A nonlinear filtering tool for analysis of hot-loop test campaings Enso Ikonen* Jenő Kovács*, ** * Systems Engineering Laboratory, Department of Process and Environmental Engineering, University of Oulu, Finland Enso.Ikonen@oulu.fi www.oulu.fi/pyosys ** Foster Wheeler Energia Oy, Varkaus, Finland Outline: Introduction model calibration, experiments & hot-loop model Global optimization Sequential optimization PF algorithm filtering & smoothing Simulation studies Discussion & conclusions
UNIVERSITY OF OULU, FINLAND 2 Introduction model vs. data model calibration state estimation coherence & PE SE for PE validates the parameters model (mechanisms, parameters,...) mismatch inadequate model inaccurate measurements unmeasured disturbances during tests fault diagnosis errors, residuals banks of models bayesian reasoning stochastic framework effective values of physical parameters tuning: measurements, physical understanding engineering sense parameter values & their uncertainties identification, numerical optimization, adaptive control belong to the (unknown) system state reason the proper value of the state based on a system model & measurements from it Kalman filter with extensions monitoring, control (MPC), optimization i smoothing, filtering, prediction
UNIVERSITY OF OULU, FINLAND 3 Dynamic tests dynamic models becoming commonly used in the industry execution of dynamic tests is time-consuming & expensive examination of test outcomes tools for assessment model vs measurements measurements vs model hypothesis evaluation state estimation monitoring, automatic control CFB test series. In addition: closed loop steps, ramps,...
UNIVERSITY OF OULU, FINLAND 4 CFB boilers Circulating fluidized d bed boilers mixed in inert material, fluidized by air closed circle via cyclone heat transfer in furnace & from flue gases multifuel capabilities oxyfuel options once-through designs Control fuel & air flows stoichiometric conditions, fluidization, temperatures, load changes emissions, corrosion,.. Unmeasured states fuel inventory, inert mass & distribution, fuel characteristics (heat value, fuel mix, particle size distribution),... FW s CFB with INTREX. hot-loop model semi-physical furnace, separator, Intrex no steam-side validated with real plants
UNIVERSITY OF OULU, FINLAND 5 hot-loop model furnace, separator, Intrex, return
UNIVERSITY OF OULU, FINLAND 6 HOPE-project HOPE = HOt-loop Parameter Estimation allow originally constant parameters to vary with time, θ k....in order to match simulations with measurements search for optimal θ k assess feasibility of estimated θ considered variables: char affinity heat transfer coefficients wing wall roof furnace wall fuel moisture data from reactivity tests minimize squared deviation in O 2 & T bed
UNIVERSITY OF OULU, FINLAND 7 Initial studies (fixed) Simulate with fixed θ nominal value at 1 simulate with 1 {0.8, 0.9, 1, 1.1, 1.2} 0.95 static gains 0.9 fh 2 O 1.1 1.05 0.85 909 80 8 [n %] O 2 [n %] 707 60 6 505
UNIVERSITY OF OULU, FINLAND 8 Initial studies (intervals) global optimization simple gradient search 0/1 st order hold simulations follow measurements well with feasible parameter change amplitudes speed & # evaluations, accuracy, robustness potential directions: advanced gradient fh 2 O 1.1 1.05 1 0.95 methods, random search, 60 parameterized trajectories, sequential methods O 2 [n %] 0.9 0.85 90 80 70 50
