Spline Interpolation Algorithm Research Articles

A Novel Classification Method with Cubic Spline Interpolation

Classification is the last, and usually the most time-consuming step in recognition. Most recently proposed classification algorithms have adopted machine learning (ML) as the main classification approach, regardless of time consumption. This study proposes a statistical feature classification cubic spline interpolation (FC-CSI) algorithm to classify emotions in speech using a curve fitting technique. FC-CSI is utilized in a speech emotion recognition system (SERS). The idea is to sketch the cubic spline interpolation (CSI) for each audio file in a dataset and the mean cubic spline interpolations (MCSIs) representing each emotion in the dataset. CSI interpolation is generated by connecting the features extracted from each file in the feature extraction phase. The MCSI is generated by connecting the mean features of 70% of the files of each emotion in the dataset. Points on the CSI are considered the new generated features. To classify each audio file according to emotion, the Euclidian distance (ED) is found between each CSI and all MCSIs of all emotions in the dataset. Each audio file is classified according to the nearest MCSI to the CSI representing it. The three datasets used in this work are Ryerson Audio-Visual Database of Emotional Speech and Song (RAVDESS), Berlin (Emo-DB), and Surrey Audio-Visual Expressed Emotion (SAVEE). The proposed work shows fast classification and high accuracy of results. The classification accuracy, i.e., the proportion of samples assigned to the correct class, using FC-CSI without feature selection (FS), was 69.08%, 92.52%, and 89.1% with RAVDESS, Emo-DB, and SAVEE, respectively. The results of the proposed method were compared to those of a designed neural network called SER-NN. Comparisons were made with and without FS. FC-CSI outperformed SER-NN on Emo-DB and SAVEE, and underperformed on RAVDESS, without using an FS algorithm. It was noticed from experiments that FC-CSI operated faster than the same system utilizing SER-NN.

A novel polynomial reconstruction algorithm‐based 1D convolutional neural network used for transfer learning in Raman spectroscopy application

AbstractWhen a convolutional neural network (CNN) model was built, the size and resolution of its input data were fixed. However, Raman spectra collected by different Raman spectrometers usually had different length, intensity range, and wavenumber interval between two adjacent data points, which made the existing CNN model difficult to be applied to a new Raman spectral data set. Therefore, this paper proposed a polynomial reconstruction algorithm as pretreatment method to obtain reconstructed spectra that would be imported into CNN model with consistent length, intensity range, and wavenumber interval. To test the effectiveness of this method, a big data set with 2563 Raman spectra of 831 minerals and synthetic organic pigments samples was constructed from the RRUFF and SOP database to pretrain a one‐dimensional CNN (1D‐CNN) model. The pretraining results showed that polynomial reconstruction algorithm used as pretreatment method was better than SG smoothing combined spline interpolation algorithm. Then two data sets were collected by different Raman spectrometers for evaluating the transfer learning performance of the trained 1D‐CNN model. Both data sets contained 390 Raman spectra from the same 39 samples of inorganic salts, organic compounds, and amino acids. One was used as calibration data to retrain the 1D‐CNN model, while the other was used as test. Based on data augmentation and 75% calibration data for retraining, the transfer learning performances of 1D‐CNN model were clearly shown in the excellent identification accuracies of 99.58%, 99.32%, and 97.69% for training, validation, and test sets, respectively, which were better than those of K‐nearest neighbor classifier. This paper provides a significant way for the wide application of CNN model in Raman spectroscopy with much more advantages in simplicity and rapidity.

Indoor Mapping of Magnetic Fields Using UAV Equipped with Fluxgate Magnetometer.

Unmanned aerial vehicles (UAVs) are used nowadays in a wide range of applications, including monitoring, mapping, or surveying tasks, involving magnetic field mapping, mainly for geological and geophysical purposes. However, thanks to the integration of ultrasound-aided navigation used for indoor UAV flight planning and development in sensorics, the acquired magnetic field images can be further used, for example, to enhance indoor UAV navigation based on the physical quantities of the image or for the identification of risk areas in manufacturing or industrial halls, where workers can be exposed to high values of electromagnetic fields. The knowledge of the spatial distribution of magnetic fields can also provide valuable information from the perspective of the technical cleanliness. This paper presents results achieved with the original fluxgate magnetometer developed and specially modified for integration on the UAV. Since the magnetometer had a wider frequency range of measurement, up to 250 Hz, the DC (Direct Current) magnetic field and low frequency industrial components could be evaluated. From the obtained data, 3D magnetic field images using spline interpolation algorithms written in the Python programming language were created. The visualization of the measured magnetic field in the 3D plots offer an innovative view of the spatial distribution of the magnetic field in the area of interest.

