Existing Interpolation Method Research Articles

Regression Trees on Grassmann Manifold for Adapting Reduced-Order Models

Low-dimensional and computationally less-expensive reduced-order models (ROMs) have been widely used to capture the dominant behaviors of high-4dimensional systems. An ROM can be obtained, using the well-known proper orthogonal decomposition (POD), by projecting the full-order model to a subspace spanned by modal basis modes that are learned from experimental, simulated, or observational data, i.e., training data. However, the optimal basis can change with the parameter settings. When an ROM, constructed using the POD basis obtained from training data, is applied to new parameter settings, the model often lacks robustness against the change of parameters in design, control, and other real-time operation problems. This paper proposes to use regression trees on Grassmann manifold to learn the mapping between parameters and POD bases that span the low-dimensional subspaces onto which full-order models are projected. Motivated by the observation that a subspace spanned by a POD basis can be viewed as a point in the Grassmann manifold, we propose to grow a tree by repeatedly splitting the tree node to maximize the Riemannian distance between the two subspaces spanned by the predicted POD bases on the left and right daughter nodes. Five numerical examples are presented to comprehensively demonstrate the performance of the proposed method, and compare the proposed tree-based method to the existing interpolation method for POD basis and the use of global POD basis. The results show that the proposed tree-based method is capable of establishing the mapping between parameters and POD bases, and thus adapt ROMs for new parameters.

A small modification of interpolation method for diffusion coefficients at boundary interfaces

In this paper, a small modification of interpolation method for diffusion coefficients at boundary interfaces is presented. A one dimension steady source-free diffusion equation with variable diffusion coefficient is taken as an example to verify the effectiveness of the modification. The existing interpolation method used in literatures for computing diffusion coefficients at boundary interfaces is analyzed, the existing method seems reasonable in physics but not in mathematics, and it is accurate only if diffusion coefficients are constant or weakly nonlinear. The conclusion that diffusion coefficients at boundary interfaces should be specified by interior nodes near the boundary, is thus derived, such as λb should be specified by λP. The modification is evaluated by solving several diffusion problems with non-linear diffusion coefficients. Numerical tests show that the modification proposed in this paper can obviously improve the accuracy of non-linear diffusion coefficients problems numerical solution. More reasonable solutions can be obtained through the modified method, Especially for the problem IX the average error is reduced from 24.94 to 9.94e−1.

DOUBLE COMPRESSION BASED LOW BANDWIDTH VIDEO TRANSMITTER

It is very difficult to imagine our modern life without data. As new technologies and data volume increase, sending them quickly is becoming one of the most important issues. Compression methods are commonly used to transfer data faster when transmitting data. Image compression is one of the data compression types used to compress digital images, to reduce their cost for storage or transmission. In this paper, we propose double compression based low bandwidth video transmitter. The device is capable of transmitting data two-stage compression. The first stage is compression based on the existing interpolation method. In the second stage, it is compressed based on the JPEG method. The relationship between bandwidth and quality in image transmission is also analyzed.

Fast simulation of non-stationary wind velocity based on time-frequency interpolation

The wind non-stationary features have a great influence on structural response analysis. The spectral representation method widely used to generate the non-stationary excitation suffers from lower efficiency when the simulation points become large. The Cholesky decomposition is a critical step and also a time-consuming procedure. Although the existing interpolation method is conducted in frequency direction, the number of Cholesky decomposition is still large. In this study, the time-frequency interpolation scheme is proposed to conduct two rounds of spline interpolation along frequency direction and time direction respectively. Then the quartic polynomial transform is developed to transform the uniform distribution of frequency into non-uniform distribution. The number of interpolation points is defined by error and computational time. Numerical example involving the simulation of fluctuating wind velocities along vertical direction shows that the proposed method reflects the target spectrum very well and maintains steadily high efficiency in the interpolation procedure of Cholesky decomposition. Comparing with existing interpolation method, more than 60% of computational time can be saved, and the accuracy of the two methods is close to each other. The time-frequency interpolation speeding up decomposition greatly is suitable for simulation of non-stationary wind velocity in large structures.

