Uncertainty quantification and stochastic modelling with EXCEL:
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| Sprache: | English |
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| Beschreibung: | xi, 531 Seiten Illustrationen |
| ISBN: | 9783030777562 |
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| 100 | 1 | |a Cursi, Eduardo Souza de |e Verfasser |0 (DE-588)1251818439 |4 aut | |
| 245 | 1 | 0 | |a Uncertainty quantification and stochastic modelling with EXCEL |c Eduardo Souza De Cursi |
| 264 | 1 | |a Cham |b Springer |c [2022] | |
| 300 | |a xi, 531 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-030-77757-9 |
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Datensatz im Suchindex
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| adam_text | Contents 1 2 Some Tips to Use EXCEL®................................................. 1.1 How to Activate the SOLVER and the ANALYSIS TOOLPACK........................................................................... 1.2 How to Include a Third-Part Add-In.................................... 1.3 Disabling Warnings on the Add-Ins..................................... 1.4 How to Activate the VBA Tools.......................................... 1.5 How to Insert a VBA Module.............................................. 1.6 How to Import a VBA Module............................................ 1.7 Matrix Formulas.................................................................... 1.8 Fixing Volatile Formulas...................................................... 1.9 Using Addresses of Cells...................................................... 1.10 Using Names in EXCEL®.................................................... 1.11 How to Run the SOLVER..................................................... 1.12 How to Include Iterative Calculations in Your Workbook............................................................................... 1.13 How to Include a Control in Your Workbook.................... 1.14 How to Include a Chart in Your Workbook........................ 1.15 How to Use a Variant to Store Anythingin a Variable... 1.16 How to Use a Collection to Store Anything in a Variable........................................................................... 1.17 How to Include a Class in Your Workbook........................ Some Useful Numerical
Methods....................................... 2.1 Linear Systems....................................................................... 2.1.1 Using the Inverse Matrix........................................ 2.1.2 Using the SOLVER................................................. 2.1.3 Using Gauss-Jordan Pivoting................................. 2.1.4 Using LU Decomposition....................................... 2.1.5 Using QR Decomposition...................................... 2.1.6 Using Relaxation Iterations.................................... 2.2 Optimization........................................................................... 2.2.1 Unconstrained Optimization Using the SOLVER in a Worksheet....................................... 2.2.2 Unconstrained Optimization Using the SOLVER in VBA.................................................... 1 1 2 3 6 7 10 11 11 12 14 16 23 25 27 30 32 33 43 43 43 45 47 49 49 50 50 51 53 VÜ
Contents viii 2.2.3 2.3 2.4 2.5 2.6 2.7 2.8 3 Constrained Optimization Using the SOLVER in a Worksheet....................................... 2.2.4 Constrained Optimization Using the SOLVER in VBA..................................................................... 2.2.5 Linear Programming Using the SOLVER in a Worksheet......................................................... 2.2.6 Linear Programming Using the SOLVER in VBA..................................................................... Nonlinear Equations............................................................... 2.3.1 Nonlinear Equations Using the SOLVER in a Worksheet......................................................... 2.3.2 Nonlinear Equations Using the SOLVER in VBA..................................................................... 2.3.3 Nonlinear Equations Using Newton-Raphson ... 2.3.4 Overdetermined Linear Systems............................ Ordinary Differential Equations........................................... 2.4.1 Runge-Kutta’s Methods.......................................... Numerical Integration............................................................ Multiobjective Optimization................................................. Interpolation of Discrete Numerical Data........................... Numerical Derivatives........................................................... 54 57 59 61 63 63 64 65 68 70 71 76 77 80 84 Probabilities with EXCEL®........................................................... 89 3.1
