ADM1 Parameter Calibration Method based on partial least squares regression framework for industrial-scale anaerobic digestion modelling

Xu, Zhehua (2019-12)

Thesis (MEng)--Stellenbosch University, 2019.

Thesis

ENGLISH ABSTRACT: Anaerobic Digestion Model 1 (ADM1) is the mainstay modelling tool for Anaerobic Digestion research and development. Its growing popularity is attributed to its sophisticated yet expandable structure. Not only does ADM1 encompass a broad range of biochemical, physicochemical and inhibition reactions, it provides the modeller a structured framework to add or remove reactions per application requirements. Two major challenges that ADM1 faces are the difficulty in translating common quality indicators into ADM1’s 26 state variables, and the complication with calibrating a large number of model parameters – 58 by default. There is currently no consensus with regards to the parameter calibration approach. Researchers utilise various sensitivity analysis techniques to identify sensitive parameters, but the selection of parameters to be calibrated relies largely on the modeller’s discretion. In some cases, decisions are simply made based on prior or expert knowledge. Since the installation, operation and maintenance of advanced instrumentation are often expensive, most industrial digesters are inadequately monitored and thus intentionally over-designed. A model that can be used on-site with acceptable accuracy could serve as a soft sensor to forecast inhibition risks and automate preventive actions. Therefore, this study aimed to develop a standardised way to calibrate parameters when optimising ADM1 models built for industrial-scale digesters. The proposed method, Partial Least Squares (PLS) Method, consists of four steps. In Step 1, a series of Monte Carlo simulations is carried out. For each Monte Carlo run, ADM1 is executed with all its model parameters sampled from independent probability distributions. These probability distributions were obtained by conducting a literature survey across 62 publications and all published parameters compiled into a domain which represents the uncertainty range of each parameter. In Step 2, a multivariate regression technique called PLS Regression (PLSR) is applied to the Monte Carlo results. The motives for employing PLSR are to reduce parameter dimensionality and to identify the underlying relationships between the model parameters and the model outputs. In Step 3, these relationships, which are mathematically described as PLS weights, loadings and latent variables, are utilised to guide parameter calibration. Lastly, the calibrated parameter set is validated against unseen data. This method successfully improved, in the absence of any modeller’s bias, the overall accuracy of a model based on data from an industrial-scale digester. The model is tasked to fit six typical plant measurements: Volatile Fatty Acids (VFA), ammonia, Volatile Suspended Solids (VSS), pH, methane gas flow & carbon dioxide gas flow. A configuration consisting of at least 500 Monte Carlo runs and two latent variables is required to produce a reasonably accurate fit. Although the use of more latent variables could enable PLSR to capture interactions of lesser weighted output variables, the model becomes increasingly prone to overfitting. However, it is envisaged that more latent variables would be necessary if more outputs are modelled. It is recommended to start the PLSR algorithm with one latent variable and only introduce more if necessary. Different parameter calibration methods produce different model outcomes. The PLS Method was benchmarked against two other methods, namely the Group Method and the “Brute Force” Method. In the former method, kinetic parameters were grouped into the three groups of sensitivities (High, Medium, Low) as suggested in the ADM1 Scientific and Technical Report. The three groups are then calibrated sequentially in order of decreasing sensitivity. The “Brute Force” Method involved calibrating all 58 parameters without any particular sequence, prioritisation or expert inputs. Lower and upper limits are, however, set as per the minimum and maximum values identified from the literature. Besides proving to be a suitable method for industrial-scale digester modelling, the PLS Method was found to exhibit several unique traits: • It is the only method that did not show signs of overfitting. • It is the only method that concluded the model optimisation with all calibrated parameter values within the surveyed minimum and maximum range. • It converges on the objective function 30-60% faster than the Group Method and 14 times quicker than the “Brute Force” Method The success is attributed to the fundamentals of PLS regression. Unlike other regression methods where parameters are adjusted independently, PLS enables parameters to be manipulated collectively in a manner that ensures maximum impact on the outputs while considering collinearities among the parameters. This guided approach effectively mitigates the so-called “curse of dimensionality” and, potentially, overfitting and thereby speeds up the calibration process.

