Nonlinear Calibration Research Articles

Inertial Measurement Unit Self-Calibration by Quantization-Aware and Memory-Parsimonious Neural Networks

This paper introduces a methodology to compensate inertial Micro-Electro-Mechanical System (IMU-MEMS) time-varying calibration loss, induced by stress and aging. The approach relies on a periodic assessment of the sensor through specific stimuli, producing outputs which are compared with the response of a high-precision sensor, used as ground truth. At any re-calibration iteration, differences with respect to the ground truth are approximated by quantization-aware trained tiny neural networks, allowing calibration-loss compensations. Due to the unavailability of aging IMU-MEMS datasets, a synthetic dataset has been produced, taking into account aging effects with both linear and nonlinear calibration loss. Also, field-collected data in conditions of thermal stress have been used. A model relying on Dense and 1D Convolution layers was devised and compensated for an average of 1.97 g and a variance of 1.07 g2, with only 903 represented with 16 bit parameters. The proposed model can be executed on an intelligent signal processing inertial sensor in 126.4 ms. This work represents a step forward toward in-sensor machine learning computing through integrating the computing capabilities into the sensor package that hosts the accelerometer and gyroscope sensing elements.

Direct Current to Digital Converter (DIDC): A Current Sensor.

This paper introduces a systematic approach to the design of Direct Current-to-Digital Converter (DIDC) specifically engineered to overcome the limitations of traditional current measurement methodologies in System-on-Chip (SoC) designs. The proposed DIDC addresses critical challenges such as high power consumption, large area requirements, and the need for intermediate analog signals. By incorporating a current mirror in a cascode topology and managing the current across multiple binary-sized branches with the Successive Approximation Register (SAR) logic, the design achieves precise current measurement. A simple comparator, coupled with an isolation circuit, ensures accurate and reliable sensing. Fabricated using the TSMC 180 nm process, the DIDC achieves 8-bit precision without the need for nonlinearity calibration, showcasing remarkable energy efficiency with an energy per conversion of 1.52 pJ, power consumption of 117 µW, and a compact area of 0.016 mm². This innovative approach not only reduces power consumption and area, but also provides a scalable and efficient solution for next-generation semiconductor technologies. The ability to conduct online measurements during both standard operations and in-field conditions significantly enhances the performance and reliability of SoCs, making this DIDC a promising advancement in the field.

Nonlinear light-output calibration of the oxygenated xylene scintillators used in OMEGA neutron time-of-flight spectrometers.

Neutron time-of-flight (nTOF) spectrometers are essential instruments for measuring and evaluating the performance of inertial confinement fusion implosions. The neutron spectrometers utilized for the OMEGA laser include two liquid-based scintillators, each consisting of a large volume filled with xylene that is coupled to four photomultiplier tubes. Analysis of the signal from these detectors requires detailed knowledge of the scintillator's light output, which is needed to fit the nTOF spectrum, from which the neutron energy spectrum is informed. The light output is nonlinearly proportional to the neutron energy, which, in turn, affects the interpretation of the neutron energy spectrum from a TOF signal. A recent campaign on OMEGA was performed to calibrate the xylene detectors and infer the shape of the light-output curve. The campaign utilized materials with increasing Z placed in the OMEGA target chamber to initiate scattering events with the 14MeV fusion neutrons. This process leads to the production of backscatter neutrons of varying energies that appear as peaks in the nTOF data. Simulations using a neutron transport code were combined with the measured deuterium-tritium neutron yields to calculate the expected backscattered neutron yields from the well-known scattering cross sections of each material. The neutron-energy dependent light output of the scintillator inferred from the experiment is compared to the light-output curve simulated with a neutron transport code for the following neutron energies: 1.5, 2.5, 6, and 14MeV.

Numerical failure modelling of natural fibre composite coupons using X-ray computed tomography based modelling

Natural fibre composites offer versatile applications across industries while being superior in sustainability aspects compared to other composite types. To unlock their full potential, it is essential to understand their complex failure involving fibre failure, matrix cracking, and debonding at the fibre-matrix interface. Efforts to address these challenges focus on advanced numerical models, probing behaviour from micro to macro scales. However, these models face complexities in handling intricate failure modes given the non-uniform nature of natural fibres. To overcome these challenges, image-based modelling using X-ray computed tomography scans is proposed. This work’s novelty lies in integrating detailed microstructure information with a nonlinear calibration procedure to accurately model damage and failure in natural fiber composites. It marks a significant step toward developing a virtual testing model, paving the way for assessing composites with varying fiber content or fiber types.

