Nonlinear Calibration Method Research Articles

Docking and pharmacophore‐based alignment comparative molecular field analysis three‐dimensional quantitative structure–activity relationship analysis of dihydrofolate reductase inhibitors by linear and nonlinear calibration methods

Comparative molecular field analysis (CoMFA) studies have been carried out on 2,4‐diamino‐5‐(2_‐arylpropargyl)pyrimidine derivatives such as dihydrofolate reductase (DHFR) anticancer inhibitors. Because of the interoperable results of CoMFA models, they are noteworthy tools in rational drug designs. However, the huge amount of fields generated by this method contributes to its poor predictive ability. In this study, we applied a CoMFA region focusing (CoMFA‐ReF) approach to weight and enhance or attenuate the contribution of lattice points on standard CoMFA interactions. In addition, the genetic algorithm (GA) is used to select interactions that are responsible for the inhibitory activities of these compounds. The selected fields were introduced to multiple linear regression, partial least squares (PLS), support vector machines (SVM), and random forest (RF) regression methods. Among the constructed models and in terms of root mean square predictions (RMSEP), the predictive power of the (CoMFA‐ReF)‐PLS (RMSEP = 0.252) was better than that of the others. The performances of the GA‐RF regression model (RMSEP = 0.383) and GA‐SVM (RMSEP = 0.387) were comparable. The pharmacophore‐based alignment has been used as an intelligent alignment algorithm in the construction of a CoMFA standard model to improve the accuracies according to the (DHFR) protein environment. Docking studies clarified the role of these compounds in the inhibitory and anticancer activities of DHFR. Copyright © 2013 John Wiley & Sons, Ltd.

Irradiation dose detection of irradiated milk powder using visible and near-infrared spectroscopy and chemometrics

The objective of this study was to examine the possibility of applying visible and near-infrared spectroscopy to the quantitative detection of irradiation dose of irradiated milk powder. A total of 150 samples were used: 100 for the calibration set and 50 for the validation set. The samples were irradiated at 5 different dose levels in the dose range 0 to 6.0kGy. Six different pretreatment methods were compared. The prediction results of full spectra given by linear and nonlinear calibration methods suggested that Savitzky-Golay smoothing and first derivative were suitable pretreatment methods in this study. Regression coefficient analysis was applied to select effective wavelengths (EW). Less than 10 EW were selected and they were useful for portable detection instrument or sensor development. Partial least squares, extreme learning machine, and least squares support vector machine were used. The best prediction performance was achieved by the EW-extreme learning machine model with first-derivative spectra, and correlation coefficients=0.97 and root mean square error of prediction=0.844. This study provided a new approach for the fast detection of irradiation dose of milk powder. The results could be helpful for quality detection and safety monitoring of milk powder.

Quantifying Antibody Binding on Protein Microarrays using Microarray Nonlinear Calibration

We present a microarray nonlinear calibration (MiNC) method for quantifying antibody binding to the surface of protein microarrays that significantly increases the linear dynamic range and reduces assay variation compared with traditional approaches. A serological analysis of guinea pig Mycobacterium tuberculosis models showed that a larger number of putative antigen targets were identified with MiNC, which is consistent with the improved assay performance of protein microarrays. MiNC has the potential to be employed in biomedical research using multiplex antibody assays that need quantitation, including the discovery of antibody biomarkers, clinical diagnostics with multi-antibody signatures, and construction of immune mathematical models.

Hand-eye and radial distortion calibration for rigid endoscopes

In this paper, we propose a non-linear calibration method for hand-eye system equipped with a camera undergoing radial distortion as the rigid endoscope. Whereas classic methods propose either a separated estimation of the camera intrinsics and the hand-eye transform or a mixed non-linear estimation of both hand-eye and camera intrinsics assuming a pin-hole model, the proposed approach enables a simultaneous refinement of the hand-eye and the camera parameters including the distortion factor with only three frames of the calibrated pattern. Our approach relies on three steps: (i) linear initial estimates of hand-eye and radial distortion with minimum number of frames: one single image to estimate the radial distortion and three frames to estimate the initial hand-eye transform, (ii) we propose to express the camera extrinsic with respect to hand-eye and world-grid transforms and (iii) we run bundle adjustment on the reprojection error with respect to the distortion parameters, the camera intrinsics and the hand-eye transform. Our method is quantitatively compared with state-of-the-art linear and non-linear methods. We show that our method provides a 3D reconstruction error of approximately 5% of the size of the 3D shape. Our experimental results show the effectiveness of simultaneously estimating hand-eye and distortion parameters for 3D reconstruction.