Estimation the internal resistance of lithium-ion-battery using a multi-factor dynamic internal resistance model with an error compensation strategy

Battery thermal management (BTM) is essential to ensure the safety of the battery pack of electric vehicles. For a variety of BTM technologies, the battery’s internal resistance always plays a critical role in the heat generation rate of the battery. Many factors (temperature, SOC and discharge rate) impact on the internal resistance, however, scant research has explored the effect of battery discharge rate on the internal resistance. This study aims to establish a multi-factor dynamic internal resistance model (MF-DIRM) with error compensation strategy to accurately estimate the internal resistance. In the present study, the internal resistance is estimated using the MF-DIRM which fuses three parameters (the temperature, SOC and discharge rate) and the procedures are two-fold: firstly, the coefficients of the binary fourth-order polynomial about the internal resistance with temperature and SOC are obtained, and then the MF-DIRM is built through the cubic spline interpolation algorithm to interpolate these coefficients at different discharge rates. Rather than measure the internal resistance, this model can estimate the internal resistance, and the estimated error does not exceed 10mΩ. Secondly, to further improve the estimation accuracy of MF-DIRM, the error function of the internal resistance is constructed as a binary cubic spline with the temperature and SOC, thereby constructing a model with error compensation strategy. The MF-DIRM combined with error compensation strategy can better estimate resistance under various conditions and the maximum value of estimation error is less than 2.5 mΩ.

Image Enhancement and Improvement Algorithm Based on Esrgan Singal Frame Remote Sensing Image

Traditional spline interpolation algorithm for reconstruction of visual effects are not good, based on Super Resolution against Network (Super - Resolution Generative Adversarial Network, SRGAN) edge character to deal with such problems as imperfect, using a generated based on the enhanced Super Resolution against Network to improve the Resolution of ordinary optical remote sensing images, the first Network generated by high Resolution data sets to train (G network), then lower Resolution test data model test, The test results and real results are put into the discrimination network (D network) to get the adversarial loss, and then the generated network is modified according to the adversarial loss. The superiority of the network is improved by introducing dense residuals to SRGAN, modifying the judgment object of the discriminator to be relatively real, and using the eigenvalue before activation to improve the perceived loss. The desert, farmland, forest and mountain data were tested on AID data set, and the algorithm in this paper could obtain the recomposition of the real image more closely. Compared with SRResNet and SRGAN algorithms, PSNR improved by about 4.0db and SSIM improved by about 0.14. This method improves the feature comprehensiveness by increasing the network fineness degree, and USES the modified perception loss to get the brightness closer to the real image, which is beneficial to improve the quality of single frame remote sensing image.

Subpixel Matching Using Double-Precision Gradient-Based Method for Digital Image Correlation.

Digital image correlation (DIC) for displacement and strain measurement has flourished in recent years. There are integer pixel and subpixel matching steps to extract displacement from a series of images in the DIC approach, and identification accuracy mainly depends on the latter step. A subpixel displacement matching method, named the double-precision gradient-based algorithm (DPG), is proposed in this study. After, the integer pixel displacement is identified using the coarse-fine search algorithm. In order to improve the accuracy and anti-noise capability in the subpixel extraction step, the traditional gradient-based method is used to analyze the data on the speckle patterns using the computer, and the influence of noise is considered. These two nearest integer pixels in one direction are both utilized as an interpolation center. Then, two subpixel displacements are extracted by the five-point bicubic spline interpolation algorithm using these two interpolation centers. A novel combination coefficient considering contaminated noises is presented to merge these two subpixel displacements to obtain the final identification displacement. Results from a simulated speckle pattern and a painted beam bending test show that the accuracy of the proposed method can be improved by four times that of the traditional gradient-based method that reaches the same high accuracy as the Newton–Raphson method. The accuracy of the proposed method efficiently reaches at 92.67%, higher than the Newton-Raphon method, and it has better anti-noise performance and stability.

