Calibration Of Model Parameters Research Articles

Comparison of the Performance of Nonlinear Time-Dependent Constitutive Models Calibrated with Minimal Test Data Applied to an Epoxy Resin

Epoxy resins are extensively employed as adhesives and matrices in fibre-reinforced composites. As polymers, they possess a viscoelastic nature and are prone to creep and stress relaxation even at room temperature. This phenomenon is also responsible for time-dependent failure or creep fracture due to cumulative strain. Several constitutive equations have been used to describe the mechanical time-dependent response of polymers. These models have been proposed over the past six decades, with minimal direct and practical confrontation. Each model is associated with a specific application or research group. This work assesses the predictive performance of four distinct time-dependent constitutive models based on experimental data. The models were deemed sufficiently straightforward to be readily integrated into practical engineering analyses. A range of loading cases, encompassing constant strain rate, creep, and relaxation tests, were conducted on a commercial epoxy resin. Model parameter calibration was conducted with a minimum data set. The extrapolative predictive capacity of the models was evaluated for creep loading by extending the tests to five decades. The selected rheological models comprise two viscoelastic models based on Volterra-type integrals, as originally proposed by Schapery and Rabotnov; one viscoplastic model, as originally proposed by Norton and Bailey; and the Burger model, in which two springs and two dashpots are combined in a serial and parallel configuration. The number of model parameters does not correlate positively to superior performance, even if it is high. Overall, the models exhibited satisfactory predictive performance, displaying similar outcomes with some relevant differences during the unloading phases.

A novel physics-based computational framework to model spacecraft solar array power under degradation: application to European Space Agency (ESA) Cluster mission

Accurate modeling and simulation (M&S) of spacecraft solar array power under degradation is essential for mission planning, remaining useful life assessment, and lifetime extension. A relevant example is ESA’s Cluster spacecraft fleet, launched in 2000 and operated at the European Space Operation Centre (ESOC), whose solar arrays have suffered severe degradation due to space radiation that has caused challenges to routine operations and mission planning. However, currently available physics-based and machine learning models have been proven ineffective in modeling the drastic reduction in power generation over the long operational life of the spacecraft.In response to these limitations, this work introduces a framework to model solar array degradation and predict power generation. It embeds a novel simplified physics-based model and a meta-heuristic optimization algorithm which exploits domain-specific knowledge and monitoring data for robust model parameter calibration and accurate power generation predictions. The results show the effectiveness of the proposed approach in avoiding overfitting and providing an accurate estimate of Cluster solar array power evolution.

Revisiting two-layer energy balance models for climate assessment

Abstract Given the pivotal role of probabilistic approaches with two-layer energy balance models in the latest climate assessment, this study aims to gain deeper insight into their advancement by comparing different approaches for generating constrained posterior ensembles. Several methodological improvements are possible both in the calibration of model parameters to the behavior of comprehensive Earth system models and in constraining the calibrated parameter ensemble with other lines of evidence. The results imply that a conventional single parameter representing evolving climate feedback characteristics is not a requirement for reliable climate projections; rather, there are potential improvements on the forcing side regarding the separation of forcing and feedbacks. Constraining the ensemble based on observational and expert-assessed climate metrics, which critically affects probabilistic climate assessment, needs to appropriately deal with different constraints on a multivariate space in a standardized and flexible way. The method introduced here is an option that fulfills the need.

Rapid stochastic spatial light modulator calibration and pixel crosstalk optimization

Holographic light potentials generated by phase-modulating liquid-crystal spatial light modulators (SLMs) are widely used in quantum technology applications. Accurate calibration of the wavefront and intensity profile of the laser beam at the SLM display is key to the high fidelity of holographic potentials. Here, we present a new calibration technique that is faster than previous methods while maintaining the same level of accuracy. By employing stochastic optimization and random speckle intensity patterns, we calibrate a digital twin that accurately models the experimental setup. This approach allows us to measure the wavefront at the SLM to within λ/170 in ~ 5 minutes using only 10 SLM phase patterns, a significant speedup over state-of-the-art techniques. Additionally, our digital twin models pixel crosstalk on the liquid-crystal SLM, enabling rapid calibration of model parameters and reducing the error in light potentials by a factor of ~ 5 without losing efficiency. Our fast calibration technique will simplify the implementation of high-fidelity light potentials in, for example, quantum-gas microscopes and neutral-atom tweezer arrays where high-NA objectives and thermal lensing can deform the wavefront significantly. Applications in the field of holographic displays that require high image fidelity will benefit from the novel pixel crosstalk calibration, especially for displays with a large field of view and increased SLM diffraction angles.

