Model Calibration Research Articles

A Reformulation of the Laminar Kinetic Energy Model to Enable Multi-mode Transition Predictions

AbstractThe paper describes the development of a novel transition/turbulence model based on the laminar kinetic energy concept. The model is intended as a base framework for data-driven improvements. Starting from a previously developed framework, mainly aimed at separated-flow transition predictions, suitable terms for model generalization are identified and reformulated for handling different transition modes, namely bypass and separated-flow modes. The ideology for the definition of new terms has its roots in mixing phenomenological and correlation-based arguments, ensuring generality and flexibility and allowing a variety of lines of action for improving model components via machine-learning approaches. The model calibration, carried out with reference to flat plate test cases subjected to different pressure gradients and freestream turbulence levels, is discussed in detail. Although the constructed model is calibrated on a group of classic flat plat cases, the validation campaign, mostly carried out on gas turbine cascades, demonstrates its ability to predict transitional flows with engineering accuracy. Finally, while the model is not specifically developed for natural transition predictions, satisfactory predictions are obtained in scenarios with low freestream turbulence for flat plate and airfoil flows.

Addressing challenges associated with training sample sizes for effective calibration of NWP precipitation forecasts

Abstract Effective calibration of precipitation forecasts produced by numerical weather prediction (NWP) models faces challenges associated with the training sample size. Newly-operationalized NWP models may only accumulate a small number of forecasts and thus may limit robust parameter inference in forecast calibration. It is necessary to investigate how the performance of forecast calibration changes with the amount of training data, to determine an effective training sample size. In this study, we thoroughly investigate the impacts of training sample size on precipitation forecast calibration based on the Seasonally Coherent Calibration (SCC) model across Australia. Overall, the performance of the model tends to stabilize in most parts of Australia when raw forecasts of 10 months or longer are used for parameter inference. Whether the training dataset cover wet months substantially affects forecast calibration. The findings of this study are critical for understanding the impacts of training sample size on forecast calibration, and will provide implications for future forecast calibration and the generation of hindcasts.

Harnessing spectrophotometry resolution power for determining ternary mixture for respiratory disorders treatment in their pharmaceutical formulation.

A ternary mixture incorporating Hydroxyzine hydrochloride (HYX), Ephedrine hydrochloride (EPH) and Theophylline (THP) frequently prescribed for the treatment of respiratory diseases. Herein, two spectrophotometric methods are designated and applied to resolve these three components in their mixture. Method A is ratio-subtraction combined with derivative spectrophotometry, where THP can be determined directly at its λmax 271 nm (neither HYX or EPH interfere), then for determination of HYX and EPH, the ternary mixture was divided by 22 μg/mL of THP and after subtraction of the plateau region, HYX can be determined directly at its λmax 234.2 nm (absence of EPH intervention). Finally, the third derivative (3D) spectrophotometric approach was utilized to estimate EPH by detecting the peak amplitude at 222 nm with Δλ = 4 and a scaling factor 100. Principal Component Regression (PCR) and Partial Least Squares (PLS), two multivariate calibration approaches, were applied effectively in Method B. This method effectively quantified the mixture under investigation by using the absorption spectra obtained from suitable solutions of the three components in the 210-230 nm region. The calibration models were evaluated using cross-validation with PCR and PLS, producing statistical characteristics that demonstrate the effectiveness of the calibration models. Synthetic and pharmaceutical preparations were also used to conduct external validation. In pharmaceutical formulation, these methods were successfully applied to analyze HYX, EPH, and THP without overlap from formulation's excipients. Moreover, the study's findings were statistically contrasted with those of earlier reported HPLC method. Appraisal approaches were used to determine whether the new spectrophotometric methods had an adverse environmental impact involving the Green Analytical Procedure Index (GAPI) and the AGREE (Analytical Greenness). These evaluations delivered information about the methods' eco-friendliness and sustainability, proving that they are in line with ecologically attributed practices. Furthermore, the Blue Applicability Grade Index (BAGI) was utilized to identify and verify the feasibility and practicality of the suggested approaches.