Estimation of within-gap regeneration height growth in managed temperate deciduous forests using bi-temporal airborne laser scanning data

Key messageMulti-temporal airborne laser scanning (ALS) data were used to estimate regeneration stem height growth within gaps in uneven-aged deciduous forests. The height and height growth measured in the field were used to calibrate and validate ALS estimates. This method provided highly precise estimates of height and unbiased height increment estimates of regeneration at stem level.ContextAssessing regeneration height growth is essential for evaluating forest dynamics and optimizing silvicultural operations. However, regeneration description at high spatiotemporal resolution has remained limited to restricted areas by the limiting cost constraints of field measurements. Highly precise airborne laser scanning (ALS) data are currently acquired over wide areas. Such datasets are promising for characterizing regeneration dynamics.AimsWe aimed to estimate height and height growth within regenerating areas at the stem level using multi-temporal ALS data.MethodsALS data were acquired from 56,150 ha of uneven-aged deciduous forest in Belgium in 2014 and 2021. Stem tops were detected using local maxima (LM) within regenerating areas in both ALS datasets and matched. Field data were collected in 2021 and used to calibrate the ALS-estimated heights using linear and non-linear models at stem level. Height growth estimation was then validated using field-measured increments.ResultsWithout height calibration, the 2021 ALS-estimated height had a − 1.06 m bias and 1.39 m root-mean-squared error (RMSE). Likewise, the 2014 ALS-estimated height had a − 0.58 m bias and 1.14 m RMSE. The non-linear calibration seemed more appropriate for small regeneration stems (height < 4 m). Using height calibration, the 2021 ALS-estimated height had a − 0.01 m bias and 0.84 m RMSE. In 2014, the bias and RMSE were 0.02 and 0.91 m, respectively. ALS-estimated height growth was unbiased and had an RMSE of 0.10 m·year−1.ConclusionsThis original method is based on the bi-temporal ALS datasets calibrated by limited field measurements. The proposed method is the first to provide unbiased regeneration height growth of regeneration stems in uneven-aged forests and new perspectives for studying and managing forest regeneration.

A Combined Sensor Design Applied to Large-Scale Measurement Systems.

The photoelectric sensing unit in a large-space measurement system primarily determines the measurement accuracy of the system. Aiming to resolve the problem whereby existing sensing units have difficulty accurately measuring the hidden points and free-form surfaces in large components, in this study, we designed a multi-node fusion of a combined sensor. Firstly, a multi-node fusion hidden-point measurement model and a solution model are established, and the measurement results converge after the number of nodes is simulated to be nine. Secondly, an adaptive front-end photoelectric conditioning circuit, including signal amplification, filtering, and adjustable level is designed, and the accuracy of the circuit function is verified. Then, a nonlinear least-squares calibration method is proposed by combining the constraints of the multi-position vector cones, and the internal parameters of the probe, in relation to the various detection nodes, are calibrated. Finally, a distributed system and laser tracking system are introduced to establish a fusion experimental validation platform, and the results show that the standard deviation and accuracy of the three-axis measurement of the test point of the combined sensor in the measurement area of 7000 mm × 7000 mm × 3000 mm are better than 0.026 mm and 0.24 mm, respectively, and the accuracy of the length measurement is within 0.28 mm. Further, the measurement accuracy of the hidden point of the aircraft hood and the free-form surface is better than 0.26 mm, which can meet most of the industrial measurement needs and expand the application field of large-space measurement systems.