Probability.............................................................................. 89 3.1.1 Mass Functions and Mass Densities...................... 90 3.1.2 The Case of Finite Populations.............................. 91 3.2 Combinatorial Probabilities with EXCEL®........................ 93 3.3 Conditional Probability, Bayes’ Formula, and Independence.......................................................................... 95 3.4 Random Variables.................................................................. 97 3.4.1 Statistics of a Random Variable............................ 98 3.4.2 Numerical Evaluation of Statistics........................ 102 3.4.3 Classical Inequalities.............................................. 104 3.4.4 Characteristic Function and Moments.................. 105 3.5 Random Vectors and Pairs of Random Variables.............. 106 3.6 Discrete and Continuous Random Variables...................... 112 3.6.1 Discrete Variables................................................... 112 3.6.2 Continuous Variables Having a PDF.................... 114 3.7 Sequences of Random Variables.......................................... 119 3.8 Samples................................................................................... 122 3.8.1 Maximum Likelihood Estimators.......................... 130 3.8.2 Samples from Random Vectors............................. 132 3.8.3 Empirical CDF and Empirical PDF...................... 136 3.9 Frequentisi Probabilities with EXCEL®.............................. 140 3.9.1 Testing Adequacy to a
Distribution...................... 141 3.9.2 Testing Independence............................................. 144 3.10 Generating Uniform Random numbers................................ 147 3.10.1 Using Built-In Functions.......................................... 147
Contents ¡X 4 5 3.10.2 Using the Data Analysis Tool................................ 3.10.3 Using VBA.............................................................. 3.11 Generating Normal Random Numbers................................ 3.11.1 Using Built-In Functions........................................ 3.11.2 Using the Analysis ToolPack................................. 3.11.3 Using VBA.............................................................. 3.12 Generating Triangular Random Numbers........................... 3.13 Generating Random Numbers by Inversion........................ 3.14 Generating Discrete Random Numbers............................... 3.14.1 Using Built-In Functions........................................ 3.14.2 Using the Analysis Toolpack................................. 3.14.3 Using VBA.............................................................. 3.15 Generating Regular Random Functions.............................. 3.16 Generating Regular Random Curves................................... 148 149 151 151 152 153 155 157 158 158 158 160 161 165 Stochastic Processes.............................................................. 4.1 Stationary and Ergodicity................................................... 4.2 Determination of the Distribution of a Stationary Process.................................................................................... 4.3 White Noise........................................................................... 4.4 Moving Average Processes.................................................. 4.5 Autoregressive
Processes...................................................... 4.6 ARMA Processes................................................................... 4.7 Markov Processes.................................................................. 4.8 Diffusion Processes............................................................... 4.8.1 Time Integral and Derivative of a Process............ 4.8.2 Simulation of the Time Integral of a White Noise........................................................................ 4.8.3 Brownian Motion.................................................... 4.8.4 Random Walks........................................................ 4.8.5 Itô’s Integrals........................................................... 4.8.6 Itô’s Calculus........................................................... 4.8.7 Numerical Simulation of Stochastic Differential Equations............................................ Representation of Random Variables............................... 5.1 The UQ Approach for the Representation of Random Variables................................................................................. 5.2 Collocation............................................................................. 5.2.1 Finding the Coefficients of the Expansion in a Worksheet........................................................ 5.2.2 Solution Using VBA............................................... 5.2.3 Solution Using an Adapted Workbook................. 5.3 Variational Approximation................................................... 5.3.1 Finding the Coefficients of the
