Modelovanje mikrofiltracije kultivacionih tečnosti primenom koncepta veštačkih neuronskih mreža

Abstract

Fokus ove doktorske disertacije je razvijanje modela zasnovanog na konceptu veštačkih neuronskih mreža za predviđanje i projektovanje mikrofiltracije kultivacionih tečnosti preko ispitivanja mogućnosti primene ovog koncepta za modelovanje fluksa permeata pri različitim uslovim a mikrofiltracij e, u sistemima sa i bez primene hidrodinamičkih metoda poboljšanja fluksa permeata i njihove kombinacije, kao i razvoj modela kojim će se objediniti eksperimentalni rezultati u cilju dobijanja jedne jedinstvene neuronske mreže za simulaciju svih metoda poboljšanja fluksa. Dodatan cilj predstavlja razvoj modela za procenu poboljšanja fluksa u stacionarnim uslovim a usled primene metoda poboljšanja fluksa permeata čija će se adekvatnost proveriti sa energetskog stanovišta. Eksperimentalna ispitivanja su obuhvatila razvoj i validaciju deset različitih modela neuronskih mreža kod kojih su nezavisne ulazne promenljive i njihovi rasponi (transmembranski pritisak, protok suspenzije i protok vazduha) utvrđeni Box-Behnken-ovim eksperimentalnim planom uz dodatne parametre vreme trajanja mikrofiltracije i temperature koji su varirani u zavisnosti od uslova izvođenja postupka mikrofiltracije. Nasuprot tome, za razvoj dinamičkog modela u svojstvu zavisno promenljive veličine razmatran je pad fluksa permeata sa vremenom, dok je za razvoj modela procene efikasnosti primenjenih metoda poboljšanja fluksa permeata razmatran fluks i specifična potrošnja energije u stacionarnim uslovima. Normalizacijom eksperimentalnih podataka izbegla se velika razlika u specifičnim težinskim koeficijentim a pojedinih ulaznih promenljivih i predupredila opasnost da te promenljive pokažu veći uticaj nego što ga imaju u realnosti, a balansiranje efekata nekontrolisanih faktora na izlaznu promenljivu izvedeno je randomizacijom na grupu za obučavanje (70% podataka), grupu za validaciju (15% podataka) i grupu za testiranje (15% podataka). Nestacionarnosti koje utiču na efikasnost algoritma obuke i arhitekture neuronskih mreža izbegnute su ispitivanjem m odela sa pet algoritama obuke (Levenberg-M arkuardt-ov algoritam obuke (trainlm), Bayes-ova regularizacija (trainbr), model rezilientnog povratnog prostiranja (trainrp), model skaliranog konjugovanog gradijenta (trainscg) i model jednostepenog sekantnog povratnog prostiranja greške unazad (trainoss)) i dve sigmoidalne aktivacione funkcije u skrivenom sloju (logistička i hiperbolična tangensna), dok je u izlaznom sloju korišćena linearna aktivaciona funkcija. Svi modeli su optimizovani primenom metode probe i greške sa osnovnim ciljem dobiti što jednostavniju mrežu, odnosno mrežu sa minimalnim brojem skrivenih neurona koja pokazuje najbolju sposobnost generalizacije. Kao indikatori nivoa generalizacije i parametara učinka obuke neuronske mreže ispitivani su koeficijent determinacije (R2) i srednja kvadratna greška (MSE), a koeficijent korelacije (r) je odabran kao dodatni parametar adekvatnosti fitovanja vrednosti utvrđenog i neuronskom mrežom procenjenog fluksa permeata. Najbolju sposobnost generalizacije i predikcije pokazao je model neuronske mreže obučavan Levenberg-M arkuardt-ovim algoritmom. Optimalan broj neurona u skrivenom sloju se kretao od 7 do 13 što ukazuje na znatnu kom pleksnost mehanizama koji utiču na fluks permeata kako je i procenjeno postavljanjem hipoteze ove doktorske disertacije. Analiza apsolutne relativne greške pokazala je veoma dobro predviđanje pošto je u rasponu od 81% do 100 % podataka imalo grešku manju od 10%, a koeficijent determinacije u rasponu od 0,98091 do 0,99976 ukazuje da mreža ne može da objasni manje od 2% varijacija u sistemu. Vrednosti koeficijenta korelacije se kreću u rasponu od 0,99041 do 0,99988 što sugeriše na dobru linearnu korelaciju između eksperimentalnih podataka i podataka predviđenih neuronskom mrežom. Pored primene koncepta fitovanja podataka ispitana je i mogućnost procene uticaja pojedinih eksperimentalnih promenljivih na fluks permeata primenom jednačine Garsona, a komparativnom analizom dobijenih simulacionih rezultata na eksperimentalim podacima koji nisu bili predstavljeni neuronskoj mreži potvrđen je generalizacijski kapacitet modela neuronske mreže.

