Proposed Interpolation Method Research Articles

Simplified Spatial Wind Vector Interpolation Method for Airport Runway Orientation Analysis

Runway orientation, guided by windrose analysis is crucial in airport planning as it directly influences aircraft performance and airport capacity. Proper alignment reduces crosswind components during takeoff and landing, ensuring safer operations and increase runway coverage. For a new airport in a location where comprehensive historical wind data is not available, prediction methods become an invaluable tool. To address this issue, this paper proposes a simplified interpolation method to predict wind data at target location based on available data from surrounding climate station readings. This paper validates the proposed method through a comparative analysis of predicted and actual windrose and its subsequent runway coverage at two prominent currently operational Indonesian airports: Soekarno Hatta International Airport in Cengkareng (CGK) and Sultan Hasanuddin International Airport in Ujung Pandang (UPG). Additionally, the study employs the proposed method to determine the optimal runway orientation for a new VVIP airport in Indonesia's new capital city (IKN), Nusantara. The analysis reveals that the proposed interpolation method yields runway heading recommendations closely aligned with those derived from actual wind data, both for the case of CGK and UPG airport. The proposed method recommends optimal runway heading between 03-21 and 08-26 for new VVIP Airport at Nusantara, new capital city of Indonesia (IKN).

Improvement Interpolation Method for Vessel Trajectory Prediction based on AIS Data

An acceptable shipping monitoring system should be able to provide early detection of vessel accidents. One of the keys to early detection is trajectory prediction. Even though the prediction results depend heavily on the historical data of the vessel trajectory, there are often missing values in the trajectory data due to disturbances in the Automatic Identification System (AIS) data transmission process. Therefore, this study proposes a preprocessing method that includes data cleaning, trajectory extraction, and a combination of Linear interpolation methods for straight-shaped trajectories and Cubic Spline interpolation for curved-shaped trajectories. Test results involving three different trajectories showed that the Gated Recurrent Units (GRU) method produces a smaller Root Mean Square Error (RMSE) value on linear interpolation. Visually, however, the GRU method with linear interpolation has a deficiency in the curved-shaped trajectories. Our studies involving the Bidirectional GRU (BiGRU), Long Short Term Memory (LSTM), and Bidirectional LSTM (BiLSTM) methods showed that the model built using the proposed interpolation method has a lower RMSE value. This study emphasizes that good predictions of vessel trajectories based on AIS data requires an additional process, namely the interpolation of vessel trajectories according to their shape.

Method for identifying the strength characteristics of concrete of a reinforced concrete crossbar during heating under conditions of fire

This paper proposes a method that makes it possible to study the patterns of changes in the concrete strength of reinforced concrete crossbars depending on the heating temperature under fire conditions by interpreting the results of their standard fire tests. For the implementation of this method, it is proposed to use similar data obtained using mathematical modeling based on the finite element method and given material properties, including the curve of concrete strength reduction recommended by the guidelines, as data included in the set of measurement results during fire tests depending on temperature. Such data are time dependences of temperature indicators at individual cross-section points and time dependence of the maximum deflection of the crossbar. The article proposes an interpolation method that makes it possible to set the temperature at any point of the section based on the approximation of the isotherms by parabolas with a variable indicator of their power. A method based on the mathematical interpretation of temperature indicators obtained using the proposed interpolation method and the curve of the dependence of the maximum deflection on time using a deformation model for describing the stress-strain state is proposed to identify the dependence of the concrete strength of reinforced concrete crossbars. The work also shows that the results obtained using the proposed method of identifying concrete strength reduction coefficients are adequate as their relative error is on average no more than 7 %. Based on the results, the possibility of its application to study the regularities of the decrease in the strength of reinforced concrete crossbars under fire conditions has been proven

Time-Series-Data Interpolation Applied to Boundary-Layer Profiles Measured on Different Flights

Turbulent boundary-layer profiles on an aircraft surface were measured during flight by pitot rakes in an experiment at subsonic speeds. Because separate flights have different flight sequences in terms of time, it is not easy to compare boundary-layer profiles measured on different flights with the corresponding premised conditions directly. Using one flight as a reference, this paper proposes a method to find the closest flight condition for each time instance from data from other flights by calculating a residual norm in combinations of flight variables. The results show that the proposed method successfully finds the best matches of the time instances from the second flight with those of the first flight. In addition, applying the interpolation method using response surface methodology further improves the accuracy of evaluation in the flight range of Mach 0.4 to Mach 0.8. The total uncertainty level of the proposed interpolation method was found to be 5.7%. Although this level of uncertainty is expected to be reduced, the effectiveness of the proposed interpolation method was presented in conjunction with an evaluation of its applicability to determine the riblet effect in reducing skin-friction drag qualitatively.

