{"product_id":"process-control-system-fault-diagnosis-a-bayesian-approach-wiley-series-in-dynamics-and-control-of-electromechanical-systems-9781118770610","title":"Process Control System Fault Diagnosis A Bayesian","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eProcess Control System Fault Diagnosis: A Bayesian Approach     Ruben T. Gonzalez, University of Alberta, Canada     Fei Qi, Suncor Energy Inc.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xiii\u003c\/p\u003e \u003cp\u003eAcknowledgements xvii\u003c\/p\u003e \u003cp\u003eList of Figures xix\u003c\/p\u003e \u003cp\u003eList of Tables xxiii\u003c\/p\u003e \u003cp\u003eNomenclature xxv\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I FUNDAMENTALS\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Motivational Illustrations 3\u003c\/p\u003e \u003cp\u003e1.2 Previous Work 4\u003c\/p\u003e \u003cp\u003e1.2.1 Diagnosis Techniques 4\u003c\/p\u003e \u003cp\u003e1.2.2 Monitoring Techniques 7\u003c\/p\u003e \u003cp\u003e1.3 Book Outline 12\u003c\/p\u003e \u003cp\u003e1.3.1 Problem Overview and Illustrative Example 12\u003c\/p\u003e \u003cp\u003e1.3.2 Overview of Proposed Work 12\u003c\/p\u003e \u003cp\u003eReferences 16\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Prerequisite Fundamentals 19\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 19\u003c\/p\u003e \u003cp\u003e2.2 Bayesian Inference and Parameter Estimation 19\u003c\/p\u003e \u003cp\u003e2.2.1 Tutorial on Bayesian Inference 24\u003c\/p\u003e \u003cp\u003e2.2.2 Tutorial on Bayesian Inference with Time Dependency 27\u003c\/p\u003e \u003cp\u003e2.2.3 Bayesian Inference vs. Direct Inference 32\u003c\/p\u003e \u003cp\u003e2.2.4 Tutorial on Bayesian Parameter Estimation 33\u003c\/p\u003e \u003cp\u003e2.3 The EM Algorithm 38\u003c\/p\u003e \u003cp\u003e2.4 Techniques for Ambiguous Modes 44\u003c\/p\u003e \u003cp\u003e2.4.1 Tutorial on Θ Parameters in the Presence of Ambiguous Modes 46\u003c\/p\u003e \u003cp\u003e2.4.2 Tutorial on Probabilities Using Θ Parameters 47\u003c\/p\u003e \u003cp\u003e2.4.3 Dempster–Shafer Theory 48\u003c\/p\u003e \u003cp\u003e2.5 Kernel Density Estimation 51\u003c\/p\u003e \u003cp\u003e2.5.1 From Histograms to Kernel Density Estimates 52\u003c\/p\u003e \u003cp\u003e2.5.2 Bandwidth Selection 54\u003c\/p\u003e \u003cp\u003e2.5.3 Kernel Density Estimation Tutorial 55\u003c\/p\u003e \u003cp\u003e2.6 Bootstrapping 56\u003c\/p\u003e \u003cp\u003e2.6.1 Bootstrapping Tutorial 57\u003c\/p\u003e \u003cp\u003e2.6.2 Smoothed Bootstrapping Tutorial 57\u003c\/p\u003e \u003cp\u003e2.7 Notes and References 60\u003c\/p\u003e \u003cp\u003eReferences 61\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Bayesian Diagnosis 62\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 62\u003c\/p\u003e \u003cp\u003e3.2 Bayesian Approach for Control Loop Diagnosis 62\u003c\/p\u003e \u003cp\u003e3.2.1 Mode M 62\u003c\/p\u003e \u003cp\u003e3.2.2 Evidence E 63\u003c\/p\u003e \u003cp\u003e3.2.3 Historical Dataset D 64\u003c\/p\u003e \u003cp\u003e3.3 Likelihood Estimation 65\u003c\/p\u003e \u003cp\u003e3.4 Notes and References 67\u003c\/p\u003e \u003cp\u003eReferences 67\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Accounting