Detection of Glutamic Acid in Oilseed Rape Leaves Using Near Infrared Spectroscopy and the Least Squares-Support Vector Machine

Amino acids are quite important indices to indicate the growth status of oilseed rape under herbicide stress. Near infrared (NIR) spectroscopy combined with chemometrics was applied for fast determination of glutamic acid in oilseed rape leaves. The optimal spectral preprocessing method was obtained after comparing Savitzky-Golay smoothing, standard normal variate, multiplicative scatter correction, first and second derivatives, detrending and direct orthogonal signal correction. Linear and nonlinear calibration methods were developed, including partial least squares (PLS) and least squares-support vector machine (LS-SVM). The most effective wavelengths (EWs) were determined by the successive projections algorithm (SPA), and these wavelengths were used as the inputs of PLS and LS-SVM model. The best prediction results were achieved by SPA-LS-SVM (Raw) model with correlation coefficient r = 0.9943 and root mean squares error of prediction (RMSEP) = 0.0569 for prediction set. These results indicated that NIR spectroscopy combined with SPA-LS-SVM was feasible for the fast and effective detection of glutamic acid in oilseed rape leaves. The selected EWs could be used to develop spectral sensors, and the important and basic amino acid data were helpful to study the function mechanism of herbicide.

Improved Iterative Calibration for Triaxial Accelerometers Based on the Optimal Observation

This paper presents an improved iterative nonlinear calibration method in the gravitational field for both low-grade and high-grade triaxial accelerometers. This calibration method assumes the probability density function of a Gaussian distribution for the raw outputs of triaxial accelerometers. A nonlinear criterion function is derived as the maximum likelihood estimation for the calibration parameters and inclination vectors, which is solved by the iterative estimation. First, the calibration parameters, including the scale factors, misalignments, biases and squared coefficients are estimated by the linear least squares method according to the multi-position raw outputs of triaxial accelerometers and the initial inclination vectors. Second, the sequence quadric program method is utilized to solve the nonlinear constrained optimization to update the inclination vectors according to the estimated calibration parameters and raw outputs of the triaxial accelerometers. The initial inclination vectors are supplied by normalizing raw outputs of triaxial accelerometers at different positions without any a priori knowledge. To overcome the imperfections of models, the optimal observation scheme is designed according to some maximum sensitivity principle. Simulation and experiments show good estimation accuracy for calibration parameters and inclination vectors.

Nonlinear Calibration of Thermocouple Sensor Using Least Squares Support Vector Regression

Calibration is an important operation in the instrumentation industry for determining the relationship between the output (s) (or response) of a measuring instrument and the value of the input (s). This paper proposes a nonlinear calibration method based on least squares support vector regression (LS-SVR) with the output voltage of thermocouple sensor as input and the measured temperature output to eliminate the nonlinear errors in detection process. Firstly, the nonlinear calibrator, expressed by power series, was established based on the principle of inverse model. And then the parameters of the calibrator were identified by LS-SVR. Through this calibrator, the desired linear characteristics of thermocouple sensor could be obtained. Finally, platinum-rhodium 30– platinum-rhodium 6-thermocouple (B-type) was taken as an example, and experimental results show that the proposed calibration method is efficient in the temperature range from 400°C to 1800°C. And the method has an advantage of analytical expression of the calibration model.

A New Binocular Camera Calibration Method Based on an Improved Genetic Algorithm

In this paper,an improved genetic algorithm was proposed,which is applicable to binocular camera calibration. On the one hand, conventional encoding method is improved so that variable search interval can be adjusted adaptively. On the other hand, crossover and mutation probability is varied by using superiority inheritance principle to avoid premature question. Experimental results show that the proposed method has a higher calibration accuracy and better robustness, compared to those of non-linear calibration methods. The proposed method is able to improve the performance of global optimization effectively.

