<Text-field style="Heading 1" layout="Heading 1">1. Implementation of the fault discrimination algorithms presented in Nathalie Verdi\303\250re and S\303\251bastien Orange. Diagnosability in the case of multifaults in nonlinear models. Journal of Process Control, 69, 2018. </Text-field>

These algorithms use the exhaustive summary of a parametrized dynamical system. From an exhausive summary, they return a vector of algebraic polynomials, called Algebraic signature, and a precomputed table of this vector. From estimation of the exhaustive summary and the knowledge of the system parameters, an estimation of the algebraic signature can be performed and the comparison of this last estimation with these precomputed tables can permit the discrimination of one or more faults acting on the system.

In the considered system, the single faults, f1, f2, f3... can be seen as supplementary parameters which are equal to 0 when no fault is acting on the system. When one or more single faults are acting simultamously on the system, we use the term multiple fault. For exemple, the multiple fault [f1, f2] is acting if f1<>0, f2<>0 and if the values of all the other single faults is 0.

<Text-field style="Heading 2" layout="Heading 2">1.1 Procedure AlgebraicSignature </Text-field>

<Text-field style="Normal" layout="Normal">Calling sequence AlgebraicSignature<Equation executable="false" style="Normal" input-equation="" display="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">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</Equation></Text-field> <Text-field style="List Item" layout="List Item" bulletsuffix="." bullet="none">IOCoeff : the list of coefficients of an exhaustive summary (composed of polynomials whose indeterminates are parameters and single faults); l_single_faults: the list of the possible single faults supposed to be equal to 0 when no faults occurs. Description This procedure returns a list of polynomials whose indeterminates are the parameters and the components of the exhaustive summary given as inputs; Each of these polynomials does not vanish when at least one multiple fault is acting and vanishes when at least an other multiple fault is acting.</Text-field>

