Modelling and control of an autogenous mill using a state space methodology and neural networks

Groenewald, Jacobus Willem de Villiers (2002-12)

Thesis (MScEng)--University of Stellenbosch, 2002.

Thesis

ENGLISH ABSTRACT: Metallurgical processes are often high dimensional and non-linear making them difficult to understand, model and control. Whereas the human eye has extensively been used in discerning temporal patterns in historical process data from these processes, the systematic study of such data has only recently come to the forefront. This resulted predominantly from the inadequacy of previously used linear techniques and the computational power required when analysing the non-linear dynamics underlying these systems. Furthermore, owing to the recent progress made with regard to the identification of non-linear systems and the increased availability of computational power, the application of non-linear modelling techniques for the development of neural network models to be used in advanced control systems has become a potential alternative to operator experience. The objective of this study was the development ofa non-linear, dynamic model of an autogenous mill for use in an advanced control system. This was accomplished through system identification, modelling and prediction, and application to control. For system identification, the attractor was reconstructed based on Taken's theorem making use of both the Method Of Delays and singular spectrum analysis. Modelling consisted of the development of multi-layer perceptron neural network, radial basis function neural network, and support vector machine models for the prediction of the power drawn by an autogenous mill. The best model was subsequently selected and validated through its application to control. This was accomplished by means of developing a neurocontroller, which was tested under simulation. Initial inspection of the process data to be modelled indicated that it contained a considerable amount noise. However, using the method of surrogate data, it was found that the time series representing the power drawn by the autogenous mill clearly exhibited deterministic character, making it suitable for predictive modelling. It was subsequently found that, when using the data for attractor reconstruction, a connection existed between the embedding strategy used, the quality of the reconstructed attractor, and the quality of the resulting model. Owing to the high degree of noise in the data it was found that the singular spectrum analysis embeddings resulted in better quality reconstructed attractors that covered a larger part of the state space when compared to the method of delays embeddings; the data embedded using singular spectrum analysis also resulting in the development of better quality models. From a modelling perspective it was found that the multi-layer perceptron neural network models generally performed the best; a multi-layer perceptron neural network model having an appropriately embedded multi-dimensional input space outperforming all the other developed models with regard to free-run prediction success. However, none of the non-linear models performed significantly better than the ARX model with regard to one-step prediction results (based on the R2 statistic); the one-step predictions having a prediction interval of 30 seconds. In general the best model was a multi-layer perceptron neural network model having an input space consisting of the FAG mill power (XI), the FAG mill load (X2), the FAG mill coarse ore feed rate (X3), the FAG mill fine ore feed rate (X4), the FAG mill inlet water flow rate (X7) and the FAG mill discharge flow rates (X9, XIO). Since the accuracy of any neural network model is highly dependent on its training data, a process model diagnostic system was developed to accompany the process model. Linear principal component analysis was used for this purposes and the resulting diagnostic system was successfully used for data validation. One of the models developed during this research was also successfully used for the development of a neurocontroller, proving its possible use in an advanced control system.

