System identification has been a major advancement in the evolution of engineering. As it is by default the first step towards a significant set of adaptive control techniques, it is imperative for engineers to apply it in order to practice control. Given that system identification could be useful in creating a digital twin, this work focuses on the initial stage of the procedure by discussing simplistic system order identification. Through specific numerical examples, this study constitutes an investigation on the most “natural” method for estimating the order from responses in a convenient and seamless way in time-domain. The method itself, originally proposed by Ho and Kalman and utilizing linear algebra, is an intuitive tool retrieving information out of the data themselves. Finally, with the help of the limitations of the methods, the potential future outlook is discussed, under the prism of forming a digital twin.

Considering the recent regulatory requirements, the overall importance of in vitro release testing (IVRT) methods regarding topical product development is undeniable, especially when addressing particulate systems. For each IVRT study, several hundreds of samples are generated. Therefore, developing rapid reversed-phase high-performance liquid chromatography (RP-HPLC) methods, able to provide a real-time drug analysis of IVRT samples, is a priority. In this study, eight topical complex drug products exhibiting distinct physicochemical profiles were considered. RP-HPLC methods were developed and fully validated. Chromatographic separations were achieved on a XBridgeTM C18 (5 µm particle size, 150 mm × 2.1 mm), or alternatively on a LiChrospher® 100 RP-18 (5 µm particle size, 125 mm × 4.6 mm) at 30 °C, under isocratic conditions using UV detection at specific wavelengths. According to the physicochemical characteristics of each drug, different mobile phases were selected. Irrespective of... [more]

Polymeric flocculants are widely used due to their ability to efficiently promote flocculation at low dosages. However, fundamental background knowledge about how they act and interact with the substrates is often scarce, or insufficient to infer the best chemical configuration for treating a specific effluent. Inductive, data-driven approaches offer a viable solution, enabling the development of effective solutions for each type of effluent, overcoming the knowledge gap. In this work, we present such an inductive workflow that combines the statistical design of experiments and predictive modelling, and demonstrates its effectiveness in the development of anionic polymeric flocculants for the treatment of a real effluent from the potato crisps manufacturing industry. Based on the results presented, it is possible to conclude that the hydrodynamic diameter, charged fraction and concentration are the parameters with a stronger influence on the characteristics of flocs obtained when using... [more]

Considering the competitive and strongly regulated pharmaceutical industry, mathematical modeling and process systems engineering might be useful tools for implementing quality by design (QbD) and quality by control (QbC) strategies for low-cost but high-quality drugs. However, a crucial task in modeling (bio)pharmaceutical manufacturing processes is the reliable identification of model candidates from a set of various model hypotheses. To identify the best experimental design suitable for a reliable model selection and system identification is challenging for nonlinear (bio)pharmaceutical process models in general. This paper is the first to exploit differential flatness for model selection problems under uncertainty, and thus translates the model selection problem to advanced concepts of systems theory and controllability aspects, respectively. Here, the optimal controls for improved model selection trajectories are expressed analytically with low computational costs. We further demo... [more]

This paper proposes an improved interval fuzzy modeling (imIFML) technique based on modified linear programming and actual boundary points of data. The imIFML technique comprises four design stages. The first stage is based on conventional interval fuzzy modeling (coIFML) with first-order model and linear programming. The second stage defines reference lower and upper bounds of data using MATLAB. The third stage initially adjusts scaling parameters in the modified linear programming. The last stage automatically fine-tunes parameters in the modified linear programming to realize the best possible model. Lower and upper bounds approximated by the imIFML technique are closely fitted to the reference lower and upper bounds, respectively. The proposed imIFML is thus significantly less conservative in cases of large variation in data, while robustness is inherited from the coIFML. Design flowcharts, equations, and sample MATLAB code are presented for reference in future experiments. Perform... [more]

Liquid−liquid equilibria (LLE) characterization is a task requiring considerable work and appreciable financial resources. Notable savings in time and effort can be achieved when the experimental plans use the methods of the optimal design of experiments that maximize the information obtained. To achieve this goal, a systematic optimization formulation based on Semidefinite Programming is proposed for finding optimal experimental designs for LLE studies carried out at constant pressure and temperature. The non-random two-liquid (NRTL) model is employed to represent species equilibria in both phases. This model, combined with mass balance relationships, provides a means of computing the sensitivities of the measurements to the parameters. To design the experiment, these sensitivities are calculated for a grid of candidate experiments in which initial mixture compositions are varied. The optimal design is found by maximizing criteria based on the Fisher Information Matrix (FIM). Three op... [more]

