Section: Software
COSMAD: Modal analysis and health monitoring Scilab toolbox
Participants : Laurent Mevel [ corresponding person ] , Neil Babou, Maurice Goursat.
With the help of Yann Veillard, Auguste Sam and Simon Berger, former engineers, Laurent Mevel and Maurice Goursat have developed a Scilab toolbox devoted to modal analysis and vibration monitoring of structures or machines subjected to known or ambient (unknown) excitation [48] , [47] .
This software (COSMAD 3.64) has been registered at the APP under the number
IDDN.FR.001.210011.002.S.A.2003.000.20700
and can be downloaded from http://www.irisa.fr/i4s/cosmad/ . A list of testcases (simulators, laboratory testbeds, real structures) for which COSMAD has been used is available from http://www.irisa.fr/i4s/cases.pdf .
COSMAD performs the following tasks :

Outputonly (O/O) subspacebased identification , working batchwise, see modules 3.5 , 6.1 and 7.1 . The problem is to identify the eigenstructure (eigenvalues and observed components of the associated eigenvectors) of the state transition matrix of a linear dynamical system, using only the observation of some measured outputs summarized into a sequence of covariance matrices corresponding to successive time shifts. An overview of this method can be found in [29] , and details in [40] , [54] , [52] and [53] .

Inputoutput (I/O) subspacebased identification , working batchwise, see modules 3.5 , 6.1 and 7.1 . The problem is again to identify the eigenstructure, but now using the observation of some measured inputs and outputs summarized into a sequence of crosscovariance matrices. This method is described in [10] .

Automatic subspacebased modal analysis , a pretuned version of the O/O and I/O identification methods above. This is described in [48] .

Automated online identification package , see modules 3.2 , 3.5 and 6.1 . The main question is to react to non stationarities and fluctuations in the evolution of the modes, especially the damping. The developed package allows the extraction of such modes using a graphical interface allowing us to follow the evolution of all frequencies and damping over time and to analyze their stabilization diagram (from which they were extracted). Automated modal extraction is performed based on the automated analysis and classification of the stabilization diagram. For this method, see [30] and [49] , [41] .

Automatic recursive subspacebased modal analysis , a sample pointwise version of the O/O and I/O identification algorithms above. For this method, see [39] .

Subspacebased identification through moving sensors data fusion , see modules 3.2 and 3.5 . The problem is to identify the eigenstructure based on a joint processing of signals recorded at different time periods, under different excitations, and with different sensors pools. The key principles are described in [7] and a consistency result can be found in [9] .

Damage detection , working batchwise, see modules 3.3 , 3.5 , and 4.2 .
Based on vibrations measurements processing, the problem is to perform early detection of small deviations of the structure w.r.t. a reference behavior considered as normal. Such an early detection of small deviations is mandatory for fatigue prevention. The algorithm confronts a new data record, summarized by covariance matrices, to a reference modal signature. The method is described in [1] , [3] .

Damage monitoring , a sample pointwise version of the damage detection algorithm above. This is described in [46] .

Online flutter onset detection , see modules 3.3 , 3.5 , 4.2 and 6.5 . This algorithm detects that one damping coefficient crosses a critical value from above. For this method see [8] [30] . An extension to detect if some subset of the whole modal parameter vector varies with respect to a threshold value, applies directly to monitoring the evolution of a set of frequencies or a set of damping coefficients with respect to their reference values [31] , [42] .

Modal diagnosis , working batchwise, see modules 3.4 , 3.5 , and 4.2 . This algorithm finds the modes the most affected by the detected deviation. For this method, see [3] .

Damage localization , see modules 3.4 , 3.5 and 4.2 .
The problem is to find the part of the structure, and the associated structural parameters (e.g. masses, stiffness coefficients) that have been affected by the damage. We state and solve this problem as a detection problem, and not an (illposed) inverse estimation problem. This is explained in [3] .

Optimal sensor positioning for monitoring . At the design stage of the monitoring system, a criterion is computed, which quantifies the relevance of a given sensor number and positioning for the purpose of structural health monitoring. For this criterion, see the articles [28] , [26] .
The modules have been tested by different partners, especially the French industrial partners, EADS, Dassault and Sopemea, within the FliTE2 project (see module 7.1 ), by partners from the past CONSTRUCTIF project
[52] and [53] , and within the framework of bilateral contracts with SNECMA and SVIBS (see modules 7.6 and 7.7 ).
This Scilab toolbox continues to play the role of a programming and development environment for all our newly designed algorithms. Moreover, offering a maintained Scilab platform turns out to be a crucial factor in convincing industrial partners to undergo joint investigations with us or to involve us within partnerships in FP7 integrated projects proposals, see module 8.1 .
As from December 2007, Neil Babou, associate engineer, has worked on finalizing the next major version of COSMAD. Identification techniques used during FliTE2 have also been implemented by F. Queyroi. Porting COSMAD to Scilab 5 has been done. A specific version for use within SNECMA is currently under way.