Evaluating NIRS for predicting faecal fibre, protein fractions and digestibility in dairy sheep and goats fed alfalfa hay and concentrate

This study evaluated the effectiveness of near-infrared spectroscopy (NIRS) in predicting faecal fibre, protein fractions and total tract apparent digestibility in dairy sheep and goats fed varying ratios of alfalfa-hay and concentrate. A total of 180 faecal samples from dairy sheep and goats were collected and chemically analysed. Faecal samples underwent also NIRS spectral acquisition and calibration models were obtained through modified partial least square regression and tested for robustness. The NIRS provided excellent estimations for N and CP as % as is (R 2 ExV 0.91 and 0.91, RPD 3.16 and 3.33, respectively), good estimation for N, CP and ND soluble CP % DM (R 2 ExV 0.90, 0.90 and 0.85, RPD 3.14, 2.90 and 2.48) and ND soluble CP expressed as % as is (R 2 ExV 0.87, RPD 2.55), approximative quantitative prediction for acid detergent insoluble crude protein (ADICP) and ADIN % acid detergent fibre (ADF) (R 2 ExV 0.79 and 0.71, RPD 1.93 and 1.78, respectively) and ADICP as % as is (R 2 ExV 0.67, RPD 1.70) but resulted to be less effective when predicting all the other components. The prediction models for total-tract digestibility (ttD) of ADICP performed best among the developed equations (R 2 ExV 0.57, RPD 1.38), but the model was not sufficient for precise predictions, suggesting a good capacity of NIRS to predict faecal N excretion but also intrinsic limitations of faecal spectra due to the partial residual nutrients content, compared to the diet. Increasing the number of calibration samples and values, the forage species, and the F:C ratios in the diet offered to the animals could improve the NIRS performance.

UroARC: A novel surgical risk calculator for older adults undergoing pelvic organ prolapse and stress urinary incontinence surgery.

Surgeries for pelvic organ prolapse (POP) and stress urinary incontinence (SUI) are commonly performed in older adults, many of whom are also frail. A surgical risk calculator for older adults undergoing POP/SUI surgeries that incorporates frailty, a factor known to increase the risk of surgical complications, would be helpful for preoperative counseling but currently does not exist. Medicare Carrier, Outpatient, and MedPAR files were examined for beneficiaries undergoing POP and SUI surgery between 2014 and 2016. A total of 15 POP/SUI categories were examined. The Claims-Based Frailty Index (CFI), a validated measure of frailty in Medicare data, and Charlson Comorbidity Index were deconstructed into their individual variables, and individual variables were entered into stepwise logistic regression models to determine which variables were most highly predictive of 30-day complications and 1-year mortality. To verify the prognostic accuracy for each model for surgical complications of interest, calibration curves and tests of model fit, including C-statistic, Brier scores, and Spiegelhalter p values, were determined. In total, 108 479 beneficiaries were included. Among these, 4.7% had CFI scores consistent with mild to severe frailty (CFI≥0.25). A total of 13 prognostic variable categories were found to be most highly predictive of postoperative complications. Calibration curves for each outcome of interest showed models were well-fit. Most models demonstrated high c-statistic values (≥0.7) and high Spiegelhalter p values (≥0.9), indicating good model calibration and excellent discrimination, and low Brier scores (<0.02), indicating high model accuracy. Urologic surgery for older Adults Risk Calculator serves as a novel surgical risk calculator that is readily accessible to both patients and clinicians that specifically factors in components of frailty. Furthermore, this calculator accounts for the heterogeneity of an aging population and can assist in individualized surgical decision-making for these common procedures.