The large amount of boron-bearing iron tailings in China is a resource for metals that needs to be more completely and efficiently utilized. In this evaluation, the ammonium sulfate roasting process was used to make a controllable phase transformation to facilitate the subsequent extraction of valuable metals from boron-bearing iron tailings. The effects of roasting temperature, roasting time, the molar ratio of ammonium sulfate to tailings, and the particle size on the extraction of elements were investigated. The orthogonal experimental design of experiments was used to determine the optimal processing conditions. XRD (X-Ray Diffractomer), scanning electron microscope (SEM), and simultaneous DSC−TG analyzer were used to assist in elucidating the mechanism of ammonium sulfate roasting. The experimental results showed that nearly all Fe, Al, and Mg were extracted under the following conditions: (1) the molar ratio of ammonium sulfate to iron tailings was 3:1; (2) the roasting temperatu... [more]

This paper proposes a multi-scale parameter identification algorithm for the lithium-ion battery (LIB) electric model by using a combination of particle swarm optimization (PSO) and Levenberg-Marquardt (LM) algorithms. Two-dimensional Poisson equations with unknown parameters are used to describe the potential and current density distribution (PDD) of the positive and negative electrodes in the LIB electric model. The model parameters are difficult to determine in the simulation due to the nonlinear complexity of the model. In the proposed identification algorithm, PSO is used for the coarse-scale parameter identification and the LM algorithm is applied for the fine-scale parameter identification. The experiment results show that the multi-scale identification not only improves the convergence rate and effectively escapes from the stagnation of PSO, but also overcomes the local minimum entrapment drawback of the LM algorithm. The terminal voltage curves from the PDD model with the iden... [more]

Theoretically simulated kinetic data were used to evaluate the performance of the most common isoconversional methods of kinetic analysis in complex-process scenarios with two independent overlapping processes exhibiting nucleation-growth kinetics, and further expand the conclusions for the autocatalytic kinetic processes with positive asymmetry. In close-to-real-life situations all the integral isoconversional methods provided practically indistinguishable E-α outcomes. The Friedman and incremental modified Vyazovkin methods results in significant over- and undershoots. However, the combined utilization of the integral and differential isoconversional methods was demonstrated to greatly contribute to the interpretation of the E-α dependences and estimation of E1 and E2—the conceptual evaluation involving positions of inflection points and plateaus is introduced. The influence of the range of applied heating rates q+ on the course of E-α dependences was studied. In this regard, the per... [more]

In this work, used lube oil was treated using natural acid-free clay. Clay was added at different amounts (5, 10, and 20 g) to 100 mL of waste engine oil at various temperatures (250, 350, 400, and 450 °C) and mixed at a speed of 800 rpm for 30 min. After settling and separation, the treated oil was diluted with kerosene before being examined using a Ultraviolet−visible (UV) spectrophotometer. In order to achieve cost-effective recycling, this process is modeled using the response surface method (RSM). Five regression models (linear, quadratic, Two Factor Interactions (2FI), cubic, and reduced-order quadratic model) were developed, then tested, and examined by calculating the statistical performance indicators (R2, R2adj, Akaike’s Information Criterion corrected (AICc), Bayesian Information Criterion (BIC), and Root Mean Square Error (RMSE)). The results obtained reveal that the modified quadratic model outperforms the rest of the models in terms of the low value of RMSE, the lowest AI... [more]

A high specific speed centrifugal pump is used in the situation of large flow and low head. Centrifugal pump parameters need to be optimized in order to raise its head and efficiency under off-design conditions. In this study, the orthogonal experiment design method is adopted to optimize the performance of centrifugal pump basing on three parameters, namely, blade outlet width b2, blade outlet angle β2 and blade wrap angle φ. First, the three-dimensional model of the centrifugal pump is established by CFturbo and SolidWorks. Then nine different schemes are designed by using orthogonal table, and numerical simulation is carried out in CFX15.0. The final optimized combination of parameters is b2 = 24 mm, β2 = 24°, φ = 112°. Under the design condition, the head and efficiency of the optimized centrifugal pump are appropriately improved, the increments of which are 0.74 m and 0.48%, respectively. However, the efficiency considerably increases at high flow rates, with an increase of 6.9% a... [more]

Nowadays, to ensure sustainability of smart materials, it is imperative to eliminate or reduce carbon footprint related to nano material production. The concept of design of experiment to provide an optimal synthesis process, with a desired yield, is indispensable. It is the researcher’s goal to get optimum value for experiments that requires multiple runs and multiple inputs. Herein, is a reliable approach of utilizing design of experiment (DOE) for response surface methodology (RSM). Thus, to optimize a facile and effective synthesis process for fluorescent carbon dots (CDs) derived from tapioca that is in line with green chemistry principles for sustainable synthesis. The predictions for fluorescent CDs synthesis from RSM were in excellent agreement with the artificial neural network (ANN) model prediction by the Levenberg−Marquardt back propagation (LMBP) algorithm. Considering R2, root mean square error (RMSE) and mean absolute error (MAE) have all revealed a positive hidden layer... [more]

