New hierarchical approach for multiple sensor fault detection and isolation. Application to an air quality monitoring network Y. Tharrault, M.-F. Harkat, G. Mourot and J. Ragot Abstract— Our work is devoted to the problem of multiple sensor fault detection and isolation using principal component analysis. Structured residuals are used for multiple fault iso- lation. These structured residuals are based on the principle of variable reconstruction. However, multiple fault isolation based on reconstruction approach leads to an explosion of the reconstruction combinations. Therefore instead of considering all the subsets of faulty variables, we determine the isolable multiple faults by removing the subsets of variables that have too high minimum fault amplitudes to ensure fault isolation. Unfortunately, in the case of a large number of variables, this scheme yet leads to an explosion of faulty scenarios to consider. An effective approach is to use multi-block reconstruction approach where the process variables are partitioned into several blocks. In the first step of this hierarchical approach, the goal is to isolate faulty blocks and then in the second step, from the faulty blocks, faulty variables have to be isolated. The proposed approach is successfully applied to multiple sensor fault detection and isolation of an air quality monitoring network. I. I NTRODUCTION Principal component analysis (PCA) has been applied successfully in the monitoring of complex systems. It is a widely used method for dimensionality reduction. Indeed PCA transforms the data to a smaller set of variables which are linear combinations of the original variables while retaining as much information as possible. The PCA model so obtained describes normal process behavior and unusual events are then detected by referencing the observed behavior against this model. For fault isolation, the structured residual approach consists in generating new residuals sensitive only to particular fault subsets. Thus, the analysis of these differ- ent residuals enables to isolate the set of faulty variables. Our work is devoted to the problem of multiple sensor fault detection and isolation (FDI) using structured residuals. These structured residuals are based on the reconstruction principle. The variable reconstruction approach estimates a set of variables using the PCA model from the remaining variables. If the faulty variables are reconstructed, the fault effect is removed which is useful for fault isolation. To avoid the combinatorial explosion of faulty scenarios related to multiple faults, Tharrault et al. [3], [4] determined useful This work was supported by EGIDE, Partenariat Hubert Currien, CMEP- TASSILI PAI 07 MDU 714 M.-F. Harkat is with Faculté des Sciences de l’Ingénieur, Uni- versité Badji Mokhtar - Annaba, BP. 12 Annaba 23000, Algeria mharkat@univ-annaba.org Y. Tharrault, G. Mourot and J. Ragot are with Centre de Recherche en Automatique de Nancy (CRAN), Nancy Université, CNRS UMR 7039, 2 avenue de la forêt de Haye, F-54516 Vandoeuvre- Lès-Nancy, France yvon.tharrault, gilles.mourot, jose.ragot@ensem.inpl-nancy.fr faulty scenarios by evaluating the existence condition of structured residuals. Unfortunately, this method does not remove residuals with poor sensitivity to faults. To improve the previous method, we take into account residual sensitivity to faults by evaluating the minimal fault magnitude to ensure fault isolation. However, in the case of a large number of variables, multiple fault isolation based on reconstruction ap- proach yet leads to explosion of reconstruction combinations. An effective approach is to use multi-block reconstruction approach where the process variables are partitioned into several blocks (subsets of measurement variables). In the first step of this hierarchical approach, the goal is to isolate the faulty subset of variables or faulty blocks and then in the second step, from the faulty blocks, faulty variables have to be isolated. Therefore, this hierarchical approach reduces considerably the number of structured residuals to design for fault isolation. The first part is a short presentation of principal component analysis. Then, in the second part, methods for fault detection and isolation are introduced. Finally, the proposed approach is successfully applied to multiple sensor fault detection and isolation of an air quality monitoring network. II. PCA MODELLING Let us consider a data matrix X ∈ℜ N×m , with row vector x T i ∈ℜ m , (i=1, . . . , N), which gathers N measurements collected on the m system variables. In the classical PCA case, data are supposed to be col- lected on a system being in a normal process operation. PCA determines an optimal linear transformation (with respect to a variance criterion) of the data matrix X: t = P T x and x = P t (1) where t ∈ R m is the principal component vector and P =  p 1 ··· p m  ∈ R m×m is the matrix of the eigenvectors associated to the eigenvalues of the covariance matrix Σ of X: Σ= P ΛP T with PP T = P T P = I m (2) where Λ = diag(λ 1 ...λ m ) is a diagonal matrix with diagonal elements in decreasing magnitude order. Once the component number ℓ to retain is determined, let us partition the eigenvalue and eigenvector matrices as follows: P = ( ˆ P ˜ P ) ˆ P ∈ℜ m×ℓ , ˜ P ∈ℜ m×(m-ℓ) (3) Λ =  ˆ Λ 0 0 ˜ Λ  ˆ Λ ∈ℜ ℓ×ℓ , ˜ Λ ∈ℜ (m-ℓ)×(m-ℓ) (4) 18th Mediterranean Conference on Control & Automation Congress Palace Hotel, Marrakech, Morocco June 23-25, 2010 978-1-4244-8092-0/10/$26.00 ©2010 IEEE 1543