Improving Effectiveness by Reducing Overconfidence in Large Catalogue Sequential Recommendation with gBCE loss

A large catalogue size is one of the central challenges in training recommendation models: a large number of items makes them memory and computationally inefficient to compute scores for all items during training, forcing these models to deploy negative sampling. However, negative sampling increases the proportion of positive interactions in the training data, and therefore, models trained with negative sampling tend to overestimate the probabilities of positive interactions – a phenomenon we call overconfidence . While the absolute values of the predicted scores/probabilities are not important for the ranking of retrieved recommendations, overconfident models may fail to estimate nuanced differences in the top-ranked items, resulting in degraded performance. In this paper, we show that overconfidence explains why the popular SASRec model underperforms when compared to BERT4Rec. This is contrary to the BERT4Rec authors’ explanation that the difference in performance is due to the bi-directional attention mechanism. To mitigate overconfidence, we propose a novel Generalised Binary Cross-Entropy Loss function (gBCE) and theoretically prove that it can mitigate overconfidence. We further propose the gSASRec model, an improvement over SASRec that deploys an increased number of negatives and the gBCE loss. Through detailed experiments on three datasets, we show that gSASRec does not exhibit the overconfidence problem. As a result, gSASRec can outperform BERT4Rec (e.g. +9.47% NDCG on the MovieLens-1M dataset), while requiring less training time (e.g. -73% training time on MovieLens-1M). Moreover, in contrast to BERT4Rec, gSASRec is suitable for large datasets that contain more than 1 million items. Finally, we show how addressing overconfidence can improve model calibration – the ability of a model to predict actual interaction probabilities accurately. By applying gBCE to the SASRec model on MovieLens-1M dataset, we reduce the models’ expected calibration error by 98.9% (from 0.966 to 0.01).

NIR Spectroscopy for the Online Monitoring of Water and Olive Oil Content in Pomace during the Extraction Process

The main challenge of this scientific work was the implementation on an industrial olive oil extraction plant of an NIR device for the multispectral analysis of pomace to predict the percentage of humidity and oil contained in it. Subsequent to the implementation of the NIR device on the oil extraction line on the solid’s outlet from the decanter, NIRS interaction measurements in the 761–1081 nm region were used to probe the pomace. NIRS calibration models for the prediction of water and oil content in the pomace were obtained and successfully tested and validated. The correlations of calibration results for oil and water content were 0.700 and 0.829, while the correlations of validation were 0.773 and 0.676, respectively. Low values of root mean square error were found for both the prediction and validation set. The results highlight the good robustness of an NIR approach based on a PLS calibration model to monitor the industrial olive oil process. The results obtained are a first step toward the large-scale implementation of NIR devices for monitoring pomace in oil mills. The possibility of knowing the oil lost in the pomace, moment by moment, would open a new frontier towards system control and the sustainability of the olive oil extraction process.

Applicability domain of a calibration model based on neural networks and infrared spectroscopy

Artificial neural networks are used as calibration models in routine analytical determinations that involve spectroscopic data. To ensure that the model will generate reliable predictions for new samples, the applicability domain must be well defined. This article describes a strategy for establishing the limits of the applicability domain when the calibration model is a feed-forward neural network. The applicability domain was defined by two limits: 1) the 0.99 quantile of the squared Mahalanobis distance calculated from the network activations of the training set and 2) the 0.99 quantile of the reconstruction error of the training spectra using either an autoencoder network or a decoder network. A new sample with a squared Mahalanobis distance and/or spectral residuals beyond these limits is said to be outside the applicability domain, and the prediction is questionable. The approach was illustrated by predicting the density of diesel fuel samples from mid-infrared spectra and the fat content in meat from near-infrared spectra. The methodology could correctly detect anomalous spectra in prediction using either the autoencoder or the decoder.

