Fusion of Redundant Information in Brake-By-Wire Systems Using a Fuzzy Voter

In safety critical systems such as brake-by-wire, fault tolerance is usually provided by virtue of having redundant sensors and processing hardware. The redundant information provided by such components should be properly fused to achieve a reliable estimate of the safety critical variable that is sensed or processed by the redundant sensors or hardware. Voting methods are well-known solutions for this category of fusion problems. In this paper, a new voting method, using a fuzzy system for decision-making, is presented. The voted output of the proposed scheme is a weighted average of the sensors signals where the weights are calculated based on the antecedents and consequences of some fuzzy rules in a rulebase. In a case study, we have tested the fuzzy voter along with the well-known majority voting method for a by-wire brake pedal that is equipped with a displacement sensor and two force sensors. Our experimental results show that the performance of the proposed voting method is desirable in the presence of short circuits to ground or supply, excessive noise and sensor drifts. Voting error (in terms of mean square error) is reduced by 82% by the proposed fuzzy voting method, compared to majority voting.

[1]  B. Parhami.  Voting algorithms , 1994 .

[2]  Kihong Park,et al.  A STUDY ON THE BRAKE-BY-WIRE SYSTEM USING HARDWARE-IN-THE-LOOP SIMULATION , 2004 .

[3]  Y. Bar-Shalom,et al.  Tracking in a cluttered environment with probabilistic data association , 1975, Autom..

[4]  R. Chakravorty,et al.  Fixed lag smoothing technique for track maintenance in clutter , 2004, Proceedings of the 2004 Intelligent Sensors, Sensor Networks and Information Processing Conference, 2004..

[5]  Parag K. Lala,et al.  Fault tolerant and fault testable hardware design , 1985 .

[6]  Richard Y. Kain,et al.  Vote assignments in weighted voting mechanisms , 1988, Proceedings [1988] Seventh Symposium on Reliable Distributed Systems.

[7]  Fuad Rahman,et al.  Multiple classifier decision combination strategies for character recognition: A review , 2003, Document Analysis and Recognition.

[8]  Robin J. Evans,et al.  A Bayesian solution and its approximations to out-of-sequence measurement problems , 2003, Inf. Fusion.

[9]  Fabrizio Smeraldi,et al.  Retinal vision applied to facial features detection and face authentication , 2002, Pattern Recognit. Lett..

[10]  Cordelia Schmid,et al.  Face Detection and Tracking in a Video by Propagating Detection Probabilities , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  Farzad Tahami,et al.  A novel driver assist stability system for all-wheel-drive electric vehicles , 2003, IEEE Trans. Veh. Technol..

[12]  Jukka Corander,et al.  A unified approach to joint modeling of multiple quantitative and qualitative traits in gene mapping. , 2002, Journal of theoretical biology.

[13]  G. R. Latif-Shabgahi,et al.  A novel algorithm for weighted average voting used in fault tolerant computing systems , 2004, Microprocess. Microsystems.

[14]  José Luis Huertas,et al.  Efficient Realization of a Threshold Voter for Self-Purging Redundancy , 2001, J. Electron. Test..

[15]  Franz Rothlauf,et al.  Population Sizing for the Redundant Trivial Voting Mapping , 2003, GECCO.

[16]  Darko Musicki,et al.  Joint Integrated Probabilistic Data Association - JIPDA , 2002, Proceedings of the Fifth International Conference on Information Fusion. FUSION 2002. (IEEE Cat.No.02EX5997).

[17]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[18]  P. Green,et al.  Global and local priors, and the location of lesions using gamma-camera imagery , 1991, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[19]  Narendra Ahuja,et al.  Detecting Faces in Images: A Survey , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  Algirdas Avizienis,et al.  The N-Version Approach to Fault-Tolerant Software , 1985, IEEE Transactions on Software Engineering.

[21]  Peter J Green,et al.  Markov chain Monte Carlo in image analysis , 1996 .

[22]  Joseph Y. Halpern.  A Counterexample to Theorems of Cox and Fine , 1996, AAAI/IAAI, Vol. 2.

[23]  Frans Voorbraak,et al.  A Computationally Efficient Approximation of Dempster-Shafer Theory , 1988, Int. J. Man Mach. Stud..

[24]  Stefan Arnborg,et al.  Bayesian Games for Threat Prediction and Situation Analysis , 2004 .

[25]  Simon Parsons,et al.  A review of uncertainty handling formalisms , 1998, Applications of Uncertainty Formalisms.

