Adaptivna estimacija teško-mjerljivih procesnih veličina

There exist many problems regarding process control in the process industry since some of the important variables cannot be measured online. This problem can be significantly solved by estimating these difficult-tomeasure process variables. In doing so, the estimator is in fact an appropriate mathematical model of the process which, based on information about easy-to-measure process variables, estimates the current value of the difficultto-measure variable. Since processes are usually time-varying, the precision of the estimation based on the process model which is built on old data is decreasing over time. To avoid estimator accuracy degradation, model parameters should be continuously updated in order to track process behavior. There are a couple of methods available for updating model parameters depending on the type of process model. In this paper, PLSR process model is chosen as the basis of the difficult-to-measure process variable estimator while its parameters are updated in several ways – by the moving window method, recursive NIPALS algorithm, recursive kernel algorithm and Just-in-Time learning algorithm. Properties of these adaptive methods are explored on a simulated example. Additionally, the methods are analyzed in terms of computational load and memory requirements.Problemi s upravljanjem mnogih procesa u industriji vezani su s nemogućnošću on-line mjerenja nekih važnih procesnih veličina. Ovaj se problem može u značajnoj mjeri riješiti estimacijom ovih teško-mjerljivih procesnih veličina. Estimator je pri tome odgovarajući matematički model procesa koji na temelju informacije o ostalim (lako-mjerljivim) procesnim veličinama procjenjuje trenutni iznos teško-mjerljive veličine. Budući da su procesi po prirodi promjenjivi, točnost estimacije zasnovane na modelu procesa izgra.enog na starim podacima u pravilu opada s vremenom. Kako bi se ovo izbjeglo, parametre modela procesa je potrebno kontinuirano prepodešavati kako bi model što bolje opisivao (trenutno) vladanje procesa. Ovisno o tipu matematičkog modela, za prepodešavanje njegovih parametara na raspolaganju je više metoda. Kao osnova estimatora teško-mjerljive veličine u radu se koristi PLSR model procesa, dok se njegovi parametri prepodešavaju na više načina – metodom pomičnog prozora, rekurzivnim NIPALS algoritmom, rekurzivnim kernel algoritmom te Just-in-Time Learning metodom. Svojstva navedenih metoda adaptacije PLSR modela procesa ispitana su na odabranom primjeru. Nadalje, metode adaptacije su analizirane i s obzirom na računalnu i memorijsku zahtjevnost

Multivariate statistical process monitoring

U industrijskoj proizvodnji prisutan je stalni rast zahtjeva, u prvom redu, u pogledu ekonomičnosti proizvodnje, kvalitete proizvoda, stupnja sigurnosti i zaštite okoliša. Put ka ispunjenju ovih zahtjeva vodi kroz uvođenje sve složenijih sustava automatskog upravljanja, što ima za posljedicu mjerenje sve većeg broja procesnih veličina i sve složenije mjerne sustave. Osnova za kvalitetno vođenje procesa je kvalitetno i pouzdano mjerenje procesnih veličina. Kvar na procesnoj opremi može značajno narušiti proizvodni proces, pa čak prouzrokovati ispad proizvodnje što rezultira visokim dodatnim troškovima. U ovom radu se analizira način automatskog otkrivanja kvara i identifikacije mjesta kvara u procesnoj mjernoj opremi, tj. senzorima. U ovom smislu mogu poslužiti različite statističke metode kojima se analiziraju podaci koji pristižu iz mjernog sustava. U radu se PCA i ICA metode koriste za modeliranje odnosa među procesnim veličinama, dok se za otkrivanje nastanka kvara koriste Hotellingova (T**2), I**2 i Q (SPE) statistike jer omogućuju otkrivanje neobičnih varijabilnosti unutar i izvan normalnog radnog područja procesa. Za identifikaciju mjesta (uzroka) kvara koriste se dijagrami doprinosa. Izvedeni algoritmi statističkog nadzora procesa temeljeni na PCA metodi i ICA metodi primijenjeni su na dva procesa različite složenosti te je uspoređena njihova sposobnost otkrivanja kvara.Demands regarding production efficiency, product quality, safety levels and environment protection are continuously increasing in the process industry. The way to accomplish these demands is to introduce ever more complex automatic control systems which require more process variables to be measured and more advanced measurement systems. Quality and reliable measurements of process variables are the basis for the quality process control. Process equipment failures can significantly deteriorate production process and even cause production outage, resulting in high additional costs. This paper analyzes automatic fault detection and identification of process measurement equipment, i.e. sensors. Different statistical methods can be used for this purpose in a way that continuously acquired measurements are analyzed by these methods. In this paper, PCA and ICA methods are used for relationship modelling which exists between process variables while Hotelling\u27s (T**2), I**2 and Q (SPE) statistics are used for fault detection because they provide an indication of unusual variability within and outside normal process workspace. Contribution plots are used for fault identification. The algorithms for the statistical process monitoring based on PCA and ICA methods are derived and applied to the two processes of different complexity. Apart from that, their fault detection ability is mutually compared

