GPS-X Technical Reference

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Miscellaneous 418 STATISTICAL PLOTS Predicted vs. Measured In this plot the predicted values are plotted against the measured values. A 45 degree line is also placed on this graph to see the deviation of data points from this line. Assuming a perfect fit, the plotted data points will plot on the 45 degree line. Visual inspection of this plot can highlight the model biases and other systematic errors in the model. A typical output from GPS-X analysis is as shown in Figure 15-4. Figure 15-4 - Predicted vs. Measured Data Plot GPS-X Technical Reference
419 Miscellaneous RESIDUAL PLOTS For a selected measured time series data, a number of residuals as show in Table 15-2 are estimated. The calculated residuals are used for plotting against time or observed data. A histogram of the standardized residuals is also made available for evaluating the model fit. Table 15-2 – Types of Residuals No. Criteria Equation 1 Residuals (O i − P i ) 2 Absolute Residual |O i − P i | 3 Squared Residual (O i − P i ) 2 4 Relative Residual (O i − P i ) O i 5 Absolute Relative Residual |O i − P i | O i 6 Squared Relative Residual ( O 2 i − P i ) O i 7 Standardized Residuals (O i − P i ) √ 1 n ∑ n i=1 (O i − P i ) 2 Histogram of Standardized Residuals A histogram of the standardized residuals are plotted to check the assumption that the errors are normally distributed. The histogram of standardized residual may also help to inspect if the residuals are randomly scattered about zero and to approximately 95 percent of the residuals lie between +2 and -2. A histogram produced for the BOD dataset is as shown in Figure 15-5. Residual Plots against Measured Data The estimated residuals can be plotted against the measured data point to see trends and biases in model outputs. A typical output of this type of plot is as shown in Figure 15-6. Residuals Plots against Time For identifying trends in estimated residuals, the time plots of the residuals may be useful. The model predictability may be affected some specific time based events and these plots may be of help to identify time periods of special events (rain fall, plant maintenance etc.) where the plant operation conditions are not captured adequately in the model. A typical output for this type of plot is as shown in Figure 15-7. GPS-X Technical Reference
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GPS-X Technical Reference GPS-X Ver
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Table of Contents iii Table of Cont
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v Table of Contents Sedimentation M
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vii Table of Contents Real Time Clo
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ix Table of Contents Figure 6-6 - P
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xi Table of Contents Figure 10-8 -
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xiii Table of Contents Figure 15-6
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xv Table of Contents Table 6-2 - Mo
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17 Modelling Fundamentals Experimen
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19 Modelling Fundamentals The proce
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21 Modelling Fundamentals Overview
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23 Modelling Fundamentals Primary a
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25 Modelling Fundamentals Vesilin
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27 GPS-X Objects CHAPTER 2 GPS-X Ob
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29 GPS- X Objects The mass balance
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31 GPS- X Objects Combining Equatio
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33 GPS-X State Variable Libraries S
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35 GPS-X State Variable Libraries C
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37 GPS-X State Variable Libraries C
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39 GPS-X Composite Variable Librari
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41 GPS-X Composite Variable Calcula
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55 Composite Variable Calculations
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61 Influent Models CHAPTER 5 Influe
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63 Influent Models Figure 5-3 - Inf
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65 Influent Models The three influe
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67 Influent Models Total runoff (Q
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69 Influent Models These inputs are
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71 Influent Models CODFractions COD
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73 Influent Models TSSCOD Figure 5-
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75 Influent Models Figure 5-13 - CN
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77 Influent Models CN and CNIP Libr
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83 Influent Models INFLUENT OBJECTS
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85 Influent Models Figure 5-22 - In
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87 Influent Models Chemical Dosage
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89 Influent Models Figure 5-29 - Ac
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91 Influent Models Figure 5-33 - Se
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93 Influent Models Figure 5-36 - Se
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95 Suspended Growth Models where: V
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97 Suspended Growth Models The baro
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99 Suspended Growth Models Oxygen M
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101 Suspended Growth Models In the
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103 Suspended Growth Models The SOT
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105 Suspended Growth Models Standar
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107 Suspended Growth Models The reg
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109 Suspended Growth Models SUMMARY
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111 Suspended Growth Models Figure
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113 Suspended Growth Models General
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115 Suspended Growth Models Number
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117 Suspended Growth Models Elevati
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121 Suspended Growth Models AERATIO
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123 Suspended Growth Models The ent
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125 Suspended Growth Models The org
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127 Suspended Growth Models Process
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129 Suspended Growth Models It i
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131 Suspended Growth Models Nitroge
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133 Suspended Growth Models Include
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135 Suspended Growth Models
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137 Suspended Growth Models Althoug
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139 Suspended Growth Models Particu
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141 Suspended Growth Models 9. Grow
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143 Suspended Growth Models 21. Sto
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145 Suspended Growth Models 33. Gro
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147 Suspended Growth Models To mode
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149 Suspended Growth Models Algebra