[26]  King Ngi Ngan,et al.  Locating facial region of a head-and-shoulders color image , 1998, Proceedings Third IEEE International Conference on Automatic Face and Gesture Recognition.

[27]  Lei Lu,et al.  Performance enhancement of the IMM estimation by smoothing , 2002, Proceedings of the Fifth International Conference on Information Fusion. FUSION 2002. (IEEE Cat.No.02EX5997).

[28]  Darren D. Cofer,et al.  Formal Verification of an Avionics Sensor Voter Using SCADE , 2004, FORMATS/FTRTFT.

[29]  Ronald Fagin,et al.  Two Views of Belief: Belief as Generalized Probability and Belief as Evidence , 1992, Artif. Intell..

[30]  S. A. Hoffman,et al.  One-step fixed-lag smoothers for Markovian switching systems , 1996, IEEE Trans. Autom. Control..

[31]  Klaus J. Kirchberg,et al.  Robust Face Detection Using the Hausdorff Distance , 2001, AVBPA.

[32]  Peter Walley,et al.  Measures of Uncertainty in Expert Systems , 1996, Artif. Intell..

[33]  Pietro Perona,et al.  A Probabilistic Approach to Object Recognition Using Local Photometry and Global Geometry , 1998, ECCV.

[34]  Hyunki Kim,et al.  The design and evaluation of all voting triple modular redundancy system , 2002, Annual Reliability and Maintainability Symposium. 2002 Proceedings (Cat. No.02CH37318).

[35]  Alireza Bab-Hadiashar,et al.  Missing data compensation for safety-critical components in a drive-by-wire system , 2005, IEEE Transactions on Vehicular Technology.

[36]  Stefan Arnborg,et al.  Robust Bayesianism: Relation to Evidence Theory , 2014, J. Adv. Inf. Fusion.

[37]  Prakash P. Shenoy,et al.  On the plausibility transformation method for translating belief function models to probability models , 2006, Int. J. Approx. Reason..

[38]  Philippe Smets,et al.  Decision making in the TBM: the necessity of the pignistic transformation , 2005, Int. J. Approx. Reason..

[39]  Yvon Savaria,et al.  Ratioed voter circuit for testing and fault-tolerance in VLSI processing arrays , 1996 .

[40]  Christof Paar,et al.  Comparison of arithmetic architectures for Reed-Solomon decoders in reconfigurable hardware , 1997, Proceedings. The 5th Annual IEEE Symposium on Field-Programmable Custom Computing Machines Cat. No.97TB100186).

[41]  Branko Ristic,et al.  Kalman Filter and Joint Tracking and Classification in the TBM framework , 2004 .

[42]  Hung T. Nguyen,et al.  On the Scoring Approach to Admissibility of Uncertainty Measures in Expert Systems , 1991 .

[43]  R. Mahler,et al.  Can the Bayesian and Dempster-Shafer approaches be reconciled? Yes , 2005, 2005 7th International Conference on Information Fusion.

[44]  Yaakov Bar-Shalom,et al.  Tracking methods in a multitarget environment , 1978 .

[45]  James M. Rehg,et al.  Statistical Color Models with Application to Skin Detection , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[46]  AnHai Doan,et al.  Geometric foundations for interval-based probabilities , 1998, Annals of Mathematics and Artificial Intelligence.

[47]  L YuilleAlan,et al.  Feature extraction from faces using deformable templates , 1992 .

[48]  Stefan Arnborg,et al.  Robust Bayesianism : Imprecise and Paradoxical Reasoning , 2004 .

[49]  Bernd Gärtner,et al.  Fast and Robust Smallest Enclosing Balls , 1999, ESA.

[50]  Abdesselam Bouzerdoum,et al.  Skin segmentation using color pixel classification: analysis and comparison , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[51]  Subhash Challa,et al.  Decentralised Fusion of Disparate Identity Estimates for Shared Situation Awareness , 2004 .

[52]  A. Tversky,et al.  Judgment under Uncertainty: Heuristics and Biases , 1974, Science.

[53]  Michele Favalli,et al.  Enabling testability of fault-tolerant circuits by means of IDDQ-checkable voters , 2000, IEEE Trans. Very Large Scale Integr. Syst..

[54]  Prakash P. Shenoy,et al.  A Comparison of Bayesian and Belief Function Reasoning , 2003, Inf. Syst. Frontiers.