Continuum Regresion in Process Modeling Based on Plant Data

Važne procesne veličine koje daju informaciju o kakvoći izlaznog proizvoda često nije moguće mjeriti senzorom nego se njihov iznos utvrđuje laboratorijskom analizom. Kako bi se omogućilo kontinuirano praćenje tijeka procesa te efikasnije upravljanje proizvodnim procesom, ovu teško mjerljivu procesnu veličinu je potrebno estimirati, tj. odrediti na temelju matematičkog modela. Za izgradnju odgovarajućeg modela procesa vrlo često su na raspolaganju samo procesni mjerni podaci pohranjeni u procesnu bazu podataka. U ovom se radu prikazuje prikladna metodologija za modeliranje procesa na temelju pogonskih podataka. Za izgradnju modela pri tome se predlažu regresijske metode zasnovane na preslikavanju ulaznog prostora u latentni potprostor. U radu se posebno istražuju svojstva kontinuum regresije (CR). Budući da neuronske mreže predstavljaju dobru osnovu za izgradnju modela na podacima, dopunski se istražuje mogućnost hibridizacije višeslojne perceptronske (MLP) neuronske mreže i CR metode, s ciljem iskorištavanja dobrih svojstava obiju metoda te izbjegavanja njihovih nedostataka u izgradnji modela procesa na pogonskim podacima. Prednosti predloženih metoda izgradnje modela procesa nad uobičajeno korištenim regresijskim metodama prikazane su na primjeru modeliranja procesa destilacije nafte na raspoloživim mjernim podacima.Important process variables which give information about the final product quality cannot often be measured by a sensor but their value is determined based on laboratory analysis. In order to perform a continuous monitoring of a process variable and an efficient process control, it is necessary to estimate this difficult-to-measure process variable, i.e. to determine it on the basis of a mathematical model. However, to build an appropriate process model in many cases there are available only process measurement data stored in a process data base. This paper gives appropriate methodology for process modeling based on plant data. Regression methods based on input space projection into a latent subspace are proposed to build a model. The paper investigates, in particular, properties of continuum regression (CR). As neural networks present a good basis for data based model building, possibility of hybridization of multilayer perceptron (MLP) neural network with CR method is additionally investigated. The aim of that is to use good properties of both methods and to avoid their weaknesses in process model building based on plant data. Advantages of the proposed methods for process model building as compared to the usually used regression methods are demonstrated by the modeling of crude oil distillation process based on the measuring data available

