Interpolation Process Research Articles

Study on the application of 3D imaging based on the γ-photon silk thread method for visualisation and detection of flow fields

As a flow display technique, the silk thread method can clearly show the state of the flow field. However, displaying the state of the flow field in industrial closed metal cavities is impossible, and results of the traditional silk thread method fail to present depth information. To address these limitations, we propose a display method based on γ-photon silk thread 3D imaging. Firstly, a flow field visualization experimental platform applicable for industrial closed metal cavity was designed. Then, aiming at the shortcomings of insufficient γ-photon scanning data and limited imaging quality in flow field visualization, an adaptive sinogram interpolation-iterative filtering reconstruction algorithm was proposed to expand the data via the adaptive interpolation processing of the sinogram in image reconstruction. Beltrami filtering was also embedded in the iterative algorithm to effectively reduce noise and artifacts in the imaging image. Finally, the internal flow field inspection of the NACA0018 airfoil and the industrial confinement turbine were used as examples to visualise the wing upper surface flow and turbine blade passage secondary flow, respectively, and the results were consistent with those of the numerical simulation analysis. As the angle of attack of the wing increased, laminar flow separation occurred, and the silk thread structure state changed to the point where the aircraft stalled. After the imaging map analysis, the stall angle ranged between (15°,19°), which is consistent with the simulation results. In the turbine blade passage secondary flow detection, the imaging map formed a horseshoe vortex with airflow separation at the central saddle point and silk threads clearly presenting the structural state of the flow field along different directions.

Fluctuations in Radiation Use Efficiency Throughout the Growth Cycle in Diploid Potato Crop

The capture of incoming solar radiation under unlimited light, water, and nutrient conditions by plant canopies and converting it into biomass has been described as radiation use efficiency (RUE). RUE has been computed as a function of biomass accumulation and intercepted photosynthetically active radiation without considering the loss of photoassimilates due to respiratory processes. This study evaluated the RUE in diploid potato crop (Solanum phureja Juz. et Buk.) across six experiments in Colombia. Total biomass was measured during the crop season from the early vegetative stage through maturity. However, this proposal involves not only the total biomass accumulated concerning the amount of photosynthetically active radiation intercepted but also took into account the losses by respiration, following Thornley respiration approach. This research demonstrates that the RUE is not a constant value as the respiration process leads to RUE values being variable in a non-linear way over time. The daily RUE simulation, conducted through an interpolation process, revealed significant variation from emergence to the end of the cycle. This indicates an error in assuming a constant RUE throughout the entire growth period, particularly in assessing its physiological impact across the entire growth and development crop cycle.

Developing an Automated Spectrophotometer with RGB LED and Light Sensor Using Arduino Microcontroller

This research used RGB LED (Red Green Blue Light Emission Diode), LDR (Light Dependent Resistant) sensors, 3D printed sampling cartridge, and Arduino Mega to create a spectrophotometer with automation software to select wavelength, calculate calibration parameters, and report the concentration of the materials being studied. Spectrophotometers are finding applications across many fields, including clinical laboratories, pharmaceuticals, molecular biology, biochemistry, and even the medical realm. This study assembled an Arduino mega system coupled with software for the automatic selection of best-fit color light, calibration curve, and actual concentration interpolation processes. Dilution solutions from multiple chemical materials were evaluated to examine their linearity of calibration curves. Our study demonstrated that the tested chemical samples revealed a significant regression coefficient of up to 0.9945 for serial dilution solutions. Relative concentrations were measured with remarkable precision, exhibiting less than 5.0 % error compared to a commercial spectrophotometer. These findings highlight the viability of the RGB spectrophotometer and emphasize its potential with the promise of further refinement in development.