Multi-Criteria Calibration of a Thermo-Mechanical Model of Steel Plate Welding in Vacuum

This paper proposes a procedurefor multi-criteria calibration of a thermo-mechanical model for numerical simulation of welding in the space vacuum. A finite-element model of a steel plate is created. Experimental and computational data are obtained. An inverse problem is formulated for the vector identification of five calibration parameters from the heat-flow model. They are evaluated for adequacy with controlled accuracy according to four criteria. An optimization problem is solved using a two-step interactive procedure. The parameter space studying method (PSI) has been applied to the study of multidimensional regions by means of quasi-uniform sounding. A Pareto-optimal set is defined. It is used to determine reduced ranked Pareto subsets by μ-selection. Salukvadze optimum is also determined.

Real-time monitoring of integrated continuous granulation/drying line system “LaVortex®” for the pharmaceutical manufacturing of acetaminophen oral dosage formulations using near-infrared spectroscopy

Granules for tableting were continuously manufactured using a fully flow-type continuous wet-granulation and drying (CGD) line system, “LaVortex®.” The raw material powder containing standard excipients and 28.8 % acetaminophen was mixed with a binder liquid (pure water), continuously wet-granulated, and dried for 600 s under 20 different granulation/drying process conditions, and the process was monitored in real-time using near-infrared (NIR) spectroscopy. Twenty granulation/drying process conditions, varying across three parameters, namely added binding water rate, agitation blades and container rotational rates, and hot drying air flow rate, were applied. Training datasets from NIR spectroscopy stably measured during the CGD process were used to construct calibration models to predict the various critical quality attributes (CQAs) of granules, such as residual moisture content, median particle size, angle of repose, and tablet hardness, using partial least squares regression (PLSR). Optimal calibration models were validated using the NIR spectroscopy test dataset. The actual granule CQA profiles evaluated using the NIR/PLSR method were almost constant up to 600 s at the end of production depending on the critical process parameters (CPPs), except for fluctuations in the initial process. These results indicate that tableting granules with various pharmaceutical properties could be obtained continuously depending on CQAs, such as the rate of water addition. Additionally, changes in CQAs could be continuously monitored by the NIR/PLSR method. Furthermore, CGD granules with various characteristic CQAs can be continuously manufactured by controlling CPPs, such as agitation blades and tube rotation rates in the agitating granulation process and drying air flow rate in the drying process under NIR spectroscopy.

Performance Assessment of Wood-Based Composite Materials Subjected to High Temperatures

This paper is based on research placed within the broader framework of the growing environmental impact requirements of building materials. Given this context, wood-based composite materials have emerged as a promising and innovative solution for structural elements. The current work aims to define a system for testing the mechanical behavior of glued laminated timber elements when exposed to high temperatures, in the neighborhood of the pyrolytic decomposition of materials. These tests monitor the transient behavior of the composite material and characterize the parameters involved in the thermo-mechanical analysis of elements constructed using this type of engineered wood product. The tests are used for the calibration of the material models involved in the numerical analysis and for the analysis of potential prototypes, considering the transient thermal load and heat propagation through the materials. By taking such tests, benchmark models and laboratory procedures are defined that can be used in the future to evaluate different materials, existing or new, and material combinations used to construct such a composite.

Model predictive control with self-learning capability for automated demand response in buildings