Continuum Regresion in Process Modeling Based on Plant Data

Važne procesne veličine koje daju informaciju o kakvoći izlaznog proizvoda često nije moguće mjeriti senzorom nego se njihov iznos utvrđuje laboratorijskom analizom. Kako bi se omogućilo kontinuirano praćenje tijeka procesa te efikasnije upravljanje proizvodnim procesom, ovu teško mjerljivu procesnu veličinu je potrebno estimirati, tj. odrediti na temelju matematičkog modela. Za izgradnju odgovarajućeg modela procesa vrlo često su na raspolaganju samo procesni mjerni podaci pohranjeni u procesnu bazu podataka. U ovom se radu prikazuje prikladna metodologija za modeliranje procesa na temelju pogonskih podataka. Za izgradnju modela pri tome se predlažu regresijske metode zasnovane na preslikavanju ulaznog prostora u latentni potprostor. U radu se posebno istražuju svojstva kontinuum regresije (CR). Budući da neuronske mreže predstavljaju dobru osnovu za izgradnju modela na podacima, dopunski se istražuje mogućnost hibridizacije višeslojne perceptronske (MLP) neuronske mreže i CR metode, s ciljem iskorištavanja dobrih svojstava obiju metoda te izbjegavanja njihovih nedostataka u izgradnji modela procesa na pogonskim podacima. Prednosti predloženih metoda izgradnje modela procesa nad uobičajeno korištenim regresijskim metodama prikazane su na primjeru modeliranja procesa destilacije nafte na raspoloživim mjernim podacima.Important process variables which give information about the final product quality cannot often be measured by a sensor but their value is determined based on laboratory analysis. In order to perform a continuous monitoring of a process variable and an efficient process control, it is necessary to estimate this difficult-to-measure process variable, i.e. to determine it on the basis of a mathematical model. However, to build an appropriate process model in many cases there are available only process measurement data stored in a process data base. This paper gives appropriate methodology for process modeling based on plant data. Regression methods based on input space projection into a latent subspace are proposed to build a model. The paper investigates, in particular, properties of continuum regression (CR). As neural networks present a good basis for data based model building, possibility of hybridization of multilayer perceptron (MLP) neural network with CR method is additionally investigated. The aim of that is to use good properties of both methods and to avoid their weaknesses in process model building based on plant data. Advantages of the proposed methods for process model building as compared to the usually used regression methods are demonstrated by the modeling of crude oil distillation process based on the measuring data available

Cardiomyopathies in children – Current opinions and our experiences Croatian retrospective epidemiological study 1988-2016

