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ADS data interpretation

Interpretation of experimental measurements using PK models & neural networks, focusing on source-driven systems & reactor criticality. Simulation and methodology for reliable interpretations of point kinetics models. Studies on global and local point kinetics.

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ADS data interpretation

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  1. ADS data interpretation S. Dulla, P. Ravetto Politecnico di Torino, Dipartimento di Energetica Torino, Italy Torino, 8 July 2010

  2. Outline • ADS data interpretation • Interpretation of experimental measurements • Analysis of the performances of PK models and role of kinetic parameters • Application of neural networks Torino, 8 July 2010

  3. Intepretation of experiments Direct analysis • Analysis of pulsed-source “experiments” (experimental data are obtained through full space-time calculation) • Source transients are simulated with PK models adopting different definition of the kinetic parameters • Capability to reproduce total power evolution, local flux signal and value of reactivity is tested • Different system configurations are considered Torino, 8 July 2010

  4. Why are we focusing on pulsed source experiments ? • This kind of experiments are under way in existing facilities to study the physics of source-driven systems • Reactivity reconstruction from local flux measurements is an important aspect • Existing methods for the interpretation of pulsed experiments in close-to-criticality systems need to be extended Torino, 8 July 2010

  5. Simulation and interpretation of source experiments • Signals from local detectors have to be (importance) averaged • Strong importance effects can be observed in source-driven problems • More suitable and problem-oriented weighting procedures must be used in inverse frameworks to construct ad-hoc kinetic parameters Torino, 8 July 2010

  6. Simulation and interpretation of source experiments • Study importance weighting procedures to generate point models that are adequate to accurately simulate local flux signal evolutions in a pulsed experiment • Re-define time-dependence of source to better represent the physical response Torino, 8 July 2010

  7. Methodology Amplitude function Shape function Integral parameters are derived by taking the balance equations factorize the neutron flux Torino, 8 July 2010

  8. Methodology and project on a weight obtaining a system of equations in time for amplitude functions with a point-like structure Torino, 8 July 2010

  9. Methodology Questions: • Choice of the shape function  ? Initial reference configuration • Well-assessed meaning for reactors departing from criticality (corresponds to the fundamental eigenstate of the homogeneous problem) • Source-dependent for subcritical source-driven systems • Choice of the weighting function ?  definition of various point kinetic models with different objectives Torino, 8 July 2010

  10. Global and Local Point Kinetics(GPK) and (LPK) weighting function  adjoint problem Source-driven adjoint critical adjoint (eigenvalue) • the adjoint source can be assumed as the local detector where the flux measurement is taken  LPK • global weighting, i.e. assuming as adjoint source the fission productivity νΣf, suitable to predict power evolution GPK Torino, 8 July 2010

  11. Pulsed-source experiments • Localized source in space and time • Analysis of the evolution of the flux after the source pulse • Comparison of different options for the construction of the point model adopted in the interpretation of the results Torino, 8 July 2010

  12. Pulsed-source experiments • Study of a source pulse in a 1D system: • Comparison of exact results with point kinetic models; • Influence of the distance of the detector from the source: • Time-delay of the response of the system • Modification of the time behavior of the source Torino, 8 July 2010

  13. Methodology x The use of global (GPK) and local (LPK) point kinetics • Definition of the adjoint to be used in the projection technique based on the purpose of the analysis • Total power prediction: adjoint associated to global neutron importance • Local flux signal retracing: detector-oriented weighting Torino, 8 July 2010

  14. Methodology • Analytical and semi-analytical study of a source pulse in a 1D system: • Comparison of exact results with point kinetic models; • Influence of the distance of the detector from the source: • Time-delay of the response of the system • Modification of the time behavior of the source Torino, 8 July 2010

  15. Pulsed experiment – power evolution GPK – more suitable for total power predictions presence of higher harmonic components GPK LPK Torino, 8 July 2010

  16. Pulsed experiments – detector signal (detector far from the source) GPK LPK Torino, 8 July 2010

  17. Pulsed experiments – detector signal (detector close to the source) PK proved to be not accurate in both options Torino, 8 July 2010