Compressive sensing ISAR imaging with low-rank constraint and anisotropic spatial total variation processing

In order to suppress random noise and remove stripe interference in ISAR imaging, a Compressive Sensing method is proposed for super-resolution ISAR imaging in this paper, which is named LR-ASTV (Low-rank and Anisotropic Spatial Total Variation) algorithm here. In this algorithm, the original echo HRRP is transformed into echo HRRP of MMV model with radial interpolation processing at first. Subsequently, an optimization objective function based on Compressive Sensing framework is formulated which includes the sparsity constraint and low-rank constraint, and this optimization problem is solved by JLRS algorithm to generate an initial ISAR image from which the random noise has been eliminated. The initial image is then subjected to further refinement using the Anisotropic Spatial Total Variation (ASTV) processing, ultimately yielding the final ISAR image with stripe interference removed. To validate the effectiveness of the LR-ASTV algorithm, ISAR imaging experiments based on simulated and measured data at different SNRs are completed, and the imaging results of the LR-ASTV algorithm are compared with those of other three algorithms including the LSM-ME2 algorithm, the JLRS algorithm and the LRPB algorithm. It can be found that the LR-ASTV algorithm has obvious superiority in suppressing random noise and removing stripe interference, and can provide ISAR images of higher clarity. The quality evaluation for ISAR images also shows that the LR-ASTV algorithm has lower image entropy index and higher image contrast index than the other three ISAR imaging algorithms.

An Adapted NURBS Interpolator with a Switched Optimized Method of Feed-Rate Scheduling

With the increasing demand for processing precision in the manufacturing industry, feed-rate scheduling is a crucial component in achieving the processing quality of complex surfaces. A smooth feed-rate profile not only guarantees machining quality but also improves machining efficiency. Although the typical offline feed-rate scheduling method possesses good processing efficiency, it may not provide an optimal solution due to the NP-hard problem caused by the feed-rate scheduling of continuous curve segments, which easily results in excess kinetic limitations and feed-rate fluctuations in a real-time interpolation. Instead, the FIR (Finite Impulse Response) method is widely used to realize interpolation in real-time processing. However, the FIR method will filter out a large number of high-frequency signals, leading to a low-processing efficiency. Further, greater acceleration or deceleration is required to ensure the interpolation passes through the segment end at a predefined feed rate and the deceleration in the feed rate profile appears earlier, which allows the interpolation to easily exceed the kinetic limitation. At present, a simple offline or online method cannot realize the global optimization of the feed-rate profile and guarantee the machining efficiency. Moreover, the current feed-rate scheduling that considers both offline and online methods does not consider the situation that the call of offline data and online prediction data will lead to a decrease in the real-time performance of the CNC system. Further, real-time feed-rate scheduling data tend to dominate the whole interpolation process, thus reducing the effect of the offline feed-rate scheduling data. Hence, based on the tool path with C3 continuity (Cubic Continuously Differentiable), this paper first presents a basic interpolation unit relevant to the S-type interpolation feed-rate profile. Then, an offline local smooth strategy is proposed to smooth the feed-rate profile and reduce the exceeding of kinetic limitations and feed-rate fluctuations caused by frequent acceleration and deceleration. Further, a global online smoothing strategy based on the data generated by offline pre-interpolation is presented. What is more, FIR login and logout conditions are proposed to further smooth the feed-rate profile and improve the real-time performance and machining efficiency. The case study validates that the proposed method performs better in kinetic results compared with the typical offline and FIR methods in both the simulation experiment and actual machining experiments. Especially, in actual processing experiments, the proposed method obtains a 28% reduction in contour errors. Further, the proposed method compared with the FIR method obtains a 15% increase in machining efficiency but only a 4% decrease compared with the typical offline method.