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151 Suspended Growth Models The sto
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153 Suspended Growth Models Decay o
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155 Suspended Growth Models SUGGEST
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157 Suspended Growth Models Special
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159 Suspended Growth Models Table 6
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161 Suspended Growth Models The GPS
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163 Suspended Growth Models where:
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165 Suspended Growth Models The max
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167 Suspended Growth Models If yo
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169 Suspended Growth Models ANAEROB
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171 Suspended Growth Models Simple
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173 Suspended Growth Models With th
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175 Suspended Growth Models Manual
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177 Suspended Growth Models Equatio
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179 Suspended Growth Models The met
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181 Suspended Growth Models Pond Mo
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183 Suspended Growth Models Special
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185 Suspended Growth Models Se
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187 Suspended Growth Models aerated
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193 Suspended Growth Models Calcula
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195 Suspended Growth Models The vap
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197 Suspended Growth Models Oxygen
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199 Suspended Growth Models Estimat
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209 Suspended Growth Models MODELLI
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211 Suspended Growth Models TEMPERA
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213 Suspended Growth Models Table 6
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215 Suspended Growth Models The PAC
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217 Suspended Growth Models CHAPTER
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219 Attached-Growth Models Each lay
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221 Attached-Growth Models Equation
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223 Attached-Growth Models The mode
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225 Attached-Growth Models The phys
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227 Attached-Growth Models Liquid F
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233 Attached-Growth Models The SBC
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237 Attached-Growth Models Operatio
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239 Attached-Growth Models Hydrauli
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241 Attached-Growth Models ADVANCED
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243 Attached-Growth Models Filtrati
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245 Attached-Growth Models Operatio
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247 Attached-Growth Models This for
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249 Attached-Growth Models HYBRID S
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251 Attached-Growth Models Figure 7
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253 Sedimentation and Flotation Mod
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267 Sand Filtration Models Floatati
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269 Sand Filtration Models The back
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271 Sand Filtration Models The mass
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273 Sand Filtration Models Figure 9
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275 Digestion Models Figure 10-1 -
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277 Digestion Models Seven yield co
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279 Digestion Models Based on the a
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281 Digestion Models Combining the
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291 Digestion Models ADM1 State Var
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293 Digestion Models AEROBIC DIGEST
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297 Other Models CHAPTER 11 Other M
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319 Others Models Figure 11-12 - Pl
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321 Others Models Physical Setup Fo
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325 Others Models BLACK BOX The Bla
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327 Tools Object Figure 11-19 - Spe
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329 Tools Object Figure 11-21 - Inp
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331 Tools Object Typical Model Outp
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333 Tools Object The variable speed
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335 Tools Object SLUDGE EFFLUENT BU
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337 Tools Object PH TOOL Take a sam
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339 Tools Object These concentratio
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341 Tools Object LOW-PASS FILTERING
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347 Tools Object PID in Position Fo
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349 Tools Object The following para
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351 Tools Object The controller tun
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355 Tools Object TIMER CONTROL The
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357 Tools Object Controller - The c
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359 Tools Object (qcon is the crypt
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361 Operating Cost Models CHAPTER 1
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363 Operating Cost Models The energ
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365 Operating Cost Models OPERATING
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Page 373 and 374: 373 Optimizer If after the reflecti
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Page 381 and 382: 381 Optimizer SUMMARY OF THE OPTIMI
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Page 409 and 410: 409 Optimizer APPENDIX C: NOMENCLAT
Page 411 and 412: 411 Optimizer APPENDIX D: REFERENCE
Page 413 and 414: 413 Miscellaneous CHAPTER 15 Miscel
Page 415 and 416: 415 Miscellaneous As compared to th
Page 417: 417 Miscellaneous A typical GPS-X o
Page 421 and 422: 421 Miscellaneous Figure 15-6 - Res
Page 423 and 424: 423 Miscellaneous REAL TIME CLOCK T
Page 425 and 426: 425 Miscellaneous Figure 15-9 - Ste
Page 427 and 428: 427 Miscellaneous Figure 15-11 - In
Page 429 and 430: 429 Miscellaneous The smoothing fun
Page 431 and 432: 431 Miscellaneous The Gear's Stiff
Page 433 and 434: Appendix A - Petersen Matrices A-1
Page 437 and 438: ASM2d in CNPLIB Appendix A - Peters
Page 439 and 440: 15 Lysis of XBP 16 Lysis of XPP 17
Page 443 and 444: NewGeneral in CNPLIB Appendix A - P
Page 445 and 446: NewGeneral in CNPLIB Appendix A - P
Page 447 and 448: Component i Process Rates Appendix
Page 449: Appendix A - Petersen Matrices A-17
Page 452 and 453: 2 Appendix A - Prefermenter Peterse
Page 460 and 461: D-2 Appendix D - References Brockwe
Page 462 and 463: D-4 Appendix D - References Hur, D.
Page 464 and 465: D-6 Appendix D - References Reilly,
Page 466: D-8 Appendix D - References Wuhrman
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