Expansion in a Worksheet........................................................ 5.3.2 Solution Using VBA............................................... 5.3.3 Solution Using an Adapted Workbook................. 171 172 178 180 181 188 199 204 215 215 219 223 226 228 230 236 243 243 250 254 256 259 265 266 268 270
Contents x 5.4 Moments Matching Method.................................................. 5.4.1 The Standard Formulation of М3.......................... 5.4.2 Constrained Optimization Formulation of М3........................................................................ 5.4.3 Multiobjective Optimization Formulation of М3........................................................................ Multidimensional Expansions............................................... 5.5.1 Case Where U Is Multidimensional...................... 5.5.2 Case Where X Is Multidimensional...................... Random Functions................................................................. Random Curves...................................................................... Mean, Variance and Confidence Intervals for Random Functions or Random Curves................................................ 272 273 Uncertain Algebraic Equations..................................................... 6.1 Uncertain Linear Systems..................................................... 6.1.1 Very Small Linear Systems.................................... 6.2 Nonlinear Equations and Adaptation of an Iterative Code........................................................................................ 6.3 Iterative Evaluation of Eigenvalues..................................... 6.3.1 Very Small Matrices............................................... Random Differential Equations.................................................... 7.1 Linear Differential Equations............................................... 7.2
Nonlinear Differential Equations.......................................... 7.3 Uncertainties on Curves Connected to Differential Equations................................................................................. 323 326 331 8 UQ in Game Theory........................................................................ 8.1 Language from Game Theory............................................... 8.2 A Simple Coin Game............................................................. 8.2.1 GT Strategies When p Is Known........................... 8.2.2 UQ Strategies When p Is Known........................... 8.2.3 Strategies When p Is Unknown.............................. 8.2.4 Strategies for the Stochastic Game........................ 8.2.5 Replicator Dynamics............................................... 8.3 A Classica! Game: Prisoner’s Dilemma............................... 8.3.1 Replicator Dynamics............................................... 8.4 The Goalie’s Anxiety at the PenaltyKick............................ 377 377 379 380 382 382 386 387 391 393 395 9 Optimization Under Uncertainty.................................................. 403 9.1 Using the Methods of Representation.................................. 404 9.2 Using the Adaptation of a Descent Method........................ 417 9.3 Combining Statistics of the Objective, the Constraints and Expansions....................................................................... 429 10 Reliability.......................................................................................... 10.1
Reliability............................................................................... 10.2 Limit State Curves................................................................. 10.3 Design Point........................................................................... 10.3.1 Multiple Failure Conditions................................... 5.5 5.6 5.7 5.8 6 7 283 284 286 286 289 292 296 306 335 348 355 359 360 367 370 433 434 443 445 449