Coupled thermal-mechanical analysis of power electronic modules with finite element method and parametric model order reduction

This work presents a new approach for performing a parametric study and examining nonlinear material behaviours of a coupled thermal-mechanical model of a Power Electronics Module (PEM) by integrating the Finite Element Method (ANSYS-FEM) with Parametric Model Order Reduction (pMOR). The considered coupling method solves the thermal and structural models concurrently compared to the widely practised sequential coupling method. Instead of constant parameter values, which are generally regarded for pMOR studies, the temperature-dependent material properties of the wire material have been parametrised in the work using the pMOR method. A generalised 2D model has been regarded here for thermal-mechanical analysis with the pMOR approach, parametrising temperature-dependent coefficient of thermal expansion (CTE) and Young’s modulus (E) of the wire material to explore their impact on wire bonds. The matrix interpolation method has been applied here for the pMOR study, and PRIMA, a Krylov subspace-based model order reduction (MOR) technique, has been exercised for local model order reductions. A new efficient process of matrix interpolation, based on the Lagrange interpolation technique, has been developed to implement matrix interpolation in the parametric reduced order model (pROM). The local reduced order models (ROMs) have a degree of freedom (DOF) of just 8, compared to the full-order models’ (FOMs) of 50,602. The pROM provides an excellent solution and reduces computational time by 84% for the presented case.

An error predict-correction formula of the load vector in the BSLM for solving three-dimensional Burgers’ equations

This paper aims to develop an algorithm reducing the computational cost of the backward semi-Lagrangian method for solving nonlinear convection–diffusion equations. For this goal, we introduce an error predict-correction formula (EPCF) of the load term for the Helmholtz system. The EPCF is built up to involve the same values as solving the perturbed Cauchy problem, which allows the reuse of the values. These reuses dramatically reduce the computational cost by eliminating the interpolation processes to evaluate the load term in most computational domains. The algorithm also produces a stable solution, even where the original solution has a sharp gradient, by introducing an indicator to distinguish the sharpness of the solution. Furthermore, the proposed algorithm discusses fast solvers of the discrete systems for the perturbed Cauchy problem, for which we utilize an eigenvalue decomposition theory. To show the adaptability and efficiency of the proposed algorithm, we apply it to the convection–diffusion equations such as two and three-dimensional viscous Burgers’ equations. Through several simulations, we confirm that the proposed algorithm for the load term radically reduces the computational cost, and the indicator for stiff components guarantees precision.

Simultaneous monitoring of the limited area ionosphere with the use of GPS and ionosonde

The importance of this study lies in its contribution to the field of ionospheric science, particularly in the monitoring and prediction of ionospheric parameters. This study focuses on comparing two techniques for spatio-temporal kriging of critical ionospheric parameters, namely the F2 layer critical frequency (foF2) and Total Electron Content (TEC), under both quiet and disturbed ionospheric conditions. The first technique, Ordinary Kriging (OK), relies solely on foF2 data, while the second technique, Kriging with External Drift (KED), incorporates the dynamic relationship between foF2 and TEC data to improve the interpolation process. This study demonstrates how KED, which utilizes dynamic secondary information, offers advantages over OK. By simultaneously monitoring the ionosphere from a single ionosonde station and collecting data from visible GPS satellites, KED enhances the accuracy of spatial structural analysis, enabling more precise estimations of ionospheric characteristics across interpolation grid nodes. The research highlights that the non-uniform distribution of ionosonde stations, especially in regions with limited foF2 data, can benefit from KED's incorporation of TEC data. Additionally, the study reveals the potential for improving TEC maps by assimilating foF2 data located at the periphery of the observation area. Furthermore, the paper discusses the determination of semivariogram structures for both foF2 and TEC data, emphasizing the spatial correlations between data points. These findings contribute to a better understanding of ionospheric behavior and the potential for enhanced ionospheric modeling.