JSFH

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

-I%mrowG6#/I+modulenameG6"I,TypesettingGI(_syslibGF'6i\m-I#miGF$6#Q!F'-I'mspaceGF$6&/%'heightGQ&0.0exF'/%&widthGQ&0.0emF'/%&depthGF4/%*linebreakGQ%autoF'-F,6(Q3AlgebraicSignatureF'/%'familyGQ,Courier~NewF'/%'italicGQ%trueF'/%+foregroundGQ+[120,0,14]F'/%0font_style_nameGQ,Maple~InputF'/%,mathvariantGQ'italicF'-I#moGF$60Q"~F'F@FFFI/FMQ'normalF'/%&fenceGQ&falseF'/%*separatorGFW/%)stretchyGFW/%*symmetricGFW/%(largeopGFW/%.movablelimitsGFW/%'accentGFW/%'lspaceGF7/%'rspaceGF7-FP60Q*&coloneq;F'F@FFFIFSFUFXFZFfnFhnFjnF\o/F_oQ,0.2777778emF'/FaoFfoFO-FP62Q%procF'F@/%%boldGFEFFFI/FMQ%boldF'/%+fontweightGF^pFUFXFZFfnFhnFjnF\oF^oF`o-I(mfencedGF$6)-F#6(-F,6(Q(IOCoeffF'F@FCFFFIFL-FP60Q",F'F@FFFIFSFU/FYFEFZFfnFhnFjnF\oF^o/FaoQ,0.3333333emF'FO-F,6(Q0l_single_faultsF'F@FCFFFIFL/%+executableGFWFSF@F[pFFFIF]pF_pF+-F06&F2F5F8/F;Q(newlineF'F/-FP60Q"#F'F@FFFIFSFUFXFZFfnFhnFjnF\oF^oF`o-F,6(Qio~Inputs~:~*~a~list,~IOCoeff,~of~coefficients~of~the~Input~Output~polynomials~;F'F@FCFFFIFLFdqF/Fhq-F,6(Qeo~~~~~~~~~~*~the~list,~l_single_faults,~of~all~the~possible~single~faults~;F'F@FCFFFIFLFdqF/Fhq-F,6(Q^p~Output~:~*~An~algebraic~signature,~AlgSign,~constructed~from~the~the~list~IOCoeff.F'F@FCFFFIFLFdqF/-FP62Q&localF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFO-F,6(Q1ListOfParametersF'F@FCFFFIFLFipFO-F,6(Q5ListOfIOcoefficientsF'F@FCFFFIFLFipFO-F,6(Q>ListMF_CorrespondingGB_IdealsF'F@FCFFFIFLFipFO-F,6(Q#mfF'F@FCFFFIFLFipFO-F,6(Q%I_mfF'F@FCFFFIFLFipFO-F,6(Q%J_mfF'F@FCFFFIFLFipFO-F,6(Q&GB_mfF'F@FCFFFIFLFipFO-F,6(Q'EnsPolF'F@FCFFFIFLFipFO-F,6(Q+IdealInterF'F@FCFFFIFLFipFO-F,6(Q(AlgSignF'F@FCFFFIFLFipFO-F,6(Q3MultipleFaultsListF'F@FCFFFIFLFipFO-F,6(Q"SF'F@FCFFFIFLFipFO-F,6(Q*System_mfF'F@FCFFFIFLFipFO-F,6(Q"iF'F@FCFFFIFL-FP60Q";F'F@FFFIFSFUF\qFZFfnFhnFjnF\oF^oFgoFdqF/FOFOFOFOFgrFOFboFO-Fbp6+-F#6&-F,6(Q#opF'F@FCFFFIFL-Fbp6)-F#6)-Fbp6+-F#6&Fhu-Fbp6)-F#6&-F,6(Q'indetsF'F@FCFFFIFL-Fbp6)-F#6%FfpFbqFSF@F[pFFFIF]pF_pFbqFSF@F[pFFFIF]pF_pFbqFSF@F[pFFFIF]pF_p/%%openGQ"|frF'/%&closeGQ"|hrF'FO-FP62Q&minusF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFO-Fbp6+-F#6&Fhu-Fbp6)-F#6%F_qFbqFSF@F[pFFFIF]pF_pFbqFSF@F[pFFFIF]pF_pF^wFawFbqFSF@F[pFFFIF]pF_pFbqFSF@F[pFFFIF]pF_p/F_wQ"[F'/FbwQ"]F'FauFdqF/FOFOFOFOFjrFOFboFO-Fbp6+-F#6&-F,6(Q$seqF'F@FCFFFIFL-Fbp6)-F#62-F,6(Q$catF'F@FCFFFIFL-Fbp6)-F#6(-F,6(Q%phi_F'F@FCFFFIFLFipFOF^uFbqFSF@F[pFFFIF]pF_pFipFOF^uFO-FP60Q"=F'F@FFFIFSFUFXFZFfnFhnFjnF\oFeoFgoFO-I#mnGF$6'Q"1F'F@FFFIFSFO-FP60Q#..F'F@FFFIFSFUFXFZFfnFhnFjnF\o/F_oQ,0.2222222emF'F`oFO-F,6(Q%nopsF'F@FCFFFIFLFjvFbqFSF@F[pFFFIF]pF_pFbqFSF@F[pFFFIF]pF_pF_xFaxFauFdqF/FOFOFOFOF]sFOFboFO-Fbp6+-F#6%F+FbqFSF@F[pFFFIF]pF_pF_xFaxFauFdqF/FOFOFOFOFhq-F,6(Qdo~Generating~the~list,~MultipleFaultsList,~of~all~the~possible~multifaultsF'F@FCFFFIFLFdqF/FOFOFOFOFetFOFboFO-Fbp6+FizF@F[pFFFIF]pF_pF^wFawFauFdqF/FOFOFOFOFhtFOFboFO-F,6(Q)combinatF'F@FCFFFIFL-FP60Q#:-F'F@FFFIFSFUFXFZFfnFhnFjnF\oF^oF`o-F,6(Q(subsetsF'F@FCFFFIFL-Fbp6)-F#6&FgvF[xFbqFSF@F[pFFFIF]pF_pFauFdqF/FOFOFOFO-FP62Q&whileF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFO-FP62Q$notF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFOFht-Fbp6+-F#6%-F,6(Q)finishedF'F@FCFFFIFLFbqFSF@F[pFFFIF]pF_pF_xFaxFO-FP62Q#doF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFOFetFOFboFO-Fbp6+-F#6)Fhu-Fbp6)-F#6%FetFbqFSF@F[pFFFIF]pF_pFipFO-Fbp6+-F#6&Fhu-Fbp6)-F#6'Fht-Fbp6+-F#6%-F,6(Q*nextvalueF'F@FCFFFIFLFbqFSF@F[pFFFIF]pF_pF_xFax-Fbp6)FizF@F[pFFFIF]pF_pFbqFSF@F[pFFFIF]pF_pFbqFSF@F[pFFFIF]pF_pF_xFaxFbqFSF@F[pFFFIF]pF_pF^wFawFO-FP62Q$endF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFOFj\lFauFdqF/FOFOFOFOFhq-F,6(Qco~Computation~of~elimination~ideals~corresponding~to~each~multiple~fault.F'F@FCFFFIFLFdqF/FOFOFOFO-FP62Q$forF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFOF`sFO-FP62Q#inF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFOFetFOFj\lFdqF/FOFOFOFOFOFOFOFOF[uFOFboFOFfpFO-FP60Q*&uminus0;F'F@FFFIFSFUFXFZFfnFhnFjnF\oFbz/FaoFczFOFjrFauFdqF/FOFOFOFOFOFOFOFOF\_lFOF^uFO-FP62Q#toF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFOFdzF[xFOFj\lFdqF/FOFOFOFOFOFOFOFOFOFOFOFO-FP62Q#ifF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFO-F,6(Q&evalbF'F@FCFFFIFL-Fbp6)-F#6&-F,6(Q'memberF'F@FCFFFIFL-Fbp6)-F#6)F_q-Fbp6+-F#6%F^uFbqFSF@F[pFFFIF]pF_pF_xFaxFipFOF`sFbqFSF@F[pFFFIF]pF_pFbqFSF@F[pFFFIF]pF_pFO-FP62Q%thenF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFOF[uFOFboFO-Fbp6+-F#61Fhu-Fbp6)-F#6%F[uFbqFSF@F[pFFFIF]pF_pFipFOF^y-Fbp6)-F#6(-F,6(Q%inv_F'F@FCFFFIFLFipFOF^uFbqFSF@F[pFFFIF]pF_p-FP60Q"*F'F@FFFIFSFUFXFZFfnFhnFjnF\o/F_oQ,0.1666667emF'/FaoFdblF_qFj`lFOFb_lFOF[zFbqFSF@F[pFFFIF]pF_pF_xFaxF+FdqF/FOFOFOFOFOFOFOFOFOFOFOFO-FP62Q%elseF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFOF[uFOFboFO-Fbp6+-F#6*FhuFealFipFOF_qFj`lFbqFSF@F[pFFFIF]pF_pF_xFaxF+FdqF/FOFOFOFOFOFOFOFOFOFOFOFOFf^lFOFi_lFdqF/FOFOFOFOFOFOFOFOFf^lFOFj\lFauFdqF/FOFOFOFOFOFOFOFOFcsFOFboFO-F,6(Q1PolynomialIdealsF'F@FCFFFIFLFc[l-F,6(Q0PolynomialIdealF'F@FCFFFIFLFealFauFdqF/FOFOFOFOFOFOFOFOFfsFOFboFOF]clFc[l-F,6(Q1EliminationIdealF'F@FCFFFIFL-Fbp6)-F#6(FcsFipFO-Fbp6+-F#6*Fhu-Fbp6)-F#6%FgrFbqFSF@F[pFFFIF]pF_pFipFOFhu-Fbp6)-F#6%FjrFbqFSF@F[pFFFIF]pF_pFbqFSF@F[pFFFIF]pF_pF^wFawFbqFSF@F[pFFFIF]pF_pFauFdqF/FOFOFOFOFOFOFOFOFisFOFboFO-F,6(Q)GroebnerF'F@FCFFFIFLFc[l-F,6(Q&BasisF'F@FCFFFIFL-Fbp6)-F#6)FfsFipFO-F,6(Q%plexF'F@FCFFFIFL-Fbp6)-F#6*FhuFbdlFipFOFhuF^dlFbqFSF@F[pFFFIF]pF_pFbqFSF@F[pFFFIF]pF_pFauFdqF/FOFOFOFOFOFOFOFOF]sFOFboFO-Fbp6+-F#6)Fhu-Fbp6)-F#6%F]sFbqFSF@F[pFFFIF]pF_pFipFO-Fbp6+-F#6+F`sFipFOFisFipFOFcsFbqFSF@F[pFFFIF]pF_pF_xFaxFbqFSF@F[pFFFIF]pF_pF_xFaxFauFdqF/FOFOFOFOFf^lFOFj\lFauFdqF/FOFOFOFOFhq-F,6(Qfs~Determination~of~a~set,~EnsPol,~of~algebraic~relations~vanishing~for~at~least~one~multifault~and~not~vanishing~for~at~least~one~multifaultF'F@FCFFFIFLFdqF/FOFOFOFOF\tFOFboFO-F,6(Q(`union`F'F@FCFFFIFL-Fbp6)-F#6&Fgx-Fbp6)-F#61-Fbp6+-F#6&Fhu-Fbp6)-F#6'F]sFj`l-Fbp6+-F#6%-F\z6'Q"2F'F@FFFIFSFbqFSF@F[pFFFIF]pF_pF_xFaxFbqFSF@F[pFFFIF]pF_pFbqFSF@F[pFFFIF]pF_pF^wFawFipFOF^uFOFhyFOF[zFOF_zFOFdz-Fbp6)-F#6&F]sFOFbqFSF@F[pFFFIF]pF_pFbqFSF@F[pFFFIF]pF_pFbqFSF@F[pFFFIF]pF_pFauFdqF/FOFOFOFOF_tFOFboFOF]clFc[l-F,6(Q*IntersectF'F@FCFFFIFL-Fbp6)-F#6&Fgx-Fbp6)-F#64F]clFc[lF`clFeglFipFOF^uFOFhyFOF[zFOF_zFOFdzF`hlFbqFSF@F[pFFFIF]pF_pFbqFSF@F[pFFFIF]pF_pFauFdqF/FOFOFOFOFhq-F,6(Q^s~Polynomials~of~EnsPol~differing~from~a~multiplicative~constant~are~removed.~Ordered~arbitrarily~they~define~an~algebraic~signatureF'F@FCFFFIFLFdqF/FOFOFOFOFbtFOFboFOF^[lFauFdqF/FOFOFOFOF\_lFOF^uFOFf_lFOFdz-Fbp6)-F#6%F\tFbqFSF@F[pFFFIF]pF_pFOFj\lFOFi_lFOF`\lFOF\`l-Fbp6)-F#6(F]clFc[l-F,6(Q0IdealMembershipF'F@FCFFFIFL-Fbp6)-F#6)F\tFj`lFipFOF_tFbqFSF@F[pFFFIF]pF_pFbqFSF@F[pFFFIF]pF_pFOF^alFOFbtFOFboFO-Fbp6+-F#6/F\tFj`l-FP60Q"/F'F@FFFIFSFUFX/FenFEFfnFhnFjnF\oFcblFeblFfdlFc[l-F,6(Q3LeadingCoefficientF'F@FCFFFIFL-Fbp6)-F#6*F\tFj`lFipFOF`el-Fbp6)-F#6&Fhu-Fbp6)-F#6&Fgv-Fbp6)-F#6&F\tFj`lFbqFSF@F[pFFFIF]pF_pFbqFSF@F[pFFFIF]pF_pFbqFSF@F[pFFFIF]pF_pFbqFSF@F[pFFFIF]pF_pFipFOFhu-Fbp6)-F#6%FbtFbqFSF@F[pFFFIF]pF_pFbqFSF@F[pFFFIF]pF_pF^wFawFOFf^lFOFi_lFOFf^lFOFj\lFauFdqF/FOFOFOFOFbtFOFbo-Fbp6+-F#6&FhuF\\mFbqFSF@F[pFFFIF]pF_pF_xFaxFauFdqF/FOFOFOFOFhq-F,6(Qcq~Printing,~for~the~user,~the~list~of~the~input~output~polynomials~used~to~define~the~algebraic~signatureF'F@FCFFFIFLFdqF/FOFOFOFO-F,6(Q'lprintF'F@FCFFFIFL-Fbp6)-F#6'FOFhu-Fbp6)-F#6&-F,6(Q'EquateF'F@FCFFFIFL-Fbp6)-F#6(FcxFipFOFfpFbqFSF@F[pFFFIF]pF_pFbqFSF@F[pFFFIF]pF_pFbqFSF@F[pFFFIF]pF_pFauFdqF/FOFOFOFO-F,6(Q+kerneloptsF'F@FCFFFIFL-Fbp6)-F#6)-F,6(Q+printbytesF'F@FCFFFIFLFOFhyFO-F,6(FEF@FCFFFIFLFbqFSF@F[pFFFIF]pF_pFauFdqF/FOFOFOFO-FP62Q'returnF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFOFbtFdqFOFf^lFOFho-FP60Q":F'F@FFFIFSFUFXFZFfnFhnFjnF\oFeoFgoFdqF/F+FbqFS

