Nonlinear Solutions Oy helps process industries improve their processes, materials, products and automation particularly with new techniques of nonlinear modelling.

Nonlinear modelling and neural networks for industrial applications - process modelling, process development, materials development, process control, process simulation, process optimisation

A site with frames may be visible here. Nonlinear Solutions Oy has provided solutions based on nonlinear models (particularly neural network based) since 1996 to several industrial sectors.

Non-linear models have been useful for a variety of purposes in process industries. One important category of applications is material properties (tailor-making of properties, reduction of variation of material properties, etc.) Another important category is process models. Such models are used for process development, for process optimisation, or process control. Non-linear models are also used for several kinds of fault prevention, fault detection, fault diagnosis purposes (e.g. paper web breaks, product defects, etc.) Nonlinear models have opened up many new possibilities, and process industries are only beginning to find them.

Nonlinear Solutions endeavours to help process industries improve their products, materials and processes through Proper use of industrial mathematics makes this possible. Our core expertise lies in the new techniques of nonlinear modelling, particularly neural networks.

Industries cooperate with us on projects which offer them clear and direct benefits from our services. Development of automation products in partnership with us is encouraged. Almost every company we work with gets tailor-made solutions.

Continuous improvement and extension of our techniques, tools and know-how is an essential part of our activity.

Nonlinear Solutions Oy provides services in various forms, primarily based on nonlinear models of processes and material behaviour. The final result can be models, software for efficient use of the models (like a LUMET system customised for a given purpose with nonlinear models implemented in it), a simulator, conclusions regarding effects of variables of interest, optimum values of variables, etc. The models are developed by Nonlinear Solutions based on production data or experimental data. Nonlinear Solutions does not sell software for developing nonlinear models, unlike most other companies. In rare solutions, the user can create the nonlinear models from experimental data.

In many cases, particularly where experimentation is expensive, Nonlinear Solutions also plans the experiments to elicit the nonlinearities in the effects of input variables, with as few experiments as possible.

Utilising knowledge about processes and materials
Nonlinear models are often entirely empirical. It is usually advantageous to take into account the knowledge and heuristics about the process or the materials in the model development. It is still better to have semi-empirical models (models with some elements of physical models combined with empiricism), whenever possible. Nonlinear Solutions has specialised know-how, expertise and experience for this purpose.

What is nonlinear modelling?
Nonlinear modelling is empirical or semi-empirical modelling which takes at least some nonlinearities into account.

There are many ways of doing that, including linear regression with nonlinear terms, polynomial regression, nonlinear regression, splines, etc. Some of the new techniques based on artificial neural networks have advantages over the traditional methods mentioned earlier. Multilayer perceptrons are capable of approximating any continuous, first order differentiable function to any desired degree of accuracy with a single series (a single layer) of certain kinds of activation functions like logistic sigmoids.

There is plenty of literature on neural networks, including several books. At least one book covers neural networks applications in chemical engineering. There is at least one series of conferences which focuses on engineering applications of neural networks.

Our contact information:

Address: PL 953, 20101 Turku, Finland
Telephone: +358 2 2154721 (will be taken out of use any day)
VAT registration number: FI 1056520 8

Some relevant links are here.

The appended words are meant to allow unfamiliar visitors find things of interest on these www pages. These are the areas in which Nonlinear Solutions can provide services. If you don't find the information of interest to you on these pages, feel free to ask us. Definition of nonlinear modelling here.