A new fast algorithm for computing the mock-Chebyshev nodes

Interpolation by polynomials on equispaced points is not always convergent due to the Runge phenomenon, and also, the interpolation process is exponentially ill-conditioned. By taking advantage of the optimality of the interpolation processes on the Chebyshev-Lobatto nodes, one of the best strategies to defeat the Runge phenomenon is to use the mock-Chebyshev nodes for polynomial interpolation. Mock-Chebyshev nodes asymptotically follow the Chebyshev distribution, and they are selected from a sufficiently large set of equispaced nodes. However, there are few studies in the literature regarding the computation of these points.In a recent paper [1], we have introduced a fast algorithm for computing the mock-Chebyshev nodes for a given set of (n+1) Chebyshev-Lobatto points using the distance between each pair of consecutive points. In this study, we propose a modification of the algorithm by changing the function to compute the quotient of the distance and show that this modified algorithm is also fast and stable; and gives a more accurate grid satisfying the conditions of a mock-Chebyshev grid with the complexity being O(n). Some numerical experiments using the points obtained by this modified algorithm are given to show its effectiveness and numerical results are also provided. A bivariate generalization of the mock-Chebyshev nodes to the Padua interpolation points is discussed.

Deep Interpolation of Remote Sensing Land Surface Temperature Data with Partial Convolutions.

Land Surface Temperature (LST) is an important resource for a variety of tasks. The data are mostly free of charge and combine high spatial and temporal resolution with reliable data collection over a historical timeframe. When remote sensing is used to provide LST data, such as the MODA11 product using information from the MODIS sensors attached to NASA satellites, data acquisition can be hindered by clouds or cloud shadows, occluding the sensors' view on different areas of the world. This makes it difficult to take full advantage of the high resolution of the data. A common solution to interpolating LST data is statistical interpolation methods, such as fitting polynomials or thin plate spine interpolation. These methods have difficulties in incorporating additional knowledge about the research area and learning local dependencies that can help with the interpolation process. We propose a novel approach to interpolating remote sensing LST data in a fixed research area considering local ground-site air temperature measurements. The two-step approach consists of learning the LST from air temperature measurements, where the ground-site weather stations are located, and interpolating the remaining missing values with partial convolutions within a U-Net deep learning architecture. Our approach improves the interpolation of LST for our research area by 44% in terms of RMSE, when compared to state-of-the-art statistical methods. Due to the use of air temperature, we can provide coverage of 100%, even when no valid LST measurements were available. The resulting gapless coverage of high resolution LST data will help unlock the full potential of remote sensing LST data.

Improved Oversampling Algorithm for Imbalanced Data Based on K-Nearest Neighbor and Interpolation Process Optimization

The problems of imbalanced datasets are generally considered asymmetric issues. In asymmetric problems, artificial intelligence models may exhibit different biases or preferences when dealing with different classes. In the process of addressing class imbalance learning problems, the classification model will pay too much attention to the majority class samples and cannot guarantee the classification performance of the minority class samples, which might be more valuable. By synthesizing the minority class samples and changing the data distribution, unbalanced datasets can be optimized. Traditional oversampling algorithms have problems of blindness and boundary ambiguity when synthesizing new samples. A modified reclassification algorithm based on Gaussian distribution is put forward. First, the minority class samples are reclassified by the KNN algorithm. Then, different synthesis strategies are selected according to the combination of the minority class samples, and the Gaussian distribution is used to replace the uniform random distribution for interpolation operation under certain classification conditions to reduce the possibility of generating noise samples. The experimental results indicate that the proposed oversampling algorithm can achieve a performance improvement of 2∼8% in evaluation metrics, including G-mean, F-measure, and AUC, compared to traditional oversampling algorithms.

PA-NeRF, a neural radiance field model for 3D photoacoustic tomography reconstruction from limited Bscan data.