Relationship between patellofemoral finite helical axis and femoral trans-epicondylar axis using a static magnetic resonance-based methodology

BackgroundTo manage patellofemoral joint disorders, a complete understanding of the in vivo patellofemoral kinematics is critical. However, as one of the parameters of joint kinematics, the location and orientation of the patellofemoral finite helical axis (FHA) remains unclear. The purpose of this study is to quantify the location and orientation of the patellar FHA, both in vivo and non-invasively at various flexion angles, and evaluate the relationship of the FHA and the trans-epicondylar axis (TEA).MethodsThe magnetic resonance (MR) images of 18 unilateral knees were collected at full extension, 30°, 60°, 90°, and maximum angle of knee flexion. Three-dimensional models of the knee joint at different flexion angles were created using the MR images, and then used to calculate the patellar tracking and FHA with a spline interpolation algorithm. By using a coordinate system based on the TEA, the FHA tracking was quantified. Six parameters concerning the location and orientation of the patellar FHA were analysed.ResultsThe average patellar FHA drew an L-shaped tracking on the midsagittal plane moving from the posteroinferior to the anterosuperior side of the TEA with knee flexion. Before 90° flexion, the patellar rotational radius decreased slightly, with an average value of 5.65 ± 1.09 cm. During 20° to 90° knee flexion, the average angle between the patellar FHA and the TEA was approximately 10° and that between the FHA and the coronal plane was maintained at about 0°, while that between the FHA and the level plane fluctuated between − 10° and 10°.ConclusionsThis study quantitatively reported the continuous location and direction of the patellar FHA during knee flexion. The patellar FHA was close to but not coincident with the femoral TEA both in location and orientation, and the patellar rotational radius decreased slightly with knee flexion. These findings could provide a clear direction for further studies on the difference in patellofemoral FHA among various types of patellofemoral disorders, and provide a foundation for the application of FHA in surgical evaluation, preoperative planning and prosthesis design, thereby assisting in the diagnosis and treatment of patellofemoral disorders.

A fully real-time spline interpolation algorithm with axial jerk constraint based on FIR filtering

Interpolators play a core and important role in CNC systems, and the scheduling of feedrate is a main task of CNC interpolators. It is routine to schedule the feedrate of linear/circular toolpaths because of their regular geometry; however, the feedrate scheduling of spline toolpaths remains challenging due to the freely and unpredictable geometric shape. Most of the existing methods require looking ahead or pre-processing to acquire sufficient toolpath information for generating drive-bounded smooth feedrate profile, which limits the integral machining efficiency. This paper presents a FIR (finite impulse response) filtering-based interpolation algorithm for spline toolpath, thus realizing the fully real-time capability without using time-consuming optimization such as looking ahead or pre-processing. The presented method merely utilizes the curvature radius information of the current interpolation point on the spline toolpath, and the scheduled feedrate can be generated within one step. Furthermore, the global tangential smoothness of the feedrate profile is guaranteed by directly applying convolution with a chain of two cascaded FIR filters. However, the FIR filtering induces interpolation error which plays as a negative cost during the one-step feedrate scheduling. To solve this issue, the principle of the filtering induced error is analyzed, so that it is computed by feed parameters and curvature radius, and the maximum error is added as an extra constraint beyond the commonly considered axial kinematic constraints. Effectiveness of the presented approach is demonstrated by both numerical illustration and experimental tests.

Fault Location of VSC Based DC Distribution Network Based on Traveling Wave Differential Current With Hausdorff Distance and Cubic Spline Interpolation