AFRIKAANSE OPSOMMING: Anaerobiese Verteerder Model 1 (ADM1) is die hoof modelleringsinstrument vir Anaerobiese Verteerder navorsing en ontwikkeling. Sy groeiende populariteit word toegeskryf aan sy gesofistikeerde tog uitbreibare struktuur. ADM1 sluit nie net ʼn wye bestek van biochemiese, fisikochemiese en inhibisie-reaksies in nie, dit verskaf ook die modelleerder met ʼn gestruktureerde raamwerk om reaksies by te voeg of weg te neem in ooreenstemming met toepassingvereistes. Twee groot uitdagings wat ADM1 in die gesig staar is hoe moeilik dit is om gewone kwaliteit aanwysers in ADM1 se 26 toestandveranderlikes oor te dra, en die komplikasie met die kalibrering van ʼn groot aantal model parameters – 58 by verstek. Daar is tans geen konsensus met betrekking tot die parameter-kalibrasie-benadering nie. Navorsers gebruik verskeie sensitiwiteit analisetegnieke om sensitiewe parameters te identifiseer, maar die keuse van parameters wat gekalibreer moet word steun grootliks op die modelleerder se diskresie. In sommige gevalle word besluite eenvoudig gemaak op voorafgaande of deskundige kennis. Aangesien die installasie, bedryf en onderhoud van gevorderde instrumentasie dikwels duur is, is meeste industriële verteerders gebrekkig gemonitor en dus opsetlik oor-ontwerp. ʼn Model wat op die perseel gebruik kan word met aanvaarbare akkuraatheid kan as ʼn sagte sensor dien wat inhibisie risiko’s kan voorspel en voorkomende aksies outomatiseer. Daarom is die doel van hierdie studie die ontwikkeling van ʼn gestandaardiseerde manier om parameters te kalibreer wanneer ADM1-modelle geoptimeer word wat vir industriële verteerders gebou is. Die voorgestelde metode, Parsiële Kleinste Kwadrate (PLS)-metode, bestaan uit vier stappe. In Stap 1, word ʼn reeks Monte Carlo-simulasies uitgevoer. Vir elke Monte Carlo lopie, is ADM1 uitgevoer met al sy modelparameter monsters geneem uit onafhanklike waarskynlikheidsverdeling. Hierdie waarskynlikheidsverdeling is verkry deur ʼn literatuuropname oor 62 publikasies en alle gepubliseerde parameters uit te voer en alle gepubliseerde parameters in ʼn definisiegebied wat die onsekerheidsbestek van elke parameter voorstel, saam te stel. In Stap 2 word ʼn meerveranderlike regressie-tegniek by name PLS Regressie (PLSR), toegepas op die Monte Carlo resultate. Die motivering om PLSR te gebruik is om parameter dimensionaliteit te verminder en om die onderliggende verhouding tussen modelparameters en die modeluitsette te identifiseer. In Stap 3 word hierdie verhoudings, wat wiskundig as PLS-gewigte, -ladings en latente veranderlikes beskryf word, gebruik om die kalibrasie van parameters te lei. Laastens word die gekalibreerde parameterstel gevalideer teen ongesiene data. Hierdie metode het, in die afwesigheid van enige modelleerder se vooroordeel, die algehele akkuraatheid van ʼn model gebaseer op data van ʼn industriële-skaal verteerder, suksesvol verbeter. Die model is die taak opgelê om ses tipiese aanlegmetings te pas: VFA, ammoniak, VSS, pH, metaangasvloei en koolstofdioksiedgasvloei. ʼn Konfigurasie wat uit ten minste 500 Monte Carlo-lopies en twee latente-veranderlikes bestaan, word benodig om ʼn redelike akkurate passing te produseer. Al kan die gebruik van meer latente veranderlikes PLSR in staat stel om interaksies van minder gewigtige uitsetveranderlikes te vang, word die model meer geneig tot oorpassing. Dit word egter verwag dat meer latente-veranderlikes nodig sal wees as meer uitsette gemodelleer word. Dit word voorgestel om die PLSR-algoritme met een latente-veranderlike te begin en slegs meer in te voeg soos nodig. Verskillende parameter kalibrasie metodes produseer verskillende model uitkomste. Die PLS-Metode is genormeer teen twee ander metodes, naamlik die Groep Metode en die “Brute Krag” Metode. In die eersgenoemde metode, is kinetiese parameters gegroepeer in drie groepe van sensitiwiteit (Hoog, Medium, Laag) soos voorgestel in die ADM1 Scientific and Technical Report. Die drie groepe word dan sekwensieel gekalibreer in orde van afnemende sensitiwiteit. Die “Brute Krag” Metode sluit kalibrasie van al 58 parameter in, sonder enige besondere orde, prioritisering of deskundige insette. Laer en hoër limiete is egter gestel soos per die minimum en maksimum waardes uit die literatuur geïdentifiseer. Buiten die bewys dat dit ʼn gepaste model is vir modellering van industriële-skaal verteerders, is die PLSMetode gevind om verskeie unieke eienskappe te vertoon: • Dit is die enigste metode wat nie tekens van oorpassing gewys het nie. • Dit is die enigste metode wat die model optimering met al die gekalibreerde parameterwaardes binne die opname se minimum en maksimum bestek, gesluit het. • Dit konvergeer 30–60% vinniger na die doelfunksie as die Groep Metode en 14 keer vinniger as die “Brute Krag” Metode. Die sukses word toegeskryf aan die grondslag van PLS-regressie. Anders as ander regressiemetodes waar parameters onafhanklik aangepas word, stel PLS-konstruksies parameters in staat om gesamentlik gemanipuleer te word op ʼn manier wat maksimum impak op die uitsette verseker terwyl kolineariteite onder parameters oorweeg word. Hierdie geleide benadering versag effektief die sogenaamde “vloek van dimensie” en, moontlik, oorpassing en daarby versnel dit die kalibrasieproses.

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