for Autodependent Modes and Evidence 68\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 68\u003c\/p\u003e \u003cp\u003e4.2 Temporally Dependent Evidence 68\u003c\/p\u003e \u003cp\u003e4.2.1 Evidence Dependence 68\u003c\/p\u003e \u003cp\u003e4.2.2 Estimation of Evidence-transition Probability 70\u003c\/p\u003e \u003cp\u003e4.2.3 Issues in Estimating Dependence in Evidence 74\u003c\/p\u003e \u003cp\u003e4.3 Temporally Dependent Modes 75\u003c\/p\u003e \u003cp\u003e4.3.1 Mode Dependence 75\u003c\/p\u003e \u003cp\u003e4.3.2 Estimating Mode Transition Probabilities 77\u003c\/p\u003e \u003cp\u003e4.4 Dependent Modes and Evidence 81\u003c\/p\u003e \u003cp\u003e4.5 Notes and References 82\u003c\/p\u003e \u003cp\u003eReferences 82\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Accounting for Incomplete Discrete Evidence 83\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 83\u003c\/p\u003e \u003cp\u003e5.2 The Incomplete Evidence Problem 83\u003c\/p\u003e \u003cp\u003e5.3 Diagnosis with Incomplete Evidence 85\u003c\/p\u003e \u003cp\u003e5.3.1 Single Missing Pattern Problem 86\u003c\/p\u003e \u003cp\u003e5.3.2 Multiple Missing Pattern Problem 92\u003c\/p\u003e \u003cp\u003e5.3.3 Limitations of the Single and Multiple Missing Pattern Solutions 93\u003c\/p\u003e \u003cp\u003e5.4 Notes and References 94\u003c\/p\u003e \u003cp\u003eReferences 94\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Accounting for Ambiguous Modes: A Bayesian Approach 96\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 96\u003c\/p\u003e \u003cp\u003e6.2 Parametrization of Likelihood Given Ambiguous Modes 96\u003c\/p\u003e \u003cp\u003e6.2.1 Interpretation of Proportion Parameters 96\u003c\/p\u003e \u003cp\u003e6.2.2 Parametrizing Likelihoods 97\u003c\/p\u003e \u003cp\u003e6.2.3 Informed Estimates of Likelihoods 98\u003c\/p\u003e \u003cp\u003e6.3 Fagin–Halpern Combination 99\u003c\/p\u003e \u003cp\u003e6.4 Second-order Approximation 100\u003c\/p\u003e \u003cp\u003e6.4.1 Consistency of Θ Parameters 101\u003c\/p\u003e \u003cp\u003e6.4.2 Obtaining a Second-order Approximation 101\u003c\/p\u003e \u003cp\u003e6.4.3 The Second-order Bayesian Combination Rule 103\u003c\/p\u003e \u003cp\u003e6.5 Brief Comparison of Combination Methods 104\u003c\/p\u003e \u003cp\u003e6.6 Applying the Second-order Rule Dynamically 105\u003c\/p\u003e \u003cp\u003e6.6.1 Unambiguous Dynamic Solution 105\u003c\/p\u003e \u003cp\u003e6.6.2 The Second-order Dynamic Solution 106\u003c\/p\u003e \u003cp\u003e6.7 Making a Diagnosis 107\u003c\/p\u003e \u003cp\u003e6.7.1 Simple Diagnosis 107\u003c\/p\u003e \u003cp\u003e6.7.2 Ranged Diagnosis 107\u003c\/p\u003e \u003cp\u003e6.7.3 Expected Value Diagnosis 107\u003c\/p\u003e \u003cp\u003e6.8 Notes and References 111\u003c\/p\u003e \u003cp\u003eReferences 111\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Accounting for Ambiguous Modes: A Dempster–Shafer Approach 112\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 112\u003c\/p\u003e \u003cp\u003e7.2 Dempster–Shafer Theory 112\u003c\/p\u003e \u003cp\u003e7.2.1 Basic Belief Assignments 112\u003c\/p\u003e \u003cp\u003e7.2.2 Probability Boundaries 114\u003c\/p\u003e \u003cp\u003e7.2.3 Dempster’s Rule of Combination 114\u003c\/p\u003e \u003cp\u003e7.2.4 Short-cut Combination for Unambiguous Priors 115\u003c\/p\u003e \u003cp\u003e7.3 Generalizing Dempster–Shafer Theory 116\u003c\/p\u003e \u003cp\u003e7.3.1 Motivation: Difficulties with BBAs 117\u003c\/p\u003e \u003cp\u003e7.3.2 Generalizing the BBA 119\u003c\/p\u003e \u003cp\u003e7.3.3 Generalizing Dempster’s Rule 122\u003c\/p\u003e \u003cp\u003e7.3.4 Short-cut Combination for Unambiguous Priors 123\u003c\/p\u003e \u003cp\u003e7.4 Notes and References 124\u003c\/p\u003e \u003cp\u003eReferences 125\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Making Use of Continuous Evidence Through Kernel Density Estimation 126\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 126\u003c\/p\u003e \u003cp\u003e8.2 Performance: Continuous vs. Discrete Methods 127\u003c\/p\u003e \u003cp\u003e8.2.1 Average False Negative Diagnosis Criterion 127\u003c\/p\u003e \u003cp\u003e8.2.2 Performance of Discrete and Continuous Methods 129\u003c\/p\u003e \u003cp\u003e8.3 Kernel Density Estimation 132\u003c\/p\u003e \u003cp\u003e8.3.1 From Histograms to Kernel Density Estimates 132\u003c\/p\u003e \u003cp\u003e8.3.2 Defining a Kernel Density Estimate 134\u003c\/p\u003e \u003cp\u003e8.3.3 Bandwidth Selection Criterion 135\u003c\/p\u003e \u003cp\u003e8.3.4 Bandwidth Selection Techniques 136\u003c\/p\u003e \u003cp\u003e8.4 Dimension Reduction 137\u003c\/p\u003e \u003cp\u003e8.4.1 Independence Assumptions 138\u003c\/p\u003e \u003cp\u003e8.4.2 Principal and Independent Component Analysis 139\u003c\/p\u003e \u003cp\u003e8.5 Missing Values 139\u003c\/p\u003e \u003cp\u003e8.5.1 Kernel Density Regression 140\u003c\/p\u003e \u003cp\u003e8.5.2 Applying Kernel Density Regression for a Solution 141\u003c\/p\u003e \u003cp\u003e8.6 Dynamic Evidence 142\u003c\/p\u003e \u003cp\u003e8.7 Notes and References 143\u003c\/p\u003e \u003cp\u003eReferences 143\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Accounting for Sparse Data Within a Mode 144\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 144\u003c\/p\u003e \u003cp\u003e9.2 Analytical Estimation of the Monitor Output Distribution Function 145\u003c\/p\u003e \u003cp\u003e9.2.1 Control Performance Monitor 145\u003c\/p\u003e \u003cp\u003e9.2.2 Process Model Monitor 146\u003c\/p\u003e \u003cp\u003e9.2.3 Sensor Bias Monitor 148\u003c\/p\u003e \u003cp\u003e9.3 Bootstrap Approach to Estimating Monitor Output Distribution Function 150\u003c\/p\u003e \u003cp\u003e9.3.1 Valve Stiction Identification 150\u003c\/p\u003e \u003cp\u003e9.3.2 The Bootstrap Method 153\u003c\/p\u003e \u003cp\u003e9.3.3 Illustrative Example 156\u003c\/p\u003e \u003cp\u003e9.3.4 Applications 160\u003c\/p\u003e \u003cp\u003e9.4 Experimental Example 164\u003c\/p\u003e \u003cp\u003e9.4.1 Process Description 164\u003c\/p\u003e \u003cp\u003e9.4.2 Diagnostic Settings and Results 167\u003c\/p\u003e \u003cp\u003e9.5 Notes and References 170\u003c\/p\u003e \u003cp\u003eReferences 170\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Accounting for Sparse Modes Within the Data 172\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 172\u003c\/p\u003e \u003cp\u003e10.2 Approaches