We introduce a novel deep-learning-based photoacoustic tomography method called Photoacoustic Tomography Neural Radiance Field (PA-NeRF) for reconstructing 3D volumetric PAT images from limited 2D Bscan data. In conventional 3D volumetric imaging, a 3D reconstruction requires transducer element data obtained from all directions. Our model employs a NeRF-based PAT 3D reconstruction method, which learns the relationship between transducer element positions and the corresponding 3D imaging. Compared with convolution-based deep-learning models, such as Unet and TransUnet, PA-NeRF does not learn the interpolation process but rather gains insight from 3D photoacoustic imaging principles. Additionally, we introduce a forward loss that improves the reconstruction quality. Both simulation and phantom studies validate the performance of PA-NeRF. Further, we apply the PA-NeRF model to clinical examples to demonstrate its feasibility. To the best of our knowledge, PA-NeRF is the first method in photoacoustic tomography to successfully reconstruct a 3D volume from sparse Bscan data.

Spatiotemporal stacking method with daily‐cycle restrictions for reconstructing missing hourly PM2.5 records

AbstractThe reliability of hourly PM2.5 data obtained from air quality monitoring stations is compromised as a result of the missing values, thereby impeding the thorough examination of crucial information. In this paper, we present a spatiotemporal (ST) stacking machine learning (ML) method with daily‐cycle restrictions for reconstructing missing hourly PM2.5 records. First, the ST neighbors for the target station with missing values are selected at a daily scale. Subsequently, the non‐null data within the ST neighbors undergo an iterative P‐BSHADE interpolation process for re‐interpolation. Next, a stacking ML model is constructed using the re‐interpolation values and several environmental factors associated with PM2.5 as the predictors, while the observed PM2.5 is taken as the independent variable. Finally, the missing values are reconstructed by inputting the predictors into the trained stacking model. The study utilized hourly PM2.5 data in the Beijing‐Tianjin‐Hebei region as a case study to assess the effectiveness of the proposed method, using daily missing ratios of 10%, 30%, and 50%, respectively. The accuracy of the proposed method was then compared to four contemporary ST interpolation methods. The results indicate that the proposed method exhibits superior performance compared to the classical methods. Specifically, it achieves a reduction in the average root mean square error and mean absolute error by at least 40.6% and 40.1%, respectively. Additionally, the proposed method demonstrates the successful recovery of extreme values in the hourly PM2.5 records, in contrast to the classical methods which often exhibit a tendency to overestimate low values and underestimate high values. Overall, the proposed method presents a viable and efficient approach to recover missing values in the hourly PM2.5 records that demonstrate evident daily periodic patterns.

Technical note: Accurate, reliable, and high-resolution air quality predictions by improving the Copernicus Atmosphere Monitoring Service using a novel statistical post-processing method

Abstract. Starting from the regional air quality forecasts produced by the Copernicus Atmosphere Monitoring Service (CAMS), we propose a novel post-processing approach to improve and downscale results on a finer scale. Our approach is based on the combination of ensemble model output statistics (EMOS) with a spatio-temporal interpolation process performed through the stochastic partial differential equation–integrated nested laplace approximation (SPDE-INLA). Our interpolation approach includes several spatial and spatio-temporal predictors, including meteorological variables. A use case is provided that scales down the CAMS forecasts on the Italian peninsula. The calibration is focused on the concentrations of several air quality pollutants (PM10, PM2.5, NO2, and O3) at a daily resolution from a set of 750 monitoring sites, distributed throughout the Italian country. Our results show the key role that conditioning variables play in improving the forecast capabilities of ensemble predictions, thus allowing for a net improvement in the calibration with respect to ordinary EMOS strategies. From a deterministic point of view, the performance of the predictive model shows a significant improvement in the performance of the raw ensemble forecast, with an almost-zero bias, significantly reduced root mean square errors, and correlations that are almost always higher than 0.9 for each pollutant; moreover, the post-processing approach is able to significantly improve the prediction of exceedances, even for very low thresholds, such as those recently recommended by the World Health Organisation. This is particularly significant if a forecasting approach is used to predict air quality conditions and plan adequate human health protection measures, even for low alert thresholds. From a probabilistic point of view, the quality of the forecast was verified in terms of reliability and credible intervals. After post-processing, the predictive probability density functions were sharp and much better calibrated than the raw ensemble forecast. Finally, we present some additional results based on a set of gridded (4 km × 4 km) maps covering the entire Italian country for the detection of areas where pollution peaks occur (exceedances of the current and/or proposed regulatory thresholds).