Probabilistic Calibration of Model Parameters with Approximate Bayesian Quadrature and Active Machine Learning

Probabilistic Calibration of Model Parameters with Approximate Bayesian Quadrature and Active Machine Learning

Discrete element model construction and dehulling simulation verification based on harvested quinoa grains.

The dry dehulling process of quinoa grains faces challenges such as poor visibility and unclear dynamic response characteristics, leading to irrational settings of the shelling process and high losses of the final processed product. Simulation methods provide an effective solution to this issue, with the accuracy of the simulation model being crucial. In this study, using the Experts in Discrete Element Modeling (EDEM) simulation software, based on the biological characteristics and mechanical properties of the grains, a method was proposed to construct a discrete-element simulation model for the double-layer bonding of the quinoa grain using the three-axis spatial coordinates method. The Plackett-Burman method, the steepest rise method and the Box-Behnken method were used to simulate the compression test. The bonding parameters of the quinoa grain were calibrated. The parameters were further validated by constructing a mechanical shear test. Finally, the process of the dehulling quinoa grain was simulated in a dry dehulling equipment. The results showed that the relative error between the simulated and actual maximum compression force of the quinoa grains was 0.32%. The breaking shear force in the simulation had a relative error of no more than 5% compared to the actual measurements. In the simulation, the dehulling rate and broken rice rate were 78.54% and 1.38%, respectively, which exceeded the bench test values (75.32% for dehulling rate and 1.24% for broken rice rate) by 3.22% and 0.14%, respectively. The error was within the acceptable range. The calibration of the discrete element model parameters for quinoa grains was accurate, reflecting the mechanical properties differences between the rice and the pericarp effectively, providing a reliable basis for optimizing the design of dry dehulling mechanisms.

Improving the Calibration of Low-Cost Sensors Using Data Assimilation.

In the context of smart agriculture, accurate soil moisture monitoring is crucial to optimise irrigation, improve water usage efficiency and increase crop yields. Although low-cost capacitive sensors are used to make monitoring affordable, these sensors face accuracy challenges that often result in inefficient irrigation practices. This paper presents a method for calibrating capacitive soil moisture sensors through data assimilation. The method was validated using data collected from a farm in Dos Hermanas, Seville, Spain, which utilises a drip irrigation system. The proposed solution integrates the Hydrus 1D model with particle filter (PF) and the Iterative Ensemble Smoother (IES) to continuously update and refine the model and sensor calibration parameters. The methodology includes the implementation of physical constraints, ensuring that the updated parameters remain within physically plausible ranges. Soil moisture was measured using low-cost SoilWatch 10 capacitive sensors and ThetaProbe ML3 high-precision sensors as a reference. Furthermore, a comparison was carried out between the PF and IES methods. The results demonstrate that the data assimilation approach markedly enhances the precision of sensor readings, aligning them closely with reference measurements and model simulations. The PF method demonstrated superior performance, achieving an 84.8% improvement in accuracy compared to the raw sensor readings. This substantial improvement was measured against high-precision reference sensors, confirming the effectiveness of the PF method in calibrating low-cost capacitive sensors. In contrast, the IES method showed a 68% improvement in accuracy, which, while still considerable, was outperformed by the PF. By effectively mitigating observation noise and sensor biases, this approach proves robust and practical for large-scale implementations in precision agriculture.