[55]  Prakash P. Shenoy,et al.  A Comparison of Methods for Transforming Belief Function Models to Probability Models , 2003, ECSQARU.

[56]  Darren D. Cofer,et al.  Formal Modeling and Analysis of an Avionics Triplex Sensor Voter , 2003, SPIN.

[57]  Jiri Matas,et al.  Feature-based affine-invariant localization of faces , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[58]  Ronald P. S. Mahler,et al.  The modified Dempster-Shafer approach to classification , 1997, IEEE Trans. Syst. Man Cybern. Part A.

[59]  David Ríos Insua,et al.  Robust Bayesian analysis , 2000 .

[60]  Hartley Slater.  J. B. Paris, the Uncertain Reasoner's Companion , 1997 .

[61]  Richard Y. Kain,et al.  Vote Assignments in Weighted Voting Mechanisms , 1991, IEEE Trans. Computers.

[62]  Alireza Bab-Hadiashar,et al.  Missing data handling by a multi-step ahead predictive filter , 2004 .

[63]  Tor Arne Johansen,et al.  Gain-scheduled wheel slip control in automotive brake systems , 2003, IEEE Trans. Control. Syst. Technol..

[64]  Stanley M. Bileschi,et al.  Advances in Component-Based Face Detection , 2002, SVM.

[65]  Stuart Bennett,et al.  Experimental comparison of voting algorithms in cases of disagreement , 1997, EUROMICRO 97. Proceedings of the 23rd EUROMICRO Conference: New Frontiers of Information Technology (Cat. No.97TB100167).

[66]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[67]  Kagan Tumer,et al.  Analysis of decision boundaries in linearly combined neural classifiers , 1996, Pattern Recognit..

[68]  D. J. Struik.  Jeffreys on Scientific Inference , 1939 .

[69]  Subhash Challa,et al.  Augmented state IMM-PDA for OOSM solution to maneuvering target tracking in clutter , 2003, 2003 Proceedings of the International Conference on Radar (IEEE Cat. No.03EX695).

[70]  P. Green.  Reversible jump Markov chain Monte Carlo computation and Bayesian model determination , 1995 .

[71]  Bing Chen,et al.  Multisensor tracking of a maneuvering target in clutter using IMMPDA fixed-lag smoothing , 2000, IEEE Trans. Aerosp. Electron. Syst..

[72]  Per Svensson,et al.  Methodology for guaranteed and robust high level fusion performance: a literature study , 2005 .

[73]  Ioannis Pavlidis,et al.  Face detection in the near-IR spectrum , 2003, SPIE Defense + Commercial Sensing.

[74]  Florentin Smarandache,et al.  Advances and Applications of DSmT for Information Fusion , 2004 .

[75]  Stuart Bennett,et al.  Smoothing voter: a novel voting algorithm for handling multiple errors in fault-tolerant control systems , 2003, Microprocess. Microsystems.

[76]  Lionel Prevost,et al.  Combining model-based classifiers for face localization , 2005, MVA.

[77]  Renaud Seguier.  A very fast adaptative face detection system , 2004 .

[78]  A. Dawid,et al.  Game theory, maximum entropy, minimum discrepancy and robust Bayesian decision theory , 2004, math/0410076.

[79]  R. Chakravorty,et al.  A single lag smoothing technique for track maintenance in clutter , 2004, IEEE Conference on Cybernetics and Intelligent Systems, 2004..

[80]  Robin J. Evans,et al.  Tracking in clutter using probabilistic data association , 1992 .

[81]  Paul A. Viola,et al.  Rapid object detection using a boosted cascade of simple features , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[82]  D. Rubin.  INFERENCE AND MISSING DATA , 1975 .

[83]  Cecilia Metra,et al.  TMR voting in the presence of crosstalk faults at the voter inputs , 2004, IEEE Transactions on Reliability.

[84]  Reza Hoseinnezhad,et al.  Position sensing in brake-by-wire callipers using resolvers , 2006, IEEE Transactions on Vehicular Technology.

[85]  D Baum,et al.  HIGH PERFORMANCE ACC SYSTEM BASED ON SENSOR FUSION WITH DISTANCE SENSOR, IMAGE PROCESSING UNIT, AND NAVIGATION SYSTEM , 1997 .

[86]  R. E. Kalman,et al.  New Results in Linear Filtering and Prediction Theory , 1961 .

[87]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .

[88]  William Dale Blair,et al.  Interacting multiple-model approach to fixed-interval smoothing , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.