Contents XI 10.4 10.5 Reliability Analysis............................................................... Hasofer-Lind Reliability Index............................................. 10.5.1 The General Case.................................................... 10.5.2 The Case of Affine Limit State Equations............ 10.5.3 The Case of a Convex Failure Region.................. Using the Reliability Index to Estimate the Probability of Failure................................................................................ 10.6.1 The Case of Affine Limit State Equations............ 10.6.2 The Case of a Convex Failure Region.................. 10.6.3 General Failure Regions......................................... The Transformations of Rosenblatt and Nataf.................... FORM and SORM................................................................. 10.8.1 FirstOrder Reliability Method(FORM)................. 10.8.2 Second Order ReliabilityMethod (SORM)........... Reliability Based Design Optimization............................... 10.9.1 The Bilevel or Double Loop Approach for a Desired ß......................................................... 10.9.2 The Bilevel or Double Loop Approach for a Desired Objective........................................... 453 455 455 466 469 Bibliography............................................................................................. 519 Index........................................................................................................... 525 10.6 10.7 10.8 10.9 473 477 478 480 487 490 491 501 508 509 515
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| adam_txt |
Contents 1 2 Some Tips to Use EXCEL®. 1.1 How to Activate the SOLVER and the ANALYSIS TOOLPACK. 1.2 How to Include a Third-Part Add-In. 1.3 Disabling Warnings on the Add-Ins. 1.4 How to Activate the VBA Tools. 1.5 How to Insert a VBA Module. 1.6 How to Import a VBA Module. 1.7 Matrix Formulas. 1.8 Fixing Volatile Formulas. 1.9 Using Addresses of Cells. 1.10 Using Names in EXCEL®. 1.11 How to Run the SOLVER. 1.12 How to Include Iterative Calculations in Your Workbook. 1.13 How to Include a Control in Your Workbook. 1.14 How to Include a Chart in Your Workbook. 1.15 How to Use a Variant to Store Anythingin a Variable. 1.16 How to Use a Collection to Store Anything in a Variable. 1.17 How to Include a Class in Your Workbook. Some Useful Numerical
Methods. 2.1 Linear Systems. 2.1.1 Using the Inverse Matrix. 2.1.2 Using the SOLVER. 2.1.3 Using Gauss-Jordan Pivoting. 2.1.4 Using LU Decomposition. 2.1.5 Using QR Decomposition. 2.1.6 Using Relaxation Iterations. 2.2 Optimization. 2.2.1 Unconstrained Optimization Using the SOLVER in a Worksheet. 2.2.2 Unconstrained Optimization Using the SOLVER in VBA. 1 1 2 3 6 7 10 11 11 12 14 16 23 25 27 30 32 33 43 43 43 45 47 49 49 50 50 51 53 VÜ
Contents viii 2.2.3 2.3 2.4 2.5 2.6 2.7 2.8 3 Constrained Optimization Using the SOLVER in a Worksheet. 2.2.4 Constrained Optimization Using the SOLVER in VBA. 2.2.5 Linear Programming Using the SOLVER in a Worksheet. 2.2.6 Linear Programming Using the SOLVER in VBA. Nonlinear Equations. 2.3.1 Nonlinear Equations Using the SOLVER in a Worksheet. 2.3.2 Nonlinear Equations Using the SOLVER in VBA. 2.3.3 Nonlinear Equations Using Newton-Raphson . 2.3.4 Overdetermined Linear Systems. Ordinary Differential Equations. 2.4.1 Runge-Kutta’s Methods. Numerical Integration. Multiobjective Optimization. Interpolation of Discrete Numerical Data. Numerical Derivatives. 54 57 59 61 63 63 64 65 68 70 71 76 77 80 84 Probabilities with EXCEL®. 89 3.1
Probability. 89 3.1.1 Mass Functions and Mass Densities. 90 3.1.2 The Case of Finite Populations. 91 3.2 Combinatorial Probabilities with EXCEL®. 93 3.3 Conditional Probability, Bayes’ Formula, and Independence. 95 3.4 Random Variables. 97 3.4.1 Statistics of a Random Variable. 98 3.4.2 Numerical Evaluation of Statistics. 102 3.4.3 Classical Inequalities. 104 3.4.4 Characteristic Function and Moments. 105 3.5 Random Vectors and Pairs of Random Variables. 106 3.6 Discrete and Continuous Random Variables. 112 3.6.1 Discrete Variables. 112 3.6.2 Continuous Variables Having a PDF. 114 3.7 Sequences of Random Variables. 119 3.8 Samples. 122 3.8.1 Maximum Likelihood Estimators. 130 3.8.2 Samples from Random Vectors. 132 3.8.3 Empirical CDF and Empirical PDF. 136 3.9 Frequentisi Probabilities with EXCEL®. 140 3.9.1 Testing Adequacy to a
Distribution. 141 3.9.2 Testing Independence. 144 3.10 Generating Uniform Random numbers. 147 3.10.1 Using Built-In Functions. 147
Contents ¡X 4 5 3.10.2 Using the Data Analysis Tool. 3.10.3 Using VBA. 3.11 Generating Normal Random Numbers. 3.11.1 Using Built-In Functions. 3.11.2 Using the Analysis ToolPack. 3.11.3 Using VBA. 3.12 Generating Triangular Random Numbers. 3.13 Generating Random Numbers by Inversion. 3.14 Generating Discrete Random Numbers. 3.14.1 Using Built-In Functions. 3.14.2 Using the Analysis Toolpack. 3.14.3 Using VBA. 3.15 Generating Regular Random Functions. 3.16 Generating Regular Random Curves. 148 149 151 151 152 153 155 157 158 158 158 160 161 165 Stochastic Processes. 4.1 Stationary and Ergodicity. 4.2 Determination of the Distribution of a Stationary Process. 4.3 White Noise. 4.4 Moving Average Processes. 4.5 Autoregressive