UNIVERSITY OF OULU, FINLAND 9 Sequential ential search View PE as a state estimation problem Solve problem sequentially natural when new data becomes available in time Monte Carlo rely on random sampling Bayesian reasoning Kalman filter, EKF Particle filter, UKF,... Particle filtering Describe unknown pdf with N particles approximation, N propagate particles using model update population with measurements (death/survival) no linear/gaussian limitations, can handle complex dynamics computationally ti heavy requires cheap computing power + memory
UNIVERSITY OF OULU, FINLAND 10 Particle filtering (markovian)
UNIVERSITY OF OULU, FINLAND 11 Particle filtering (bayesian)
Particle filtering (SIR) ENSO IKONEN SYSTEMS ENGINEERING LABORATORY UNIVERSITY OF OULU, FINLAND 12
Particle filtering (interpretations) ENSO IKONEN SYSTEMS ENGINEERING LABORATORY UNIVERSITY OF OULU, FINLAND 13
UNIVERSITY OF OULU, FINLAND 14 Simulations (hot-loop model) discrete-time statespace form hot-loop states (660) past inputs (20) interpolation unknown parameters (5 2) random walk model, N(0, 0.01 2 ) ½ < θ k < 2 outputs (108 2) measurement noise (gaussian) :N(0 02 2 O 2 N(0, 0.2 )%-vol T bed : N(0, 5 2 ) o C 1-step-ahead simulations sequence length x # particles (=lots of..) assuming initially in steady state N=500 (# particles)
Simulations (algorithm) ENSO IKONEN SYSTEMS ENGINEERING LABORATORY UNIVERSITY OF OULU, FINLAND 15
Simulations (PF) O [n %] 2 T [n %] furnacebed 80 70 60 60 58 56 60 58 56 estimated moisture & heat transfer coefficients predicted O 2 & T bed measured O 2 & T bed quantiles in MC a random trajectory a trajectory a random trajectory t ftc fh O 3 2 1.2 1.15 1.1 1.05 1 0.95 0.9 0.85 1.55 1.5 1.45 1.4
Simulations (smoothing) O [n %] 2 T [n n %] furnacebed 80 70 N sample eff, k K 10 3 10 2 10 1 estimated moisture & heat transfer coefficients predicted O 2 & T bed measured O 2 & T bed quantiles in MC 60 0.9 10 0 N=500 0.85 60 58 56 60 58 56 a random trajectory a trajectory a random trajectory t fh O 2 ftc 3 1.2 1.15 1.1 1.05 1 0.95 1.55 1.5 1.45 1.4
Simulations (filtering) 90 1.2 80 1.1 O 2 [n %] 70 fh 2 O 1 0.9 60 0.8 filter distributions k k using data up to (but not exceeding) k
Simulations (UKF) UKF (unscented Kalman filter) 1.2 SIR (particle filter) 1.2 1.1 1.1 fh 2 O 1 fh 2 O 1 0.9 0.9 0.8 0.8 PF 500 particles (500 simulations in parallel) UKF 5 sigma-points (5 model simulations in parallel)
UNIVERSITY OF OULU, FINLAND 20 Discussion ssion & Conclusions Bayesian state estimation for model calibration / experiment test assessment both model & measurements are efficiently used, the role of the two can be transparently interpreted theoretically solid estimates/predictions are not limited to, expectations, or prior distributions simple to implement for any simulation model
UNIVERSITY OF OULU, FINLAND 21 Discussion ssion & Conclusions ii For more info, see: Ikonen, E., J. Kovacs & J. Ritvanen (2013) Circulating fluidized bed hotloop analysis, tuning, and stateestimation using particle filtering. International Journal of Innovative Computing, Information and Control, 9 (8), pp 3357 3376. Thank you! Hultgren, M., J. Kovacs & E. Ikonen (2013) Input and State Estimation Tool for Dynamic CFB Models. 18 th Nordic Process Control Workshop 22-23 Aug 2013, Oulu, Finland. SYTE / Department of Process and Environmental Engineering http://www.oulu.fi/pyosys Enso.Ikonen@oulu.fi Future directions user feedback from engineers => further developments smoothing UKF algorithms? how to illustrate/use sequences of multidimensional distributions?
Simulations (smoothing) 80 O 2 [n %] 70 60 back
Simulations (smoothing) 60 %] T ebed [n % furnace 58 56 60 58 56 back
Simulations (smoothing) 1.2 1.15 1.1 2 O fh 2 1.05 1 0.95 0.9 0.85 back
Simulations (smoothing) 1.55 1.5 ft TC 3 1.45 1.4 back