JWST-FEAST: Feedback in Emerging extrAgalactic Star clusTers: Calibration of Star Formation Rates in the Mid-infrared with NGC 628

New JWST near-infrared imaging of the nearby galaxy NGC 628 from the JWST Cycle 1 program Feedback in Emerging extrAgalactic Star clusTers (JWST-FEAST) is combined with archival JWST mid-infrared imaging to calibrate the 21 μm emission as a star formation rate (SFR) indicator at ∼120 pc scales. The Paα (1.8756 μm) hydrogen recombination emission line targeted by FEAST provides a reference SFR indicator that is relatively insensitive to dust attenuation, as demonstrated by combining this tracer with Hubble Space Telescope Hα imaging. Our analysis is restricted to regions that appear compact in nebular line emission and are sufficiently bright to mitigate effects of both age and stochastic sampling of the stellar initial mass function. We find that the 21 μm emission closely correlates with the nebular line emission, with a power law with exponent = 1.07 ± 0.01, in agreement with past results. We calibrate a hybrid SFR indicator using a combination of Hα and 24 μm (extrapolated from 21 μm) tracers and derive the proportionality constant between the two tracers, b = 0.095 ± 0.007, which is ∼3–5 times larger than previous derivations using large regions/entire galaxies. We model these discrepancies as an increasing contribution to the dust heating by progressively older stellar populations for increasing spatial scale, in agreement with earlier findings that star formation is hierarchically distributed in galaxies. Thus, the use of hybrid SFR indicators requires prior knowledge of the mean age of the stellar populations dominating the dust heating, which makes their application uncertain. Conversely, nonlinear calibrations of SFRs from L(24) alone are more robust, with a factor ≲ 2.5 variation across the entire range of L(24) luminosities from H ii regions to galaxies.

Quantification of nisin concentration from fluorescence-based antimicrobial activity assay using Bayesian calibration.

Bacteriocins are ribosomally synthesized peptides with the innate ability to kill or inhibit growth of other bacteria. In recent years, bacteriocins have received increased interest, as their antimicrobial activity enhances food safety and shelf life by combatting pathogens such as Listeria monocytogenes. They also have application potential as an active pharmaceutical compound to combat multidrug-resistant pathogens. As new bacteriocins continue to be discovered, accelerated workflows for screening, identification, and process development have been developed. However, antimicrobial activity measurement is often still limited with regards to quantification and throughput. Here, we present the use of a non-linear calibration model to infer nisin concentrations in cultivation supernatants of Lactococcus lactis ssp. lactis B1629 using readouts of pHluorin2 fluorescence-based antimicrobial activity assays.

Calib-RT: an open source python package for peptide retention time calibration in DIA mass spectrometry data.

The data independent acquisition (DIA) mass spectrometry (MS) method is increasingly popular in the field of proteomics. But the loss of the correspondence between peptide ions and their spectra in DIA makes the identification challenging. One effective approach to reduce false positive identification is to calculate the deviation between the peptide's estimated retention time (RT) and measured RT. During this process, scaling the spectral library RT into the estimated RT, known as the RT calibration, is a prerequisite for calculating the deviation. Currently, within the DIA algorithm ecosystem, there is a lack of engine-independent and readily usable RT calibration toolkits. In this work, we introduce Calib-RT, a RT calibration method tailored to the characteristics of RT data. This method can achieve the nonlinear calibration across various data scales and tolerate a certain level of noise interference. Calib-RT is expected to enrich the open source DIA algorithm toolchain and assist in the development of DIA identification algorithms. Calib-RT is released as an open source software under the MIT license and can be installed from PyPi as a python module. The source code is available on GitHub at https://github.com/chenghui03/Calib_RT.

Designing optimal sensor arrays: leveraging hard modeling for improved performance.

In a sensor array system with the ability to design multiple sensor elements, selecting the optimal sensor elements can maximize the efficiency of the sensor array in responding to various analytes. This paper proposes the application of hard chemical modeling as a means to identify the optimal subset of indicator displacement assay (IDA)-based sensors in the array, aiming to achieve maximum performance for detection or quantification. The model governing all reactions in the IDA sensor and the model of the pure spectrum of active species are first determined. Next, by applying the model of the pure spectrum of active species (including the indicator and indicator-receptor complex) to each sensor element and taking into account the system's nonlinearity, corrected concentration profiles of active species are derived using the generalized classical least square (G-CLS) method. These corrected concentration profiles are utilized as the output signal for each sensor element. Finally, the dynamic ranges (DR) of each sensor element and subsequently the DR for all possible sensor arrays are determined.To assess the effectiveness of the sensor array through dynamic range analysis, an IDA-based sensor system comprising five different elements was designed. It was observed that sensors with a larger dynamic range, when arranged together in an array, are more efficient for the quantitative identification of analytes. However, simply increasing the number of elements in the sensor array may not necessarily enhance its effectiveness; instead, it could amplify the noise within the system. Additionally, multivariate fitting regression with Gaussian function (MFRG), a nonlinear calibration method, was applied to assess the prediction ability of all possible designed sensor arrays.

