Since two of the three unknown parameters are locally identifiable and the remaining one is globally identifiable the model is structurally locally identifiable.
If, in addition, we can assume that then the second moment invariant implies that . Hence, in this case, both k2e and k1e are globally identifiable and so the model becomes structurally globally identifiable.
2. Consider the model given by:
The first Taylor series coefficient is given by:
and so the parameter c is unique for the output – it is globally identifiable.
The second coefficient is given by:
and so 1 = k1(1 – k2) is also unique. The third coefficient is given by:
and so 2 = k1(1 – 2k2) is also unique. Dividing these two expressions gives
and so k2 is unique. Since k1(1 – k2) this means that k1 is unique.
Summarising: All of the parameters k1, k2 and c are unique for the given output and hence globally identifiable. Therefore the model is structurally globally identifiable.
For the given measured values:
Dividing second equation by first gives
Substituting into the first equation gives:
3. (i) For the given system to be at steady state:
From the second equation either or .
Substituting into the first equation yields a contradiction since a > 0.