Compared with AC power system, DC distribution network is a low-damping system without natural zero crossing. The DC fault current will reach its peak value within a few milliseconds, posing a great threat to power electronic devices. Therefore, the rapid and high-precision identification of DC line faults is one of the technical difficulties faced by the VSC based DC distribution network. In this paper, a new fault location method based on traveling wave differential current with Hausdorff distance and cubic spline interpolation is proposed. First, the forward and reverse traveling waves at both ends of the VSC based DC lines are extracted, the Karenbauer transform is used to decouple the positive and negative electrodes to obtain accurate fault information. Then, the internal relationship between the differential current and the fault current is obtained according to the principle of traveling wave transmission invariance, the cubic spline interpolation algorithm is used to solve the traditional sampling frequency limitation, and the positive differential current in the interception time window is smoothly displaced. At last, the Hausdorff distance algorithm is used to analyze the correlation between the translational differential current and the reverse differential current. The fault location corresponds to the highest correlation. The proposed method uses the time-domain information at both ends of the VSC based DC lines, and it is less affected by the transition resistance. Lots of simulation experiments prove that it has a strong anti-noise interference ability and high reliability, and is less affected by the sampling frequency after cubic spline interpolation. Compared with traveling wave algorithm based on Pearson correlation coefficient, the method in this paper shows a significantly shortened error, 27% on average.

Retracted] Interpolation Method for Visual Simulation of Engine Exhaust Flame

Propulsive force and exhaust fluid temperature are important indicators in the performance of an engine. An investigation of the effects of propellant composition, plane flight conditions, and engine operating environment on rocket thrust and the range of smoke plume temperature can provide references in the design of engine mechanics at the optimization of propellant composition, in monitoring of target identification and in the evolving of stealth of stealth technology. In order to understand the characteristics of the engine tail flame, a visual simulation of the engine tail flame was carried out by combining the engine operating conditions with the tail flame conditions. Based on the advantages of the bicubic spline interpolation algorithm and the Kriging interpolation algorithm, this paper proposes a hybrid interpolation algorithm, which performs color mapping and three‐dimensional space separation in the engine plume data set and model, and visualizes the engine and engine plume. The simulation realizes real‐time monitoring of the functions of various engine components through characteristic colors. The research results show that the hybrid interpolation method can effectively visualize the engine exhaust flame. The simulated plume has a relatively obvious temperature peak at 0.7 m, and the temperature of the plume flow field is significantly higher than that of the frozen plume flow field by about 200 ~1000 K. This shows that the algorithm in this paper helps to visualize the expression of engine tail flame information.

A Signal Reconstruction Method Based on Quadratic Spline Interpolation Applied in Power Quality Analysis for SCM-TTU

Aiming at the accurate and quick analysis of power quality especially of harmonic problem in power system, interpolation approaches should be applied if the samples collected by hardware are not matched with Fast Fourier Transform (FFT) calculation. A quadratic spline interpolation algorithm is proposed on Single Chip Micyoco-Transformer Terminal Unit (SCM-TTU) in this paper. This algorithm considers the continuous of interpolation function and also the first derivative in order to improve the accuracy. It could be applied before FFT calculation to avoid the mismatch of sampling rates. A simulation with mathematic example and also an application with SCM-TTU contains the harmonics from 2nd to 50th orders are experimented, results are presented to show the effectiveness.

Optimal Kernel ELM and Variational Mode Decomposition for Probabilistic PV Power Prediction

A probabilistic prediction interval (PI) model based on variational mode decomposition (VMD) and a kernel extreme learning machine using the firefly algorithm (FA-KELM) is presented to tackle the problem of photovoltaic (PV) power for intra-day-ahead prediction. Firstly, considering the non-stationary and nonlinear characteristics of a PV power output sequence, the decomposition of the original PV power output series is carried out using VMD. Secondly, to further improve the prediction accuracy, KELM is established for each decomposed component and the firefly algorithm is introduced to optimize the penalty factor and kernel parameter. Finally, the point predicted value is obtained through the summation of predicted results of each component and then using the nonlinear kernel density estimation to fit it. The cubic spline interpolation algorithm is applied to obtain the shortest confidence interval. Results from practical cases show that this probabilistic prediction interval could achieve higher accuracy as compared with other prediction models.

An Improved LWD Azimuth Gamma Imaging Model Based on HSI Space

In recent years, in the process of oil and gas exploration and development, the situation of drilling tools drilling out of the reservoir often occurs. Due to the lack of directional indication, the traditional LWD(Logging While Drilling) natural gamma measurement technology cannot guide drilling tools to return to the reservoir efficiently. In order to solve this problem, this paper improves the traditional radiometric gamma measurement technology and establishes a set of azimuth gamma imaging model. Firstly, the basic imaging model is established based on HSI (Hue, Saturation, Intensity) color space. Then, the study focuses on the design of the gamma data quality control algorithm, which can effectively suppress the original gamma data noise. In addition, the cubic spline interpolation algorithm is selected to support the model to obtain 360° omni-directional gamma data. Finally, the image processing technology based on fast grayscale grouping is applied in this study, which greatly improves the imaging effect. Field application shows that the model runs stably on site, and the azimuth gamma image is well indicative. It can monitor the relative position relationship between the borehole trajectory and the formation, which effectively improves the reservoir encounter rate, and has high application and promotion value.