and Algorithms 172\u003c\/p\u003e \u003cp\u003e10.2.1 Approach for Component Diagnosis 173\u003c\/p\u003e \u003cp\u003e10.2.2 Approach for Bootstrapping New Modes 176\u003c\/p\u003e \u003cp\u003e10.3 Illustration 181\u003c\/p\u003e \u003cp\u003e10.3.1 Component-based Diagnosis 184\u003c\/p\u003e \u003cp\u003e10.3.2 Bootstrapping for Additional Modes 188\u003c\/p\u003e \u003cp\u003e10.4 Application 194\u003c\/p\u003e \u003cp\u003e10.4.1 Monitor Selection 195\u003c\/p\u003e \u003cp\u003e10.4.2 Component Diagnosis 195\u003c\/p\u003e \u003cp\u003e10.5 Notes and References 198\u003c\/p\u003e \u003cp\u003eReferences 199\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II APPLICATIONS\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Introduction to Testbed Systems 203\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Simulated System 203\u003c\/p\u003e \u003cp\u003e11.1.1 Monitor Design 203\u003c\/p\u003e \u003cp\u003e11.2 Bench-scale System 205\u003c\/p\u003e \u003cp\u003e11.3 Industrial Scale System 207\u003c\/p\u003e \u003cp\u003eReferences 207\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Bayesian Diagnosis with Discrete Data 209\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 209\u003c\/p\u003e \u003cp\u003e12.2 Algorithm 210\u003c\/p\u003e \u003cp\u003e12.3 Tutorial 213\u003c\/p\u003e \u003cp\u003e12.4 Simulated Case 216\u003c\/p\u003e \u003cp\u003e12.5 Bench-scale Case 217\u003c\/p\u003e \u003cp\u003e12.6 Industrial-scale Case 219\u003c\/p\u003e \u003cp\u003e12.7 Notes and References 220\u003c\/p\u003e \u003cp\u003eReferences 220\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Accounting for Autodependent Modes and Evidence 221\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 221\u003c\/p\u003e \u003cp\u003e13.2 Algorithms 222\u003c\/p\u003e \u003cp\u003e13.2.1 Evidence Transition Probability 222\u003c\/p\u003e \u003cp\u003e13.2.2 Mode Transition Probability 226\u003c\/p\u003e \u003cp\u003e13.3 Tutorial 228\u003c\/p\u003e \u003cp\u003e13.4 Notes and References 231\u003c\/p\u003e \u003cp\u003eReferences 231\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Accounting for Incomplete Discrete Evidence 232\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Introduction 232\u003c\/p\u003e \u003cp\u003e14.2 Algorithm 232\u003c\/p\u003e \u003cp\u003e14.2.1 Single Missing Pattern Problem 232\u003c\/p\u003e \u003cp\u003e14.2.2 Multiple Missing Pattern Problem 236\u003c\/p\u003e \u003cp\u003e14.3 Tutorial 238\u003c\/p\u003e \u003cp\u003e14.4 Simulated Case 241\u003c\/p\u003e \u003cp\u003e14.5 Bench-scale Case 242\u003c\/p\u003e \u003cp\u003e14.6 Industrial-scale Case 244\u003c\/p\u003e \u003cp\u003e14.7 Notes and References 246\u003c\/p\u003e \u003cp\u003eReferences 246\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Accounting for Ambiguous Modes in Historical Data: A Bayesian Approach 247\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Introduction 247\u003c\/p\u003e \u003cp\u003e15.2 Algorithm 248\u003c\/p\u003e \u003cp\u003e15.2.1 Formulating the Problem 248\u003c\/p\u003e \u003cp\u003e15.2.2 Second-order Taylor Series Approximation of p(E|M,Θ) 248\u003c\/p\u003e \u003cp\u003e15.2.3 Second-order