Data validation for very large scale systems in mineral industry
Résumé
This communication suggests a method for the hierarchical treatment of measurement balances of static systems through homogeneous multilinear equations. Due to errors caused by sensors, the measurements taken from a physical system are generally noisy and do not verify these balance equations (total or partial flows). The problem consists in obtaining an estimation of the exact values, which verify the balance equations. The solution is classically obtained by minimizing a quadratic criterion of the error terms, taking into account the balance constraints. A large scale system of nonlinear equations must the be solved. Several forms of hierarchical treatment may be used and also suboptimal solutions have been proposed. The proposed algorithm is based on the mathematical decomposition of the whole system into serial sub-systems. This decomposition is systematic in all cases and allows a direct iteration calculus. The main numerical difficulty is to take into account the coordination factors between each level ; after some algebraic manipulations it is possible to eliminate all the Lagrange multipliers of the problem and to express on a very convenient form the coordination factors. Each level of calculus is reduced to a simple projection of the measurements on the constraints space and moreover the same parametrized routine can be used for each level. An example is given with measurements on a mineralurgical process with quadrilinear models using volumic flowrate, density, granulometric distribution, and chemical analysis. The method has also been tested for processes described by more than one thousand variables.
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