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24th may 2006 1 Use of genetic algorithm for designing redundant sensor network Carine Gerkens Systèmes chimiques et conception de procédés Département de chimie appliquée Université de Liège

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224th may 2006 Synopsis Objectives Data validation Algorithm description Optimization Case study Parallelization Global parallelization Distributed genetic algorithms Conclusions

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324th may 2006 Objectives Using concepts for data reconciliation in chemical processes, create an algorithm able to Design a sensor network that allows to Limit the annualised cost of the measurement system for a chemical plant Evaluate process key variables with a prescribed accuracy Secure redundancy even in case of one sensor failure Give the solution for quite large plants within a reasonable time Problem solved by Bagajewicz (linear mass balances) and Madron (graph oriented method)

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424th may 2006 Data validation All measurements are erroneous Some important variables (efficiency, conversion…) can not be measured Data validation Thanks to redundancy: correct each measurement as slightly as possible to verify all conservation equations (linear or not, mass and energy balances, link equations) Estimate non measured variables and their accuracy from reconciled measured variables and accuracies Hypothesis: Hypothesis: Gaussian distribution of measurement errors Accuracies influenced by the number, the location and the precision of sensors Sensor network design Sensor network design

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524th may 2006 Redundancy Redundancy is more than repeating the same measurement on the same variable several times (temporal redundancy) It is also installing several identical sensors (spacial redundancy) estimating the same variable thanks to different sensors (stuctural redondancy) F F1 P F2 = f( P) T1T2 Q F3 = Q / Cp (T2-T1)

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624th may 2006 Data validation(2) Constrained optimization problem (linearised eq) Unconstrained optimization problem (Lagrange ) Unconstrained optimization problem (Lagrange ) Optimality

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724th may 2006 Data validation(3) Solve the system: Solution:

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824th may 2006 Data validation(4) Validated accuracies

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924th may 2006 Algorithm description Sensor database Belsim-Vali validation model Optimization criteria Key variables Sensor network optimization Problem feasability? Sensor requirements Sensor database - Cost - Accepted range - Uncertainty Key variables - Variables - Required standart deviation Sensor requirements - existing sensor - impossible placement Optimization criteria - Cost - Target accuracies - Singularity of the validation problem - Safeguard against one sensor failure - Several operating points Sensor network optimization Problem feasability? For all possible sensors : -M singular? -Target accuracies reached? Belsim-Vali validation model -For all operating points -Validated values of all variables -Jacobian matrices A and B

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1024th may 2006 Optimization The problem to optimise is Large scale Generally multimodal Not derivable Genetic algorithm Developed by John Holland Solution described by a set of binary decisions (genes) corresponding to the decision to install a sensor at a given location

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1124th may 2006 Optimization(2) Random search algorithm based on reproduction and natural selection mechanisms Biological systems are robust, efficient and flexible Artificial systems try to translate nature but less perfomant Robustness of GA proved empirically Combine survival of best individuals with information exchange Exploit parents information to create better children

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1224th may 2006 Optimization(3) Mecanisms used: Selection Reproduction (50%) One-point-crossover (50%) Jump mutation (1%)

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1324th may 2006 Optimization(2) First population chosen randomly with a high probability for each sensor to be chosen Population of 20 chromosomes Evaluation of each chromosome’s fitness Sensitivity matrix inversion (Chen et Stadherr) sparse matrix The best individual is kept at each generation Stop criterion: best remains unchanged during x generations Final solution better than initial one (but not necessary the global minimum)

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1424th may 2006 Ammonia synthesis loop 224 variables178 constraint equations 117 potential sensors58 key parameters Case study: ammonia loop Optimes.exe

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1524th may 2006 Search history: ammonia loop (2) Case of redundant sensor network Processor M (dothan) 1.6 GHz Processor M (dothan) 1.6 GHz Stop criterion : 200 generations Stop criterion : 200 generations 100 objective function evaluations per second 100 objective function evaluations per second Solution obtained after 76 seconds Solution obtained after 76 seconds Objective function : 1822.9 Cost : 1850 units 361 generations 7241 objective function evaluations

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1624th may 2006 Solution : case of redundant sensor network 39 sensors : 1 chromatograph, 7 mass flowmeters, 20 temperature sensors, 11 pressure gauges

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1724th may 2006 Solution : case of one sensor failure 67 sensors : 2 chromatograph, 13 mass flowmeters, 31 temperature sensors, 21 pressure gauges Computing time : 1h45

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1824th may 2006 Case study: reformer 1263 variables 1116 constraint equations 473 potential sensors 9 key parameters Case of redundant sensor network Processor Pentium IV Processor Pentium IV Stop criterion : 200 generations Stop criterion : 200 generations 9 objective function evaluations per minut 9 objective function evaluations per minut Solution obtained after 6 days Solution obtained after 6 days

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1924th may 2006 Case study: reformer (2) Objective function : 1955.1 units Cost : 1960 units 1618 generations 77665 objective function evaluations Solution: 72 sensors : 3 chromatographs, 10 mass flowmeters, 45 temperature sensors, 13 pressure gauges, 1 density sensor

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2024th may 2006 Parallelisation Why? Large computing time for middle size problems share the computing work between several processors share the computing work between several processors reduce the computing time reduce the computing time techniques are compared by efficiency techniques are compared by efficiency Parallelisation allows to Impossible to deal with larger size problems

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2124th may 2006 Global parallelisation Evaluation of chromosomes’fitness Population evolution, comparison of fitness Best efficiency if Fastest operations Use of MPI (Message Passing Interface) Carried out by master processor Weak loss of efficiency Shared between processors Slowest operations

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2224th may 2006 Global parallelisation (2) Case of a redundant sensor network:

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2324th may 2006 Distributed Genetic Algorithm Global parallelisation : fall of efficiency with the number of processors DGA : better efficiency? Chromosomes distributed in sub-populations Migration operator : chromosomes transfert Migrating chromosomes chosen randomly Parameters : Sub-populations’size: 10 chromosomes Number of migrating chromosomes : 2 Number of migrating chromosomes : 2 Number of sub-populations : 5 Number of sub-populations : 5 Number of generations before migration : 5

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2424th may 2006 Results comparison

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2524th may 2006 Conclusions The solution found is better than the initial network but there is no guarantee of overall optimum Accuracies on key parameters are acceptable Both parallelization techniques allow to reduce the computing time Distributed genetic algorithm gives better results than global parallelization

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2624th may 2006 Future work Adaptation to dynamic problems Create an algorithm of dynamic data validation Design of networks able to identify process faults

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2724th may 2006 Acknowledgements Walloon Region European Social Funds

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2824th may 2006 Questions?

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