A Novel Analog Interpolation Method for Heterodyne Laser Interferometer

Laser interferometer technology is used in the precision positioning stage as an encoder. For better resolution, laser interferometers usually work with interpolation devices. According to the interpolation factor, these devices can convert an orthogonal sinusoidal signal into several square-wave signals via digital processing. The bandwidth of the processing will be the limitation of the moving speed of the positioning stage. Therefore, the user needs to make a trade-off between the interpolation factor and the moving speed. In this investigation, a novel analog interpolation method for a heterodyne laser interferometer has been proposed. This method is based on the principle of the lock-in amplifier (LIA). By using the proposed interpolation method, the bandwidth of the laser encoder system can be independent of the interpolation factor. This will be a significant benefit for the ultra-high resolution encoder system and the laser interferometers. The concept, design, and experiment are revealed in this manuscript. The experimental results show that the proposed interpolation method can reach nanometer resolution with a heterodyne laser interferometer, and the bandwidth of the signal is independent of the resolution.

Testing for Local Spatial Association Based on Geographically Weighted Interpolation of Geostatistical Data with Application to PM2.5 Concentration Analysis

Using local spatial statistics to explore local spatial association of geo-referenced data has attracted much attention. As is known, a local statistic is formulated at a particular sampling unit based on a prespecific proximity relationship and the observations in the neighborhood of this sampling unit. However, geostatistical data such as meteorological data and air pollution data are generally collected from meteorological or monitoring stations which are usually sparsely located or highly clustered over space. For such data, a local spatial statistic formulated at an isolate sampling point may be ineffective because of its distant neighbors, or the statistic is undefinable in the sub-regions where no observations are available, which limits the comprehensive exploration of local spatial association over the whole studied region. In order to overcome the predicament, a local-linear geographically weighted interpolation method is proposed in this paper to obtain the predictors of the underlying spatial process on a lattice spatial tessellation, on which a local spatial statistic can be well formulated at each interpolation point. Furthermore, the bootstrap test is suggested to identify the locations where local spatial association is significant using the interpolated-value-based local spatial statistics. Simulation with comparison to some existing interpolation and test methods is conducted to assess the performance of the proposed interpolation and the suggested test methods and a case study based on PM2.5 concentration data in Guangdong province, China, is used to demonstrate their applicability. The results show that the proposed interpolation method performs accurately in retrieving an underlying spatial process and the bootstrap test with the interpolated-value-based local statistics is powerful in identifying local patterns of spatial association.

Improving the phase reconstruction accuracy of simultaneous phase-shifted lateral shearing interferometry using a polarization redundant sub-region interpolation method.

In a simultaneous phase-shifted lateral shearing interferometry, a division of focal plane polarization camera is generally used as the phase-shifting device. However, acquiring simultaneous phase-shift interferograms in a single frame suffers from a lack of spatial resolution, significantly affecting the phase reconstruction accuracy. A polarization redundant sub-region interpolation (PRSI) method is proposed to solve this problem. This interpolation method distinguishes smooth regions from stripe fringe regions by calculating the polarization redundancy error of the synchronous phase shift interferogram. After sub-regional processing, resolution reconstruction is performed in the smoothed area using a fast convolutional bilinear interpolation method. In the streak detail region, the resolution reconstruction is performed based on the strength of the correlation between the orthogonal and non-orthogonal polarization channels crossing the streak region. The PRSI method can quickly reconstruct the lost pixels and accurately recover the stripe detail information. Experiment results show that the proposed interpolation method outperforms the existing dominant methods in terms of visual reconstruction effect and quantitative index of phase reconstruction.