Production economics issues: production capacity, tonnage, CIF or FOB price, raw material cost, (labor) labour cost, value addition, market demand, worldwide supply, overproduction, consumption, overcapacity, profitability, product quality, overquality, consumer confidence, purchase department, index, shipment, load, etc. All these things have something to do with production economics. Mathematics related issues: Neural network models, or simply neural networks, also referred to as neural net models, or neural nets, are used to approximate nonlinearities. The central issue in most cases is non-linearity, (nowadays written as nonlinearity). Non-linearities are addressed by non-linear function approximation, which is based on approximation theory, which also covers basic concepts of regression, non-linear regression, which are also found in statistical theory, in most books on statistics. Clustering: k-means clustering, topology preserving clustering, cluster formation are some issues addressed in certain kinds of nonlinear modelling. Process industry/process control related: process industry is the prime beneficiary of these techniques; process industries benefit in terms of industrial process control, particularly advanced process control, self-tuning adaptive control, process guidance, process supervision, monitoring, model based process control, nonlinear model based control, model based nonlinear control, nonlinear control, control based on process models, statistical process control, process automation, etc. Nonlinear process modelling is often the basis of advanced control algorithms. A nonlinear process model can be empirical or semi-empirical, but process models based on physical modelling normally turn out to be too simplistic for real processes. Nonlinear process modeling is not based on a large number of assumptions and simplifications unlike physical models. Physical modelling normally requires assumptions and simplifications, and therefore a physical model is useful as good theory, but for industrial purposes physical modeling is not the most beneficial. Stochastic processes are not the only ones which benefit from stochastic models. Stochastic modelling can be useful in various situations, Monte-Carlo simulation can be utilised for various processes. A simulator based on such models can often be slow. Simulators based on empirical models, including dynamic simulation, are usually quite fast. A dynamic simulator can incorporate a nonlinear simulation model. A non-linear model is often the core of such simulators. Non-linear models for simulation can be of various kinds.

modelling related: semi-empirical models, semi-empirical modelling, semi-empirical modeling, semi-empirical model empirical models, empirical modelling, empirical model, empirical modeling; artificial intelligence, process optimisation, process optimization, optimise, optimize

linear modelling: multivariate analysis, chemometrics, principal component analysis, PCA, PLS, multivariate techniques

industrial value: improve materials, improve products, improve processes, improving production economics, improve quality, quality control, statistical quality control, reduce waste, reduce rejects, reduce wastage, increase efficiency, increase yield, improve yield, increase production increase productivity, reduce size, reduce volume, product development, process development, research, materials science, materials engineering, materials technology, chemical engineering, reduce energy consumption, reduce raw material consumption, reduce power consumption, electricity

Energy industry: heat, power generation, reduce emission, reduce emissions, reduce pollution, reduce emissions of pollutants, NOx, sulphur, sulfur, oxides, SO2, SO3, CO, carbon monoxide, unburnt, dioxin, dioxins, particle, particles, particulate, dust - keywords for power plants, boilers, as well as combustion issues of automobile engines, related combustion processes, exhaust gas recycle (EGR), selective catalytic reduction (SCR), fossil fuels, biofuels, waste, air staging, secondary air, air ratio, burners, cost reduction by reducing fuel consumption, improving energy efficiency while reducing emissions is possible with appropriate nonlinear models - ask for more information

for metallurgy: metal industry, which includes iron and steel industry, aluminium and copper producers; steel processing, etc. besides secondary metallurgy can benefit from nonlinear modelling; Many issues in metallurgical engineering can be handled better with nonlinear modelling; Nonlinear Solutions has worked with material behaviour of metals and alloys, particularly steels.

Nonlinear Solutions has provided several nonlinear models to Rautaruukki, SSAB, Fundia, Ovako Steel, etc. (a few articles available) stainless steel models for Avesta Sheffield and Outokumpu Polarit in Tornio, both companies are now Avesta Polarit, some cooperation with Sandvik, special models for titanium steel

special steels: boron steel, niobium steel, besides more common manganese steels, high silicon, wires with low carbon HSLA corten cast iron, high chromium content alloy, solder, etc. Material properties including tensile strength, yield strength, elongation at break, reduction of area have been modelled. A Lumet system for Jominy hardenability has also been developed. Nonlinear models were provided to Ovako Steel a few years back. Rockwell hardness, Vickers hardness, Brinell hardness, Charpy impact strength, Izod, fatigue strength, etc. can be modelled well.

Nonlinear Solutions has also provided nonlinear models of machinability. Machinability of stainless steels is more complicated.

Copper and aluminum: oxygen-free copper, cryogenic, RRR, residual resistivity ratio; nonlinear models were provided to Outokumpu Poricopper, an article on this topic appears in the magazine Wire Industry.