This paper presents an optimal management strategy, called Building Optimizer, based on a Model Predictive Control (MPC) approach with self-learning capabilities for buildings. The proposed MPC is a key enabler of cooperative demand response strategies at community level, ensuring the allocation of an optimal demand profile at each participating member of the community according to an optimal consumption reference defined by a complementary agent at community level. In this way, the proposed solution can contribute to provide demand response services exploiting the unlocked residential flexibility. The MPC calculates the optimal setpoints of the HVAC system’s terminal units, considering the expected usage of the buildings and the outdoor conditions, and exploiting the building’s thermal inertia. The models embedded in the MPC are grey-box models representing a thermal zone of the building. An adaptive MPC is proposed to mitigate the high uncertainty present in building management due to the time-variant characteristics of the building and the uncertain internal heat gains due to occupancy and other disturbances. For that, the reduced models incorporate self-learning capabilities implemented as Moving Horizon Estimators that perform a continuous calibration based on real-time measurements. This solution allows full automation for model calibration and management of the terminal units. This paper presents a case study to assess the thermal comfort assurance and power flexibility provision potential of the proposed solution. First, the Building Optimizer is compared to a regular benchmark consisting of an on–off controller, evaluating the performance of each controller for indoor temperature tracking. For the assessment of the flexibility provision, a baseline MPC with fixed model parameters obtained by an offline calibration is used for comparison to the Building Optimizer with self-learning capabilities. Different flexibility scenarios are simulated, considering different restrictions regarding thermal comfort and various flexibility request signals. Notably, the Building Optimizer outperforms the baseline MPC in all scenarios, particularly guaranteeing thermal comfort. Incorporating self-learning capabilities enhances controller performance by mitigating the effect of uncertainty, allowing the Building Optimizer to shift up to 13.08% of peak periods into valley periods, and tracking a flexibility request scenario of 10% with no discomfort.

Soil sampling design matters - Enhancing the efficiency of digital soil mapping at the field scale

Optimisation of sampling design (methods chosen to select the samples) and sample size (number of samples) remains a key challenge in digital soil mapping, especially in the area of precision farming with the expected economic benefits from the introduction of new technologies. As the existing information is available in the form of relevant environmental covariates, its combination with non-parametric machine learning techniques requires careful planning from the initial field sampling to the final production of digital soil maps. The aim of this study is to compare widely used covariate-wise sampling designs combined with variable sample sizes for supervised prediction of common soil drivers of agricultural productivity (pH, soil organic carbon, soil macronutrients) in a real case study of a field (35 ha) with heterogeneous soil properties. From a total of 200 samples, we evaluated different sample sets where 10, 30 and 60 field samples were selected by conditioned Latin Hypercube Sampling (cLHS) and Feature Space Coverage Sampling (FSCS) to calibrate random forest (RF) models. The evaluation was performed on independently in-situ sampled test points. In addition to these datasets, we also compared the investigated methods with Simple Random Sampling (SRS) in a numerical benchmark experiment with increasing sample size, comparing the global accuracies of the predicted maps on the test points, but using interpolated maps as the artificial true population for each soil characteristic. The results of the study in both the field experiment and the numerical experiment showed slightly better results for the FSCS method, especially when the number of samples was small. At smaller training sample sizes, the risk of insufficiently accurate prediction models was slightly lower for FSCS and the difference decreased as the sample size increased. Nevertheless, sample size proved to be the most important factor in the accuracy of RF models, regardless of the sampling technique. The results suggest that a sample size between 18 and 30 training samples (0.6 to 1 sample ha−1) seems plausible for covariate-wise predictions using RF at field scale in our case study. The relative importance of each auxiliary variable for each RF calibration was also assessed for the field experiment. The results showed that the additional introduction of spatial proxies overshadowed the importance of other covariates, but only significantly improved the model calibration at larger sample sizes. The calibrated models without spatial proxies showed the strongest effect of remotely sensed surface characteristics.

Longitudinal dispersivity estimation according to heat and mass groundwater transport model calibration for Baikalsk paper and mill site

The paper presents the results of the numerical three-dimensional model of groundwater heat and mass transfer in the territory of Baikalsk paper and mill site calibration based on the materials of groundwater composition and properties twenty-year monitoring, which showed that the longitudinal dispersion at heat transfer is an order of magnitude greater than at mass transfer.

A Prospective Study on Risk Prediction of Preeclampsia Using Bi-Platform Calibration and Machine Learning.