<Text-field style="Heading 2" layout="Heading 2">1.2 Procedure SingleFaultCharacterization</Text-field>

<Text-field style="Normal" layout="Normal">Calling sequence <Equation executable="false" style="Normal" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVE8U2luZ2xlRmF1bHRDaGFyYWN0ZXJpemF0aW9uRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdGMS8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvRjNRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVE8U2luZ2xlRmF1bHRDaGFyYWN0ZXJpemF0aW9uRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdGMS8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvRjNRJ25vcm1hbEYn</Equation><Equation executable="false" style="Normal" input-equation="" display="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">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</Equation> * AlgSign: the algebraic signature returned by the procedure AlgebraicSignature or a sublist of it; * <Equation executable="false" style="Normal" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZELUkjbWlHRiQ2JVEoaW9jb2VmZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi5RIn5GJ0YvRjIvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjsvJSlzdHJldGNoeUdGOy8lKnN5bW1ldHJpY0dGOy8lKGxhcmdlb3BHRjsvJS5tb3ZhYmxlbGltaXRzR0Y7LyUnYWNjZW50R0Y7LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSi1GNjYuUSI6RidGL0YyRjlGPEY+RkBGQkZERkYvRklRLDAuMjc3Nzc3OGVtRicvRkxGUUY1LUYsNiVRJHRoZUYnL0YwRjsvRjNRJ25vcm1hbEYnLUY2Ni1GOEZXRjlGPEY+RkBGQkZERkZGSEZLLUYsNiVRJWxpc3RGJ0ZWRldGWS1GLDYlUSNvZkYnRlZGV0ZZLUYsNiVRLWNvZWZmaWNpZW50c0YnRlZGV0ZZRmhuRllGU0ZZLUYsNiVRJklucHV0RidGVkZXRlktRiw2JVEnT3V0cHV0RidGVkZXRlktRiw2JVEscG9seW5vbWlhbHNGJ0ZWRldGWS1GLDYlUSV1c2VkRidGVkZXRlktRjY2LlEjdG9GJy8lJWJvbGRHRjtGV0Y5RjxGPkZARkJGREZGRkhGS0ZZLUYsNiVRKGNvbXB1dGVGJ0ZWRldGWS1GLDYlUShBbGdTaWduRidGL0YyLUY2Ni1RIjtGJ0ZXRjkvRj1GMUY+RkBGQkZERkZGSEZSLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHRkovJSZkZXB0aEdGXnEvJSpsaW5lYnJlYWtHUShuZXdsaW5lRictRiw2I1EhRicvJTBmb250X3N0eWxlX25hbWVHUSVUZXh0RidGVw==</Equation>* Cond: An optional argument which is a list, possibly empty, of contrains on the parameters and faults including, possibly, initial conditions. Description This procedure returns a list of 2-tuple composed of single fault(s) fi whose presence in a multiple fault can be charaterized by a non vanishing component, AlgSign[k], of AlgSign, i.e. such that fi<>0 iff AlgSign[k]<>0.</Text-field>

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

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

<Text-field style="Heading 2" layout="Heading 2">1.3 Procedure <Equation executable="false" style="Heading 2" input-equation="" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlFDRXhwZWN0ZWRWYWx1ZXNPZkFsZ2VicmFpY1NpZ25hdHVyZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSxib2xkLWl0YWxpY0YnLyUrZm9udHdlaWdodEdRJWJvbGRGJw==">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlFDRXhwZWN0ZWRWYWx1ZXNPZkFsZ2VicmFpY1NpZ25hdHVyZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSxib2xkLWl0YWxpY0YnLyUrZm9udHdlaWdodEdRJWJvbGRGJw==</Equation></Text-field>

<Text-field style="Normal" layout="Normal">Calling sequence <Equation executable="false" style="Normal" input-equation="" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVFDRXhwZWN0ZWRWYWx1ZXNPZkFsZ2VicmFpY1NpZ25hdHVyZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVFDRXhwZWN0ZWRWYWx1ZXNPZkFsZ2VicmFpY1NpZ25hdHVyZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==</Equation><Equation executable="false" style="Normal" input-equation="" display="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">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</Equation><Equation executable="false" style="2D Math" input-equation="" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlFDRXhwZWN0ZWRWYWx1ZXNPZkFsZ2VicmFpY1NpZ25hdHVyZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlFDRXhwZWN0ZWRWYWx1ZXNPZkFsZ2VicmFpY1NpZ25hdHVyZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn</Equation><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> * AlgSign: an algebraic signature returned by the procedure AlgebraicSignature or a sublist of it; * <Equation executable="false" style="Normal" input-equation="" display="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">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</Equation>* l_single_fault: a list of single faults which are supposed to be equal to 0 when no fault occurs, * Cond: a first optional argument which is a list, possibly empty, of contrains on the parameters and faults including, possibly, the initial conditions; * <Equation executable="true" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEkTFNGRicvJSdpdGFsaWNHUSV0cnVlRicvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GNlEnbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEkTFNGRicvJSdpdGFsaWNHUSV0cnVlRicvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GNlEnbm9ybWFsRic=</Equation>: a second optional argument which is a list of 2-tuple composed of single fault(s) f_i whose presence in a multiple fault can be charaterized by a non vanishing component. Description The output of this procedure is a list of 2-uplets. The first component is list of (multiple) faults. The second one is the corresponding vector, EV, composed of 0, 1 and -1 with the following convention: * EV[k] is set to 0 if AlgSign[k] is guaranted to vanish; * EV[k] is set to 1 if AlgSign[k] is guarented to never vanish; * EV[k] is set to -1 in the other cases.</Text-field>