Many widely-used polymers are made via free-radical polymerization. Mathematical models of polymerization reactors have many applications such as reactor design, operation, and intensification. The method of moments has been utilized extensively for many decades to derive rate equations needed to predict polymer bulk properties. In this article, for a comprehensive list consisting of more than 40 different reactions that are most likely to occur in high-temperature free-radical homopolymerization, moment rate equations are derived methodically. Three types of radicals—secondary radicals, tertiary radicals formed through backbiting reactions, and tertiary radicals produced by intermolecular chain transfer to polymer reactions—are accounted for. The former tertiary radicals generate short-chain branches, while the latter ones produce long-chain branches. In addition, two types of dead polymer chains, saturated and unsaturated, are considered. Using a step-by-step approach based on the me... [more]

In this study, we present the details of an optimization method for parameter estimation of one-dimensional groundwater reactive transport problems using a parallel genetic algorithm (PGA). The performance of the PGA was tested with two problems that had published analytical solutions and two problems with published numerical solutions. The optimization model was provided with the published experimental results and reasonable bounds for the unknown kinetic reaction parameters as inputs. Benchmarking results indicate that the PGA estimated parameters that are close to the published parameters and it also predicted the observed trends well for all four problems. Also, OpenMP FORTRAN parallel constructs were used to demonstrate the speedup of the code on an Intel quad-core desktop computer. The parallel code showed a linear speedup with an increasing number of processors. Furthermore, the performance of the underlying optimization algorithm was tested to evaluate its sensitivity to the va... [more]

Process development, especially in regulated industries, where quality-by-design approaches have become a prerequisite, is cost intensive and time consuming. A main factor is the large number of experiments needed. Process modelling can reduce this number significantly by replacing experiments with simulations. However, this requires a validated model. In this paper, a process and model development workflow is presented, which focuses on implementing, parameterizing, and validating the model in four steps. The presented methods are laid out to gain, create, or generate the maximum information and process knowledge needed for successful process development. This includes design of experiments and statistical evaluations showing process robustness, sensitivity of target values to process parameters, and correlations between process and target values. Two case studies are presented. An ion exchange capture step for monoclonal antibodies focusing on high accuracy and low feed consumption;... [more]

In this work, a closed-loop identification method based on a reinforcement learning algorithm is proposed for multiple-input multiple-output (MIMO) systems. This method could be an attractive alternative solution to the problem that the current frequency-domain identification algorithms are usually dependent on the attenuation factor. With this method, after continuously interacting with the environment, the optimal attenuation factor can be identified by the continuous action reinforcement learning automata (CARLA), and then the corresponding parameters could be estimated in the end. Moreover, the proposed method could be applied to time-varying systems online due to its online learning ability. The simulation results suggest that the presented approach can meet the requirement of identification accuracy in both square and non-square systems.

Multi-component polymers can provide many advantages over their homopolymer counterparts. Terpolymers are formed from the combination of three unique monomers, thus creating a new material that will exhibit desirable properties based on all three of the original comonomers. To ensure that all three comonomers are incorporated (and to understand and/or predict the degree of incorporation of each comonomer), accurate reactivity ratios are vital. In this study, five terpolymerization studies from the literature are revisited and the ‘ternary’ reactivity ratios are re-estimated. Some recent studies have shown that binary reactivity ratios (that is, from the related copolymer systems) do not always apply to ternary systems. In other reports, binary reactivity ratios are in good agreement with terpolymer data. This investigation allows for the comparison between previously determined binary reactivity ratios and newly estimated ‘ternary’ reactivity ratios for several systems. In some of the... [more]

In the present study, the effects of operating parameters, namely, rotor speed, feed rate, and inlet air velocity, on the cut diameter of a cage-type separator were studied. The design of experiments (DOE) method was used to investigate the relationship between the operating parameters and the cut size. The experimental results were statistically analyzed using MINITAB 16 software. Both the rotor speed and air inlet velocity had significant main effects on the cut size. The feed rate was also significant but had a weak effect with respect to the rotor speed and inlet air velocity effects. The cut size decreased with an increase in rotor speed and increased with an increase in air inlet velocity. However, the cut size slightly decreased with an increase in feed rate. An empirical multiple-variable linear model for predicting the cut size of the classification was created and presented. The results derived from the statistical analysis were in good agreement with those from the experimen... [more]