Preeclampsia is a pregnancy syndrome characterized by complex symptoms which cause maternal and fetal problems and deaths. The aim of this study is to achieve preeclampsia risk prediction and early risk prediction in Xinjiang, China, based on the placental growth factor measured using the SiMoA or Elecsys platform. A novel reliable calibration modeling method and missing data imputing method are proposed, in which different strategies are used to adapt to small samples, training data, test data, independent features, and dependent feature pairs. Multiple machine learning algorithms were applied to train models using various datasets, such as single-platform versus bi-platform data, early pregnancy versus early plus non-early pregnancy data, and real versus real plus augmented data. It was found that a combination of two types of mono-platform data could improve risk prediction performance, and non-early pregnancy data could enhance early risk prediction performance when limited early pregnancy data were available. Additionally, the inclusion of augmented data resulted in achieving a high but unstable performance. The models in this study significantly reduced the incidence of preeclampsia in the region from 7.2% to 2.0%, and the mortality rate was reduced to 0%.

Regionalized multiple-point statistical simulation for calibrating process-based geologic models to seismic data

Calibrating process-based geologic models to seismic data is critical and has been challenging for decades. The traditional approach to data calibration involves tuning the model input parameters by trial-and-error or through an automated inverse procedure. This can improve the model calibration to data but can hardly reach a fully satisfactory result. We adopt a multiple-point statistics (MPS) approach where a process-based geologic model is used as a training image for statistical pattern recognition. First, we define a rock-physics model from the process-based geologic model and derive its seismic attributes through seismic forward modeling. Then, we use the process-based model and its seismic attributes as coupled training images for geologic pattern recognition and regeneration under seismic data constraints. The method differs from the conventional MPS method in several ways: (1) the training image is a process-based geologic model of the reservoir of interest, thus defined on the same grid of the reservoir model; (2) the training image is generally nonstationary but there is no need to partition the nonstationary training image into pseudostationary ones; (3) the geologic facies and seismic constraint are related through seismic forward modeling instead of statistical inference, thus there is no need to convert seismic data to facies proportion or probability; (4) multiple-point statistics are based on Bayes’ law and Gaussian kernel approximation of conditional probability instead of a somehow arbitrary probability combination scheme or a heuristic rule; and (5) the method does not involve an iterative optimization procedure. Therefore, it also differs from the neural-network-based machine-learning approach, where the data conditioning is achieved through an iterative optimization procedure. These differences make our method advantageous for calibrating process-based geologic models. The two examples with synthetic data illustrate the effectiveness of the method. The first one is derived from a satellite image of a river delta, and the second one from the Stanford VI reservoir model.

A Survey of Data-Driven Construction Materials Price Forecasting

The construction industry is heavily influenced by the volatility of material prices, which can significantly impact project costs and budgeting accuracy. Traditional econometric methods have been challenged by their inability to capture the frequent fluctuations in construction material prices. This paper reviews the application of data-driven techniques, particularly machine learning, in forecasting construction material prices. The models are categorized into causal modeling and time-series analysis, and characteristics, adaptability, and insights derived from large datasets are discussed. Causal models, such as multiple linear regression (MLR), artificial neural networks (ANN), and the least square support vector machine (LSSVM), generally utilize economic indicators to predict prices. The commonly used economic indicators include but are not limited to the consumer price index (CPI), producer price index (PPI), and gross domestic product (GDP). On the other hand, time-series models rely on historical price data to identify patterns for future forecasting, and their main advantage is demanding minimal data inputs for model calibration. Other techniques are also explored, such as Monte Carlo simulation, for both price forecasting and uncertainty quantification. The paper recommends hybrid models, which combine various forecasting techniques and deep learning-advanced time-series analysis and have the potential to offer more accurate and reliable price predictions with appropriate modeling processes, enabling better decision-making and cost management in construction projects.