JSFH

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-I%mrowG6#/I+modulenameG6"I,TypesettingGI(_syslibGF'6hdn-I#miGF$6#Q!F'-I'mspaceGF$6&/%'heightGQ&0.0exF'/%&widthGQ&0.0emF'/%&depthGF4/%*linebreakGQ%autoF'-F,6(QCExpectedValuesOfAlgebraicSignatureF'/%'familyGQ,Courier~NewF'/%'italicGQ%trueF'/%+foregroundGQ+[120,0,14]F'/%0font_style_nameGQ,Maple~InputF'/%,mathvariantGQ'italicF'-I#moGF$60Q"~F'F@FFFI/FMQ'normalF'/%&fenceGQ&falseF'/%*separatorGFW/%)stretchyGFW/%*symmetricGFW/%(largeopGFW/%.movablelimitsGFW/%'accentGFW/%'lspaceGF7/%'rspaceGF7-FP60Q*&coloneq;F'F@FFFIFSFUFXFZFfnFhnFjnF\o/F_oQ,0.2777778emF'/FaoFfoFO-FP62Q%procF'F@/%%boldGFEFFFI/FMQ%boldF'/%+fontweightGF^pFUFXFZFfnFhnFjnF\oF^oF`o-I(mfencedGF$6'-F#66-F,6(Q(AlgSignF'F@FCFFFIFL-FP60Q",F'F@FFFIFSFU/FYFEFZFfnFhnFjnF\oF^o/FaoQ,0.3333333emF'FO-F,6(Q*l_iocoeffF'F@FCFFFIFLFipFO-F,6(Q0l_single_faultsF'F@FCFFFIFLFipFOFO-F,6(Q%CondF'F@FCFFFIFLFbo-Fbp6)-F#6%F+/%+executableGFWFSF@FFFIFS/%%openGQ"[F'/%&closeGQ"]F'FipFO-F,6(Q:l_CharaterizedSingleFaultF'F@FCFFFIFLFboFhqF\rFSF@FFFIFSF+-F06&F2F5F8/F;Q(newlineF'F/-FP62Q&localF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFO-F,6(Q1ListMF_CorAlgRelF'F@FCFFFIFLFipFO-F,6(Q3MultipleFaultsListF'F@FCFFFIFLFipFO-F,6(Q"SF'F@FCFFFIFLFipFO-F,6(Q"RF'F@FCFFFIFLFipFO-F,6(Q.MultipleFaultF'F@FCFFFIFLFipFO-F,6(Q*System_mfF'F@FCFFFIFLFipFO-F,6(Q"iF'F@FCFFFIFLFipFO-F,6(Q$EasF'F@FCFFFIFLFipFO-F,6(Q$EsfF'F@FCFFFIFLFipFO-F,6(Q/l_mf_as_expValF'F@FCFFFIFLFipFO-F,6(Q%i_mfF'F@FCFFFIFLFipFO-F,6(Q-l_expect_valF'F@FCFFFIFLFipFO-F,6(Q"kF'F@FCFFFIFLFipFO-F,6(Q$BGIF'F@FCFFFIFLFipFO-F,6(Q%eqnsF'F@FCFFFIFL-FP60Q";F'F@FFFIFSFUF\qFZFfnFhnFjnF\oF^oFgoFgrF/-FP60Q"#F'F@FFFIFSFUFXFZFfnFhnFjnF\oF^oF`o-F,6(QM~Inputs:~~*~an~algebraic~signature~AlgSign~;F'F@FCFFFIFLFgrF/F^v-F,6(Qbp~~~~~~~~~~*~the~list,~l_iocoeff,~of~input~output~coefficients~used~to~compute~AlgSign~;F'F@FCFFFIFLFgrF/F^v-F,6(QZ~~~~~~~~~~*~the~list,~l_single_faults,~of~single~faults~;F'F@FCFFFIFLFgrF/F^v-F,6(Qep~~~~~~~~~~*~the~list,~Cond,~parameters~cnstrains~including~eventually~initial~conditions~;F'F@FCFFFIFLFgrF/F^v-F,6(Q`r~~~~~~~~~~*~the~list,~l_CharaterizedSingleFault,~eventually~empty,~of~2-uplet~composed~of~single~faults~f_i~and~of~a~F'F@FCFFFIFLFgrF/F^v-F,6(Q\p~~~~~~~~~~~~~~component,~AlgSign_i,~of~AlgSign~such~that~f_i<>0~iff~AlgSign_i<>0.F'F@FCFFFIFLFgrF/F^v-F,6(Q_p~Output:~~*~the~list~giving,~for~each~single~fault,~the~expected~values~of~AlgSign~;F'F@FCFFFIFLFgrF/F^v-F,6(Q]t~~~~~~~~~~*~(with~the~following~convention:~0~if~the~component~of~AlgSign~is~assured~to~vanish,~1~if~it~can~not~vanish~and~-1~in~the~other~cases).F'F@FCFFFIFLFgrF/FOFOFOFO-F,6(Q+kerneloptsF'F@FCFFFIFL-Fbp6'-F#6)-F,6(Q+printbytesF'F@FCFFFIFLFO-FP60Q"=F'F@FFFIFSFUFXFZFfnFhnFjnF\oFeoFgoFO-F,6(FWF@FCFFFIFLF\rFSF@FFFIFSF[vFgrF/FOFOFOFOFasFOFboFO-Fbp6)FjqF@FFFIFS/F_rQ"|frF'/FbrQ"|hrF'F[vFgrF/FOFOFOFOF^v-F,6(Qdo~Generating~the~list,~MultipleFaultsList,~of~all~the~possible~multifaultsF'F@FCFFFIFLFgrF/FOFOFOFOFdsFOFboFO-F,6(Q)combinatF'F@FCFFFIFL-FP60Q#:-F'F@FFFIFSFUFXFZFfnFhnFjnF\oF^oF`o-F,6(Q(subsetsF'F@FCFFFIFL-Fbp6'-F#6&-F,6(Q'indetsF'F@FCFFFIFL-Fbp6'-F#6%FbqF\rFSF@FFFIFSF\rFSF@FFFIFSF[vFgrF/FOFOFOFO-FP62Q&whileF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFO-FP62Q$notF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFOFds-Fbp6)-F#6%-F,6(Q)finishedF'F@FCFFFIFLF\rFSF@FFFIFSF^rFarFO-FP62Q#doF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFOFasFOFboFO-Fbp6)-F#6)-F,6(Q#opF'F@FCFFFIFL-Fbp6'-F#6%FasF\rFSF@FFFIFSFipFO-Fbp6)-F#6&Fi[l-Fbp6'-F#6'Fds-Fbp6)-F#6%-F,6(Q*nextvalueF'F@FCFFFIFLF\rFSF@FFFIFSF^rFar-Fbp6'FjqF@FFFIFSF\rFSF@FFFIFSF\rFSF@FFFIFSF^rFarF\rFSF@FFFIFSFjxF\yFO-FP62Q$endF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFOFb[lF[vFgrF/FOFOFOFOF^v-F,6(Q\q~Determination,~for~each~multiplefault,~MultipleFault,~of~the~corresponding~semi~algebraic~systemF'F@FCFFFIFLFgrF/FOFOFOFOF^sFOFboFOFhqF[vFgrF/FOFOFOFO-FP62Q$forF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFOFjsFO-FP62Q#inF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFOFasFOFb[lFgrF/FOFOFOFOFOFOFOFOF]tFOFboFO-F,6(Q'EquateF'F@FCFFFIFL-Fbp6'-F#6(F_qFipFO-Fbp6)-F#6&-F,6(Q$seqF'F@FCFFFIFL-Fbp6'-F#62-F,6(Q$catF'F@FCFFFIFL-Fbp6'-F#6(-F,6(Q%phi_F'F@FCFFFIFLFipFOF`tF\rFSF@FFFIFSFipFOF`tFOFcxFO-I#mnGF$6'Q"1F'F@FFFIFSFO-FP60Q#..F'F@FFFIFSFUFXFZFfnFhnFjnF\o/F_oQ,0.2222222emF'F`oFO-F,6(Q%nopsF'F@FCFFFIFL-Fbp6'-F#6%F_qF\rFSF@FFFIFSF\rFSF@FFFIFSF\rFSF@FFFIFSF^rFarF\rFSF@FFFIFSF[vFgrF/FOFOFOFOFOFOFOFOFg]lFOF`tFO-FP62Q#toF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFOFb`lFazFOFb[lFgrF/FOFOFOFOFOFOFOFOFOFOFOFO-FP62Q#ifF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFO-F,6(Q&evalbF'F@FCFFFIFL-Fbp6'-F#6&-F,6(Q'memberF'F@FCFFFIFL-Fbp6'-F#6)Fbq-Fbp6)-F#6%F`tF\rFSF@FFFIFSF^rFarFipFOFjsF\rFSF@FFFIFSF\rFSF@FFFIFSFO-FP62Q%thenF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFOF]tFOFboFO-Fbp6)-F#6.Fi[l-Fbp6'-F#6%F]tF\rFSF@FFFIFSFipFOFbqF]blFO-FP60Q+&NotEqual;F'F@FFFIFSFUFXFZFfnFhnFjnF\oFeoFgoFO-Fj_l6'Q"0F'F@FFFIFSF\rFSF@FFFIFSF^rFarF+FgrF/FOFOFOFOFOFOFOFOFOFOFOFO-FP62Q%elseF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFOF]tFOFboFO-Fbp6)-F#6.Fi[lFhblFipFOFbqF]blFOFcxFOF_clF\rFSF@FFFIFSF^rFarF+FgrF/FOFOFOFOFOFOFOFOFOFOFOFOFa]lFOF\alFgrF/FOFOFOFOFOFOFOFOFa]lFOFb[lF[vFgrF/FOFOFOFOFOFOFOFOF^sFOFboFO-Fbp6)-F#6)Fi[l-Fbp6'-F#6%F^sF\rFSF@FFFIFSFipFO-Fbp6)-F#6(FjsFipFOF]tF\rFSF@FFFIFSF^rFarF\rFSF@FFFIFSF^rFarF+FgrF/FOFOFOFOFa]lFOFb[lF[vFgrF/FOFOFOFOFctFOFboFO-Fbp6)-F#6&Fh^l-Fbp6'-F#63FdrF]bl-Fbp6)-F#6%-Fj_l6'Q"2F'F@FFFIFSF\rFSF@FFFIFSF^rFarFipFOF`tFOFcxFOFi_lFOF]`lFOFb`l-Fbp6'-F#6%FdrF\rFSF@FFFIFSF\rFSF@FFFIFSF\rFSF@FFFIFSF^rFarF[vFgrF/FOFOFOFOFftFOFboFO-Fbp6)-F#6&Fh^l-Fbp6'-F#63FdrF]bl-Fbp6)-F#6%Fi_lF\rFSF@FFFIFSF^rFarFipFOF`tFOFcxFOFi_lFOF]`lFOFb`lFdelF\rFSF@FFFIFSF\rFSF@FFFIFSF^rFarF[vFgrF/FOFOFOFOF^v-F,6(Q\p~Determination~of~the~expected~values,~l_mf_as_expVal,~of~the~algebraic~signatureF'F@FCFFFIFLFgrF/FOFOFOFOFitFOFboFOFhqF[vFgrF/FOFOFOFO-F,6(Q'printfF'F@FCFFFIFL-Fbp6'-F#6+F+-I#msGF$6#Q$%-sF'FOFipFO-F_gl6#Q@Processing~of~the~multifault~:~F'F+F\rFSF@FFFIFSF[vFgrF/FOFOFOFOFg]lFOF\uFOFi`lFOFb`lF]dlFOFb[lFgrF/FOFOFOFOFOFOFOFOFOFgfl-Fbp6'-F#6,F+-F_gl6#Q$~%aF'FOFipFOF^s-Fbp6)-F#6%F\uF\rFSF@FFFIFSF^rFarF`flF\rFSF@FFFIFSF[vFgrF/FOFOFOFOFOFOFOFOF_uFOFboFOFhqF[vFgrF/FOFOFOFOFOFOFOFOFg]lFOFbuFOFi`lFOFb`l-Fbp6'-F#6%FfpF\rFSF@FFFIFSFOFb[lFOFOFOF^v-F,6(Qft~Testing~whether~it~is~possible~to~complete~the~list~of~expected~values,~l_expect_val,~with~an~eventual~characterization~given~by~l_CharaterizedSingleFaultF'F@FCFFFIFLFgrF/FOFOFOFOFOFOFOFOFOFOFOFOF\alFOFfal-Fbp6'-F#6)Ffp-Fbp6)-F#6%FbuF\rFSF@FFFIFSF^rFarFipFOFctF\rFSF@FFFIFSFOFablFgrF/FOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOF\alFOFfal-Fbp6'-F#6+Fft-Fbp6)-F#6(-F,6(Q*ListToolsF'F@FCFFFIFLFdy-F,6(Q'SearchF'F@FCFFFIFLFghlF\rFSF@FFFIFSF^rFarFipFOF^sF\hlF`flF\rFSF@FFFIFSFOFablFOF_uFOFboFO-Fbp6)-F#6)Fi[l-Fbp6'-F#6%F_uF\rFSF@FFFIFSFipFOFi_lF\rFSF@FFFIFSF^rFarF+FgrF/FOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFbclFOF_uFOFboFO-Fbp6)-F#6)Fi[lFajlFipFOF_clF\rFSF@FFFIFSF^rFarF+FgrFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFa]lFOF\alFOF[vFgrFOFOFOFOFOFOFOFOFOFOFOFOFbclF^v-F,6(Qft~Testing~whether~the~component~AlgSign[k]~of~AlgSign~vanishes~or~does~not~vanish~when~the~multiple~fault~occurs~using~emptiness~tests~of~SemiAlgebraic~setsF'F@FCFFFIFLFgrF/FOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFeuFOFboFOF^sF\hlF]elF[vFgrF/FOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFgsFOFboFO-F,6(Q.RegularChainsF'F@FCFFFIFLFdy-F,6(Q/PolynomialRingF'F@FCFFFIFL-Fbp6'-F#6%-Fbp6)-F#6&Fi[l-Fbp6'-F#6+F^z-Fbp6'-F#6%FeuF\rFSF@FFFIFSFO-FP62Q&unionF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFOF^z-Fbp6'-F#6%FeqF\rFSF@FFFIFSF\rFSF@FFFIFSF\rFSF@FFFIFSF^rFarF\rFSF@FFFIFSF[vFgrF/FOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFhuFOFboFO-Fbp6)-F#62FfpF[ilFOF\clFOF_clFipFOFi[lF^\mFipFOFi[lFe\mF\rFSF@FFFIFSF^rFarF[vFgrF/FOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOF\alFOF_al-Fbp6'-F#6*F\[mFdy-F,6(Q6SemiAlgebraicSetToolsF'F@FCFFFIFLFdy-F,6(Q(IsEmptyF'F@FCFFFIFL-Fbp6'-F#6(FhuFipFOFgsF\rFSF@FFFIFSF\rFSF@FFFIFSFOFablFOF_uFOFboFOFejlF+FgrF/FOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFbclFOFOFOFOFhuFOFboFO-Fbp6)-F#62FfpF[ilFOFcxFOF_clFipFOFi[lF^\mFipFOFi[lFe\mF\rFSF@FFFIFSF^rFarF[vFgrF/FOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOF\alFOF_alF]]mFOFablFOF_uFOFboFOF]jlFOFgrF/FOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFbclFOF_uFOFboFO-Fbp6)-F#6*Fi[lFajlFipFO-FP60Q*&uminus0;F'F@FFFIFSFUFXFZFfnFhnFjnF\oF``l/FaoFa`lFi_lF\rFSF@FFFIFSF^rFarFOFgrFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFa]lFOF\alFOF[vFgrFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFOFa]lFOF\alFOF[vFgrF/FOFOFOFOFOFOFOFOFOFOFOFOFa]lFOF\alFgrF/FOFOFOFOFOFOFOFOFa]lFOFb[lF[vFgrF/FOFOFOFOFOFOFOFOFitFOFboFO-Fbp6)-F#6)Fi[l-Fbp6'-F#6%FitF\rFSF@FFFIFSFipFO-Fbp6)-F#6*F^sF\hlF`flFipFOF_uF\rFSF@FFFIFSF^rFarF\rFSF@FFFIFSF^rFarF+FgrF/FOFOFOFOFa]lFOFb[lF[vFgrF/FOFOFOFOFiw-Fbp6'-F#6)F`xFOFcxFO-F,6(FEF@FCFFFIFLF\rFSF@FFFIFSF[vFgrF/FOFOFOFO-FP62Q'returnF'F@F[pFFFIF]pF_pFUFXFZFfnFhnFjnF\oF^oF`oFOFitFgrFOFa]lFOFhoFO-FP60Q":F'F@FFFIFSFUFXFZFfnFhnFjnF\oFeoFgoF\rFS

