Added computation om probability of maximum fault isolation performance

code/main.ipynb

@@ -101,7 +101,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Plot the 7 first residuals in all fault modes. The residuals plotted in red are supposed to alarm for the fault according to the fault sensitivity matrix."
+    "Plot the 7 first residuals in all fault modes. The residuals plotted in red are supposed to alarm for the fault according to the fault sensitivity matrix.\n",
+    "\n",
+    "(Fig. 4 in the paper)"
    ]
   },
   {
@@ -153,7 +155,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Plot the ideal fault isolability matrix corresponding to the fault sensitivity matrix."
+    "Plot the ideal fault isolability matrix corresponding to the fault sensitivity matrix. \n",
+    "\n",
+    "(Fig. 6 in the paper)"
    ]
   },
   {
@@ -175,7 +179,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Compute consistency based diagnoses and the corresponding confusion matrix based on all 42 thresholded residuals. The confusion matrix should be compared with the ideal fault isolation matrix above."
+    "Compute consistency based diagnoses and the corresponding confusion matrix based on all 42 thresholded residuals. The confusion matrix should be compared with the ideal fault isolation matrix above.\n",
+    "\n",
+    "(Fig. 7 in the paper)"
    ]
   },
   {
@@ -222,7 +228,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Plot the confusion matrix for the random forest classifier for training data"
+    "Plot the confusion matrix for the random forest classifier for training data\n",
+    "\n",
+    "(Fig. 8 in the paper)"
    ]
   },
   {
@@ -231,7 +239,8 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "C = np.diag([1/sum(thdata['mode']==mi) for mi in range(nf)])@confusion_matrix(thdata['mode'], rf.predict(thdata['res']))*100\n",
+    "s = np.diag([1/sum(thdata['mode']==mi) for mi in range(nf)])\n",
+    "C = s@confusion_matrix(thdata['mode'], rf.predict(thdata['res']))*100\n",
     "\n",
     "plt.figure(31, clear=True, figsize=(6, 6))\n",
     "du.PlotConfusionMatrix(C/100)\n",
@@ -245,7 +254,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Plot the variable importance, sorted, to get a ranking of predictor/residual usefullness in the classifier. Note that this classifier is not meant to be used in the diagnosis system."
+    "Plot the variable importance, sorted, to get a ranking of predictor/residual usefullness in the classifier. Note that this classifier is not meant to be used in the diagnosis system.\n",
+    "\n",
+    "(Fig. 10 in the paper)"
    ]
   },
   {
@@ -268,13 +279,16 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Compute performance measures on false-alarm (FA), missed detection (MD), and an aggregated fault isolation (FI) when selecting residuals according to the ranking computed above.\n",
+    "Compute performance measures on false-alarm (FA), missed detection (MD), aggregated fault isolation (FI) and the probability of maximum isolability performance (FI-max)\n",
+    "when selecting residuals according to the ranking computed above.\n",
     "\\begin{align*}\n",
     "  p_{\\text{FA}} &= 1 - P(NF\\in D|NF)\\\\\n",
     "  p_{\\text{MD}} &= \\frac{1}{n_{f}}\\sum_{f_{i}\\in \\tilde{\\mathcal{F}}} P(NF\\in D|f_{i})\\\\\n",
     "  p_{\\text{FI}} &= \\frac{1}{n_{f}^{2}}\\sum_{f_{i}\\in \\tilde{\\mathcal{F}}} P(NF\\notin\n",
-    "  D|f_{i})\\sum_{f_{j}\\in \\tilde{\\mathcal{F}}}|P(f_{j}\\in D|f_{i})-I_{ij}|\n",
-    "\\end{align*}"
+    "  D|f_{i})\\sum_{f_{j}\\in \\tilde{\\mathcal{F}}}|P(f_{j}\\in D|f_{i})-I_{ij}|\\\\\n",
+    "  p_{\\text{FI-max}} &= P(D=F_{f_i}|f_i)\n",
+    "\\end{align*}\n",
+    "where $F_{f_i}$ is the set of faults nont structurally isolable from fault $f_i$."
    ]
   },
   {
@@ -286,20 +300,32 @@
     "pfa = np.zeros(nr-1)\n",
     "pmd = np.zeros(nr-1)\n",
     "pfi = np.zeros(nr-1)\n",
+    "pmfi = np.zeros((nr-1, nf))\n",
+    "\n",
+    "# Make sure isolability matrix for NF corresponds to diagnosis statement \n",
+    "# computed by DiagnosesAndConfusionMatrix\n",
+    "imk = du.IsolabilityMatrix(data['fsm'])\n",
+    "imk[0] = np.zeros(nf)\n",
+    "imk[0, 0] = 1  \n",
     "\n",
     "for k in range(1, nr):\n",
-    "    imk = du.IsolabilityMatrix(data['fsm'][sortIdx[0:k]])\n",
-    "    _, C = du.DiagnosesAndConfusionMatrix(thdata, residx=sortIdx[0:k])\n",
+    "    dx, C = du.DiagnosesAndConfusionMatrix(thdata, residx=sortIdx[0:k])\n",
     "    pfa[k-1] = 1-C[0,0]\n",
     "    pmd[k-1] = np.mean(C[1:,0])\n",
-    "    pfi[k-1] = np.mean(np.diag(1-C[1:, 0])@np.abs(C[1:, 1:]-im[1:, 1:]))"
+    "    pfi[k-1] = np.mean(np.diag(1-C[1:, 0])@np.abs(C[1:, 1:]-im[1:, 1:]))\n",
+    "    \n",
+    "    for fi in range(nf):\n",
+    "        pmfi[k-1, fi] = np.mean(np.all(dx[thdata['mode'] == fi] == imk[fi, :],\n",
+    "                                       axis=1))"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Plot the three performance measures agains the number of selected residuals."
+    "Plot the three aggregated performance measures agains the number of selected residuals.\n",
+    "\n",
+    "(Fig. 11 in the paper)"
    ]
   },
   {
@@ -326,7 +352,31 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Compute and display confusion matrices corresponding to selecting 10, 12, 26, and 27 residuals. The results should be compared to the confusion matrix above where all 42 residuals were used."
+    "Plot the probability of maximum fault isolation performance for each fault.\n",
+    "\n",
+    "(Fig. 12 in the paper)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "plt.figure(figsize=(10, 10))\n",
+    "for k in range(nf):\n",
+    "    plt.plot(pmfi[:, k], label=thdata['modes'][k])\n",
+    "plt.legend(loc='upper right')\n",
+    "BoxOff()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Compute and display confusion matrices corresponding to selecting 10, 12, 26, and 27 residuals. The results should be compared to the confusion matrix above where all 42 residuals were used.\n",
+    "\n",
+    "(Fig. 13 in the paper)"
    ]
   },
   {