Penerapan Metode Interpolasi Linear dan Geometric Mean Filter Pada Citra Resolusi Rendah Hasil Resampling

In addition to the color representation contained in a digital image, the size of the image will also greatly affect the image processing process. In some cases of image acquisition, sometimes the size of the image obtained does not correspond to the desired one. Pattern recognition processes, such as vehicle license plate recognition, may result in incorrect output if the size of the processed input image is not appropriate. Therefore, determining the size of a digital image is very important in further image processing. To solve such problems can be done by enlarging the size of the image through the process of interpolation or resampling. Image magnification is the process of enlarging the size of a digital image from its original size to a new and different size based on the desired magnification scale. However, as a result of enlarging the image obtained there is always a blur, so the image will look like a checkerboard (split). This situation occurs because during the magnification process the resolution of the new image becomes lower. Thus, additional methods are needed to improve the image quality of the resampling results. This study aims to improve the low-resolution image quality of resampling results by applying Linear Interpolation and Geometric Mean Filter methods. The test results showed that the Linear Interpolation method was able to produce a new image that was larger than the original image and the Geometric Mean Filter method could improve the image quality of the enlarged image so that the details of the information in the image are better and clearly seen visually. And to find out if the image enlarged from the Linear Interpolation and Geometric Mean Filter is good or not, we will use the Mean Squared Error (MSE) and Peak Signal to Noise Ratio (PSNR) methods. Keywords : Image, Interpolasi Linear,Geometric Mean Filter, PSNR, MSE.

Forecasting superstore fruit and vegetable sales based on ARIMA-LSTM

In the context of a fresh food supermarket, managing perishable vegetables, which have a notably limited shelf life, maintaining optimal stock levels becomes imperative for safeguarding profitability. This research paper intricately explores the analysis of numerous datasets using Power Query and Power BI, with a pivotal focus on devising a succinct coding system. To ensure data quality, outliers are meticulously eliminated using advanced techniques like linear interpolation and Z-Score processing. The ARIMA time series model is employed to predict the sales volume for each category in July, having been trained on data from June 2022 to June 2023, adeptly capturing historical sales patterns and emerging trends. Additionally, a parameter-tuned LSTM recurrent neural network, optimized with Adam's algorithm, is utilized to refine predictions, considering its inherent memory capabilities. A thoughtfully designed weighted average approach combines outputs from both models, strategically minimizing overfitting and enhancing prediction accuracy. The resultant research fortifies inventory management optimization, bolstering the supermarket's profitability while effectively meeting customer demands.

Sweep interpolation: a cost-effective semi-Lagrangian scheme in the Global Environmental Multiscale model

Abstract. The interpolation process is the most computationally expensive step of the semi-Lagrangian (SL) approach for solving advection and is commonly used in numerical weather prediction (NWP) models. It has a significant impact on the accuracy of the solution and can potentially be the most expensive part of model integration. The sweep algorithm, which was first described by Mortezazadeh and Wang (2017), performs SL interpolation with the same computational cost as a third-order polynomial scheme but at the accuracy of the fourth order. This improvement is achieved by using two third-order backward and forward polynomial interpolation schemes in two consecutive time steps. In this paper, we present a new application of the sweep algorithm within the context of global forecasts produced with Environment Climate Change Canada's Global Environmental Multiscale (GEM) model. Results show that the SL scheme with sweep interpolation is computationally more efficient compared to a conventional SL scheme with fourth-order polynomial interpolation, especially when a very large number of passive tracers are advected. An additional advantage of this new approach is that its implementation in a chemical and weather forecast model requires minimum modifications of the interpolation weighting coefficients. An analysis of the computational performance for a set of theoretical benchmarks as well as a global ozone forecast experiment show that up to 15 % reduction in total wall clock time is achieved. Forecasting experiments using the global version of the GEM model and the new interpolation show that the sweep interpolation can perform very well in predicting ozone distribution, especially in the tropopause region, where transport processes play a significant role.