Focus of this doctoral dissertation is to develop a model based on the artificial neural networks concept for predicting and designing cultivation broth microfiltration by examining the feasibility of this concept for modeling permeate flux under different microfiltration conditions, in systems with and without hydrodynamic im provem ent methods, as well the development of a model that will combine the experimental results in order to obtain a single neural network to simulate all methods of flux improvement. An additional goal is the development of a model in quasi steady state in term so fadequacy of flux enhancement methods application, which will be checked from the energy point of view. Experimental tests included the development and validation of ten different models оf neural networks in which the independent input variables and their ranges (transmembrane pressure, suspension flow and air flow) were determined by Box-Behnken's experimental plan with added microfiltration parameters time and temperature, varied depending on the conditions of the microfiltration procedure. In contrast, for the development оf a dynamic model as a dependent variable, the decrease in permeate flux with time was considered, while for the development of a model for evaluating the efficiency оf applied permeate flux im provement methods, flux and specific energy consumption in quasi steady state conditions were considered. Normalization of experimental data avoided a large difference in specific weight coefficients of individual input variables and prevented the danger that these variables show a greater impact than they have in reality, and balancing the effects of uncontrolled factors on the output variable was performed by randomization on the training group (70% o f data), a validation group (15% of data) and a testing group (15% of data). Non-stationarities affecting the efficiency of the training algorithm and neural network architecture were avoided by testing the model with five diferent training algorithms (Levenberg-M arquardt training algorithm (trainlm), Bayesian regularization (trainbr), resilient backpropagation algorithm (trainrp), scaled conjugate gradient method (trainscg) and a one-step secant m ethod (trainoss)) and two sigmoid activation functions in the hidden layer (logistic and hyperbolic tangent), while a linear activation function was used in the output layer. All models are optimized by applying the trial and error method with the basic goal of having the simplest possible network, ie a network with a minimum num ber o f hidden neurons that shows the best ability to generalize. Determ ination coefficient (R2) and mean square error (MSE) were examined as indicators of generalization level and neural network training performance parameters, and correlation coefficient (r) was selected as an additional param eter o f adequacy оf fitting the value of determined and neural network estimated permeate flux. The best ability to generalize and predict was shown by a model of a neural network trained by the Levenberg-M arquardt algorithm. The optimal num ber of neurons in the hidden layer ranged from 7 to 13, which indicates a significant complexity of the mechanisms that affect the permeate flux, as assessed by the hypothesis of this doctoral dissertation. Absolute relative error analysis showed very good prediction as in the range of 81% to 100 % of the data had an error of less than 10 %, and the coefficient of determination in the range of 0.98091 to 0.99976 indicates that the network cannot explain less than 2 % variation in the system. The values оf the correlation coefficient range from 0.99041 to 0.99988 suggests a good linear correlation between the experimental data and the data predicted by the neural network. In addition to the application of the concept of data fitting, the relative importance of input variables was also investigated by applying the Garson equation. Comparative analysis of the obtained simulation results on experimental data that were not presented to the neural network confirmed the generalization capacity of the neural network model.