Miscellaneous: nitrogen, nitride, nitrides, nitriding, oxygen, oxide, oxides, zinc, galvanising, plastic coating, brass, rolling, extrusion, annealing, tempering, oil-tempered

General issues: material properties, mechanical properties, thermal properties, electrical properties, rheology, rheological fluid consistency, wet strength, flatness, workability, non-Newtonian pastes - ask for more information

cement and concrete: (an article on compressive strength and degree of compaction available) cement kiln, clinker, free lime, energy economy, reduce energy consumption (an article in International Cement Review) properties of wet concrete, properties of hardened concrete, construction - ask Nonlinear Solutions how you can cooperate on this topic

powder metallurgy: particle size distribution, chemical composition, oxygen, hot isostatic pressing, HIP, atomisation, atomization; Anval, Erasteel, Carpenter, etc. all know about nonlinear modelling and Nonlinear Solutions;

Continuous casting is an important process in steel production. In some situations, near net shape casting is performed where dimensional accuracy is more important. A dynamic model for ladle furnace, nonlinear dynamic model for LD converter, models for AOD converter, energy consumption in electric arc furnace (EAF) modelled with nonlinear modelling; induction furnace, preheating oven, rolling various products including, hot rolled plates cold strips wire rods for drawing, drawn wires, annealed wire, tempered wire cable extruded profile, extruded profiles HRC CRC

Nonlinear models for scrap melting can help in improving energy efficiency (energy economy, reduction of energy consumption)

Lumet systems for material properties delivered, provided tailor-made solutions for several companies plastics technology: polymer engineering, plastics processing, plastics converting, converters, injection moulding, molding, rotational, blow moulding, composites, rubber, elastomers can all benefit from nonlinear modelling. Polymerization: polymerise various monomers, polymerize

(There is a nice article in British Plastics and Rubber about nonlinear modelling in polymer sector industries, with examples from Borealis Polymers, Nextrom, etc. See also the article on improving production economics of extrusion processes in BP&R)

polymerisation process modelling, polymerization process modeling, polymer structure, polymerization catalysis, polymerisation catalysis, catalysts Ziegler-Natta, metallocenes, melt index, melt flow rate, MFR, molecular weight distribution, bimodal, xylene solubles, DSC enthalpy, crystallinity, glass transition temperature, softening point, other transitions, melt strength, viscoelasticity, nucleation, crystallisation, crystallization, results of compounding - ask for more information

Polymers: All kinds of polymers can benefit from nonlinear modelling including polyacrylates polycarbonates polyethylene HDPE LLDPE LDPE PEX PE-X XLPE PTFE teflon polypropylene PP mPP BOPP; homopolymers as well as copolymers; comonomer random heterophasic; Even polyvinyl chloride (PVC); polymers for medical applications (medical polymers), biopolymers, biodegradable or bioabsorbable polymers, (ask us for more information on modelling of kinetics of biodegradation, strength retention or loss, permeability, diffusivity, from limited experimental data). Nonlinear modelling has been used for (i) co-polymerization models, (ii) models of material properties, or structure-property relationship models for biopolymers and copolymers, (iii) biopolymer degradation or erosion or absorption kinetics and (iv) drug release rates/profiles, besides very many other things.

also starch based polymers, natural polymers - all these can benefit from nonlinear modelling

polymer foams: polyurethane polystyrene PVC polyamides fibre fibres spinning and various other processes, spinnerette (spinneret, spineret) extrusion coating, tubes, pipes, cables, OFC, excess length, heat treatment, shrinkage, crosslinking, hot set, flame retardant, bromine, bromide, density, weight, compressive strength, flexural modulus, tensile modulus, insulation, dielectric strength, thermal conductivity, cell structure, porosity; polylactide, glycolide, decomposition; biodegradation - quality improvement, cost reduction by reducing waste, raw material consumption, energy consumption - There is a nice article on LUMET systems for extrusion processes in BP&R of September 2008 - ask for Nonlinear Solutions for more information

Nonlinear modelling is useful in bioinformatics also in several ways. In the medical and biotechnology sectors, there are plenty of good applications of nonlinear modelling. From process modelling of biochemical processes and separation (e.g. chromatographic), nonlinear models are useful for pharmacokinetics, in vivo - in vitro correlations, for predicting drug release profiles, etc. Formulation development can be speeded up significantly by nonlinear modelling. Tablet properties (including dissolution rates, drug delivery rates) can be predicted better with nonlinear models. Another area is material behaviour of various kinds of materials used as implants. Quantitative structure-activity relationship (QSAR); molecular modelling, solubility, dissolution rates, boiling point, biological activity, strong correlations between structure and observed properties - molecular mining like data mining; use in drug design, drug screening - ask Nonlinear Solutions how you can cooperate on this topic