Nonlinear optimization of optical camera multiparameter via triple integrated Gradient-based optimizer algorithm

Metaheuristic techniques are widely used to solve various complex real-world problems. Camera calibration is a critical task in machine vision, which aims to determine the optical camera parameters through 2D image features and corresponding 3D spatial features. To overcome the limitations of traditional methods, such as weak local optima avoidance and low calibration accuracy, a triple integrated Gradient-based optimizer (TIGBO_CC) is proposed for nonlinear optimization of optical camera parameters. Several improvements are made to the original Gradient-based optimizer (GBO). First, in the exploration phase, a fitness-distance balance is adopted to select the most contributing candidate to guide the update of the solution. Second, a random search technique is adopted in the exploitation phase. The switching between the original mode and the additional mode follows the probability. Finally, a neighborhood local search is also introduced. Small-step fine search is performed near the optimal solution to improve the quality of the final solution. TIGBO_CC is evaluated on 12 classical functions, the CEC2020 test suite, and the CEC2022 test suite. The experiments include sensitivity analysis, effectiveness analysis, scalability analysis, function value, convergence curve, box plot, Friedman test, Wilcoxon test, etc. Furthermore, a nonlinear camera calibration model is established. Taking the mean reprojection error as the objective function, TIGBO_CC solves the optimal optical camera parameters by minimizing this function. In different scenarios, the calibration method based on TIGBO_CC has high precision and strong reproducibility. Comprehensive analysis shows that TIGBO_CC has excellent optimization ability and practicality.

Global phase accuracy enhancement of structured light system calibration and 3D reconstruction by overcoming inevitable unsatisfactory intensity modulation

Mainstream fringe projection profilometry (FPP) faces challenges in measuring low signal-to-noise ratio intensity modulation areas, especially in shadow areas on objects and black areas on calibration plates, causing pseudo phases and obvious nonlinear calibration errors in 3D measurement. To address these issues concurrently, we proposed a cyclic phase-shifts difference (CPSD) module based on phase-shifting gratings. CPSD uses double-layer circulation difference to retain the pixels with higher light intensity eliminating the influence of ambient light and finally creates a mask removing and correcting black and shadow areas. Without further post-processing and projection operation, we achieved the global phase accuracy enhancement and obtained high-precision 3D point clouds without pseudo points. The method’s efficacy was proven through experiments on three kinds of calibration planes, achieving a significant reduction in mean absolute error (MAE) and standard deviation (STD) in plane reconstruction (up to 50.9% and 56.1% respectively). We believe that CPSD has enormous potential for wide application across various FPP-related fields. (Code and data are avaliable at: https://github.com/LiYiMingM/CPSD_shadow_and_black_area_phase_correction_in_SL3D)

Comparative study of linear and nonlinear calibration algorithm for extrapolation ability of near infrared spectroscopy quantitative analysis

The determination of the o-nitrotoluene (o-MNT) content in separation process of mononitrotoluene (MNT) is of interest, since it affects the purity of m-nitrotoluene (m-MNT) and p-nitrotoluene (p-MNT). In real-world applications, the calibration model inevitably requires dealing with complex extrapolation problems. Therefore, this study extracted the spectral features of the o-nitrotoluene based on the interval selection algorithm. The linear calibration method (partial least squares (PLS)) and nonlinear calibration methods (support vector machine (SVM), back propagation (BP), random forest (RF), extreme learning machine (ELM)) were used to build the calibration models based on o-nitrotoluene samples in different concentration ranges, and the prediction accuracy and robustness of the calibration model were compared. The results indicate that the effectiveness of different calibration methods is different when going from prediction accuracy to robustness. The prediction accuracy and robustness of RF models are not satisfactory. BP models, which are capable of producing very accurate results in terms of prediction accuracy, are not able to solve extrapolation problems. PLS model has more advantages in model prediction accuracy. ELM has shown the best behavior in terms of robustness of model, but is inferior to PLS in terms of prediction accuracy.