The main sensitivity parameters of the Holmquist−Johnson−Cook constitutive model for coal were obtained from a variety of tests such as uniaxial compression, uniaxial cyclic loading, splitting and triaxial compression tests, as well as the indirect derivation equation of a briquette. The mechanical properties of briquettes under dynamic impact were investigated using a split Hopkinson pressure bar experiment. Based on the experimental measurement of the Holmquist−Johnson−Cook constitutive model, the numerical simulation of briquette was performed using ANSYS/LS-DYNA software. A comparison between experimental and simulation results verified the correctness of simulation parameters. This research concluded that the failure of briquette at different impact velocities started from an axial crack in the middle of the coal body, and the sample was swollen to some extent. By the increase of impact velocity, the severity of damage in the coal body was increased, while the size of the coal blo... [more]

A data-driven strategy for the online estimation of important kinetic parameters was assessed for the copolymerization of ethylene with 1,9-decadiene using a metallocene catalyst at different diene concentrations and reaction temperatures. An initial global sensitivity analysis selected the significant kinetic parameters of the system. The retrospective cost model refinement (RCMR) algorithm was adapted and implemented to estimate the significant kinetic parameters of the model in real time. After verifying stability and robustness, experimental data validated the algorithm performance. Results demonstrate the estimated kinetic parameters converge close to theoretical values without requiring prior knowledge of the polymerization model and the original kinetic values.

Structural identifiability is a critical aspect of modelling that has been overlooked in the vast majority of Li-ion battery modelling studies. It considers whether it is possible to obtain a unique solution for the unknown model parameters from experimental data. This is a fundamental prerequisite of the modelling process, especially when the parameters represent physical battery attributes and the proposed model is utilised to estimate them. Numerical estimates for unidentifiable parameters are effectively meaningless since unidentifiable parameters have an infinite number of possible numerical solutions. It is demonstrated that the physical phenomena assignment to a two-RC (resistor⁻capacitor) network equivalent circuit model (ECM) is not possible without additional information. Established methods to ascertain structural identifiability are applied to 12 ECMs covering the majority of model templates used previously. Seven ECMs are shown not to be uniquely identifiable, reducing the... [more]

Biological systems can be described mathematically to model the dynamics of metabolic, protein, or gene-regulatory networks, but locating parameter regimes that induce a particular dynamic behavior can be challenging due to the vast parameter landscape, particularly in large models. In the current work, a Pythonic implementation of existing bifurcation objective functions, which reward systems that achieve a desired bifurcation behavior, is implemented to search for parameter regimes that permit oscillations or bistability. A differential evolution algorithm progressively approximates the specified bifurcation type while performing a global search of parameter space for a candidate with the best fitness. The user-friendly format facilitates integration with systems biology tools, as Python is a ubiquitous programming language. The bifurcation−evolution software is validated on published models from the BioModels Database and used to search populations of randomly-generated mass-action... [more]

The computation and modeling of extents has been proposed to handle the complexity of large-scale model identification tasks. Unfortunately, the existing extent-based framework only applies when certain conditions apply. Most typically, it is required that a unique value for each extent can be computed. This severely limits the applicability of this approach. In this work, we propose a novel procedure for parameter estimation inspired by the existing extent-based framework. A key difference with prior work is that the proposed procedure combines structural observability labeling, matrix factorization, and graph-based system partitioning to split the original model parameter estimation problem into parameter estimation problems with the least number of parameters. The value of the proposed method is demonstrated with an extensive simulation study and a study based on a historical data set collected to characterize the isomerization of α -pinene. Most importantly, the obtained resul... [more]

Synthetic biology design challenges have driven the use of mathematical models to characterize genetic components and to explore complex design spaces. Traditional approaches to characterization have largely ignored the effect of strain and growth conditions on the dynamics of synthetic genetic circuits, and have thus confounded intrinsic features of the circuit components with cell-level context effects. We present a model that distinguishes an activated gene’s intrinsic kinetics from its physiological context. We then demonstrate an optimal experimental design approach to identify dynamic induction experiments for efficient estimation of the component’s intrinsic parameters. Maximally informative experiments are chosen by formulating the design as an optimal control problem; direct multiple-shooting is used to identify the optimum. Our numerical results suggest that the intrinsic parameters of a genetic component can be more accurately estimated using optimal experimental designs, an... [more]

Synthetic biology seeks to design biological parts and circuits that implement new functions in cells. Major accomplishments have been reported in this field, yet predicting a priori the in vivo behaviour of synthetic gene circuits is major a challenge. Mathematical models offer a means to address this bottleneck. However, in biology, modelling is perceived as an expensive, time-consuming task. Indeed, the quality of predictions depends on the accuracy of parameters, which are traditionally inferred from poorly informative data. How much can parameter accuracy be improved by using model-based optimal experimental design (MBOED)? To tackle this question, we considered an inducible promoter in the yeast S. cerevisiae. Using in vivo data, we re-fit a dynamic model for this component and then compared the performance of standard (e.g., step inputs) and optimally designed experiments for parameter inference. We found that MBOED improves the quality of model calibration by ∼60%. Results furt... [more]