Calibration and experiments of discrete element flexible model parameters for kiwifruit stalk

A method combining experimental and simulation optimization was used to calibrate parameters to enhance the accuracy of discrete element model parameters during kiwifruit stem separation. First, physical experiments were conducted to determine the intrinsic and contact parameters of kiwifruit stalk. Second, the mechanical parameters of the kiwifruit stalks were determined using three-point bending and shear tests. On this basis, simulation tests were conducted on kiwifruit stalks by combining the Hertz-Mindlin model with a bonding model, and the optimal combination of bonding parameters was confirmed using the bending strength and maximum shear force. Finally, a discrete element model of the kiwifruit was built with the determined bonding parameters and simulated, and the reliability of the model was verified through mechanical tests. The results showed that the density was 867.5 kg/m3, Poisson's ratio was 0.26, the modulus of elasticity was 3.25 × 108 Pa, the recovery coefficient between the fruit stalks and steel parts was 0.365, and the average values of the static and dynamic friction coefficients between the kiwifruit stalks and steel parts were 0.268 and 0.152, respectively. The kiwifruit stem bonding parameters were normal stiffness per unit area kn=7.201×1011 N/m3, shear stiffness per unit area kt=2.379×1011 N/m3, critical normal stress σmax=5.937×108 Pa, critical shear stress tmax = 2.354×109 Pa, and bonded disc radius Rj=0.164 mm. Compared with the results of the mechanical tests, the relative errors of the bending strength and maximum shear of the discrete element model were 2.13% and 2.84%, respectively. The results showed that the discrete element model improves the simulation of the bending and shearing processes of kiwifruit stalks and is capable of characterizing the physical properties of kiwifruit stalks. The results of this study provide a theoretical foundation for the optimal design of end effectors.

Bayesian parameter calibration of a one-dimensional hemodynamic model

In this work, we couple a Bayesian optimization approach with a one-dimensional blood-flow model (known as ADAN86) to achieve a flexible and efficient strategy for the calibration of model parameters when in-vivo patient-specific data is available. The optimization step is addressed in the frequency domain, minimizing the discrepancies between the first harmonics of the in-vivo and predicted flow/pressure signals. The model parameters can be locally or globally perturbed, modifying the reference values in the same proportion for the whole system (global) or by region to account for the specificities of each location (local).To test the proposed strategy, two cases are considered. The first one involves parameter calibration in a synthetic patient, where some parameters are locally modified, and the optimization process is compared in local and global scenarios. The second case addresses parameter optimization in a patient with in-vivo flow/pressure data, comparing the local and global calibration approaches.The results show that the coupling between the Bayesian optimization process and the ADAN86 models yields an efficient strategy for the parameter calibration problem, which is naturally parallelizable and promising for data assimilation in computational hemodynamics.

Variational Neural Network Embedded with Digital Twins for Probabilistic Structural Damage Quantification

Quantifying structural damage using online monitoring data is crucial for condition-based maintenance to ensure aviation safety. However, most data-driven methods hardly use accumulated domain knowledge, making it difficult to address parameter variability across different structures due to manufacturing as well as compromising result interpretability. To address these challenges, this study proposes a physics-decoded variational neural network for structural damage quantification and model parameter calibration. The innovation of this method lies in seamlessly integrating a reduced-order digital twin containing damage states and influencing parameters as a decoder within the variational neural network and training a data-driven physical feature extraction model using the variational inference. This architecture enables the individualized, real-time structural damage quantification and parameter calibration across an entire fleet, while accounting for uncertainties. Validation on typical damaged aeronautical panels demonstrates that the proposed method accurately predicts structural damage states and quantifies associated uncertainties, thereby ensuring high interpretability and accuracy. This approach is expected to be integrated into the airframe digital twin framework to enable condition-based maintenance across a fleet.

Utilizing realistic loading histories for the calibration of nonlinear components in seismic analysis

