GPS-X Technical Reference

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Optimizer 400 The overall variation explained is calculated as: Equation 14.33 The % variation explained is not a model adequacy test but is useful because it shows how much of the variation in the data is accounted for by the fitted model. This test is only reported when the maximum likelihood or sum of squares objective functions are used. Significance of Regression This test involves testing the null hypothesis that all the model parameters are zero against the alternative hypothesis that all the parameters are not zero. The following sum of squares ratio is calculated for each response variable: Equation 14.34 where SSreg j is the weighted regression sum of squares for target variable j and is defined by: Equation 14.35 The sum of squares ratio follows an F-distribution if the errors in the measurements are independent, normally distributed random variables and if the model parameters are all zero. GPS-X Technical Reference
401 Optimizer GPS-X reports the F-value for each target variable and reports the probability that it is n p from an F-distribution with p-1 and j degrees of freedom. If the probability is larger than the chosen significance level it provides evidence that the parameters are all zero and the regression is not significant for the corresponding target variable. The significance level is entered in the General Data > System > Parameters > Optimizer form in the Significance of the Regression sub-section. If the probability value is smaller than the significance level it indicates that the F-value does not follow an F-distribution and therefore we accept the alternative hypothesis that the model parameters are not all zero. In this case the regression is significant for the corresponding target variable and the variation explained by the regression is greater than expected by chance. For a model to be useful for predictive purposes the F-values should be large and the probability values should be close to zero. GPS-X provides messages that summarize the results of the significance test. The significance test is based on linear regression theory and is only approximate for nonlinear models. This test is only reported when the maximum likelihood or the sum of squares objective functions are used. Lack of Fit Test This test determines whether the variance of the residuals is acceptable compared to the user supplied estimate of the measurement variance or the measurement variance calculated using replicate measurements. This serves as a model adequacy test. For each target variable, the following sum of squares ratio is calculated: Equation 14.36 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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203 Suspended Growth Models Enterin
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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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229 Attached-Growth Models This con
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231 Attached-Growth Models The next
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233 Attached-Growth Models The SBC
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235 Attached-Growth Models Based on
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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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283 Digestion Models The Operationa
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285 Digestion Models Kinetic and St
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287 Digestion Models The rest of th
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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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299 Others Models High volume for p
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301 Others Models The sludge pretre
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303 Others Models With a large over
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305 Others Models Dosage Controller
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307 Others Models The set of above
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309 Others Models There are three p
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311 Others Models DISINFECTION UNIT
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313 Others Models DEWATERING Four m
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315 Others Models The optimal polym
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317 Others Models DISC AND BELT MIC
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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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323 Others Models Exponential const
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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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343 Tools Object Control Variable P
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345 Tools Object The individual mod
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347 Tools Object PID in Position Fo
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Page 361 and 362: 361 Operating Cost Models CHAPTER 1
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Page 369 and 370: 369 Operating Cost Models CALIBRATI
Page 371 and 372: 371 Operating Cost Models Category
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 387 and 388: 387 Optimizer APPENDIX A: MAXIMUM L
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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
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Page 419 and 420: 419 Miscellaneous RESIDUAL PLOTS Fo
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Page 423 and 424: 423 Miscellaneous REAL TIME CLOCK T
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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
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2 Appendix A - Prefermenter Peterse
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D-2 Appendix D - References Brockwe
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D-4 Appendix D - References Hur, D.
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D-6 Appendix D - References Reilly,
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D-8 Appendix D - References Wuhrman
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