Reducing volume and shape errors in front tracking by divergence-preserving velocity interpolation and parabolic fit vertex positioning

Volume conservation and shape preservation are two well-known issues related to the advection and remeshing in front tracking. To address these issues, this paper proposes a divergence-preserving velocity interpolation method and a parabolic fit vertex positioning method for remeshing operations for three-dimensional front tracking. Errors in preserving the divergence of the velocity field when interpolating the velocity from the fluid mesh to the vertices of the triangles of the front are a primary reason for volume conservation errors when advecting the front. The proposed interpolation method preserves the discrete divergence of the fluid velocity by construction and is compared in this work with other known interpolation methods in divergence-free and non-divergence-free test cases, with respect to volume conservation and shape preservation of the front. The presented interpolation method conserves the volume and shape up to an order of magnitude better than the conventionally used interpolation methods and is within the range of higher order interpolation methods at lower computational cost. Additionally, the parabolic fit vertex positioning method for remeshing operations locally approximates the front with a smooth polynomial surface, improving volume conservation and shape preservation by an order of magnitude compared to conventional remeshing algorithms.

Online interpolation of 5-axis machining toolpaths with global blending

Modern high-speed 5-axis machining toolpaths consist of densely discretized tool center points (TCP) and tool orientation vectors (TOV). This paper presents a global interpolation technique that can blend very densely discretized 5-axis toolpaths within user defined blending tolerance and interpolate them in real-time using minimal computational expense. Instead of geometric splines, Finite Impulse Response (FIR) low-pass filtering is used to blend TCP and TOV and interpolate them smoothly for synchronized 5-axis motion generation. Global blending errors of TCP and TOV are modeled based on path geometry, tool motion kinematics and dynamics of the FIR filter. These global blending errors are confined by modulating the machining feedrate. In other words, machining feedrate is adjusted, i.e. reduced and increased, to control the global blending accuracy along the 5-axis machining toolpath. A windowing scheme is proposed to solve this new feedrate scheduling problem. Since the proposed interpolation method is based on digital filtering (convolution), it enables online (real-time) interpolation of densely discretized 5-axis machining toolpaths in a real-time and at the same time provides control over the frequency spectrum of interpolated trajectories. The proposed global blending strategy delivers significant reduction in machining cycle-time as compared to conventional local blending techniques and generates smoother, frequency-controlled trajectories with a fraction of the computational effort required as compared to spline-based interpolation. Illustrative examples and experimental results are provided to showcase functionality and validate effectiveness of the proposed technique.

Spatiotemporal Variation of Aerosol Optical Depth Based on 3-D Spatiotemporal Interpolation

To solve the problem of low coverage of MODIS aerosol optical depth (AOD) products, this paper proposes a three-dimensional spatiotemporal interpolation method to predict missing values for time series AOD products. In this study, ordinary Kriging interpolation and three-dimensional spatiotemporal interpolation are applied to analyze the dynamics of AOD in Beijing-Tianjin-Hebei urban agglomeration (BTHUA), China, and the performances of the two methods are compared. The results show that the three-dimensional spatiotemporal interpolation has better performance in predicting missing data of AOD products. The proposed interpolation method provides a feasible solution for the establishment of long-term MODIS aerosol products with temporal and spatial consistency, and also provides effective data support for the study of urban environmental changes.

ЗАСТОСУВАННЯ ІНТЕРПОЛЯЦІЇ КУБІЧНИМИ СПЛАЙНАМИ В ІНТЕЛЕКТУАЛЬНІЙ ІНФОРМАЦІЙНІЙ СИСТЕМІ ПРОГНОЗУВАННЯ ФАЗОВОЇ СТАБІЛЬНОСТІ ТВЕРДИХ РОЗЧИНІВ

This research work is devoted to the use of cubic spline interpolation to solve the current problem of predicting the phase stability of solid solutions. The theory of isomorphic substitutions in Urusov crystals was used to calculate the mixing energies (interaction parameters) and critical decomposition temperatures (stability temperatures) of solid solutions. The proposed intelligent information system (IIS) automates the construction of diagrams, which allows to predict the thermodynamic stability of solid solutions. IIS also provides interactive features for user convenience. The obtained results can be useful in choosing the ratio of components in "mixed" matrices, the amount of activator in luminescent, laser and other practically important materials, as well as in matrices for immobilization of toxic and radioactive waste. The results of the application of interpolation on large segments, ie with a relatively large number of nodes, are often unsatisfactory. On the one hand, at large distances between nodes the interpolation accuracy decreases, and on the other hand, with increasing number of nodes due to the influence of high-order polynomials there are oscillations of the interpolation curve, because only in this way the curve can be forced to pass through given points. This state does not correspond to the real dependence resulting from the tabular values of the nodes. Therefore, it is proposed to use spline interpolation, which has a number of important advantages. First, it is high convergence. In contrast to Lagrange interpolation polynomials, the sequence of cubic splines on a uniform grid of nodes always converges to a continuous interpolated function. Secondly, we have minimal sensitivity to the error of the original data. Small changes in the values of the function at one or more adjacent interpolation points do not significantly affect the behavior of the spline at some distance from these points. As a consequence of the above - higher interpolation accuracy. As a result of the research the calculation of unknown coefficients for the proposed splines is formalized and the advantages of practical application of the proposed interpolation method are determined. The IIS of phase stability of solid solutions was improved using interpolation by cubic splines, as a result, the accuracy of the results was increased by 4.96%.