  18. Some remarks… • Similar performances of all options in reproducing the power evolution • Results with poor accuracy in flux prediction when the detector is placed far from the source • Strong higher harmonic effects for the flux for detectors near the source • LPK shows better performance in preserving areas (important when area methods are used in the interpretation of measurements) Torino, 8 July 2010

  19. Pulsed-source experimentsFlux at detector position • Flux response at spatial points far from the source is mainly influenced by the time delay of the neutron signal detected It is necessary to modify the time behavior of the source in order to simulate the real signal • Evaluation of time of flight to detector position • Evaluation of mean travel time (which distribution?) • Convolution of external source with system response (use of Green function) Torino, 8 July 2010

  20. Treatment of source delay x0 x1>x0 • Time of flight  • Mean travelling time  • Source shift • Source convolution: Torino, 8 July 2010

  21. Treatment of source delay Exact solution Point kinetics Convolution with Green function Torino, 8 July 2010

  22. Treatment of source delay Exact solution Point kinetics Convolution with Green function Torino, 8 July 2010

  23. Use of pk in transient evaluation • 3-group solution in a MUSE-like configuration (1D) • Localized perturbations of cross sections • Evaluation of power and local flux using pk with local and global weighting core shield source reflector Torino, 8 July 2010

  24. Use of PK in transient evaluation    Transient 1: a,1< 0 =729pcm • P/P0= 1.286 Pgpk= (Pgpk-P)/P[%]=-1.78 Monochromatic detectors d,g a,g< 0 Improved performances with LPK • (x ,3)/ 0(x ,3)=1.320   GPK[%]=-4.36   LPK[%]=-1.45 • (x,3)/ 0(x,3)=1.309   GPK[%]=-3.56   LPK[%]=-1.56 • (x ,1)/ 0(x ,1)=1.368   GPK[%]=-7.72   LPK[%]=-0.65 • (x,2)/ 0(x,2)=1.316   GPK[%]=-4.05   LPK[%]=-1.46 • (x,1)/ 0(x ,1)=1.316   GPK[%]=-4.05   LPK[%]=-1.45 • (x,2)/ 0(x ,2)=1.300   GPK[%]=-2.92   LPK[%]=-1.63 • (x ,2)/ 0(x ,2)=1.326   GPK[%]=-4.78   LPK[%]=-1.34 • (x,3)/ 0(x ,3)=1.297   GPK[%]=-2.68   LPK[%]=-1.69 • (x,1)/ 0(x,1)=1.377   GPK[%]=-8.33   LPK[%]=-0.46 Torino, 8 July 2010

  25. Use of LPK in transient evaluation    Transient 1: a,1< 0 =729pcm Transient 2: a,2< 0 =1157pcm Transient 3: a,3< 0 =499pcm Torino, 8 July 2010

  26. Reactivity evaluationin pulsed-source experiments c b a • 3-group evaluation of a subcritical system • Evaluation of reactivity from LPK for different detectors (at 3 spatial positions a-b-c and within each of 3 energy groups) Torino, 8 July 2010

  27. Reactivity evaluationin pulsed-source experiments c b a keff=0.97 1° group 2° group 3° group GPK 0 Torino, 8 July 2010

  28. Reactivity evaluationin pulsed-source experiments c b a keff=0.99 1° group 2° group 3° group GPK 0 Torino, 8 July 2010

  29. Inverse analysis • The inverse analysis is usually based on PK • The reference solution for the power is best-fitted by the solution of the PK model • The obtained parameters are used for the direct simulation of other source transients time behavior of the source (known) Parameters for best-fitting Torino, 8 July 2010

  30. Inverse analysis 2 ms 5 ms 0.1 ms • Best-fit for 1 ms pulse, keff=0.98 • Parameters used to fit pulses of 2, 5 and 0.1 ms Fitting values: =/=−1521.7 s−1 S0= 298.4 p.u./s Best-fit Values of direct analysis: =/=−1039.5 s−1 S0= 179.1 p.u./s Torino, 8 July 2010

  31. Inverse analysis • The same approach can be devised in a multipoint framework • different subdomains in the phase space interacting • Coupling coefficients can be best-fitted • Spatial and spectral effect can be reproduced more accurately Torino, 8 July 2010

