Structural analysis for fault diagnosis faults f ( t ) observation y - PowerPoint PPT Presentation

Jubilee Symposium 2019: Future Directions of System Modeling and Simulation 2 Model based diagnosis, basic idea System Structural analysis for fault diagnosis faults f ( t ) observation y ( t ) residual r ( t ) + actuators u ( t ) of equation based models 0.5 0 − − 0.5 Industrial applications often more difficult … − 1 0 5 10 15 20 25 30 35 40 45 Erik Frisk <erik.frisk@liu.se> Model • Models are complex, non-linear, includes lookup-tables, to big to handle prediction ˆ y ( t ) Department of Electrical Engineering x = g ( x, u ) ˙ by hand, … Linköping University, Sweden y = h ( x, u ) • Fault isolation, not only fault detection • Models are uncertain, which, by definition is not modeled Jubilee Symposium — Future Direc4ons of System Modeling and Simula4on 
 Sept. 30, Lund, Sweden 3 4 Modeling languages A Matlab toolbox — faultdiagnosistoolbox.github.io • Simulink and Modelica are used (in industry) Models for • Mainly simulation • optimization • not so much for diagnosis analysis and design • Support for Simulink and Modelica would Main designer, coding, and algorithms Simulation make methods industrially more accessible Erik Frisk (http://users.isy.liu.se/fs/frisk/) <erik.frisk@liu.se> • We in Linköping has thought about this for Professor, Linköping University, Sweden some time; diagnostic methods useful for such models Coding and algorithms • Maybe have to compromise between general Mattias Krysander (http://users.isy.liu.se/fs/matkr/) <mattias.krysander@liu.se> applicability and optimality/guarantees/… Associate professor, Linköping University, Sweden Optimization

Jubilee Symposium 2019: Future Directions of System Modeling and Simulation 5 6 DAEs and equation based models for diagnosis Basic approach to diagnosis system design • Non-causal models — inherent in the diagnosis problem • A signal is known or unknown; it does not matter if it is an input or Model output signal to the system • — unknown, known, and fault signals 
 x , z , f F (· x , x , z , f ) = 0 • Submodels — inherently differential-algebraic 
 · x 1 = f 1 ( x 1 , x 2 , z , f ) Sub-model 
 · · x 1 = f 1 ( x 1 , x 2 , z , f ) Residual 
 x 2 = f 2 ( x 1 , x 2 , z , f ) With 
 Generator y 1 = h 1 ( x 1 , x 2 , z , f ) y 1 = h 1 ( x 1 , x 2 , z , f ) Redundancy y 2 = h 2 ( x 1 , x 2 , z , f ) 8 7 Differential index and diagnosis filter design Structural models • Standard definition on differential index is for just-determined models but Structural model can be directly extended to over-determined models, i.e., models with A structural model only models that variables are related! redundancy, 
 · Example relating variables: V , i , ω x 1 = f 1 ( x 1 , x 2 , z , f ) e 1 : V = iR (1 + f R ) + L di dt + K a i ω y 1 = h 1 ( x 1 , x 2 , z , f ) • If sub-model is low-index, standard observer design techniques can be Unknown variables i θ ω α T T m T l f R f i f ω f T V y i y ω y T utilized for a fault detector in the form 
 X X X X · ̂ e 1 x 1 = g 1 ( ̂ x 1 , ̂ x 2 , z ) + Kg r ( ̂ x 1 , ̂ x 2 , z ) Coarse model description, no parameters or analytical expressions 0 = g a ( ̂ x 1 , ̂ x 2 , z ) Can be obtained early in design process with little engineering e ff ort r = g r ( ̂ x 1 , ̂ x 2 , z ) Large-scale model analysis possible using graph theoretical tools • Thus low-index sub-models are of particular interest for detector synthesis Very useful!

Jubilee Symposium 2019: Future Directions of System Modeling and Simulation 9 10 Structural representation of engine model Fundamental algorithmic tool: Dulmage-Mendelsohn decomposition Engine model e1 e2 e3 e4 X 0 X 1 X 2 X n − 1 X n X ∞ e5 · · · e6 e7 e8 e9 • Basic tool in many structural e10 e11 e12 e13 e14 I D e15 I D analysis algorithms b 0 e16 M − e17 e18 e19 I D e20 e21 I D e22 e23 e24 I D • Smart reordering or e25 I D e26 e27 e28 e29 I D e30 I D e31 rows(equations) and columns b 1 e32 e33 e34 I D e35 I D e36 e37 (variables) e38 e39 I D e40 I D e41 b 2 e42 e43 e44 e45 e46 • Partitions the model into three e47 e48 e49 e50 e51 M 0 e52 ... e53 parts e54 e55 e56 e57 e58 e59 e60 e61 b n − 1 e62 • Under determined e63 e64 e65 e66 e67 e68 e69 e70 e71 • Exactly determined b n e72 e73 • Incidence matrix of variable e74 e75 e76 e77 e78 e79 dependency graph e80 I D • Over determined e81 e82 e83 e84 I D e85 e86 e87 • Edges represents connections e88 e89 • The overdetermined part with e90 e91 M + b ∞ e92 e93 e94 redundancy is the one interesting W_es W_e T_em PSI_c DELTA_theta Tq_e_f Tq_e_p W_ac y_W_af y_T_amb • I/D-edges correspond to W_af p_t p_ic T_ic W_ic W_th Aeff_th W_wg Aeff_wg T_af p_af W_c T_cout T_c p_c T_imcr p_im T_im T_ti p_em dh_is W_twg T_turb T_t alpha_th omega_e W_ig W_fr Tq_c eta_c omega_tc PI_c W_t Tq_t eta_t PI_t u_wg wg_pos T_e T_amb p_amb PSI_th PI_wg PSIli_wg m_af m_c m_ic T_fwd_flow_ic m_im m_em m_t PI_cnolim U_c PHI_model W_ccorr Tq_e_cs Tq_e_cb eta_ign W_i_p FMEP S_p BMEP C_eta_vol T_in eta_vol W_fc T_tout Tflow_wg dmdt_af dTdt_af dmdt_c dTdt_c dmdt_ic dTdt_ic dmdt_im dTdt_im dmdt_em dTdt_em dmdt_t dTdt_t dwgdt_pos fp_af fw_af fw_th fw_c fc_vol fw_t fx_th fyw_af fyp_im fyp_ic fyT_ic y_p_ic y_p_im y_T_ic y_omega_e y_alpha_th y_u_wg y_wfc y_p_amb domegadt_tc for diagnosis differentiation and integration 11 Outline of the talk 1. Diagnosability and sensor placement analysis 2. Testable (sub-)models and detector synthesis 3. A Modelica perspective 4. An automotive use-case Diagnosability analysis and sensor selection Presentation will be more what than how