Hysteretic models that simulate the hysteretic response of key structural components are generally employed in the nonlinear seismic analysis of structures. The calibration of hysteretic model parameters is crucial for achieving accurate analysis results in structural seismic assessment. The calibration process is commonly conducted by tuning hysteretic model parameters to align with the experimental results of a single component tested under standardized reverse-cyclic loading protocols. The underlying assumption of such a calibration method is that a structural model at the system level, using a well-tuned hysteretic model capable of accurately replicating the test results of a single component under a standardized incremental cyclic loading protocol, can predict the dynamic response of the structural system subjected to ground motion excitations with an acceptable level of accuracy. However, due to the simplified and often unrealistic loading protocols used for model calibrations, this assumption has been challenged recently by both numerical and experimental studies. In this paper, calibration methods utilizing more realistic loading histories are evaluated and compared to more conventional incremental cyclic loading-based protocols. The evaluation of calibration methods is carried out by quantifying the calibration relevance, utilizing a framework of virtual experiments that incorporates uncertainties in hysteretic model parameters. Analyses are conducted based on a case study of BRB components and BRBFs. Additionally, four calibration error quantification methods, considering characteristics in the transitional and plastic ranges of hysteresis curves of BRB, are proposed and compared. The results demonstrate that it is in fact advantageous to use realistic loading histories in component calibration of BRBs. An improved formulation of the calibration error is also proposed for the optimization of hysteretic parameters.

Kalibrasi Parameter Model Tangki Berbasis Metaheuristik untuk Transformasi Seri Data Hujan Menjadi Limpasan Periode Harian

The fundamental weakness of the Tank model are the large number of parameters and their continuous values, which make it ineffective for solving practical problems. This article proposes a metaheuristic-based automatic calibration method to enhance the Tank model’s performance and applicability in transforming rainfall data series into runoff in a watershed. The metaheuristic methods involved include the Differential Evolution (DE) algorithm, Particle Swam Optimization (PSO), synthesis of chaotic search-opposition based learning-differential evolution-quantum mechanism (CODEQ) algorithm and Shuffled Complex Evolution (SCE). The models resulting from the integration of the Tank model with these metaheuristic methods are called the Tank-DE, Tank-PSO, Tank-CODEQ and Tank-SCE models. The four models were tested in the Welang Watershed (473.39 Km2), located in Pasuruan Regency, East Java, using a 15-year hydroclimatology dataset from 2006 to 2020. The 2006-2010 dataset served as the training dataset forTank model parameter calibration, while the 2011-2020 dataset was used for model validation. Calibration results show that all models achieved an accuracy level equivalent to an average RMSE of 0.05 m3/s. However, during validation, there were slight differences in high flow response results. Compared to the training dataset, the model output responded effectively to both low and high flows but tended to produce slightly higher discharge at intermediate flows, with an average difference of 1.33 m3/s. When compared to the test dataset, the model outputs tended to overestimate high flow rates (average difference of 1.63 m3/s) and underestimated low flow rates, with minor deviations.Keywords: tank model, metaheuristic, transformation, rainfall-streamflow, Welang Watershed.

Tillage Depth Detection and Control Based on Attitude Estimation and Online Calibration of Model Parameters

Aiming at solving the problems of inaccurate tillage depth detection and unstable tillage depth control, this study proposes a tillage depth detection and control method based on attitude estimation and online calibration of model parameters. First, a tillage depth detection model based on the attitude measurement of the plow is established. The attitude estimation method is designed to measure the horizontal attitude of the plow. An adaptive Kalman filter is utilized to perform an online calibration of the model parameters between the rotation angle of the lifting arm and the pitch angle of the plow. The dynamic and accurate detection of tillage depth is achieved using the tillage depth detection model. Second, a tillage depth control device using an STM32 microcontroller is developed in this study. The PID controller controls the tractor’s suspension system to adjust the plow through the solenoid valve, thus achieving stable control of the tillage depth. Finally, the experimental results obtained from simulation and field tests show that the tillage depth can be stably controlled within the set target interval during the tractor plowing operation, proving the effectiveness and feasibility of the proposed tillage depth detection and control method.