Pulp and paper: board, paperboard, fibreboard (fiberboard), MDF, particle-board, wood chips, timber, etc. Fiber or fibre length is a key issue for many properties; laboratory variables like tensile and tear strength, formation index, printability can be improved with nonlinear models, paper web breaks can be reduced with one solution offered by Nonlinear Solutions, several quality variables can be improved with nonlinear models; sophisticated nonlinear models for paper coating by different processes; extrusion coating, spraying, spray drying, calandering (calendering) - ask Nonlinear Solutions how you can cooperate on this topic

mechanical and chemical pulping, TCMP, kappa number, lignin, delignification, nonlinear models of bleaching with various processes including peroxide, chlorate, semi-empirical models of paper drying, or for pulp drying; calander, supercalander, supercalandering, - ask for more information; retention, latex, latexes, cationic resins, anionic resins, precipitated calcium carbonate, press felts, paper machine fabrics are produced by companies like Tamfelt, Albany, Voith. If you want better control over permeability of the fabrics, talk with us.

Suominen nonwovens is one of the nonwoven products company which has worked with us.

nonwoven, non-woven, polypropylene, polyamide, polyester, fibre spinning (melt, wet, dry), air cooling rate, melt strength, viscoelasticity, etc.

There is a nice article in International Fiber Journal on nonlinear modelling of fibre properties with neural networks, relating process variables of melt spinning with several fiber properties. The models can be used to improve the quality, increase production rate, or reduce breaks. Ask Nonlinear Solutions for more information.

Semiconductor industry: semiconductors, silicon wafers, chips, MEMS, CVD - ask for our interesting article which shows the advantage of using nonlinear modelling techniques instead of the conventional alternatives; LPCVD, ALCVD (ALD), ALE, MBE, etc. can be modelled well with nonlinear modelling; epitaxy, chemical vapour deposition vapor Czochralski growth single crystal silicon gallium arsenide silicon carbide, oxide, insulator, SOI - quality improvement, cost reduction by reducing waste, raw material consumption, energy consumption possible with appropriate nonlinear models - ask for more information

Food processing: processes like drying, mixing, grinding, roasting, extrusion, crystallisation, thickening, dissolution, fermentation, sprouting, distillery brewery processes, concentration, aging, packaging, freezing, etc; - ask Nonlinear Solutions how you can cooperate on this topic

Engineering in general: heat transfer, mass transfer, fluid mechanics, thermodynamics, solubility, conductivity, diffusivity, thermal, diffusion, mixing, stirring, homogenisation, homogenization, fluidisation ( fluidization ), fluidised bed ( fluidized bed ) drying, nonlinear models for spray drying process control, dryer, spray, sprayer, cooler, heater, distillation, concentration, incineration, oxidation, reduction, particle size distribution, dissolution, electrolysis - ask Nonlinear Solutions how you can cooperate on this topic

Water treatment and purification (drinking water as well as waste water) is another area where nonlinear models turn out to be very useful. Ask for more information from the contact page. Keywords: dosage, filtration, coagulation, sedimentation, pH, turbidity, alkalinity, COD, TOC, potassium permanganate, alum, aluminium, ferric sulphate, ferric sulfate, lime, limestone, chlorine, activated sludge, fertiliser, incineration, etc. - ask Nonlinear Solutions how you can cooperate on this topic

Nonlinear Solutions is located in Finland, in Europe, close to Sweden. Therefore, most of our work has been with companies in Finland and Sweden. However, at present, more interesting areas for process development, product development and materials science research and development are in some other countries of Europe, including Germany, Switzerland, Netherlands and Belgium. There is some amount of interest in UK also. From the point of view of production growth, nonlinear modelling has a greater potential in China, India, Russia, Brazil, Argentina, Chile, Mexico, and several Asian countries.

See also this page of TEKES.