Bayesian Combination 250\u003c\/p\u003e \u003cp\u003e15.2.4 Optional Step: Separating Monitors into Independent Groups 252\u003c\/p\u003e \u003cp\u003e15.2.5 Grouping Methodology 253\u003c\/p\u003e \u003cp\u003e15.3 Illustrative Example of Proposed Methodology 254\u003c\/p\u003e \u003cp\u003e15.3.1 Introduction 254\u003c\/p\u003e \u003cp\u003e15.3.2 Offline Step 1: Historical Data Collection 255\u003c\/p\u003e \u003cp\u003e15.3.3 Offline Step 2: Mutual Information Criterion (Optional) 255\u003c\/p\u003e \u003cp\u003e15.3.4 Offline Step 3: Calculate Reference Values 256\u003c\/p\u003e \u003cp\u003e15.3.5 Online Step 1: Calculate Support 257\u003c\/p\u003e \u003cp\u003e15.3.6 Online Step 2: Calculate Second-order Terms 258\u003c\/p\u003e \u003cp\u003e15.3.7 Online Step 3: Perform Combinations 260\u003c\/p\u003e \u003cp\u003e15.3.8 Online Step 4: Make a Diagnosis 262\u003c\/p\u003e \u003cp\u003e15.4 Simulated Case 265\u003c\/p\u003e \u003cp\u003e15.5 Bench-scale Case 268\u003c\/p\u003e \u003cp\u003e15.6 Industrial-scale Case 269\u003c\/p\u003e \u003cp\u003e15.7 Notes and References 270\u003c\/p\u003e \u003cp\u003eReferences 271\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Accounting for Ambiguous Modes in Historical Data: A Dempster–Shafer Approach 272\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Introduction 272\u003c\/p\u003e \u003cp\u003e16.2 Algorithm 272\u003c\/p\u003e \u003cp\u003e16.2.1 Parametrized Likelihoods 272\u003c\/p\u003e \u003cp\u003e16.2.2 Basic Belief Assignments 273\u003c\/p\u003e \u003cp\u003e16.2.3 The Generalized Dempster’s Rule of Combination 275\u003c\/p\u003e \u003cp\u003e16.3 Example of Proposed Methodology 276\u003c\/p\u003e \u003cp\u003e16.3.1 Introduction 276\u003c\/p\u003e \u003cp\u003e16.3.2 Offline Step 1: Historical Data Collection 277\u003c\/p\u003e \u003cp\u003e16.3.3 Offline Step 2: Mutual Information Criterion (Optional) 277\u003c\/p\u003e \u003cp\u003e16.3.4 Offline Step 3: Calculate Reference Value 278\u003c\/p\u003e \u003cp\u003e16.3.5 Online Step 1: Calculate Support 279\u003c\/p\u003e \u003cp\u003e16.3.6 Online Step 2: Calculate the GBBA 280\u003c\/p\u003e \u003cp\u003e16.3.7 Online Step 3: Combine BBAs and Diagnose 283\u003c\/p\u003e \u003cp\u003e16.4 Simulated Case 283\u003c\/p\u003e \u003cp\u003e16.5 Bench-scale Case 284\u003c\/p\u003e \u003cp\u003e16.6 Industrial System 286\u003c\/p\u003e \u003cp\u003e16.7 Notes and References 287\u003c\/p\u003e \u003cp\u003eReferences 287\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Making use of Continuous Evidence through Kernel Density Estimation 288\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Introduction 288\u003c\/p\u003e \u003cp\u003e17.2 Algorithm 289\u003c\/p\u003e \u003cp\u003e17.2.1 Kernel Density Estimation 289\u003c\/p\u003e \u003cp\u003e17.2.2 Bandwidth Selection 289\u003c\/p\u003e \u003cp\u003e17.2.3 Adaptive Bandwidths 290\u003c\/p\u003e \u003cp\u003e17.2.4 Optional Step: Dimension Reduction by Multiplying Independent Likelihoods 291\u003c\/p\u003e \u003cp\u003e17.2.5 Optional Step: Creating Independence via Independent Component Analysis 291\u003c\/p\u003e \u003cp\u003e17.2.6 Optional Step: Replacing Missing Values 292\u003c\/p\u003e \u003cp\u003e17.3 Example of Proposed Methodology 293\u003c\/p\u003e \u003cp\u003e17.3.1 Offline Step 1: Historical Data Collection 295\u003c\/p\u003e \u003cp\u003e17.3.2 Offline Step 3: Mutual Information Criterion (Optional) 296\u003c\/p\u003e \u003cp\u003e17.3.3 Offline Step 4: Independent Component Analysis (Optional) 298\u003c\/p\u003e \u003cp\u003e17.3.4 Offline Step 5: Obtain Bandwidths 298\u003c\/p\u003e \u003cp\u003e17.3.5 Online Step 1: Calculate Likelihood of New Data 301\u003c\/p\u003e \u003cp\u003e17.3.6 Online Step 2: Calculate Posterior Probability 302\u003c\/p\u003e \u003cp\u003e17.3.7 Online Step 3: Make a Diagnosis 302\u003c\/p\u003e \u003cp\u003e17.4 Simulated Case 302\u003c\/p\u003e \u003cp\u003e17.5 Bench-scale Case 304\u003c\/p\u003e \u003cp\u003e17.6 Industrial-scale Case 304\u003c\/p\u003e \u003cp\u003e17.7 Notes and References 307\u003c\/p\u003e \u003cp\u003eReferences 307\u003c\/p\u003e \u003cp\u003eAppendix 308\u003c\/p\u003e \u003cp\u003e17.A Code for Kernel Density Regression 308\u003c\/p\u003e \u003cp\u003e17.A.1 Kernel Density Regression 308\u003c\/p\u003e \u003cp\u003e17.A.2 Three-dimensional Matrix Toolbox 310\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Dynamic Application of Continuous Evidence and Ambiguous Mode Solutions 313\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 Introduction 313\u003c\/p\u003e \u003cp\u003e18.2 Algorithm for Autodependent Modes 313\u003c\/p\u003e \u003cp\u003e18.2.1 Transition Probability Matrix 314\u003c\/p\u003e \u003cp\u003e18.2.2 Review of Second-order Method 314\u003c\/p\u003e \u003cp\u003e18.2.3 Second-order Probability Transition Rule 315\u003c\/p\u003e \u003cp\u003e18.3 Algorithm for Dynamic Continuous Evidence and Autodependent Modes 316\u003c\/p\u003e \u003cp\u003e18.3.1 Algorithm for Dynamic Continuous Evidence 316\u003c\/p\u003e \u003cp\u003e18.3.2 Combining both Solutions 318\u003c\/p\u003e \u003cp\u003e18.3.3 Comments on Usefulness 319\u003c\/p\u003e \u003cp\u003e18.4 Example of Proposed Methodology 320\u003c\/p\u003e \u003cp\u003e18.4.1 Introduction 320\u003c\/p\u003e \u003cp\u003e18.4.2 Offline Step 1: Historical Data Collection 320\u003c\/p\u003e \u003cp\u003e18.4.3 Offline Step 2: Create Temporal Data 320\u003c\/p\u003e \u003cp\u003e18.4.4 Offline Step 3: Mutual Information Criterion (Optional, but Recommended) 321\u003c\/p\u003e \u003cp\u003e18.4.5 Offline Step 5: Calculate Reference Values 322\u003c\/p\u003e \u003cp\u003e18.4.6 Online Step 1: Obtain Prior Second-order Terms 322\u003c\/p\u003e \u003cp\u003e18.4.7 Online Step 2: Calculate Support 323\u003c\/p\u003e \u003cp\u003e18.4.8 Online Step 3: Calculate Second-order Terms 323\u003c\/p\u003e \u003cp\u003e18.4.9 Online Step 4: Combining Prior and Likelihood Terms 324\u003c\/p\u003e \u003cp\u003e18.5 Simulated Case 325\u003c\/p\u003e \u003cp\u003e18.6 Bench-scale Case 326\u003c\/p\u003e \u003cp\u003e18.7 Industrial-scale Case 326\u003c\/p\u003e \u003cp\u003e18.8 Notes and References 327\u003c\/p\u003e \u003cp\u003eReferences 327\u003c\/p\u003e \u003cp\u003eIndex 329\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default 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