Validation of four resistivity mixing models on field time lapse geoelectrical measurements from fine-grained soil undergoing freeze-thaw cycles

Resistivity mixing models relate porosity, phase composition and specific resistivities of ground materials to their bulk (effective) electrical properties. These models were typically derived for calculating hydrocarbon saturation from geophysical logs. In permafrost monitoring applications, they have been used to link ground electrical response to its phase composition, with focus on unfrozen water vs. ice content, and to derive changes in ground ice content from repeated resistivity acquisitions. Such quantitative interpretations rely on validity of the mixing models in a context different from the one they were derived in. To increase the reliability of the permafrost forecasts that are based on repeated resistivity surveys, we undertook validation of four selected resistivity mixing model formulations: i) the original Archie's law, ii) the Archie's law with an ice-content dependent cementation exponent m (Archie-M), iii) a modification of the Archie's law for multiple conducting phases (Archie-N), and iv) the geometric mean model (GM). The model application context was permafrost monitoring and fate forecasting on natural fine-grained soil undergoing cycles of freezing and thawing, based on indirect (geophysical), in-situ time-lapse resistivity measurements. The purpose of the calibrated resistivity models was to derive the phase composition of the ground from in-situ resistivity measurements, with acceptable quantitative reliability, notably with respect to the amount and changes of ice and water content. In our validation framework, daily temperature-dependent soil phase distribution was converted into an effective resistivity distribution of the ground using each of the four resistivity mixing models. From the effective resistivity model, an apparent resistivity response was forward calculated and compared to time-lapse field apparent resistivity measurements from a permafrost monitoring field site. The performance metrics were i) the root mean square error between the forward-calculated and field-measured apparent resistivities throughout the freeze-thaw season, ii) the percentage of field apparent resistivity data explained by each resistivity model, and iii) the plausibility of the calibrated model parameter estimates. We found that despite different current conducting mechanisms involved in each of the resistivity mixing model formulations, the quantitative performance of the four evaluated models was very similar. The four models typically reproduced the field-measured resistivity variations within one to two standard deviations (STD) of the field measurements, depending on the time of the year and depth in the soil profile. In the active layer, the Archie-M model most consistently reproduced the field data within 1 STD throughout the freezing and frozen periods of the year (September – May). Meanwhile, the GM best matched the actual values of resistivities during freezing. The GM also recovered porosities of the three model layers close to the true values measured on borehole samples. All the tested models were challenged by accurately simulating the thawing period – overestimating resistivities in the temperature range from −5 °C to −2 °C and underestimating them between −2 °C and thawing point. Consequently, the choice between the models should depend on the specifics of a particular application, such as available calibration data, desired parameters or ground properties to resolve, sensitivity of the modeling framework etc. An application-specific validation of several resistivity mixing models and quantification of performance of the chosen resistivity model may be called for. Additionally, the possibility of using different mixing model and water content parameterizations should be investigated, to adequately address complex ground resistivity structures and phase change processes typical of permafrost ground.

Understanding Climate Change by Modeling the Earth's Atmosphere as a Well‐Stirred Tank

AbstractComing to terms with climate change by understanding climate processes and their policy implications is essential not only for climate scientists and policymakers, but also for the general public, for industrial practitioners, and for engineers, including process system engineers. We have developed a simplified linear climate model (SLCM) to enable non‐specialists to explore the essential physical and chemical processes caused by greenhouse gas emissions. Trading‐off simplicity and accuracy, achieved by calibrating model parameters using established simple climate models, the SLCM allows (i) determining the climate impact of given past and future emissions, (ii) determining the amounts of CO2 removal needed to compensate for any unavoidable emissions of CH4 and N2O from agriculture, and (iii) back‐calculating emission pathways to meet specified global warming targets.

Combining Biology-based and MRI Data-driven Modeling to Predict Response to Neoadjuvant Chemotherapy in Patients with Triple-Negative Breast Cancer.