Improved Quantum Particle Swarm Optimization Algorithm for Offline Path Planning in AUVs

This paper proposes an offline path planning method based on the Improved Quantum Particle Swarm Optimization (IQPSO) algorithm for Autonomous Underwater Vehicles (AUVs) in the underwater environment. The spherical modelling method is adopted to represent irregular underwater obstacles as spheres with a specified radius. Then, the IQPSO algorithm is developed to solve the problem of the limitations of the convergence and optimization ability of the traditional Quantum Particle Swarm Optimization (QPSO) algorithm and to identify the best path for AUVs. In this algorithm, to satisfy the three factors of path safety, path length and angle change of the path point, the fitness function is constructed to achieve multi-objective optimization. A smooth path is designed using the cubic spline interpolation algorithm. Different scenes or the same scene with different obstacles are designed to verify the effectiveness of the algorithm. The simulation results show that compared with PSO algorithm, QPSO algorithm, EGA algorithm and DENPSO algorithm, the path generated by IQPSO algorithm in various scenes is shorter, smoother and more stable.

Analytical sensitivity analysis of flexible aircraft with the unsteady vortex-lattice aerodynamic theory

The unsteady vortex-lattice method provides a medium-fidelity tool for calculation of low-speed aerodynamic loads based on the potential-flow theory. It has long been favored in research on the aeroelasticity and flight dynamics for flexible aircraft with high aspect ratios. However, the unsteady vortex-lattice method is established in the discrete time domain which brings difficulties to modeling aeroelastic system for stability analysis. An analytical aerodynamic sensitivity calculation scheme is developed in this paper to formulate the aeroelastic equations of motion with UVLM aerodynamics. A free wake model is used to simulate accurate vortex shedding and subsequent wake propagation. Using a small perturbation method, the aerodynamic governing equations are linearized around the equilibrium condition, where the analytical sensitivities can be derived. The surface spline interpolation algorithm is adopted to implement the structure-aerodynamic coupling. Both aerodynamic sensitivities with respect to structural motions and circulation strengths of vortices are obtained. In numerical studies, a time-marching transient response analysis scheme is used to obtain the distributed aerodynamic loads and structural deformations. Analytical sensitivity results are validated by the finite difference method. The proposed analytical sensitivity calculation framework is demonstrated to be applicable to commonly used beam-based flexible wing models, as well as the shell-based finite element models with higher fidelity. The derived sensitivity formulations and related numerical implementations can build the foundation for further studies on aeroelastic optimization and stability analysis.

A Cable-Mapping Algorithm Based on Ground-Penetrating Radar

The demand for mapping the buried cables is increasing dramatically with the rapid expansion of urban area, but there are few specific procedures and approaches to map underground cables without disturbing the normal electricity supply. In this letter, a cable-mapping approach based on the ground-penetrating radar (GPR) is proposed, which consists of two parts. First, the parallel scan lines are established along which the GPR is moved to obtain the B-scan images; the hyperbolic shapes on these obtained images are identified and fitted; and the locations and depths of the detected sample points of the buried cables could be derived from these hyperbolas. Then, due to different terrain and surrounding obstacles, as well as the use of pipe-jacking technology, <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> the underground cables may not be straight. The detected points are interpolated by a three-dimensional spline interpolation algorithm to obtain a smooth 3-D curve with location and depth information. Compared with the 2-D model, the 3-D curve could visualize the direction of buried cables more intuitively. Also, in comparison with other interpolation algorithms, the error caused by the proposed interpolation is minimized on the chosen data sets. Experiments on real-world data sets are conducted, and the obtained results demonstrate the effectiveness of the proposed model. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> Pipe-jacking is a trenchless technology for buried utilities [1].

Computer-assisted prediction of atherosclerotic intimal thickness based on weight of adrenal gland, interleukin-6 concentration, and neural networks.