Pixelwise Dynamic Convolution Neural Network for LiDAR Depth Data Interpolation

A light detecting and ranging (LiDAR) system is an important means that takes an omni-directional view to collect precise surrounding 3D information in high sampling frequency. However, due to the architecture of a LiDAR sensor, LiDAR data typically contains much less information in the vertical direction compared to the horizontal direction. In addition, LiDAR data are often defected during measurement. There have been previous researches about LiDAR data interpolation using a high-resolution reference image. However, they suffer from the calibration error due to vibration or shock during operation and do not consider defected data. Here, we propose a reference-free interpolation method with considering the defected LiDAR data using a two-step network architecture. Our proposed method is designed first to exploit the rich information in the horizontal direction of the LiDAR data to restore the defected data and then increase the vertical resolution of LiDAR data. Since the proposed interpolation method is a reference-free approach, it if free from the calibration issue. We confirm that our proposed method shows better performance than existing interpolation methods and is effective as a pre-processing function in other applications. For example, our proposed method can improve the performance of the human segmentation. We also propose a pixelwise dynamic convolution layer as a component of the proposed interpolation method. The proposed dynamic convolution layer adaptively processes each pixel with variable kernels, while existing dynamic layers only use fixed kernels. Experimental results show that the proposed dynamic layer is more effective than existing dynamic layers for LiDAR data interpolation.

Ray tracing in thermally loaded optical systems

AbstractHigh‐power laser beams are usually imaged with the help of suitable optics. The propagation of such beams, through optical systems, often result in a focus shift. This is mainly due to the deposited power in the beam acting as a heat source in the optical elements. Finally, the resulting change in temperature leads to both, a deformation of the lens surface, and a change of the refractive index in the lens. Ray tracing and the finite element method are needed in order to analyze the above effects. The accuracy and the computational time of focus shift calculations, in both simulation techniques, are strongly influenced by the interpolation of the data. This paper will present, a newly proposed interpolation method, allowing a fast and accurate interpolation of data using an unstructured finite element grid. This method will specifically focus on the accurate calculation of laser beam thermal load inside an optical lens.

An interpolation-based lattice Boltzmann method for non-conforming orthogonal meshes

We propose an interpolation-based lattice Boltzmann formulation that is applicable to non-conforming orthogonal meshes. This interpolation configuration allows the use of localized and directional refinement that reduces mesh sizes and makes them well adapted for solving flows in various configurations, including aerodynamic shapes in free streams. The novel aspect of the proposed method lies in the interpolation scheme selection algorithm, which uses local mesh topology for choosing a suitable combination of nodes and polynomial terms. The objective of this study consists of validating the scheme accuracy with well documented laminar incompressible flow test cases. The results demonstrate the capability of the proposed interpolation method to successfully solve closed and open flows with either straight or curved walls. Simulations for the flow over a NACA 0012 airfoil show that the aerodynamic coefficients are captured correctly using a mesh with large aspect ratio cells near the wall and in the airfoil wake.

Solar PV Modelling and Parameter Extraction Using Iterative Algorithms

In the present work, improvement of Newton’s method with high order convergence has been suggested. This improvement is based on Two-Point Bracketing method. The proposed method Inverse Quadratic Interpolation method requires two steps per iteration. By means of the numerical equation of the one diode model of PV equivalent circuit, included five values of R from 1 to 5 ohms (load resistance of the circuit). The results obtained explain that the new suggested technique is easy to use, more accurate and efficient than other numerical methods are presented here.