Purpose To combine deep learning and biology-based modeling to predict the response of locally advanced, triple-negative breast cancer before initiating neoadjuvant chemotherapy (NAC). Materials and Methods In this retrospective study, a biology-based mathematical model of tumor response to NAC was constructed and calibrated on a patient-specific basis using imaging data from patients enrolled in the MD Anderson A Robust TNBC Evaluation FraMework to Improve Survival trial (ARTEMIS; ClinicalTrials.gov registration no. NCT02276443) between April 2018 and May 2021. To relate the calibrated parameters in the biology-based model and pretreatment MRI data, a convolutional neural network (CNN) was employed. The CNN predictions of the calibrated model parameters were used to estimate tumor response at the end of NAC. CNN performance in the estimations of total tumor volume (TTV), total tumor cellularity (TTC), and tumor status was evaluated. Model-predicted TTC and TTV measurements were compared with MRI-based measurements using the concordance correlation coefficient and area under the receiver operating characteristic curve (for predicting pathologic complete response at the end of NAC). Results The study included 118 female patients (median age, 51 years [range, 29-78 years]). For comparison of CNN predicted to measured change in TTC and TTV over the course of NAC, the concordance correlation coefficient values were 0.95 (95% CI: 0.90, 0.98) and 0.94 (95% CI: 0.87, 0.97), respectively. CNN-predicted TTC and TTV had an area under the receiver operating characteristic curve of 0.72 (95% CI: 0.34, 0.94) and 0.72 (95% CI: 0.40, 0.95) for predicting tumor status at the time of surgery, respectively. Conclusion Deep learning integrated with a biology-based mathematical model showed good performance in predicting the spatial and temporal evolution of a patient's tumor during NAC using only pre-NAC MRI data. Keywords: Triple-Negative Breast Cancer, Neoadjuvant Chemotherapy, Convolutional Neural Network, Biology-based Mathematical Model Supplemental material is available for this article. Clinical trial registration no. NCT02276443 ©RSNA, 2024 See also commentary by Mei and Huang in this issue.

Comparison of synergy extrapolation and static optimization for estimating multiple unmeasured muscle activations during walking

BackgroundCalibrated electromyography (EMG)-driven musculoskeletal models can provide insight into internal quantities (e.g., muscle forces) that are difficult or impossible to measure experimentally. However, the need for EMG data from all involved muscles presents a significant barrier to the widespread application of EMG-driven modeling methods. Synergy extrapolation (SynX) is a computational method that can estimate a single missing EMG signal with reasonable accuracy during the EMG-driven model calibration process, yet its performance in estimating a larger number of missing EMG signals remains unknown.MethodsThis study assessed the accuracy with which SynX can use eight measured EMG signals to estimate muscle activations and forces associated with eight missing EMG signals in the same leg during walking while simultaneously performing EMG-driven model calibration. Experimental gait data collected from two individuals post-stroke, including 16 channels of EMG data per leg, were used to calibrate an EMG-driven musculoskeletal model, providing “gold standard” muscle activations and forces for evaluation purposes. SynX was then used to predict the muscle activations and forces associated with the eight missing EMG signals while simultaneously calibrating EMG-driven model parameter values. Due to its widespread use, static optimization (SO) applied to a scaled generic musculoskeletal model was also utilized to estimate the same muscle activations and forces. Estimation accuracy for SynX and SO was evaluated using root mean square errors (RMSE) to quantify amplitude errors and correlation coefficient r values to quantify shape similarity, each calculated with respect to “gold standard” muscle activations and forces.ResultsOn average, compared to SO, SynX with simultaneous model calibration produced significantly more accurate amplitude and shape estimates for unmeasured muscle activations (RMSE 0.08 vs. 0.15, r value 0.55 vs. 0.12) and forces (RMSE 101.3 N vs. 174.4 N, r value 0.53 vs. 0.07). SynX yielded calibrated Hill-type muscle–tendon model parameter values for all muscles and activation dynamics model parameter values for measured muscles that were similar to “gold standard” calibrated model parameter values.ConclusionsThese findings suggest that SynX could make it possible to calibrate EMG-driven musculoskeletal models for all important lower-extremity muscles with as few as eight carefully chosen EMG signals and eventually contribute to the design of personalized rehabilitation and surgical interventions for mobility impairments.