  32. Multipoint inverse analysis • From the integral parameter (single number) to a set of integral coefficients (matrix) • Suitable for systems with decoupled regions • More accurate description of the transient (performed preliminary calculations) • The single-point approach can be retreived applying Henry projection procedure on the multipoint model Torino, 8 July 2010

  33. Remarks • The concept of integral parameters seems to lose significance for ADS • Important to define clearly how an integral quantities is obtained to avoid misinterpretations • Subcritical systems are more point-like with respect to critical systems • Still there is the problem of how to construct a PK model suitable for subcritical systems • Transients of interest in experiments involve source modification, thus introducing unavoidabily spatial/spectral effects Torino, 8 July 2010

  34. Application of neural networks Torino, 8 July 2010

  35. ADS experiment analyzed • YALINA-BOOSTER reactor • Small and highly-enriched reactor • Decoupled system • Fast booster • Thermal region • Reflector • Neutron flux measures at specific positions (detectors) • Source transients Torino, 8 July 2010

  36. Yalina experimental facility Yalina reactor (Minsk, Belarus) Strong decoupling between the regions, for safety reasons Torino, 8 July 2010

  37. Subcriticality evaluation • Reconstruction of reactivity from experimental flux measurements (detector responses) • The standard approach is based on the inversion of a balance model (as said before) • A simplified model of neutron kinetics is usually adopted  PK Torino, 8 July 2010

  38. Review of classical techniques • Inverse problems are mathematically ill-posed • Sensitivity of results to noise on input data • Often point kinetic equations (PK) are used to interpret the power signal, since inversion can be performed analytically • Problems concerning PK in reactivity determination • power not experimentally available • power does not behave exactly point-like • detector energy and position strongly influence results Torino, 8 July 2010

  39. Review of classical techniques • Possible improvements involve use of: • Tailored adjoint functions to simulate detector response • Correction factors for accounting for spatial position of detector and energy selectivity • Still, a lumped parameter model cannot adequately simulate a space-energy transient for a source pulse in an ADS Problem of inversion making use of more complex spatial-spectral models ¡¡ Artificial Neural Network inversion !! Torino, 8 July 2010

  40. Neural-based inversion Neuron basic computational unit (neuron) accepts an input and provides an output depending on the value of two adjustable parameters - weight and bias Artificial Neural Network can learn patterns and functional relationships present in a set of training data it is proved in literature its robustness and capability of operation with a data “corrupted” by experimental noise Torino, 8 July 2010

  41. Construction of the training set NKE Training set: Torino, 8 July 2010

  42. NN inversion steps: training Supervised training (change adjustable parameters to minimize the difference output/target) Torino, 8 July 2010

  43. ANN inversion steps: direct use of net Pulsed experiments bridge between experiments & subcriticality evaluation Torino, 8 July 2010

  44. ANN inversion steps: generalization NKE comparison ANN Torino, 8 July 2010

  45. Problem setting Initially zero flux Single pulse simulation (1μs) 6-precursor families (delayed emission) 1D/3-group diffusion model Use of 4 detector signals for interpretation Test case s: source f1, f2: fast region v1, v2: decoupling region t: thermal region p, g: reflecting region Torino, 8 July 2010

  46. Detector and power evolutions D2 D1 power D3 D4 keff=0.95-0.96-0.97- 0.98 Torino, 8 July 2010

  47. Training set transients corresponding to 500 reactivities 100 sampling times Network details 2 layer network 120-1 structure Computational time of the training Pentium III, 2.4GHz About 2 minutes Network design Torino, 8 July 2010

  48. Analysis of cases out of training set Results: generalization • 10 test cases are reported to show performance of AAN on new data • error is of the order of 100 pcm • in order to reduce it one should enlarge the training set dimension => more neuron in the network => longer training and new network design required… Torino, 8 July 2010

  49. Multi-step approach keff = 0.93–0.98 • Successive refinement instead of bigger training set • ANN can be used for the successive refinement, provided that same training set size k* keff = [k*-Δk, k*+Δk] k** Torino, 8 July 2010

  50. Results: generalization First guess (keff=0.93–0.98) After refinement (keff=0.96-0.98) Torino, 8 July 2010

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