3. Other software: SASSI and CLASSI

The two most used tools to do ISS calculations with spatial variability for nuclear power are the CLASSI and SASSI software. The method implemented in*Code_Aster* is similar to that of SASSI [bib8, bib9].

Just like DYNA_ISS_VARI in Code_Aster, SASSI makes it possible on the one hand to determine transfer functions (unit excitation) and on the other hand to calculate temporal responses taking into account spatial variability.

The calculation of the transfer functions is carried out according to the same principle in the two codes (Code_Aster and SASSI): a spectral decomposition (POD) of the coherence matrix is performed, the mode answer POD is determined by mode POD in order to recompose its response DSP as described in this note.

For calculating temporal responses, there is a difference between the SASSI methodology and the implementation in Code_Aster. More specifically, SASSI introduces a random phase for each mode POD [bib9]:

(3.1)\[ q (\ omega) =\ sum _ {k} H (\ omega) G (\ omega) G (\ omega) {\ omega) {\ phi} _ {\ lambda} _ {k} (\ omega)} {e}} {e}} ^ {e} ^ {i {\ eta}} ^ {i {eta}} ^ {\ eta} ^ {k} (\ omega)} {u} _ {0} (\ omega)\]

Where \({\eta }^{k}(\omega )\) are random variables that are uniform over the \([-\pi ,\pi ]\) interval. We then determine \(m\) answers and \(m\) SRO to retain the average. However, the introduction of the random phase is not useful if the problem is considered as a problem of filtering (deterministic) a deterministic signal (the accelerogram) as described above. It can also be checked that the expected value of the expression () is equal to the expression ().

The method used by CLASSI is different, insofar as we remain within the framework of classical stochastic dynamics: we solve a linear filtering problem (as is the case for DYNA_ISS_VARI when no seismic signal is given). The DSP of seismic excitation is approximated directly using an algorithm that makes the equivalence between DSP and SRO. The SRO response is obtained in the same way from the DSP response, namely by determining the SRO corresponding to the DSP of the calculated response [bib9].