Some relevant words in Finnish to make it easier for people to find this site:

Nonlinear Solutionsin toimintaan liittyviä joitakin avainsanoja suomeksi

epälineaarinen malli mallintaminen mallinnus mallitus ratkaisu approksimointi approximointi teoria tilastollinen menetelmä epälineaarinen regressio funktio sovitus neuroverkko neuraaliverkko hermoverkko

Muut matemaattiset aiheet: monimuuttuja analyysi, pääkomponentti analyysi, regressio analyysi, varianssi, varianssianalyysi, klusterointi, klusteri, k-means, itse-organisoituva

matemaattinen empiirinen mallintaminen, empiiristä, fysikaalinen, fysikaalista, semi-empiirinen, tekoäly, automaatio, prosessi, prosessien mallintaminen, prosessien mallinnus, prosessitekniikka, tekniikka säätö ohjaus, mallipohjainen säätö, epälineaarinen säätö, valvonta, etävalvonta, säätäjä, prosessiteollisuus, käyttö sovellus sovellutus sovelluksia sovellutuksia hyöty hyödyntää prosessiteollisuudessa parantaa laatua, laadunvalvonta, vähentää raaka-aineiden, raaka-aineen kulutusta

parantaa tuotantotaloutta, vähentää energian kulutusta, vähentää päästöjä, nostaa tehokkuutta, parantaa tuotteita, tuote tuotteet tuotekehitys kehitys tutkimus tutkimusta materiaali, parantaa materiaaleja

rauta, valurauta, teräs, terästä, teräksiä, ruostumaton, ruostumatonta, titaaniteräs, mikroseostettu, kupari, hapeton, hopea, messinki, juotos, titaani, johtavuus, lujuus, murtolujuus, myötölujuus, (hyviä esimerkkejä toimittamistamme ratkaisuista) venymä, murtovenymä, murtokurouma, kovuus, karkenevuus, puristuslujuus, lastuttavuus, kokojakauma, pulveri, pulverimetallurgia, hehkutus, valokaariuuni, romu sulatus, alumiini profiili, pursotus, extruusio tai ekstruusio (useita artikkeleita jotka selittävät miten epälineaarinen mallintaminen auttaa parantamaan laatua, nostamaan linjanopeutta), puristus, kuumavalssaus, valssaus, valsaus, kylmävalssaus, sinkitys, päällystys, maalaus, muovimaalaus, pinnoitus, muovipinnoitus, jne.

polymeeri polymeerit polymeereja poymerointi polyeteeni polypropeeni polystyreeni muovit sulaindeksi extruusio pursotus puristus sulan lämpötila linjanopeus ruuvin kierrosluku ruiskuvalu ruiskupuristus jäähdytysaika sykliaika puhallusmuovaus kehruu sulan lujuus muovimaalaus lateksi päällystys paksuuden säätö

sellu massa paperi metsä viira viirat huopa kalanteri kuivaus vaaleus formaatio painettavuus

soodakattila kattila voimala hiili poltto polttoaine tuuli tuulivoima hyötysuhde sähkö kombi voimala päästö p??st?t p??st?j? (my?s hyv? demonstraatio-esimerkki) höyry, voimansiirto, kaapeli HVC MVC pii puolijohde puolijohteet pii karbiidi oksiidi betoni puristuslujuus tiivistys (artikkeli saatavilla) vapaa kalkki sementti uuni, meesa, meesauuni, klinkkeri, energian kulutus

elintarvike, prosessointi, jalostus, kuivaus, sekoitus, jauhatus, paisto, extruusio, kiteytys, sakeutus, linkous, liuos, pakastaminen, huokoisuus, pakkaminen, pakkaus, l?p?isy, l?p?isevyys, liukeneminen, sakeuttaminen, puristus, pursotus, vanheneminen, funktionaalinen funktionaaliset, erotusprosessi erotusprosessit erotusprosesseja kromatografia kromatografiset proteiini proteinien erotus (my?s hyv? demonstraatio-esimerkki), puhdistus, kalvoerotus, membraani, hiilihydratti hiilihydraatti sokeri t?rkkelys t?rkki amylaasi