AFRIKAANSE OPSOMMING: Metallurgiese prosesse is gewoonlik hoogs dimensioneel en nie-lineêr, wat dit moeilik maak om te verstaan, modelleer, en te beheer. Alhoewel die menslike oog alreeds wyd gebruik word om temporale patrone in historiese proses data te onderskei, het die sistematiese studie van hierdie tipe data eers onlangs na vore gekom. Dit is hoofsaaklik na aanleiding van die onvoldoende resultate wat verkry is deur van voorafgaande lineêre tegnieke gebruik te maak, asook die beperkende berekenings vermoë wat beskikbaar was vir analise van onderliggend nie-lineêre dinamiese stelsels. 'n Verder bydraende faktor is die onlangse vordering wat gemaak is met betrekking tot die identifikasie van nie-lineêre stelsels en die toename in beskikbaarheid van rekenaar-vermoë. Die toepassing van nie-lineêre modellerings tegnieke vir die ontwikkeling van neurale netwerke om gebruik te word in gevorderde beheerstelsels, het 'n potensiële alternatief geword tot operateur ondervinding. Die doelwit van hierdie studie was die ontwikkeling van 'n gevorderde beheerstelsel vir 'n outogene meul gebaseer op 'n nie-lineêre, dinamiese model. Dit is bereik deur middel van stelsel-identifikasie, modellering en voorspelling, en laastens implementering van die beheerstelsel. Vir stelsel-identifikasie is die attraktor van die stelsel bepaal soos gebaseer op Taken se teorema deur gebruik te maak van beide die metode van vertraging en enkelvoudige spektrum analise. Modellering van die stelsel vir die voorspelling van krag-verbruik deur die outogene meul het bestaan uit die ontwikkeling van multilaag-perseptron-neurale netwerke, radiaalbasisfunksie-neurale netwerke, en steunvektor-masjien-modelle. Die beste model is daarna gekies vir validasie deur middel van toepassing vir beheer. Dit is bereik deur 'n neurobeheerder te ontwikkel en te toets deur middel van simulasie. Die aanvanklike inspeksie van proses data wat gebruik sou word vir modellering het egter getoon dat die data 'n aansienlike hoeveelheid geraas bevat. Nietemin, deur die gebruik van 'n surrogaat-data-metode, is dit bevind dat die tyd-reeks wat die krag verbruik van die outogene meul beskryf, duidelik deterministiese karakter toon en dat dit dus wenslik is om 'n nie-lineêre voorspellings-model, soos 'n neurale netwerk te gruik. Gevolglik is gevind dat, wanneer die data vir attraktor hersamestelling gebruik word, 'n verband bestaan tussen die ontvouing-strategie wat gebruik word, die kwaliteit van die gerekonstrueerde attraktor, en die kwaliteit van die daaropvolgende model. As gevolg van die geraas in die data is gevind dat die ontvouing gebaseer op enkelvoudige spektrum analise 'n beter kwaliteit attraktor hersamestelling lewer. So ook is gevind dat 'n groter deel van die toestandruimte gedek word in vergelyking met die metode van vertraging-ontvouing. Deur gebruik te maak van enkelvoudige spektrum-analise, het die dataontvouing ook beter kwaliteit modelle opgelewer. Vanuit 'n modellerings-perspektief is gevind dat die multilaag-perseptron-neurale netwerk-modelle in die algemeen die beste gevaar het. 'n Multilaag-perseptronneurale netwerk met 'n gepaste ontvoude multidimensionele invoer-spasie het die beste gevaar van al die ontwikkelde modelle met betrekking tot vryloopvoorspellings. Geen van die nie-lineêre modelle het egter beduidend (op 'n R2 basis) beter gevaar as die ARX model wanneer daar na die eenstap-voorspellings (oor 'n 30 sekonde interval) gekyk word nie. Die multilaag-perseptron-neurale netwerk met 'n invoer-spasie bestaande uit die meul krag-verbruik (XI), die meullading (X2), die meul growwe-erts voertempo (X3), die meul fyn-erts voertemp ('4), die meul inlaat-water vloeitempo (X7) en die meul uitlaat vloeitempo's (X9, XIO) het in die algemeen die beste gevaar. Aangesien die akkuraatheid van emge neurale netwerk afhanklik is van die data waarmee dit aanvanklik opgestel is, is 'n diagnostiese proses modelontwikkel om die proses-model te vergesel. Lineêre hoofkomponent analise is vir hierdie doel aangewend en die gevolglike diagnostiese stelsel is suksesvol aangewend vir datavalidasie. Een van die modelle ontwikkel gedurende hierdie navorsing is ook suksesvol gebruik vir die ontwikkeling van 'n neurobeheerder wat dien as bewys dat die model goed gebruik kan word in 'n gevorderde beheerstelsel.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/52940
This item appears in the following collections: