An optimal experimental design framework for fast kinetic model identification based on artificial neural networks

Data Reconciliation in Reaction Systems using the Concept of Extents

This study examined the modelling and optimisation of the electrocoagulation-flocculation (ECF) recovery of aquaculture effluent (AQE) using aluminium electrodes. The response surface methodology (RSM), artificial neural network (ANN), and adaptive neuro-fuzzy inference system (ANFIS) were used for the modelling, while the optimisation tools were the numerical RSM and genetic algorithm (GA). Furthermore, the kinetics of the ECF process was studied to provide insight into the mechanism governing the ECF of AQE. The experimental design was performed using the central composite design (CCD) of the RSM. The ANFIS modelling was accomplished via the Grid Partition (GP) of the data set, while the ANN used the multi-layer perceptron (MLP) based feed-forward system. Statistically, the prediction accuracy of the models followed the order: ANFIS (R2: 0.9990), ANN (R2: 0.9807), and RSM (R2: 0.9790). The process optimisation gave optimal turbidity (TD) removal efficiencies of 98.98, 97.81, and 96.01% for ANFIS-GA, ANN-GA, and RSM optimisation techniques, respectively. The ANFIS-GA gave the best optimization result at optimum conditions of pH 4, current intensity (3 A), electrolysis time (7.2min), settling time (23min), and temperature (43.8°C). In the kinetics study, the experimental data was analysed using pseudo-first-order (0.8787), pseudo-second-order (0.9395), and Elovich (R2: 0.9979) kinetic models; the Elovich model gave the best correlation with the experimental data showing that the process is governed by electrostatic interaction mechanism. This study effectively demonstrated that ECF recovery of AQE can effectively be modelled using RSM, ANN, and ANFIS and be optimised using RSM, ANN-GA, and ANFIS-GA techniques, and the order of performance is ANFIS > ANN > RSM and ANFIS-GA > ANN-GA > RSM, respectively.

Model Predictive Control (MPC) is a solution towards more energy-efficient waste treatment without compromising on treatment quality. A key component is the process model describing how the inputs and outputs correlate. MPC uses this model to predict future outputs over a finite horizon to decide on step changes to make at the input. These step changes are made so that the output reaches and maintains at a user specified set point. For MPC to be effective, the process model needs to accurately describe the process behaviour. This is a difficult challenge in waste treatment processes due to a combination of slow response, process complexity, and large disturbances. This research project investigated two research avenues towards developing better modelling techniques. This would result in more accurate models or achieve a sufficiently accurate model with fewer experiments. The first avenue is Constrained Model Identification (CMI). Model identification is an optimisation problem to estimate the model parameters. In CMI, process knowledge from first principles and operator experience is translated into optimisation constraints to aid data-driven model identification. The second avenue is Sequential Optimal Experiment Design (SOED). This uses the concept of measuring a value representing information content of a dataset. Like MPC, SOED uses the model to make output predictions. The expected output response to a sequence of input steps form a dataset, and SOED is an optimisation problem to maximise the information content of that expected dataset, by changing the input step sequence. Once optimised, this step sequence is applied in the next experiment. The third part of this work focused on farm-fed anaerobic digestion. It is a renewable energy technology fuelled by agricultural waste. They rely on government incentives to be profitable, but these incentives have steadily been decreased. This project investigated methods to help farmers in the day-to day operation of the unit, including biogas production estimation, automated fault identification and partial diagnosis.

This article, written by Technology Editor Dennis Denney, contains highlights of paper SPE 94357, "Treating Uncertainties in Reservoir-Performance Prediction With Neural Networks," by J.P. Lechner, SPE, OMV A.G., and G. Zangl, SPE, Schlumberger Information Solutions, prepared for the 2005 SPE Europec/EAGE Annual Conference, Madrid, Spain, 13–16 June. In development projects, reservoir parameters are known only within certain ranges, which results in various realizations of the subsurface. Because of the computational time involved, simulation models to obtain a probability distribution of possible outcomes cannot cover all possible parameter combinations. Creating a response surface based on a reduced number of simulation runs becomes necessary. Such a response surface can be used to approximate results for several variations of input parameters. An approach in which reservoir response is captured by an artificial neural network (ANN) has been investigated. The trained ANN model was used in Monte Carlo simulations to generate the probability distribution of possible outcomes. Introduction Often, simulation models are built to design field-development plans. Because of the low level of information during the early development stage, a range of uncertainty in the prediction scenarios must be considered. Such uncertainties can be handled with ANNs. Numerical models (simulation models) are detailed and powerful predictive tools that can answer many questions regarding subsurface engineering. However, especially in the early development phase, uncertainties are large, and prediction results will span a broad range. To take into account the whole range of possible outcomes of reservoir simulation, optimization routines would have to run the numerical models perhaps thousands of times. Although the most likely solution that respects subsurface uncertainties is of interest, the most profitable solution for reservoir management must be found. Because of the computational time involved, these methodologies often are not used. Building a response surface that can predict many possible outcomes of a numerical simulation by processing a large variety of input parameters could provide a solution to this problem. The response surface must cover the non-linear dependencies between input and output parameters. Experimental design and response-surface modeling has been used to delineate subsurface uncertainty. Common applications include determining the probability distribution of original oil in place from geological models, quantifying uncertainty in predevelopment or preredevelopment projects, predicting production performance from different realizations of a geological model, and optimizing the location of new wells to maximize net profit. Methodology Fig. 1 shows the proposed workflow. As a first step, a limited number of simulation runs is carried out to define the most sensitive input parameters. In these runs, parameters are altered one at a time, either to the minimum or to the maximum. After selecting the most influential input parameters, three values (minimum, best-estimate, and maximum) are defined, and an experimental design is set up. The experimental design aims at obtaining the maximum information with a minimum number of simulation runs. However, practice showed that a minimum number of training data sets are required by the ANN to be able to make sufficiently accurate predictions. With these data sets containing varying input parameters and the corresponding output, an ANN is trained and tested with several additional simulation runs. After defining the probability distribution of the input parameters, the trained ANN is used as a proxy function for a Monte Carlo simulation. Thereby, a probability distribution of the desired output parameter (e.g., cumulative production after a certain number of years) is gained. The quality of the ANN is measured by the root-mean-square error of the deviation between the predicted and the actual output.

Industrial noise can be successfully mitigated with the combined use of passive and Active Noise Control (ANC) strategies. In a noisy area, a practical solution for noise attenuation may include both the use of baffles and ANC. When the operator is required to stay in movement in a delimited spatial area, conventional ANC is usually not able to adequately cancel the noise over the whole area. New control strategies need to be devised to achieve acceptable spatial coverage. A three-dimensional actuator model is proposed in this paper. Active Noise Control (ANC) usually requires a feedback noise measurement for the proper response of the loop controller. In some situations, especially where the real-time tridimensional positioning of a feedback transducer is unfeasible, the availability of a 3D precise noise level estimator is indispensable. In our previous works [1,2], using a vibrating signal of the primary source of noise as an input reference for spatial noise level prediction proved to be a very good choice. Another interesting aspect observed in those previous works was the need for a variable-structure linear model, which is equivalent to a sort of a nonlinear model, with unknown analytical equivalence until now. To overcome this in this paper we propose a model structure based on an Artificial Neural Network (ANN) as a nonlinear black-box model to capture the dynamic nonlinear behaveior of the investigated process. This can be used in a future closed loop noise cancelling strategy. We devise an ANN architecture and a corresponding training methodology to cope with the problem, and a MISO (Multi-Input Single-Output) model structure is used in the identification of the system dynamics. A metric is established to compare the obtained results with other works elsewhere. The results show that the obtained model is consistent and it adequately describes the main dynamics of the studied phenomenon, showing that the MISO approach using an ANN is appropriate for the simulation of the investigated process. A clear conclusion is reached highlighting the promising results obtained using this kind of modeling for ANC.