juomavedenk?sittely, juomavesi, veden k?sittely, puhdistus vedenk?sittely, j?te, j?tevesi, j?teveden k?sittely, aktiiviliete, j?tevedenk?sittely, selkeytys, pH, sameus, alkaliniteetti, kalkki, ferrisulfaatti, ferrosulfaatti, fosfori, typenpoisto, orgaaninen kuorma, jne. Nonlinear Solutions sijaitsee Suomessa, Euroopassa, l?hell? Ruotsia. Siksi suuri osa ty?st?mme on ollut Suomen ja Ruotsin yritysten kanssa. Ruotsi ei en?? ole t?rkein vientimaa. T?ll? hetkell? my?s Saksa, Sveitsi, Alankomaat ja Belgia ovat mielenkiintoisia prosessien kehityksen, tuotekehityksen ja materiaalitutkimuksen kannalta. Tuotannon kasvu on kuitenkin enemm?n kehitysmaissa - Kiina, Intia, Ven?j?, Brasilia, Argentina, Chile, ja muu Aasia.

H?r finns lite information och n?gra ord om Nonlinear Solutions verksamhet i Sverige och Finland.

Icke-linj?ra modeller utnyttjas i ett antal olika till?mpningar inom processindustri. Ett viktigt anv?ndningsomr?de ?r modellering av materialegenskaper av bl. a. metallprodukter (st?l, koppar, aluminium, m?ssing, osv), papper och massa, cement och betong, plastprodukter (termoplaster, termoset, gummi), glas, keramik, byggmaterial, osv.

N?gra ord p? svenska:

icke-linj?r modell modeller icke-linj?r modellering l?sning l?sningar l?sningsmetoder approximering approximationer, teori statistiskt statistik metod metoder regression funktion anpassning neurala n?tverk n?t multivariatanalys, huvudkomponent analys, PLS regression, kemometri, k-means klustrering

empirisk modellering, fysikalisk, semi-empirisk, artificiell intelligens, automation, process, processmodellering, processteknik, teknik, reglering, styrning, ?vervakning, regulator, processindustri, anv?ndning, till?mpning, till?mpningar, f?rdel, nytta, utnyttja, f?rb?ttra kvalitet, kvalitetskontroll, f?rminska, r?varu f?rbrukning, ?tg?ng, konsumtion

f?rb?ttra produktionsekonomin, f?rminskning av eller minska energif?rbrukningen, minska utsl?ppen, ?ka effektiviteten, f?rb?ttra produkter, produkt, produktutveckling, utveckling, forskning, material, f?rb?ttra materialer, j?rn, st?l, rostfritt, titanst?l, mikrolegerad, koppar, syrefri, silver, m?ssing, l?dfog, l?dning, titan, ledningsf?rm?ga, h?llfasthet, brotth?llfasthet, brottgr?ns, str?ckgr?ns, t?jning, h?rdbarhet, h?rdning, storleksf?rdelning, pulver, pulvermetallurgi, aluminium, profil, extrusion, pressning, varmvalsning, valsning, kallvalsning, f?rzinkning, bel?ggning, bestrykning, m?lning, plastm?lning, ytbel?ggning, plastbel?ggning, bestryckning, gl?dgning, ljusb?gsugn

polymer, polymerer, polyeten, polypropen, polystyren, plaster, plast, sm?ltindex, cellulosa, massa, papper, skog, skogsprodukt, vira, f?lt, kalander, torkning, ljushet, formation, formationsindex, tryckbarhet, kraftverk, kol, f?rbr?nning, br?nsle, vind, effektivitet, verkningsgrad oms?ttningsgrad, el, elektricitet, kombination, kisel, halvledare, karbid, oxid, betong, tryckh?llfasthet, t?tning, fri kalk, cement ugn, klinker, energif?rbrukning

livsmedel, processering, raffinering, torkning, blandning, malning, stekning, extrusion, kristallisering av socker, margarin, osv., f?rtjockning, koncentration, centrifugering, l?sning, frysning, porositet, packning, f?rpackning, genomsl?pplighet, uppl?sning, pressning, f?r?ldring, funktional, separering, separation, separationsprocess, kromatografi, protein, reng?ring, membran, avskiljning, kolhydrat, socker, st?rkelse, amylas

Vi har utvecklat modeller f?r vattenrening ocks?.

The site of Abhay Bulsari is still being written.