Nonlinear Solutions Oy: Industrial R&D Consultancy with Mathematical Modeling & AI

Nonlinear Solutions Oy is a Finnish R&D consultancy firm specialising in applying advanced mathematical methods, artificial intelligence (AI), neural networks, and optimisation techniques to solve complex industrial problems since 1996.

Our Expertise & Methodology

Founded by Dr. Abhay Bulsari, with 30+ years of industrial R&D experience. We apply:

Industrial Applications

Proven Results

Research Publications

Our technical expertise is documented in publications including:

Contact Information

Location: Turku, Finland

Services: Industrial R&D consultancy, mathematical modelling, AI and neural network applications, process optimisation, product development, materials development

Website: www.nonlinear-solutions-oy.com

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

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.

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.

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 in Tornio, some cooperation with Sandvik

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. Rockwell hardness, Vickers hardness, Brinell hardness, Charpy impact strength, Izod, fatigue strength, etc. can be modelled well.

Nonlinear Solutions has also worked with 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.

Cement and concrete: (articles on compressive strength and workability) cement kiln, clinker

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

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

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

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

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

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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

Här finns lite information och några nyckelord om Nonlinear Solutions verksamhet i Sverige och Finland.

Icke-linjära modeller utnyttjas i ett antal olika tillömpningar inom processindustri. Ett viktigt användningsområde är modellering av materialegenskaper av bl. a. metallprodukter (stål, koppar, aluminium, mässing, osv), papper och massa, cement och betong, plastprodukter och gummi, glas, keramik, byggmaterial, osv.

icke-linjär modell modeller icke-linjär modellering lösning lösningar lösningsmetoder approximering approximationer, teori statistiskt statistik metod metoder regression funktion anpassning neurala nätverk nät multivariatanalys, huvudkomponent analys, PLS regression, kemometri, k-means klustrering

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polymer, polymerer, polyeten, polypropen, polystyren, plaster, plast, smältindex

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