Effective kinetic models of heterogeneous catalytic processes are an indispensable tool for reactor design, optimization, and control. Under the assumption of using functional forms like power laws, model parameters are traditionally fitted to kinetic data measured along local line scans. A local line scan involves systematically varying one individual reaction parameter, such as a reactant concentration or temperature, at a time. This approach typically involves numerous separate kinetic measurements and is susceptible to the uncertainty of these line scans in determining the model's parameters. Here, we explore the use of profile reactors in combination with a fully automated adaptive design approach for an efficient identification of effective kinetic models. Originally developed to provide operando information along the axis of tubular reactors, profile reactors provide a complex line scan that encapsulates kinetic information across all reaction conditions probed along the tube. The proposed Model-Driven Adaptive Design with Profiles algorithm harnesses this extensive dataset to strategically guide the selection of initial reaction conditions for subsequent profile reactor measurements. This approach ensures that each line scan provides maximally complementary information, thereby significantly enhancing the efficiency and accuracy of kinetic model identification.

Synthesis and characterization of Alg/Gel/n-HAP/MNPs porous nanocomposite adsorbent for efficient water conservancy and removal of methylene blue in aqueous environments: Kinetic modeling and artificial neural network predictions

The current study looks at the effectiveness of the removal of nickel (II) from aqueous solution using an adsorption method in a laboratory‐size reactor. An artificial neural network (ANN) and an adaptive neuro‐fuzzy inference system (ANFIS) were used in this study to predict blend hydrogels adsorption potential in the removal of nickel (II) from aqueous solution. Four operational variables, including initial Ni (II) concentration (mg/L), pH, contact duration (min), and adsorbent dose (mg/L), were used as an input with removal percentage (%) as the only output; they were studied to assess their impact on the adsorption study in the ANFIS model. In contrast, 70% of the data was used for training, while 15% of the data was used in testing and validation to build the ANN model. Feedforward propagation with the Levenberg–Marquardt algorithm was employed to train the network. The use of ANN and ANFIS models for experiments was used to optimize, construct, and develop prediction models for Ni (II) adsorption using blend hydrogels. The adsorption isotherm and kinetic models were also used to describe the process. The results show that ANN and ANFIS models are promising prediction approaches that can be applied to successfully predict metal ions adsorption. According to this finding, the root mean square errors (RMSE), absolute average relative errors (AARE), average relative errors (ARE), mean squared deviation (MSE), and R 2 for Ni (II) in the training dataset were 0.061, 0.078, 0.017, 0.019, and 0.986, respectively, for ANN. In the ANFIS model, the RMSE, AARE, ARE, MSE, and R 2 were 0.0129, 0.0119, 0.028, 0.030, and 0.995, respectively. The adsorption process was spontaneous and well explained by the Langmuir model, and chemisorption was the primary control. The morphology, functional groups, thermal characteristics, and crystallinity of blend hydrogels were all assessed.

We consider the problem of A-optimal design of experiment under a Bayesian probabilistic model with both categorical and continuous response variables. The utility function of the local design problem is derived by applying Bayesian experimental design framework. We also develop an efficient optimization algorithm to obtain the local optimal design by combining the particle swarm optimization and the blocked coordinate descent methods. In addition, we discuss two different ways of constructing the global optimal design based on the algorithm for local optimal design. Simulation studies are presented to illustrate the efficiency of our approach.