A Fast Linear Calibration of Computer Stereo Vision System

Computer stereo vision has been paid high attention in areas such as industry measurement and automatic control. Calibration of stereo vision system is a key step to implement vision measurement. Nonlinear calibration method involves too many parameters and too complex function, so the processing of optimization is difficult and slow. In this paper, two digital cameras are used to set up stereo vision system which provides convenient experimental operation. The binocular stereo vision system is calibrated using linear calibration model. The results indicate that the method is stable and fast with high precision and practicability.

Neural network (ANN) approach to biodiesel analysis: Analysis of biodiesel density, kinematic viscosity, methanol and water contents using near infrared (NIR) spectroscopy

The use of ethanol and biodiesel, which are alternative fuels or biofuels, has increased in the last few years. Modern official standards list 25 parameters that must be determined to certify biodiesel quality, and these analyses are expensive and time-consuming. Near infrared (NIR/NIRS) spectroscopy (4000–12,820 cm −1) is a cheap and fast alternative to analyse biodiesel quality, when compared with infrared, Raman, or NMR methods, and quality control can be done in realtime (on-line).We compared the performance of linear and non-linear calibration techniques – namely, multiple linear regression (MLR), principal component regression (PCR), partial least squares regression (PLS), polynomial and Spline-PLS versions, and artificial neural networks (ANN) – for prediction of biodiesel properties from near infrared spectra. The model was created for four important biodiesel properties: density (at 15 °C), kinematic viscosity (at 40 °C), water content, and methanol content. We also investigated the influence of different pre-processing methods (Savitzky–Golay derivatives, orthogonal signal correction) on the model prediction capability. The lowest root mean squared errors of prediction (RMSEP) of ANN for density, viscosity, water percentage, and methanol content were 0.42 kg m −3, 0.068 mm 2 s −1, 45 ppm, and 51 ppm, respectively. The artificial neural network (ANN) approach was superior to the linear (MLR, PCR, PLS) and “quasi”-non-linear (Poly-PLS, Spline-PLS) calibration methods.

Non-Liner Error Compensation of the New Vibration Accelermeter Based on Neural Network

A new type of piezoelectric vibration acceleration sensor was studied, which sensitive element consists of cymbal transducer and a buffer chip. The nonlinear characteristic of voltage sensitivity of this vibration acceleration sensor was investigated. Using the general principles of nonlinear calibration method of BP neural network, established the mathematic model of nonlinear calibration of output voltage sensitivity for this piezoelectric vibration acceleration sensor, and then accomplished the computer simulation programming using MATLAB algorithm. The computer simulation results showed that the nonlinear error of output voltage sensitivity for this piezoelectric vibration acceleration sensor can be less than 0.1‰ after six-steps training using artificial neural network. The effect of the compensation is better than that of commonly piecewise linear interpolation method, and with the characteristic of simple structure and high accuracy.

Bagging for robust non-linear multivariate calibration of spectroscopy

This paper presents the application of the bagging technique for non-linear regression models to obtain more accurate and robust calibration of spectroscopy. Bagging refers to the combination of multiple models obtained by bootstrap re-sampling with replacement into an ensemble model to reduce prediction errors. It is well suited to “non-robust” models, such as the non-linear calibration methods of artificial neural network (ANN) and Gaussian process regression (GPR), in which small changes in data or model parameters can result in significant change in model predictions. A specific variant of bagging, based on sub-sampling without replacement and named subagging, is also investigated, since it has been reported to possess similar prediction capability to bagging but requires less computation. However, this work shows that the calibration performance of subagging is sensitive to the amount of sub-sampled data, which needs to be determined by computationally intensive cross-validation. Therefore, we suggest that bagging is preferred to subagging in practice. Application study on two near infrared datasets demonstrates the effectiveness of the presented approach.