ObjectiveAtherosclerosis (AS) is the main pathological basis of ischemic cardio-cerebrovascular diseases, and the intimal thickness (IT) of large arteries is regarded as a powerful evaluation indicator for AS. We established an effective neural network model for automatic prediction of the IT and analyzed the high-risk warning indicators of IT.MethodsThe weight of the left adrenal (WLA) was evaluated. The serum interleukin-6 (IL-6) concentration was measured by enzyme-linked immunosorbent assay. The statistical methods included neural network modeling, a cubic spline interpolation algorithm, Spearman’s rho test, and linear fit.ResultsThirty-seven rabbits were classified into a control group (n = 11), high-fat diet group (n = 13), and high-fat diet plus chronic stress group (n = 13). The neural network model was successfully established and verified by comparing the predicted IT with the actual IT. The high-risk warning indicator of IT was identified as follows: 0.445 g < WLA < 0.610 g and 60 ng/L< IL-6 < 80 ng/L.ConclusionsThe neural network model based on WLA and IL-6 could predict the IT of AS. When 0.445 g < WLA < 0.610 g and 60 ng/L < IL-6 < 80 ng/L, the risk to developing AS is very high.

A Study on an Automatic Multi-Focus System for Cell Observation

This study is concerned with the mechanism and structure of an optical microscope and an automatic multifocus algorithm for automatically selecting sharp images from multiple foci of a cell. To obtain precise cell images quickly, a z-axis actuator with a resolution of 0.1 μm was designed to control an optical microscope Moreover, a lighting control system was constructed to select the color and brightness of light that best suit the object being viewed. Cell images are captured by the instrument and the sharpness of each image is determined using Gaussian and Laplacian filters. Next, cubic spline interpolation and peak detection algorithms are applied to automatically find the most vivid points among multiple images of a single object. A cancer cell imaging experiment using propidium iodide staining confirmed that a sharp multipoint image can be obtained using this microscope. The proposed system is expected to save time and effort required to extract suitable cell images and increase the convenience of cell analysis.

Periodic Steady State Assessment of Microgrids with Photovoltaic Generation Using Limit Cycle Extrapolation and Cubic Splines

This paper proposes a fast and accurate time domain (TD) methodology for the assessment of the dynamic and periodic steady state operation of microgrids with photovoltaic (PV) energy sources. The proposed methodology uses the trapezoidal rule (TR) technique to integrate the set of first-order differential algebraic equations (DAE), generated by the entire electrical system. The Numerical Differentiation (ND) method is used to significantly speed-up the process of convergence of the state variables to the limit cycle with the fewest number of possible time steps per cycle. After that, the cubic spline interpolation (CSI) algorithm is used to reconstruct the steady state waveform obtained from the ND method and to increase the efficiency of the conventional TR method. This curve-fitting algorithm is used only once at the end part of the algorithm. The ND-CSI can be used to assess stability, power quality, dynamic and periodic steady state operation, fault and transient conditions, among other issues, of microgrids with PV sources. The results are successfully validated through direct comparison against those obtained with the PSCAD/EMTDC simulator, widely accepted by the power industry.

The liquid level monitoring with sub-millimeter resolution by discrete wavelength sampling method

The liquid level fiber sensor with a measurement range of about 50 cm is fabricated through a kind of single-no-core-single mode (SNS) structure. It is found that the change of liquid level will only induce the wavelength shifts of the whole interference spectrum. The liquid level monitoring with sub-millimeter resolution can be achieved by the proposed discrete wavelength sampling method. In the experiment, the transmit interference spectrum is sampled by a tunable laser with a step of 0.5 nm, then constructed by cubic spline interpolation algorithm. The wavelength shifts can be obtained through a minimum variance demodulation algorithm. Experiment results exhibit an excellent linear response (R2 = 0.99993) and the high sensitivity response to different liquid refractive index (RI). And the sensitivity of the sensor is 23.38 pm/mm with the liquid RI of 1.3505. In particular, the sensing resolution of the liquid level can reach 0.5 mm. This anti-electromagnetic interference technique with such high resolution and large sensing range can find the promising applications of monitoring the left fuel in the aircraft tanker, the surface evaporation in the water resource cycle, etc.