This paper presents data-driven modeling and a results analysis. Group method data handling (GMDH), multivariable regression (MVR), artificial neuron network (ANN), and new proposed GMDH-featured ANN machine learning algorithms were implemented to model a field telemetry equivalent mud circulating density (ECD) dataset based on surface and subsurface drilling parameters. Unlike the standard GMDH-ANN model, the proposed GMDH-featured ANN utilizes a fully connected network. Based on the considered eighteen experimental modeling designs, all the GMDH regression results showed higher R-squared and minimum mean-square error values than the multivariable regression results. In addition, out of the considered eight experimental designs, the GMDH-ANN model predicts about 37.5% of the experiments correctly, while both algorithms have shown similar results for the remaining experiments. However, further testing with diverse datasets is necessary for better evaluation.

Nucleophilic aromatic substitutions (SNAr) are key chemical transformations in pharmaceutical and agrochemical synthesis, yet their complex mechanisms (concerted or two-step) complicate kinetic model identification. Accurate kinetic models for SNAr are essential for scale-up, optimization, and control of the reaction process, but conventional methods struggle with mechanism uncertainty driven by substrates, nucleophiles, and reaction conditions, with data collection being difficult due to its source-intensive nature. We address this using DoE-SINDy, a data-driven framework for generative modelling without complete theoretical understanding. A benchmark study on the SNAr reaction of 2,4-difluoronitrobenzene with morpholine in ethanol was conducted, incorporating parallel and consecutive side-product formation. Ground-truth kinetic models validated in prior studies were used to generate in-silico data under varying noise levels and sampling intervals. DoE-SINDy successfully identified the true kinetic model with minimal runs, quantifying the impact of key design factors such as inlet concentrations, residence time, sample size and experimental budget on model identification.

The need for efficient computational screening of molecular candidates that possess desired properties frequently arises in various scientific and engineering problems, including drug discovery and materials design. However, the large size of the search space containing the candidates and the substantial computational cost of high-fidelity property prediction models makes screening practically challenging. In this work, we propose a general framework for constructing and optimizing a virtual screening (HTVS) pipeline that consists of multi-fidelity models. The central idea is to optimally allocate the computational resources to models with varying costs and accuracy to optimize the return-on-computational-investment (ROCI). Based on both simulated as well as real data, we demonstrate that the proposed optimal HTVS framework can significantly accelerate screening virtually without any degradation in terms of accuracy. Furthermore, it enables an adaptive operational strategy for HTVS, where one can trade accuracy for efficiency.

Mathematical models of complex biological systems, such as metabolic or cell-signalling pathways, usually consist of sets of nonlinear ordinary differential equations which depend on several non-measurable parameters that can be hopefully estimated by fitting the model to experimental data. However, the success of this fitting is largely conditioned by the quantity and quality of data. Optimal experimental design (OED) aims to design the scheme of actuations and measurements which will result in data sets with the maximum amount and/or quality of information for the subsequent model calibration. New methods and computational procedures for OED in the context of biological systems are presented. The OED problem is formulated as a general dynamic optimisation problem where the time-dependent stimuli profiles, the location of sampling times, the duration of the experiments and the initial conditions are regarded as design variables. Its solution is approached using the control vector parameterisation method. Since the resultant nonlinear optimisation problem is in most of the cases non-convex, the use of a robust global nonlinear programming solver is proposed. For the sake of comparing among different experimental schemes, a Monte-Carlo-based identifiability analysis is then suggested. The applicability and advantages of the proposed techniques are illustrated by considering an example related to a cell-signalling pathway.

In environmental and water resource (EWR) engineering, different types of design problems exist, such as operation design, monitoring design, detection design, and remediation design. This chapter is devoted to the subject of experimental design for model calibration and parameter estimation. Experimental design plays a critical role in model construction because the reliability of a model is mainly dependent on the quantity and quality of data used for its calibration. In other words, the experimental design dictates how data should be collected in field campaigns and how many observations are needed. An optimal experimental design (OED), when it is executed, should provide the maximum amount of information with the minimum cost. Basic concepts, theories, and methods of OED are well established in statistics and have been applied to various scientific and engineering disciplines.

Weight loss of frozen bread dough under isothermal and fluctuating temperature storage conditions