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

<Text-field style="Heading 1" layout="Heading 1">2. Application to a mechanical system with two degrees of freedom</Text-field>

The mechanical system, studied in this section, is outlined in the figure hereafter. It is composed of two masses m1 and m2 with three spring stiffness k1, k2 and k3 free to move on a horizontal axis. The frictions are ignored. The parameters k1, k2, k3, m1, m2 and d are known and the position of mass m1 and m2 are respectively denoted by x1 and x2.

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We assume that * three additive faults f1, f2, f3 are respectively acting on the three spring stiffness k1, k2 and k3; * a fault, f4, is acting on the first output y1 = x1+f4; * the second output is y2=x2-x1. No fault is acting on the system if and only if all the single faults, f1 .. f4 are equal to 0. The objective is to determine, a priori, if the mathematical model is able to discriminate (multiple) faults acting on the system.

<Text-field style="Heading 2" layout="Heading 2">2.0 Studied system and exhaustive summary Assignements of the variables of the studied system</Text-field>

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Computation of the exhaustive summary

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Note that there are two IO polynomials since there are two outputs (See L. Denis-Vidal, G. Joly-Blanchard, C. Noiret, and M. Petitot. An algorithm to test identifiability of non-linear systems. In Proceedings of 5th IFAC Symposium on Nonlinear Control Systems, volume 7, pages 174\342\200\223178, St Petersburg, Russia, 2001.)

<Text-field style="Heading 2" layout="Heading 2">2.1 Computation of the algebraic signature</Text-field>

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

Note that f1 = 0 iff the component - phi_1+k1 of AlgSign is vanishing. The same remark can be done for f2 and k2+phi2

<Text-field style="Heading 2" layout="Heading 2">2.2 Computation of the expected values of the algebraic signature without taking into account constraints on the parameters</Text-field>

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

Recall that, in the vectors giving the expected values of the algebraic signature, * 0 means that the component always vanishes, * 1 that it never vanishes; * -1 in the other cases. Which single faults can be discriminated ? Is there a component of this algebraic signature whose values characterize the presence of the single fault f2 in the multiple fault ? In the next execution block, for each single fault fi, a component of the algebraic signature characterizing the presence of fi in any multiple fault is searched.

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<Text-field style="Heading 2" layout="Heading 2">2.3 Computation of the expected values of the algebraic signature taking into account constraints on the parameters</Text-field>

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

What can be said about this output ?

Use the procedure SingleFaultCharaterization to confirm your observation. Remark that this function admits a fourth (optional) argument : the list of conditions, Cond.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEjLi5GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRictRiw2LVEiLkYnRi9GMkY1RjdGOUY7Rj1GPy9GQkZGRkQvJStleGVjdXRhYmxlR0Y0Ri8=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

<Text-field style="Heading 2" layout="Heading 2">2.4 Complexity Assume that the presence of a single fault fi in any multiple fault can be characterized by at least one component of the algebraic signature. Let n be the number of single faults and m the number of components of the algebraic signature. What is the maximum and the minimum numbers of emptyness tests of semialgebraic sets realized by each of the two following approaches? * Use of the procedure <Equation executable="false" style="Heading 2" input-equation="" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KFFDRXhwZWN0ZWRWYWx1ZXNPZkFsZ2VicmFpY1NpZ25hdHVyZUYnLyUlc2l6ZUdRIzEyRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EqWzAsMTI4LDBdRicvJSxtYXRodmFyaWFudEdRLGJvbGQtaXRhbGljRicvJStmb250d2VpZ2h0R1ElYm9sZEYn">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KFFDRXhwZWN0ZWRWYWx1ZXNPZkFsZ2VicmFpY1NpZ25hdHVyZUYnLyUlc2l6ZUdRIzEyRicvJSdpdGFsaWNHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1EqWzAsMTI4LDBdRicvJSxtYXRodmFyaWFudEdRLGJvbGQtaXRhbGljRicvJStmb250d2VpZ2h0R1ElYm9sZEYn</Equation> knowing that each value of the output corresponds to one or two test(s). * Use of the procedure SingleFaultCharacterization knowing that, for each fault f1, ..., fn, and for the m components of the algebraic signature, at most 2 tests are realized. </Text-field>

<Text-field style="Heading 3" italic="false" bold="false" layout="Heading 3">Answer Procedure <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> Procedure <Equation executable="false" style="2D Math" input-equation="" 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JSFH

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