Non-dispersive infrared SF6 sensor with temperature compensation using ISSA_BP neural network

Sulfur hexafluoride (SF6) is a widely used gas in the power industry, and its concentration monitoring is of great importance in power systems. In this study, a non-dispersive infrared (NDIR) gas sensor was developed for monitoring SF6 with a response time (t90) of 3–4 s. A dual-channel structure was designed to minimize the influence of other factors such as light sources. However, the sensor’s output signal is susceptible to temperature drift and non-linear characteristics. To address these challenges, a new compensation algorithm of improved sparrow search algorithm based on the backpropagation neural network (ISSA_BP) is presented to improve the temperature dependence and to correct the nonlinear errors of the sensors. The ISSA_BP algorithm extracts features from sensor-collected signals and predicts the concentration of SF6 gas by the BP neural network. The levy flight strategy and sine-cosine factor are employed within the sparrow search algorithm (SSA) to improve the efficiency and accuracy of the method. The experimental results show that the proposed model outperforms the state-of-the-art approaches, achieving an average relative error of 0.02 within the range of −10°C to 45°C and gas concentrations from 0 ppm to 5000 ppm, which is 3% lower than the industry standard. Compared with traditional approaches, the measurement accuracy is improved approximately by 0.02–0.03, confirming that the proposed algorithm has a high reference value for temperature compensation and nonlinear calibration, which is applicable in the production of infrared sensors for industrial settings.

Application of bi-directional long short-term memory in separating NO and SO2 ultraviolet differential absorption spectrum signals

To safeguard the environment, it is crucial to monitor the emissions of nitrogen oxide (NO) and sulfur dioxide (SO2), harmful pollutants generated during fossil fuel combustion in industries. However, accurately measuring ultra-low concentrations of SO2 and NO remains a challenge. In this study, we developed an optical measurement system based on ultraviolet differential optical absorption spectroscopy (UV-DOAS) to address this issue. The 200–230 nm cross-sensitivity band was chosen for SO2 and NO. Experimental data with a mixed gas concentration range of 1–25 ppm for SO2 and NO was utilized. We proposed a fast algorithm based on Bi-directional Long Short-Term Memory (Bi-LSTM) to extract the differential optical density, overcoming the mutual interference between SO2 and NO. A nonlinear calibration model was employed to invert the separated differential absorption spectra and determine the gas concentrations. The results demonstrated a detection limit (DL) of 0.27 ppm and a full-scale error of 3.15 % for SO2, while for NO, the DL was 0.32 ppm and the full-scale error was 2.81 %. The uncertainties in SO2 and NO detection were calculated as 1.73 % and 1.96 %, respectively.

Design and evaluation of a novel dual-channel complementary potentiometer for rotation measurement

The main objective of this work is to develop a novel Dual-Channel Complementary (DCC) potentiometer to enhance the measurement accuracy of the conventional rotational potentiometer. Its principle is utilizing the complementary characteristic of the signals, which exist a specific phase offset, from different channels to reduce the effect of their inherent nonlinearity on measurement accuracy, and increase the measurement accuracy. A data-driven multi-channel information fusion method has been proposed to fuse the signals of the Dual-Channel Complementary (DCC) potentiometer, which could achieve data fusion and sensor nonlinearity calibration in one go. Prototype has been developed to evaluate the efficiency of the proposed DCC principle and information fusion method. Experimental results reveal that compared to the conventional rotational potentiometer, the RMS value of the measurement error of the DCC potentiometer could achieve a reduction of about 99.5%. The overall measurement performance of the DCC potentiometer could be significantly enhanced.

Performance of the IMPACT and CRASH prognostic models for traumatic brain injury in a contemporary multicenter cohort: a TRACK-TBI study.