Generative interpolation via a diffusion probabilistic model

Seismic data interpolation is essential in a seismic data processing workflow, recovering data from sparse sampling. Traditional and deep-learning-based methods have been widely used in the seismic data interpolation field and have achieved remarkable results. In this paper, we develop a seismic data interpolation method through the novel application of diffusion probabilistic models (DPMs). DPM transforms the complex end-to-end mapping problem into a progressive denoising problem, enhancing the ability to reconstruct complex situations of missing data, such as large proportions and large-gap missing data. The interpolation process begins with a standard Gaussian distribution and seismic data with missing traces and then removes noise iteratively with a UNet trained for different noise levels. Our DPM-based interpolation method allows interpolation for various missing cases, including regularly missing, irregularly missing, consecutively missing, noisy missing, and different ratios of missing cases. The ability to generalize to different seismic data sets is also discussed in this paper. Numerical results of synthetic and field data indicate satisfactory interpolation performance of the DPM-based interpolation method in comparison with the f- x prediction filtering method, the curvelet transform method, the low-dimensional manifold method (LDMM), and the coordinate attention-based UNet method, particularly in cases with large proportions and large-gap missing data. Diffusion is all we need for seismic data interpolation.

Estimating the Lebesgue constant for the Chebyshev distribution of nodes

In this paper an approach to estimation of the Lebesgue constant for the Lagrange interpolation process with nodes in the zeros of Chebyshev polynomials of the first kind is done. Two-sided estimation of this constant is carried out by using the logarithmic derivative of the Euler gamma function and of the Riemann zeta function. The choice of interpolation nodes is due to the fact that with a fixed number of Chebyshev nodes, the Lebesgue constant tends to its minimum value, thus reducing the error of algebraic interpolation and providing less sensitivity to rounding errors. The expressions for the upper and the lower bounds of this constant are represented as finite sums of an asymptotic alternating series. Based on the expressions obtained, these boundaries are calculated depending on the number of nodes of the interpolation process. The error of each of the boundaries’ value is estimated based on the first discarded term in the corresponding asymptotic series. The results of the calculations are presented in tables showing deviations of the Lebesgue constant from its lower and upper estimated bounds. Dependence of the values’ errors on the number of Chebyshev nodes is depicted in these tables as well. It is numerically shown that with an increase in the number of these nodes, the estimation boundaries rapidly get close to each other. The presented results can be used in the theory of interpolation to estimate the norm of the operator matching a function to its interpolation polynomial and to estimate a deviation of the constructed perturbed polynomial from the unperturbed one.

LONG SHORT-TERM MEMORY FOR PREDICTION OF WAVE HEIGHT AND WIND SPEED USING PROPHET FOR OUTLIERS

The reason fishermen lose control is wave height and wind speed. The impact is also felt by all users of the marine sector. This research uses the Long Short Term Memory (LSTM) method because this method has accurate values in the forecasting process with a lot of historical data and uses the Prophet method to detect outliers with Newton interpolation to replace the detected outlier data. The total number of data was 2074 obtained from BMKG Perak Surabaya from January 2020 to November 2022 at four research points, namely north, northeast, east and south points. The test results provide varying error values with MAPE as the model evaluation value. The error value for sea wave height at the north, northeast, east and south points is 13.32 respectively; 13.32; 9.32 and 8.85 with data without interpolation. Meanwhile, the error value in the wind speed data is 14.74; 14.85; 15.14 and 14.52 with a 3rd order Newton interpolation process at the northeast and east points. MAPE values below 20% prove that the LSTM model is good for predicting wave height and wind speed data at four points in Sumenep Regency. The system implementation is made into a web-based application.