Self-Consistent Algorithm for Calibrating Spectrometers to Picometer Accuracy over the Entire Wavelength Range

Spectrometer calibration accuracies are of high importance for a wide range of applications. Typically, one calibrates the spectrometer with a calibration lamp, providing distinct and well-defined calibration lines. However, for small spectral ranges, where only two calibration lines are present, the calibration becomes inaccurate. We present a high-precision nonlinear wavelength calibration method, which is based on two or more reference lines from a calibration lamp. The additional key element introduced is a Fabry-Perot multilayer structure that yields multiple sharp transmission maxima of similar intensity over the full spectrometer range under broad-band illumination (e.g., white-light source). An iterative algorithm is put forward to obtain a self-consistent calibration of picometer precision over the full spectrometer range. In regions distant from calibration lines the accuracy is enhanced by at least a factor of two compared to conventional methods.

Enhanced Accuracy of Force Application for AFM Nanomanipulation Using Nonlinear Calibration of Optical Levers

The atomic force microscope (AFM) has been widely used as a nano-effector with a function of force sensing to detect interaction forces between an AFM tip and a sample, thereby controlling the process of the nanomanipulation. However, both the extent and accuracy of force application are significantly limited by the nonlinearity of the commonly used optical lever with a nonlinear position-sensitive detector (PSD). In order to compensate the nonlinearity of the optical lever, a nonlinear calibration method is presented. This method applies the nonlinear curve fit to a full-range position-voltage response of the photodiode, obtaining a continuous function of its voltage-related sensitivity. Thus, interaction forces can be defined as integrals of this sensitivity function between any two responses of photodiode voltage outputs, instead of rough transformation with a single conversion factor. The lateral position-voltage response of the photodiode, a universally acknowledged puzzle, was directly characterized by an accurately calibrated force sensor composed of a tippless piezoresistive microcantilever and corresponding electronics, regardless of any knowledge of the cantilevers and laser measuring system. Experiments using a rectangular cantilever (normal spring constant 0.24 N/m) demonstrated that the proposed nonlinear calibration method restrained the sensitivity error of normal position-voltage responses to 3.6% and extended the force application range.

The Research on the Static Calibration of Fingertip Force Sensor for Underwater Dexterous Hand on RBF Neural Network

The fingertip force sensor is the key for the complex task of the dexterous underwater hand, in order to safely grasp an unknown object using the dexterous underwater hand and accurately perceive its position in the fingers, a sensor should be developed, which can detect the force and position simultaneously. Furthermore, this sensor should be used underwater. It is difficult to employ the accustomed calibration method for the characteristic of the fingertip force sensor, and the accustomed method is not able to assure the precision. A calibration method based on RBF (Radial-Basis Function) neural network is introduced. Furthermore, the calibration system and program are also designed. The calibration experiment of the sensor is carried out. The results show the nonlinear calibration method based on RBF neural network assure the precision of the sensor, which meets the demand of research on the underwater dexterous hand.

Identical Projective Geometric Properties of Central Catadioptric Line Images and Sphere Images with Applications to Calibration

Central catadioptric cameras are imaging devices that use mirrors to enhance the field of view while preserving a single effective viewpoint. Lines and spheres in space are all projected into conics in the central catadioptric image planes, and such conics are called line images and sphere images, respectively. We discovered that there exists an imaginary conic in the central catadioptric image planes, defined as the modified image of the absolute conic (MIAC), and by utilizing the MIAC, the novel identical projective geometric properties of line images and sphere images may be exploited: Each line image or each sphere image is double-contact with the MIAC, which is an analogy of the discovery in pinhole camera that the image of the absolute conic (IAC) is double-contact with sphere images. Note that the IAC also exists in the central catadioptric image plane, but it does not have the double-contact properties with line images or sphere images. This is the main reason to propose the MIAC. From these geometric properties with the MIAC, two linear calibration methods for central catadioptric cameras using sphere images as well as using line images are proposed in the same framework. Note that there are many linear approaches to central catadioptric camera calibration using line images. It seems that to use the properties that line images are tangent to the MIAC only leads to an alternative geometric construction for calibration. However, for sphere images, there are only some nonlinear calibration methods in literature. Therefore, to propose linear methods for sphere images may be the main contribution of this paper. Our new algorithms have been tested in extensive experiments with respect to noise sensitivity.