Validation of the prognostic index for spine metastasis (PRISM) for stratifying survival in patients treated with spinal stereotactic body radiation

PurposeThe Prognostic Index for Spinal Metastasis (PRISM) is a scoring system derived from prospective data from a single institution that stratifies patients undergoing spine stereotactic radiosurgery (SSRS) for spinal metastases into subgroups by overall (OS). We sought to further demonstrate its generalizability by performing validation with a large dataset from a second high-volume institution, Mayo Clinic. Methods and materialsEight hundred seventy-nine patients—424 from Mayo Clinic and 455 from MD Anderson Cancer Center (MDACC)—who received SSRS between 2007 and 2019 were identified. Patients were stratified by PRISM criteria, and overall survival (OS) for the PRISM groups for each cohort was compared using Kaplan-Meier estimations and univariate Cox proportional analyses. Model calibration and concordance indices (C-indices) were calculated for each cohort to assess the quality of the scoring system. ResultsPatient and tumor characteristics varied significantly between both cohorts including histology, sex, performance status, and number of organs involved (all P < 0.001). Median OS was 30.3 and 22.1 months for the Mayo and MDACC cohorts, respectively. Kaplan-Meier survival curves revealed robust separation between prognostic groups within both cohorts. The Mayo cohort showed median OS of 57.1, 37.0, 23.7, and 8.8 months for Groups 1, 2, 3, and 4, respectively. Univariate analysis revealed hazard ratios of 3.0 (95 % confidence interval [CI], 1.9–4.9), 5.2 (95 % CI, 3.2–8.3), and 12.9 (95 % CI, 7.8–21.4) for groups 2, 3 and 4, respectively all P < 0.001). The C-indices were 0.69 and 0.66 for the unstratified and stratified scores for the Mayo cohort, and 0.70 and 0.68 for the MDACC cohort, respectively. ConclusionThese data demonstrate robust validation of the PRISM score to stratify OS in patients treated with SSRS by a large external cohort, despite substantial differences among the cohorts. Overall, the PRISM scoring may help guide optimal treatment selection for patients with spine metastases.

Precision Calibration in Wire-Arc-Directed Energy Deposition Simulations Using a Machine-Learning-Based Multi-Fidelity Model

Thermal simulation is essential in wire-arc-directed energy deposition (W-DED) to accurately estimate temperature distributions, impacting residual stress and distortion in components. Proper calibration of simulation models minimizes inaccuracies caused by varying material properties, machine settings, and environmental conditions. The lack of standardized calibration methods further complicates thermal predictions. This paper introduces a novel calibration method integrating both machine learning, as the high-fidelity (HF) model, and response surface modeling, as the low-fidelity (LF) model, within a multi-fidelity (MF) framework. The approach utilizes Bayesian optimization to effectively explore the search space for optimal solutions. A two-tiered model employs the LF model to identify feasible regions, followed by the HF model to refine calibration parameters, such as thermal efficiency (η), convection coefficient (h), and emissivity (ε), which are difficult to determine experimentally. A three-factor Box–Behnken design (BBD) is applied to explore the design space, requiring only thirteen parameter configurations, conserving resources and enabling robust model training. The efficacy of this MF model is demonstrated in multi-layer W-DED calibration, showing strong alignment between experimental and simulated temperatures, with a mean absolute error (MAE) of 7.47 °C. This method offers a replicable framework for broader additive manufacturing processes.

Pupil-centric imaging model for zoom camera calibration.

Zoom camera calibration has always been challenging, as arbitrary zoom/focus settings change the camera parameters. Current calibration methods are based on the pinhole imaging model, which results in coupled calibration parameters due to the lack of geometric/physical constraints. In this Letter, we present a novel, to the best of our knowledge, pupil-centric imaging model that accounts for the camera's radial, decentering, and mustache distortions at various zoom settings using exit pupil offsets and a non-frontal lens-sensor model. Therefore, we provide a reasonable physical explanation for the different distortion effects. Global optimization is performed based on the proposed initial camera calibration and bundle adjustment under several zoom and autofocus setting combinations. Experiments using three representative zoom cameras demonstrate the effectiveness of the proposed method. Its relative measurement accuracy is better than that of current state-of-the-art methods.