Processes. 4.6 ARMA Processes. 4.7 Markov Processes. 4.8 Diffusion Processes. 4.8.1 Time Integral and Derivative of a Process. 4.8.2 Simulation of the Time Integral of a White Noise. 4.8.3 Brownian Motion. 4.8.4 Random Walks. 4.8.5 Itô’s Integrals. 4.8.6 Itô’s Calculus. 4.8.7 Numerical Simulation of Stochastic Differential Equations. Representation of Random Variables. 5.1 The UQ Approach for the Representation of Random Variables. 5.2 Collocation. 5.2.1 Finding the Coefficients of the Expansion in a Worksheet. 5.2.2 Solution Using VBA. 5.2.3 Solution Using an Adapted Workbook. 5.3 Variational Approximation. 5.3.1 Finding the Coefficients of the
Expansion in a Worksheet. 5.3.2 Solution Using VBA. 5.3.3 Solution Using an Adapted Workbook. 171 172 178 180 181 188 199 204 215 215 219 223 226 228 230 236 243 243 250 254 256 259 265 266 268 270
Contents x 5.4 Moments Matching Method. 5.4.1 The Standard Formulation of М3. 5.4.2 Constrained Optimization Formulation of М3. 5.4.3 Multiobjective Optimization Formulation of М3. Multidimensional Expansions. 5.5.1 Case Where U Is Multidimensional. 5.5.2 Case Where X Is Multidimensional. Random Functions. Random Curves. Mean, Variance and Confidence Intervals for Random Functions or Random Curves. 272 273 Uncertain Algebraic Equations. 6.1 Uncertain Linear Systems. 6.1.1 Very Small Linear Systems. 6.2 Nonlinear Equations and Adaptation of an Iterative Code. 6.3 Iterative Evaluation of Eigenvalues. 6.3.1 Very Small Matrices. Random Differential Equations. 7.1 Linear Differential Equations. 7.2
Nonlinear Differential Equations. 7.3 Uncertainties on Curves Connected to Differential Equations. 323 326 331 8 UQ in Game Theory. 8.1 Language from Game Theory. 8.2 A Simple Coin Game. 8.2.1 GT Strategies When p Is Known. 8.2.2 UQ Strategies When p Is Known. 8.2.3 Strategies When p Is Unknown. 8.2.4 Strategies for the Stochastic Game. 8.2.5 Replicator Dynamics. 8.3 A Classica! Game: Prisoner’s Dilemma. 8.3.1 Replicator Dynamics. 8.4 The Goalie’s Anxiety at the PenaltyKick. 377 377 379 380 382 382 386 387 391 393 395 9 Optimization Under Uncertainty. 403 9.1 Using the Methods of Representation. 404 9.2 Using the Adaptation of a Descent Method. 417 9.3 Combining Statistics of the Objective, the Constraints and Expansions. 429 10 Reliability. 10.1
Reliability. 10.2 Limit State Curves. 10.3 Design Point. 10.3.1 Multiple Failure Conditions. 5.5 5.6 5.7 5.8 6 7 283 284 286 286 289 292 296 306 335 348 355 359 360 367 370 433 434 443 445 449
Contents XI 10.4 10.5 Reliability Analysis. Hasofer-Lind Reliability Index. 10.5.1 The General Case. 10.5.2 The Case of Affine Limit State Equations. 10.5.3 The Case of a Convex Failure Region. Using the Reliability Index to Estimate the Probability of Failure. 10.6.1 The Case of Affine Limit State Equations. 10.6.2 The Case of a Convex Failure Region. 10.6.3 General Failure Regions. The Transformations of Rosenblatt and Nataf. FORM and SORM. 10.8.1 FirstOrder Reliability Method(FORM). 10.8.2 Second Order ReliabilityMethod (SORM). Reliability Based Design Optimization. 10.9.1 The Bilevel or Double Loop Approach for a Desired ß. 10.9.2 The Bilevel or Double Loop Approach for a Desired Objective. 453 455 455 466 469 Bibliography. 519 Index. 525 10.6 10.7 10.8 10.9 473 477 478 480 487 490 491 501 508 509 515 |
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| index_date | 2024-07-03T19:11:13Z |
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| isbn | 9783030777562 |
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| spelling | Cursi, Eduardo Souza de Verfasser (DE-588)1251818439 aut Uncertainty quantification and stochastic modelling with EXCEL Eduardo Souza De Cursi Cham Springer [2022] xi, 531 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Erscheint auch als Online-Ausgabe 978-3-030-77757-9 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033222074&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cursi, Eduardo Souza de Uncertainty quantification and stochastic modelling with EXCEL |
| title | Uncertainty quantification and stochastic modelling with EXCEL |
| title_auth | Uncertainty quantification and stochastic modelling with EXCEL |
| title_exact_search | Uncertainty quantification and stochastic modelling with EXCEL |
| title_exact_search_txtP | Uncertainty quantification and stochastic modelling with EXCEL |
| title_full | Uncertainty quantification and stochastic modelling with EXCEL Eduardo Souza De Cursi |
| title_fullStr | Uncertainty quantification and stochastic modelling with EXCEL Eduardo Souza De Cursi |
| title_full_unstemmed | Uncertainty quantification and stochastic modelling with EXCEL Eduardo Souza De Cursi |
| title_short | Uncertainty quantification and stochastic modelling with EXCEL |
| title_sort | uncertainty quantification and stochastic modelling with excel |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033222074&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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