Uvod: Na kardiomiopatije (KM) otpada 3 – 5% svih bolesnika za koje se skrbe pedijatrijski kardiolozi. Nalaze se u svim dobnim skupinama, od fetalne do adolescentne dobi, a u timskom radu obuhvaćaju uz kardiologiju više pedijatrijskih supspecijalnosti (neurologija, metabolizam, genetika). Zbog novih spoznaja i mogućnosti liječenja stupanj preživljenja sve je viši. Cilj: Primarni je cilj prikazati KM-e opsežnom retrospektivnom epidemiološkom studijom prema suvremenoj klasifikaciji, primjenom najnovijih dijagnostičkih metoda i terapijskih pristupa te prožimanjem s ostalim supspecijalnostima. Sekundarni je cilj pokazati da kardiomiopatije više nisu „rijetke, nevažne i neizlječive“, nego su česte, važne i lječive. Rezultati studije: U razdoblju od siječnja 1988. do prosinca 2016. (28 godina) u Referentnom centru za pedijatrijsku kardiologiju Klinike za pedijatriju KBC-a Zagreb hospitalizirano je 315 bolesnika s dijagnozom kardiomiopatije, 183 muškog (58,1%) i 132 ženskog (41,9%) spola. U tri različita razdoblja (10 godina, 12 godina, 6 godina) služili smo se klasifikacijom KM-a iz 1996. godine. Sva tri razdoblja imaju obilježja populacijske, a posljednja dva imaju obilježja i kliničke epidemiološke studije. U sva tri razdoblja najčešća je dilatacijska kardiomiopatija (DKM) (42,5%), a slijede hipertrofična (HKM) (37,1%) i restrikcijska (RKM) (6,7%). Njihovi su relativni odnosi u stalnoj ravnoteži. Uočava se znatan porast entitetskih oblika: aritmogena desnoventrikularna kardiomiopatija (ADVKM) i nekompaktna kardiomiopatija (NKKM), i to od 5,8% (1988. – 1998.) na 16,2% (2010. – 2016.). Smanjen je broj KM-a nepoznata uzroka: kod DKM-a 24,4%, a kod HKM-a tek 18,8%. U posljednjih 18 godina zabilježili smo smrtnost od 7,4% (14/194), od čega 50% (7/14) otpada na DKM. Rezultat je to timskog rada, ciljane medikamentne terapije, elektroterapije (elektrostimulator – ES, srčana resinkronizacija – CRS, implantabilni kardioverterski defibrilator – ICD) i kardiokirurške terapije (operacija prema Morrowu, zaomčavanje (engl. banding) plućne arterije – PAB), uključujući i presadbu srca od 2011. godine (8 bolesnika). Zaključak: Kardiomiopatije su nakon prirođenih srčanih grješaka najteže bolesti u skrbi pedijatrijskog kardiologa, nalažu skladan timski rad više skupina stručnjaka te svladavanje brojnih dijagnostičkih i terapijskih metoda. Dilatacijske kardiomiopatije najčešći su uzrok smrti i najčešća indikacija za presadbu srca u djece.Introduction: Cardiomyopathies (CM) account for 3-5% of patients in the care of pediatric cardiologists. They are found in all age groups, from fetal to adolescent age, and along with cardiology, teams from several other pediatric subspecialties (neurology, metabolism, genetics) are also included. New findings have led to a high survival rate. Goal: The primary goal is to present CM as an important part in the work of pediatric cardiologist through an elaborate epidemiological study, current classifications, the latest diagnostic methods and treatments, as well as the intertwining with other subspecialties. The secondary goal is to show that CM are no longer “uncommon, insignificant and terminal”, but are common, significant and treatable diseases. Results: From January 1988 to December 2016 (28 years) in the Referral Center for Pediatric Cardiology, Department of Pediatrics, Clinical Hospital Centre, 315 patients were diagnosed with cardiomyopathy,183 males (58.1%) and 132 females (41.9%). In three different periods (10 , 12 and six years) a classification from 1996 was used (10). All three periods have features of a population study, whereas the latter two also have features of an epidemiological study. In all three periods there was a predominance of dilated cardiomyopathies (DCM) (42.5%) , followed by hypertrophic cardiomyopathies (HCM) (37.1%) and restrictive cardiomyopathies (RCM) (6.7%) . Their relative relations were in constant balance. A significant increase of some entity forms, arrhythmogenic right ventricular cardiomyopathies (ARVCM) and non-compaction cardimyopathies (NCCM) has been observed, from 5.8% (1988-1998) to 16.2% (2010-2016). Owing to advances in diagnostic methods, number of unclassified CM has been decreasing significantly. The cause remained unknown in only 24.4% of DCM patients, and in 18.8% of HCM patients. In the last 18 years the mortality rate of 7.4% (14/194) has been recorded, 50% (7/14) due to DCM. That is the result of teamwork, targeted medical therapy, electrotherapy (electrical stimulation - ES, cardiac resynchronisation - CRS, implantable cardioverter defibrilator - ICD) and surgical therapy (Morrow, pulmonary artery banding - PAB), including heart transplantaton since 2011 (8 patients). Conclusion: Cardiomyopathies are after congenital heart defects the most severe diseases under care of pediatric cardiologists. They require fluent teamwork of several expert groups, and mastering of numerous diagnostic and therapeutic methods. Dilated cardiomyopathies are the most common cause of death and the indication for heart transplatation in children

Kardiomiopatije u djece - Današnja stajališta i naša iskustva Hrvatska retrospektivna epidemiološka studija 1988. - 2016. [Cardiomyopathies in children - Current opinions and our experiences Croatian retrospective epidemiological study 1988-2016]

INTRODUCTION: Cardiomyopathies (CM) account for 3-5% of patients in the care of pediatric cardiologists. They are found in all age groups, from fetal to adolescent age, and along with cardiology, teams from several other pediatric subspecialties (neurology, metabolism, genetics) are also included. New findings have led to a high survival rate. ----- GOAL: The primary goal is to present CM as an important part in the work of pediatric cardiologist through an elaborate epidemiological study, current classifications, the latest diagnostic methods and treatments, as well as the intertwining with other subspecialties. The secondary goal is to show that CM are no longer “uncommon, insignificant and terminal”, but are common, significant and treatable diseases. ----- RESULTS: From January 1988 to December 2016 (28 years) in the Referral Center for Pediatric Cardiology, Department of Pediatrics, Clinical Hospital Centre, 315 patients were diagnosed with cardiomyopathy,183 males (58.1%) and 132 females (41.9%). In three different periods (10 , 12 and six years) a classification from 1996 was used (10). All three periods have features of a population study, whereas the latter two also have features of an epidemiological study. In all three periods there was a predominance of dilated cardiomyopathies (DCM) (42.5%) , followed by hypertrophic cardiomyopathies (HCM) (37.1%) and restrictive cardiomyopathies (RCM) (6.7%) . Their relative relations were in constant balance. A significant increase of some entity forms, arrhythmogenic right ventricular cardiomyopathies (ARVCM) and non-compaction cardimyopathies (NCCM) has been observed, from 5.8% (1988-1998) to 16.2% (2010-2016). Owing to advances in diagnostic methods, number of unclassified CM has been decreasing significantly. The cause remained unknown in only 24.4% of DCM patients, and in 18.8% of HCM patients. In the last 18 years the mortality rate of 7.4% (14/194) has been recorded, 50% (7/14) due to DCM. That is the result of teamwork, targeted medical therapy, electrotherapy (electrical stimulation - ES, cardiac resynchronisation - CRS, implantable cardioverter defibrilator - ICD) and surgical therapy (Morrow, pulmonary artery banding - PAB), including heart transplantaton since 2011 (8 patients). Conclusion: Cardiomyopathies are after congenital heart defects the most severe diseases under care of pediatric cardiologists. They require fluent teamwork of several expert groups, and mastering of numerous diagnostic and therapeutic methods. Dilated cardiomyopathies are the most common cause of death and the indication for heart transplatation in children

Upravljanje procesom sušenja zrna u kontinuiranim gravitacijskim sušarama

Opisana je kontinuirana gravitacijska sušara za zrno i proces sušenja koji se u njoj odvija. Analizirana je potreba i mogućnost uvođenja automatskog upravljanja ovim procesom. Predložena je struktura sustava automatskog vođenja cjelokupnim postrojenjem za sušenje zrna kao jedna od smjernica za daljnji razvoj ovih postrojenja. Postavljena je globalna struktura matematičkog modela procesa sušenja zrna u kontinuiranoj gravitacijskoj sušari. Detaljnije je istražena faza konstantne brzine sušenja kao potproces koji se odvija u gornjoj sekciji ove sušare. Izveden je matematički model gornje sekcije za sušenje. Odabran je pogodan algoritam upravljanja ovom sekcijom, odnosno (pot)procesom sušenja zrna koji se u njoj odvija.Continuous gravity dryer and drying process which takes place in it are described. The need and possibility of automatic control of the drying process are analysed. Structure of the automatic control system has been proposed as being one of the guidelines for future development of those driers. Global structure of the mathematical model of the drying process in a continuous gravity dryer is shown. The phase of constant rate of the drying has been analysed in more detail as a subprocess in the upper section of the dryer. A mathematical model of the upper drying section has been derived. Appropriate control algorithm of this section, i.e. of the (sub)process of grain drying in it, has been chosen

Upravljanje procesom sušenja zrna u kontinuiranim gravitacijskim sušarama

Opisana je kontinuirana gravitacijska sušara za zrno i proces sušenja koji se u njoj odvija. Analizirana je potreba i mogućnost uvođenja automatskog upravljanja ovim procesom. Predložena je struktura sustava automatskog vođenja cjelokupnim postrojenjem za sušenje zrna kao jedna od smjernica za daljnji razvoj ovih postrojenja. Postavljena je globalna struktura matematičkog modela procesa sušenja zrna u kontinuiranoj gravitacijskoj sušari. Detaljnije je istražena faza konstantne brzine sušenja kao potproces koji se odvija u gornjoj sekciji ove sušare. Izveden je matematički model gornje sekcije za sušenje. Odabran je pogodan algoritam upravljanja ovom sekcijom, odnosno (pot)procesom sušenja zrna koji se u njoj odvija.Continuous gravity dryer and drying process which takes place in it are described. The need and possibility of automatic control of the drying process are analysed. Structure of the automatic control system has been proposed as being one of the guidelines for future development of those driers. Global structure of the mathematical model of the drying process in a continuous gravity dryer is shown. The phase of constant rate of the drying has been analysed in more detail as a subprocess in the upper section of the dryer. A mathematical model of the upper drying section has been derived. Appropriate control algorithm of this section, i.e. of the (sub)process of grain drying in it, has been chosen

Estimation of difficult-to-measure process variables based on plant operational data

Primjenom estimatora moguće je nadomjestiti mjerenje teško-mjerljive procesne veličine. Estimacija se pri tome oslanja na informacije o drugim procesnim veličinama koje se mjere senzorima, tzv. lako-mjerljivim veličinama. Kako bi se estimacija mogla kontinuirano provoditi potrebno je raspolagati matematičkim modelom procesa koji povezuje odabrane lako-mjerljive veličine s teško-mjerljivom veličinom koja se estimira. Budući da u praksi najčešće nema dovoljno a priori znanja o procesu, izgradnja modela procesa se zasniva na podacima dobivenim mjerenjem. Pri tome se polazi od neke opće strukture modela koja može aproksimirati bilo koju funkciju ulazno-izlaznog preslikavanja a parametri modela se procjenjuju na temelju raspoloživih mjernih podataka. S ekonomskog stajališta najpovoljnija je izgradnja modela procesa na temelju pogonskih podataka sadržanih u procesnoj bazi podataka. Kada se modelira na ovim podacima uobičajeni pristupi izgradnji modela često zapadaju u ozbiljne matematičke probleme i rezultiraju modelom loših predikcijskih svojstava. Za izgradnju modela na pogonskim podacima u radu se predlažu metode zasnovane na projekciji ulaznog prostora u latentni prostor i regresiji na ovim novim (latentnim) varijablama. S matematičkog stajališta ovakav model predstavlja kompoziciju dviju funkcija kojima se parametri optimiraju kroz zasebne kriterije, što u pravilu omogućava bolje strukturiranje modela procesa za određenu zadaću modeliranja, kao i pouzdaniju procjenu parametara modela. Kako su svojstva modela uglavnom određena načinom preslikavanja ulaznog prostora u latentni, u radu je težište istraživanja stavljeno upravo na ovaj aspekt izgradnje modela. Nekoliko odabranih metoda preslikavanja detaljnije su istražene kroz primjere izgradnje modela dvaju procesa.By using an estimator, it is possible to substitute the measuring of difficult-to-measure process variable in which process the estimation relies on information about other process variables that are measured by sensors (so called easy-to-measure variables). In order to perform a continuous estimation, we need a mathematical model of the process which connects the chosen easy-to-measure variables with a difficult-to-measure variable that is being estimated. As there is usually not enough preliminary knowledge about the process, the process model building is based on the available measuring data. The basis is a general model structure which can approximate any function of input-output mapping, including presumptions of model dimension and estimation of its parameters based on the available measuring data. In economic terms, the most suitable model process building is the one based on plant data contained in the process data base. When modeling on these data the usual approaches to model building very often face serious mathematical problems and result in a model with unsatisfactory prediction properties. To build a model using plant data, the thesis proposes methods based on input space projection into a latent space and on regression on these new (latent) variables. From a mathematical point of view, this model presents a composition of two multivariable functions, the parameters of which are optimised through separate criterion functions, which allows better model structuring for a specific modeling task and more reliable model parameters estimation. As model properties are mostly defined by way of input space mapping, the thesis focuses on this aspect of model building. Several selected methods of input mapping are investigated in two cases of model process building