Jubilee Symposium 2019: Future Directions of System Modeling and Simulation 13 14 Diagnosability analysis - Problem formulation Structurally detectable and isolable faults Engine model e1 e2 e3 e4 • Given a dynamic model e5 e6 e7 e8 • Let be the equation that is affected by fault e9 e f i f i e10 e11 e12 e13 e14 I D e15 • Q1: Which faults are I D e16 e17 e18 e19 I D X 0 X 1 X 2 X n − 1 X n X ∞ e20 I D e21 · · · • A fault is (structurally) detectable iff 
 e22 f i e23 structurally detectable? e24 I D e25 I D e26 e27 e28 e29 I D M 0 b 0 e30 I D e31 e32 e f i ∈ M + e33 • Q2: What are the structural e34 I D e35 I D e36 e37 e38 e39 I D e40 I D e41 isolability properties of the e42 M 1 b 1 e43 e44 e45 e46 e47 e48 • Fault not detectable, is detectable model? e49 f 1 f 2 e50 e51 M 2 b 2 e52 e53 e54 e55 e56 e57 e58 e59 • A fault is isolable form a fault iff 
 e60 . ... e61 f i f j e62 . . e63 e64 e65 e66 e67 e68 M n − 1 b n − 1 f 1 e69 e70 e f i ∈ ( M ∖ e f j ) + e71 e72 e73 e74 e75 e76 M n b n e77 e78 e79 e80 I D e81 e82 e83 • Take home: Structural diagnosability can be 
 e84 I D e85 e86 e87 e88 e89 e90 e91 determined by a series of 
 e92 e93 e94 M ∞ f 2 b ∞ W_af W_es W_th W_e T_em T_t PSI_c DELTA_theta Tq_e_cs Tq_e_f Tq_e_p W_i_p T_in W_ac y_T_ic y_W_af y_u_wg y_T_amb p_t p_ic T_ic W_ic Aeff_th W_wg Aeff_wg T_af p_af W_c T_cout T_c p_c T_imcr p_im T_im T_ti p_em dh_is W_twg T_turb alpha_th omega_e W_ig W_fr Tq_c eta_c omega_tc PI_c W_t Tq_t eta_t PI_t u_wg wg_pos T_e T_amb p_amb PSI_th PI_wg PSIli_wg m_af m_c m_ic T_fwd_flow_ic m_im m_em m_t PI_cnolim U_c PHI_model W_ccorr Tq_e_cb eta_ign FMEP S_p BMEP C_eta_vol eta_vol W_fc T_tout Tflow_wg dmdt_af dTdt_af dmdt_c dTdt_c dmdt_ic dTdt_ic dmdt_im dTdt_im dmdt_em dTdt_em dmdt_t dTdt_t domegadt_tc dwgdt_pos fp_af fw_af fw_th fw_c fc_vol fw_t fx_th fyw_af fyp_im fyp_ic fyT_ic y_p_ic y_p_im y_omega_e y_alpha_th y_wfc y_p_amb Dulmage-Mendelsohn decompositions (fast) 15 16 A more detailed structure decomposition Diagnosability of an engine model Dulmage-Mendelsohn decomposition of model 'SECS' Dulmage-Mendelsohn decomposition of model 'SECS' 0 0 Isolability matrix for 'Engine model' 50 100 100 fp_af 150 fw_af 200 200 Injected fault fw_th 250 300 300 fw_c 350 D I D D D I D I D I D I D I D fc_vol I I I Equations 400 Equations 400 D I D D I D D I D I D I D I D I D fw_t I D I D ID I D 450 ID ID I D I D I D I D I D I D I D I D 500 I D I D I D fx_th 500 I D I D I D ID ID ID ID ID ID I D I D I D D I I f21 f22 I I D I 550 D D I I I I D D f21 f22 f18 fyw_af f1 600 f4 f7 f8 f5 600 f6 f3 D I D I f16 f14 f13 f11 f17 f9 f7 f5 f19 fyp_im f1 f8 f10 f15 650 f2 D I f12 fyp_ic 700 D I D I 700 D I 750 fyT_ic f12 800 I D D I 800 D I D I D D I I f4 f2 D I I D f3 f13 f16 fp_af fw_af fw_th fw_c fc_vol fw_t fx_th fyw_affyp_imfyp_ic fyT_ic 850 f17 f9 f11 I D f15 f10 f20 f19 f14 f6 f20 f18 Diagnoses 0 100 200 300 400 500 600 700 800 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 Variables Variables