Inferring trade directions in fast markets

The reliability of trade classification algorithms that identify the liquidity demander in financial markets transaction data has been questioned due to an increase in the frequency of quote changes. Hence, this paper proposes a new method. While established algorithms rely on an ad hoc assignment of trades to quotes, the proposed full-information (FI) algorithm actively searches for the quote that matches a trade. The FI algorithm outperforms the existing ones, particularly at low timestamp precision: For data timestamped at seconds misclassification is reduced by half compared to the popular Lee-Ready algorithm. These improvements also carry over into empirical applications such as the estimation of transaction costs. The recently proposed interpolation method and bulk volume classification algorithm do not offer improvements.

Analysis and assasment method of the Chirchik river flow for water supply and water use

The scientific work is devoted to studying hydroecological problems and methods for assessing the transformation of river water on the example of the Chirchik River, which flows through large industrial centers of the Republic of Uzbekistan and the territory of its capital, Tashkent. Investigations of quantitative and qualitative transformation of river water runoff were carried out using the interpolation method. The main task is to describe the method of interpolation of hydrometeorological data of the territories; For such system, the center in this work adopted a material point that characterizes the movement of the whole system; for this research, such as the hydrometeorological parameters of the territory. The data of the hydrometeorological service of the Republic of Uzbekistan were used when interpolating climatic parameters, which are the main determining factors in the formation and transformation of the river flow of Chirchik. In the proposed interpolation method, a combined system is created, consisting of a landscape-natural component, a system representing a moving mass with a single center. The meteorological parameters of the territory are taken as elements of the mass system, which have their centers of change-movement. The performed test calculations showed that the difference in meteorological parameters affects the position of their centers; each parameter: atmospheric pressure, precipitation, humidity, and temperature, etc., has its center.

Optimal design for kernel interpolation: Applications to uncertainty quantification

The paper is concerned with classic kernel interpolation methods, in addition to approximation methods that are augmented by gradient measurements. To apply kernel interpolation using radial basis functions (RBFs) in a stable way, we propose a type of quasi-optimal interpolation points, searching from a large set of candidate points, using a procedure similar to designing Fekete points or power function maximizing points that use pivot from a Cholesky decomposition. The proposed quasi-optimal points results in smaller condition number, and thus mitigates the instability of the interpolation procedure when the number of points becomes large. Applications to parametric uncertainty quantification are presented, and it is shown that the proposed interpolation method can outperform sparse grid methods in many interesting cases. We also demonstrate the new procedure can be applied to constructing gradient-enhanced Gaussian process emulators.

Inferring Trade Directions in Fast Markets

The reliability of established trade classification algorithms that identify the liquidity demander in financial markets transaction data has been questioned due to an increase in the frequency of quote changes. Hence, this paper proposes a new method. While established algorithms rely on an ad hoc assignment of trades to quotes, the new algorithm actively searches for the quote that matches a trade. Using an ideal data set that identities the liquidity demander I impose various deficiencies to simulate more typical data sets and find that the new method considerably outperforms the existing ones, particularly at lower timestamp precisions: at data timestamped to seconds the misclassification rate is reduced by half. These improvements also carry over into empirical applications. A risk-averse investor would pay up to 33 basis points per annum to base her portfolio allocation on transaction cost estimates obtained from the new method instead of the popular Lee-Ready algorithm. The recently proposed interpolation method (Holden and Jacobsen, 2014) and the bulk volume classification algorithm (Easley, de Prado and O’Hara, 2012), on the other hand, do not offer improvements.

An efficient method for modeling terrain and complex terrain boundaries in constrained wind farm layout optimization

A novel and efficient approach for modeling irregular domain boundaries and enforcing complex land-based constraints in wind farm layout optimization is presented. The presented method can be used to enforce constraints and represent complex domains for which an analytical expression is not available. The developed approach uses support vector domain description to obtain an analytical expression of the domain from data points sampled from the various regions for wind turbine placements. Such an analytical, continuous, differentiable description can then be used for wind farm layout optimization using gradient based and non-gradient based optimization algorithms. The applicability of the method was demonstrated on a wind farm layout optimization problem where several regions of the terrain were restricted. The method was shown to accurately and efficiently model regular, irregular, convex, non-convex and discontinuous domains/regions using only scattered data sampled from the domains. An efficient method for terrain modeling and interpolation is also presented. The proposed interpolation method uses quadtree decomposition to decompose the large interpolation problem into several smaller interpolation problems thereby reducing the complexity of the interpolation. The framework developed (libSVDD) is also made publicly available.