3D Reconstruction of Ground Crops Based on Airborne LiDAR Technology

Due to its light weight and high scanning accuracy, LiDAR (Light Detection and Ranging) has been widely used in surveying, unmanned, and instant map construction. In agriculture, LiDAR can directly collect point cloud data of ground crops. After the processing of denoising, interpolation and other algorithms, the 3D digital model of ground crops will be established to be able to timely observe crop growth. Its high degree of automation. This paper first sets up a hardware system for airborne LiDAR, then the principle of point cloud data generation and the derivation of coordinate system transformation are discussed. The various possible errors in the system are analyzed in detail and the simple control error scheme is given then. After that the method of processing 3D point cloud data is expounded and a combined interpolation method based on existing interpolation method is proposed to improve the effect of 3D reconstruction. At last, the experimental verification was carried out to collect point cloud data of a variety of crops. And the 3D digital model of each crop was established using MATLAB.

Simple median‐based EP PP scheme for enhancement of reconstructed Bayer colour filter array images

In this study, the median-based edge-preserving (EP) modification is revisited and has been shown to improve effectively the quality of a reconstructed Bayer colour filter array image in terms of the composite peak signal-to-noise ratio (CPSNR) performance index. Along this research direction, the authors propose an EP-modified signal-correlation-based (SCB) post-processing (PP), called EP-SCB, as an enhancement to any existing interpolation method. The Bayer image reconstruction system they consider thus consists of two operational phases. The first phase performs an initial estimation of the missing red, green and blue colours by using an existing interpolation method, whereas the second phase applies EP-SCB PP. Since a certain class of images may not fulfil the premise of having small variations in local colour difference, which is assumed by SCB-type interpolation, thereby resulting in a deterioration in CPSNR after EP-SCB PP, a threshold test on local variance ratio is also devised to conditionally switch off the second phase. Experimental results show that the EP-SCB PP with variance-ratio test gives a worst average CPSNR than the original interpolation methods tested in none of the Kodak and IMAX image groups experimented.

Piecewise Positivity Preserving Cubic Bezier Interpolation for Estimating Solar Radiation Missing Value in Penang, Malaysia

Complete solar radiation data is important in variety of disciplines such as solar radiation development system or solar project which is strongly affected by hourly variation of the solar radiation. However, the available data may contain missing data for several days in the absence of measurement due to several factors such as instrument failure and human errors. In this study, the secondary data of solar radiation at Penang, Malaysia taken from Malaysian Meteorology Department was investigated. In order to fill the gap of the above missing values, the interpolation method based on positivity preserving Bezier curves to ensure that the solar radiation are always positive is proposed. This paper start with the derivation of positivity preserving condition for Bezier curves by imposing lower bound of the Bezier control points. The proposed method is tested using simulated missing value of solar radiation dataset. Result from RMSE and Coefficient of Determination (r2) for different set of missing value from 10, 30 and 50%, show that the proposed method produce a better result compared to existing interpolation method without implementing positivity preserving condition. Finally, the proposed method was used to fill the gap of missing values of solar radiation at Penang, Malaysia.

Statistical methods for interpolating missing meteorological data for use in building simulation

Building performance simulation is increasingly used to aid in decision making about the design, construction, retrofit, operation, and maintenance of new and existing buildings. Such simulations require a complete set of meteorological data sampled at regular intervals. A data file with even a single missing measurement value becomes useless for simulation. Unfortunately, it is extremely rare to find such a perfect body of data. Measurement errors and sensor failure are frequent occurrences in meteorological data collection and are among a host of reasons for missing measurement values. To overcome this problem, simulation users may rely on Typical Meteorological Years (TMYs) instead of actual historical data, or they may apply an existing interpolation method to fill the gaps in historical data. Historical data is often preferable, since TMYs fail to account for atypical weather conditions. Clearly, this could lead to poor decision making when the decision outcomes are strongly affected by the occurrence of atypical conditions. This paper presents several methods for statistical interpolation between discrete weather-data points. A normalization procedure is first used to transform meteorological data into a set of Gaussian-distributed sample data. Next, a vector autoregressive model is calibrated using the normalized site-specific meteorological data, and is then used to determine the most likely value for one or more missing data points. Variations of the model are described to address specific combinations of missing data, and the methods are validated for several cities in the USA. Results show that the normalization procedure is the most important contributor towards a significant improvement in accuracy relative to other interpolation methods.

An efficient model-based multirate method for reconstruction of audio signals across long gaps

This paper presents an efficient model-based interpolator for reconstructing long portions of missing samples in audio signals. A simple modification to an existing interpolation method is proposed, optimizing the balance between computational requirements and qualitative performance. Moreover, a post-processing multirate interpolation scheme is introduced to further enhance the quality of the restored signals. Subjective quality assessments of the reconstructed signals via listening tests substantiate the improved performance of the proposed algorithm