The International Mission on Prognosis and Analysis of Clinical Trials in Traumatic Brain Injury (IMPACT) and Corticosteroid Randomization After Significant Head Injury (CRASH) prognostic models for mortality and outcome after traumatic brain injury (TBI) were developed using data from 1984 to 2004. This study examined IMPACT and CRASH model performances in a contemporary cohort of US patients. The prospective 18-center Transforming Research and Clinical Knowledge in Traumatic Brain Injury (TRACK-TBI) study (enrollment years 2014-2018) enrolled subjects aged ≥ 17 years who presented to level I trauma centers and received head CT within 24 hours of TBI. Data were extracted from the subjects who met the model criteria (for IMPACT, Glasgow Coma Scale [GCS] score 3-12 with 6-month Glasgow Outcome Scale-Extended [GOSE] data [n = 441]; for CRASH, GCS score 3-14 with 2-week mortality data and 6-month GOSE data [n = 831]). Analyses were conducted in the overall cohort and stratified on the basis of TBI severity (severe/moderate/mild TBI defined as GCS score 3-8/9-12/13-14), age (17-64 years or ≥ 65 years), and the 5 top enrolling sites. Unfavorable outcome was defined as GOSE score 1-4. Original IMPACT and CRASH model coefficients were applied, and model performances were assessed by calibration (intercept [< 0 indicated overprediction; > 0 indicated underprediction] and slope) and discrimination (c-statistic). Overall, the IMPACT models overpredicted mortality (intercept -0.79 [95% CI -1.05 to -0.53], slope 1.37 [1.05-1.69]) and acceptably predicted unfavorable outcome (intercept 0.07 [-0.14 to 0.29], slope 1.19 [0.96-1.42]), with good discrimination (c-statistics 0.84 and 0.83, respectively). The CRASH models overpredicted mortality (intercept -1.06 [-1.36 to -0.75], slope 0.96 [0.79-1.14]) and unfavorable outcome (intercept -0.60 [-0.78 to -0.41], slope 1.20 [1.03-1.37]), with good discrimination (c-statistics 0.92 and 0.88, respectively). IMPACT overpredicted mortality and acceptably predicted unfavorable outcome in the severe and moderate TBI subgroups, with good discrimination (c-statistic ≥ 0.81). CRASH overpredicted mortality in the severe and moderate TBI subgroups and acceptably predicted mortality in the mild TBI subgroup, with good discrimination (c-statistic ≥ 0.86); unfavorable outcome was overpredicted in the severe and mild TBI subgroups with adequate discrimination (c-statistic ≥ 0.78), whereas calibration was nonlinear in the moderate TBI subgroup. In subjects ≥ 65 years of age, the models performed variably (IMPACT-mortality, intercept 0.28, slope 0.68, and c-statistic 0.68; CRASH-unfavorable outcome, intercept -0.97, slope 1.32, and c-statistic 0.88; nonlinear calibration for IMPACT-unfavorable outcome and CRASH-mortality). Model performance differences were observed across the top enrolling sites for mortality and unfavorable outcome. The IMPACT and CRASH models adequately discriminated mortality and unfavorable outcome. Observed overestimations of mortality and unfavorable outcome underscore the need to update prognostic models to incorporate contemporary changes in TBI management and case-mix. Investigations to elucidate the relationships between increased survival, outcome, treatment intensity, and site-specific practices will be relevant to improve models in specific TBI subpopulations (e.g., older adults), which may benefit from the inclusion of blood-based biomarkers, neuroimaging features, and treatment data.

MiniRead: A simple and inexpensive do-it-yourself device for multiple analyses of micro-organism growth kinetics.

Fitness in micro-organisms can be proxied by growth parameters on different media and/or temperatures. This is achieved by measuring optical density at 600 nm using a spectrophotometer, which measures the effect of absorbance and side scattering due to turbidity of cells suspensions. However, when growth kinetics must be monitored in many 96-well plates at the same time, buying several 96-channel spectrophotometers is often beyond budgets. The MiniRead device presented here is a simple and inexpensive do-it-yourself 96-well temperature-controlled turbidimeter designed to measure the interception of white light via absorption or side scattering through liquid culture medium. Turbidity is automatically recorded in each well at regular time intervals for up to several days or weeks. Output tabulated text files are recorded into a micro-SD memory card to be easily transferred to a computer. We propose also an R package which allows (1) to compute the nonlinear calibration curves required to convert raw readings into cell concentration values, and (2) to analyze growth kinetics output files to automatically estimate proxies of growth parameters such as lag time, maximum growth rate, or cell concentration at the plateau.

An Interpretable Nonlinear Decoupling and Calibration Approach to Wheel Force Transducers

An Interpretable Nonlinear Decoupling and Calibration Approach to Wheel Force Transducers

An Improved Quadratic Spline Model Using Curvature Tip Compression - Particle Swarm Optimization to Forecast Accurately the Nonlinear Fluid Calibration Curve

An Improved Quadratic Spline Model Using Curvature Tip Compression - Particle Swarm Optimization to Forecast Accurately the Nonlinear Fluid Calibration Curve