Estimation of difficult-to-measure process variables based on plant operational data

Primjenom estimatora moguće je nadomjestiti mjerenje teško-mjerljive procesne veličine. Estimacija se pri tome oslanja na informacije o drugim procesnim veličinama koje se mjere senzorima, tzv. lako-mjerljivim veličinama. Kako bi se estimacija mogla kontinuirano provoditi potrebno je raspolagati matematičkim modelom procesa koji povezuje odabrane lako-mjerljive veličine s teško-mjerljivom veličinom koja se estimira. Budući da u praksi najčešće nema dovoljno a priori znanja o procesu, izgradnja modela procesa se zasniva na podacima dobivenim mjerenjem. Pri tome se polazi od neke opće strukture modela koja može aproksimirati bilo koju funkciju ulazno-izlaznog preslikavanja a parametri modela se procjenjuju na temelju raspoloživih mjernih podataka. S ekonomskog stajališta najpovoljnija je izgradnja modela procesa na temelju pogonskih podataka sadržanih u procesnoj bazi podataka. Kada se modelira na ovim podacima uobičajeni pristupi izgradnji modela često zapadaju u ozbiljne matematičke probleme i rezultiraju modelom loših predikcijskih svojstava. Za izgradnju modela na pogonskim podacima u radu se predlažu metode zasnovane na projekciji ulaznog prostora u latentni prostor i regresiji na ovim novim (latentnim) varijablama. S matematičkog stajališta ovakav model predstavlja kompoziciju dviju funkcija kojima se parametri optimiraju kroz zasebne kriterije, što u pravilu omogućava bolje strukturiranje modela procesa za određenu zadaću modeliranja, kao i pouzdaniju procjenu parametara modela. Kako su svojstva modela uglavnom određena načinom preslikavanja ulaznog prostora u latentni, u radu je težište istraživanja stavljeno upravo na ovaj aspekt izgradnje modela. Nekoliko odabranih metoda preslikavanja detaljnije su istražene kroz primjere izgradnje modela dvaju procesa.By using an estimator, it is possible to substitute the measuring of difficult-to-measure process variable in which process the estimation relies on information about other process variables that are measured by sensors (so called easy-to-measure variables). In order to perform a continuous estimation, we need a mathematical model of the process which connects the chosen easy-to-measure variables with a difficult-to-measure variable that is being estimated. As there is usually not enough preliminary knowledge about the process, the process model building is based on the available measuring data. The basis is a general model structure which can approximate any function of input-output mapping, including presumptions of model dimension and estimation of its parameters based on the available measuring data. In economic terms, the most suitable model process building is the one based on plant data contained in the process data base. When modeling on these data the usual approaches to model building very often face serious mathematical problems and result in a model with unsatisfactory prediction properties. To build a model using plant data, the thesis proposes methods based on input space projection into a latent space and on regression on these new (latent) variables. From a mathematical point of view, this model presents a composition of two multivariable functions, the parameters of which are optimised through separate criterion functions, which allows better model structuring for a specific modeling task and more reliable model parameters estimation. As model properties are mostly defined by way of input space mapping, the thesis focuses on this aspect of model building. Several selected methods of input mapping are investigated in two cases of model process building