Assessment of the Choked Flow Model of RELAP5 for Application of Inverse Quantification Methods

In the framework of deterministic safety analysis, best estimate plus uncertainty methodologies can provide a more informative detailed analysis of transients than conservative approaches. However, one important step in the application of such methodologies is derivation of uncertainty of the physical models. Probability density functions of the physical model parameters are obtained by applying inverse uncertainty quantification (IUQ) methods to experimental data. The present work deals with evaluation of the experimental database and assessment of the simulation model, which are required steps prior to the application of IUQ methods. The U.S. Nuclear Regulatory Commission system code RELAP5 has been applied for simulation of three experimental databases on choked/critical flow: Sozzi-Sutherland, Super MobyDick, and Marviken Critical Flow Tests. First, the adequacy of the experimental data to the specific target domain is carried out, to then proceed to calibration of the input model parameters by combining the use of Gaussian Process metamodels and optimization schemes. The assessment of the simulation models is performed by evaluating independently accuracy, precision, and consistency through four statistical indicators, including a novel indicator to evaluate the consistency of the results. The final results indicate that the model is capable of reproducing the selected experimental database and overall average accuracy, precision, and consistency below the 10% threshold and can be used for application of IUQ methods.

Maximizing similarity: Using correlation coefficients to calibrate kinetic parameters in population balance models

Crystallization plays a crucial role as a separation and purification technique, particularly in the chemical and pharmaceutical industries. By adjusting process parameters, the productivity, product quality, and efficiency of downstream processes can be improved. In complex processes, model-based design becomes invaluable. Population Balance Models (PBMs) have successfully aided the chemical industry in achieving more effective production processes for decades. These models can utilize various input data sources to identify the dominant mechanisms and calibrate model parameters. While inline particle monitoring tools serve as excellent qualitative descriptors, challenges arise from experimentation and data interpretation, hindering their direct application in the kinetic parameter estimation of PBMs. In this study, we present a novel approach that utilizes information from inline particle monitoring tools for the kinetic parameter estimation of PBMs, bypassing the associated obstacles. Our pioneering approach relies on offline product size data and the correlation-based utilization of inline particle monitoring information. The paper compares this novel strategy with two parameter estimation techniques: the classical method using solute concentration and product size data and a somewhat naïve approach, which assumes that the inline particle monitoring data can directly be compared with the simulations. The prediction capabilities are evaluated through two in-silico case studies. The results indicate that the precision and predictive capability of the correlation-based technique are comparable to the classical approach, both for noisy data and for a system undergoing significant agglomeration and deagglomeration. The use of Pearson's correlation coefficient yields the best results in the novel cases. These findings in in-silico datasets provide a foundation and motivation for the practical application of this idea, unleashing the so-far hidden model development potential of such measurements.

Advancing SWAT Model Calibration: A U-NSGA-III-Based Framework for Multi-Objective Optimization

In recent years, remote sensing data have revealed considerable potential in unraveling crucial information regarding water balance dynamics due to their unique spatiotemporal distribution characteristics, thereby advancing multi-objective optimization algorithms in hydrological model parameter calibration. However, existing optimization frameworks based on the Soil and Water Assessment Tool (SWAT) primarily focus on single-objective or multiple-objective (i.e., two or three objective functions), lacking an open, efficient, and flexible framework to integrate many-objective (i.e., four or more objective functions) optimization algorithms to satisfy the growing demands of complex hydrological systems. This study addresses this gap by designing and implementing a multi-objective optimization framework, Py-SWAT-U-NSGA-III, which integrates the Unified Non-dominated Sorting Genetic Algorithm III (U-NSGA-III). Built on the SWAT model, this framework supports a broad range of optimization problems, from single- to many-objective. Developed within a Python environment, the SWAT model modules are integrated with the Pymoo library to construct a U-NSGA-III algorithm-based optimization framework. This framework accommodates various calibration schemes, including multi-site, multi-variable, and multi-objective functions. Additionally, it incorporates sensitivity analysis and post-processing modules to shed insights into model behavior and evaluate optimization results. The framework supports multi-core parallel processing to enhance efficiency. The framework was tested in the Meijiang River Basin in southern China, using daily streamflow data and Penman–Monteith–Leuning Version 2 (PML-V2(China)) remote sensing evapotranspiration (ET) data for sensitivity analysis and parallel efficiency evaluation. Three case studies demonstrated its effectiveness in optimizing complex hydrological models, with multi-core processing achieving a speedup of up to 8.95 despite I/O bottlenecks. Py-SWAT-U-NSGA-III provides an open, efficient, and flexible tool for the hydrological community that strives to facilitate the application and advancement of multi-objective optimization in hydrological modeling.