which states how many times each of the 6 MSO equations has to be differentiated to be able to derive the ARR.