Comparison of linear and nonlinear calibration methods for phase-measuring profilometry

In phase-shifting-based fringe-projection surface-geometry measurement, phase unwrapping techniques produce a continuous phase distribution that contains the height information of the 3-D object surface. Mapping of the phase distribution to the height of the object has often involved complex derivations of the nonlinear relationship. In this paper, the phase-to-height mapping is formulated using both linear and nonlinear equations, the latter through a simple geometrical derivation. Furthermore, the measurement accuracies of the linear and nonlinear calibrations are compared using measurement simulations where noise is included at the calibration stage only, and where noise is introduced at both the calibration and measurement stages. Measurement accuracies for the linear and nonlinear calibration methods are also compared, based on real-system measurements. From the real-system measurements, the accuracy of the linear calibration was similar to the nonlinear calibration method at the lower range of depth. At the higher range of depth, however, the nonlinear calibration method had considerably higher accuracy. It seems that as the object approaches the projector and camera for the higher range of depth, the assumption of linearity based on small divergence of light from the projector becomes less valid.

Measurement of soybean fatty acids by near‐infrared spectroscopy: Linear and nonlinear calibration methods

AbstractA key element of successful development of new soybean cultivars is availability of inexpensive and rapid methods for measurement of FA in seeds. Published research demonstrated applicability of NIR spectroscopy for FA profiling in oilseeds. The objectives of this study were to investigate the applicability of NIR spectroscopy for measurement of FA in whole soybeans and compare performance of calibration methods. Equations were developed using partial least squares (PLS), artificial neural networks (ANN), and support vector machines (SVM) regression methods. Validation results demonstrated that (i) equations for total saturates had the highest predictive ability (r2=0.91–0.94) and were usable for quality assurance applications, (ii) palmitic acid models (r2=0.80–0.84) were usable for certain research applications, and (iii) equations for stearic (r2=0.49–0.68), oleic (r2=0.76–0.81), linoleic (r2=0.73–0.76), and linolenic (r2=0.67–0.74) acids could be used for sample screening. The SVM models produced significantly more accurate predictions than those developed with PLS. ANN calibrations were not different from the other two methods. Reduction in the number of calibration samples reduced predictive ability of all equations. The rate of performance degradation of SVM models with sample reduction was the lowest.

Método para a correção da distorção de imagens obtidas por videofluoroscopia

OBJETIVO: Operacionalizar um protocolo para a correção de imagens obtidas por videofluoroscopia a partir de um modelo matemático descrito por Baltzopoulos (1995) e avaliar a magnitude do erro pelos métodos de calibração linear e não linear. MATERIAIS E MÉTODOS: As imagens foram obtidas por meio de um videofluoroscópio da marca Axion Siemens Iconos R100 de um indivíduo realizando exercício de extensão de joelho. Para a correção das imagens foi utilizado padrão de calibração não-linear. O processamento dos dados foi realizado em placa de captura da marca Silicon Graphics 320 e posteriormente analisado em um "software" Matlab. RESULTADOS: Para demonstrar a aplicabilidade do método foi avaliada a deformação do ligamento patelar. A utilização do padrão de calibração linear produziu um erro máximo de 0,086 mm, enquanto o padrão de calibração não linear atingiu um valor máximo de 0,019 mm. Já com relação ao erro médio, a calibração linear atingiu o valor de 0,024 mm, e a não linear apresentou um valor de 0,007 mm. CONCLUSÃO: Os resultados evidenciam a necessidade de utilização de um procedimento de calibração não linear.

Estimation of the Physical Wood Properties of Pinus Taeda L. Radial Strips Using Least Squares Support Vector Machines

Near infrared (NIR) spectroscopy offers a rapid method for estimating many important wood properties, including air-dry density, microfibril angle ( MFA) and SilviScan estimated stiffness (EL(SS)). Wood property calibrations may be improved by using non-linear calibration methods. In this study, we compare calibrations developed using partial least squares (PLS) regression and least-squares support vector machine (LS-SVM) regression, a relatively new technique for modelling multivariate, non-linear systems. LS-SVM regression provided the strongest calibration statistics for all wood properties. For an equivalent number of latent variables, the predictive performance of the MFA LS-SVM calibrations were superior to those of the corresponding PLS calibration, while predictive results for air-dry density and EL(SS) were similar for both calibration methods.