Adjacent Vectors Research Articles

Distance similarity entropy: a sensitive nonlinear feature extraction method for rolling bearing fault diagnosis

Entropy-based methods are widely used in machinery fault diagnosis for characterizing system disorder and complexity. However, conventional entropy techniques often fail to capture local signal variations when analyzing relationships between vectors, especially in complex settings. This leads to incomplete representations of subtle features and dynamic behaviors, resulting in inaccurate estimations of system complexity and affecting diagnostic accuracy and reliability. To address these limitations, a novel distance similarity entropy (DSEn) is proposed in this paper: (1) It leverages element-wise distances to precisely capture local shifts and subtle distortions between subsequences. (2) It employs a Gaussian kernel function for vector similarity, enhancing signal pattern analysis by preserving subtle differences and mitigating the impact of outliers. (3) It uses probability density estimation of distance similarities between adjacent vectors to track changes in internal signal patterns, enabling more accurate and sensitive estimations of signal complexity. Synthetic signal experiments demonstrate that DSEn excels in detecting dynamic time series changes and characterizing signal complexity. Tests on two bearing datasets reveal that DSEn's extracted features show significant differences, highlighted by Hedges’ g effect size. Compared to other commonly used entropies (SampEn, PermEn, FuzzEn, DistEn, etc.), DSEn shows superior fault identification accuracy, computational efficiency, and noise resistance.

Disturbance‐rejection adjacent vector model predictive control strategy based on extended state observer for EV converter

AbstractConventional single‐vector model predictive control (MPC) can suffer from low control accuracy, while multi‐vector MPC is often criticized for its complexity and heavy computational burden. In order to address these issues, an adjacent vector‐based MPC is investigated in this paper for an electric vehicle battery charging and discharging converter. The voltage vector selection table based on the principle of using adjacent vectors has been designed and this reduces the number of iterations and thus the computational burden. A threshold is used in the adjacent vector‐based MPC to coordinate the use of the single and multi‐vector MPCs considering a balance between the control accuracy and computational burden. In addition, to enhance the robustness of MPC to parameter changes, an extended state observer for active disturbance rejection control has been used to derive the predictive model, and an adjacent vector‐based MPC using extended state observer is studied. The method does not need accurate system parameters. Instead, it only requires the system input and output measurements to calculate the predicted current. The robustness of the controller against the parameter mismatch is enhanced compared to alternative approaches and the experimental results verify the feasibility and effectiveness of the proposed strategy.

Designing an OAM fiber with a two-layer seven-core structure to support 322 OAM-mode transmissions

In this paper, a two-layer seven-core structural fiber (TLSCSF) is proposed to support and improve the propagation of more orbital angular momentum (OAM) mode beams, thus increasing the transmission capacity and spectrum efficiency (SE) of an optical communication system. The TLSCSF is composed of seven sub-cores, each containing two inner and outer layers of core rings and a central air hole. The two core rings are prepared using two materials with different doping concentrations. The supported OAM modes can be propagated in the fiber core ring. A finite element method (FEM) is used to analyze the designed fiber, and the calculated results show that the TLSCSF can stably transmit 322 OAM modes without higher order radial modes in the wavelength range of 1.5∼1.6 um. The corresponding effective refractive index difference between two adjacent vector modes (HE/EH) is more than 10−4. The measured effective mode areas (Aeff) and the confinement losses (CL) of HE or EH modes are larger than 54 um2 and smaller than 10−10 dB m−1, respectively. Moreover, the calculated dispersion variations and the mode qualities are lower than 230 ps nm−1 km−1 and more than 90%, respectively. Finally, the 10ps walk-off lengths of all vector modes supported by TLSCSF at a wavelength of 1.55 um are also evaluated, where the measured results show that except for HE2,1 and EH1,1, all other modes achieve a 10ps walk-off length of the order of 103 to 105. Consequently, the TLSCSF can contributes to improving the channel capacity and SE by supporting 322 fundamental radial OAM modes with robust performances in an optical communication system.

Adaptive Weighted Data Fusion for Line Structured Light and Photometric Stereo Measurement System.

Line structured light (LSL) measurement systems can obtain high accuracy profiles, but the overall clarity relies greatly on the sampling interval of the scanning process. Photometric stereo (PS), on the other hand, is sensitive to tiny features but has poor geometrical accuracy. Cooperative measurement with these two methods is an effective way to ensure precision and clarity results. In this paper, an LSL-PS cooperative measurement system is brought out. The calibration methods used in the LSL and PS measurement system are given. Then, a data fusion algorithm with adaptive weights is proposed, where an error function that contains the 3D point cloud matching error and normal vector error is established. The weights, which are based on the angles of adjacent normal vectors, are also added to the error function. Afterward, the fusion results can be obtained by solving linear equations. From the experimental results, it can be seen that the proposed method has the advantages of both the LSL and PS methods. The 3D reconstruction results have the merits of high accuracy and high clarity.

Indexing Topological Numbers on Images by Transferring Chiral Magnetic Textures

AbstractTopological analysis is widely adopted in various research fields to unveil intricate features and structural relationships implied in geometrical objects. Especially, in the fields of data analysis, exploring the topological properties of various images offers rich insights into the intrinsic geometrical information within them. In this study, a novel approach is proposed to investigate the topological properties of arbitrary grayscale images by employing a straightforward procedure used in 2D magnetism studies to calculate topological numbers. This method utilizes machine learning techniques to transfer chiral magnetic textures onto the images. Then, the topological number is then computed directly from the converted images by integrating the solid angles formed by adjacent spin vectors. The method successfully identifies the topological numbers of various grayscale images, showing stable performances against small noises. Furthermore, two applications of the method: are demonstrated topological analysis of the Modified National Institute of Standards and Technology (MNIST) dataset and the counting of blood cells in microscopic images.

An improved manifold-projection trajectory based method for chemical kinetic mechanism reduction

An improved manifold-projection trajectory based dimension reduction algorithm (MTDR) to automatically generate skeletal chemical kinetic mechanisms was proposed and validated in this study. This algorithm is implemented by constructing an approximate manifold-based trajectory of the combustion system using Euclidean distances between two adjacent points and cosine similarities between two adjacent vectors in the manifold space, and then evaluating the importance of species by calculating the error of manifold-based trajectories before and after the projection of the manifold. In this method, the nature of the combustion system is well reflected since the combustion process information can be captured by the location of the state point in the manifold space. The calculation during the reduction process is simplified by using the manifold-based trajectory instead of the complex differential equations. Compared to our previous work, this study improves the prediction accuracy of the reduced mechanisms through a more comprehensive error evaluation in the mechanism reduction process. The detailed mechanisms of fuels including iso-cetane, iso-octane and gasoline surrogate mixtures of toluene, iso-octane and n-heptane were reduced to portray the prowess of the algorithm. It’s demonstrated that the number of species of the fuels is reduced from 492, 254 and 1389 to 95, 87 and 427 within an acceptable error, respectively. Meanwhile, the case of iso-octane mechanism reduction was chosen to compare the performance of MTDR with traditional methods including path flux analysis (PFA) and directed relation graph with error propagation and sensitivity analysis (DRGEPSA), and it is shown that the MDTR can generate more compact mechanism under a broad range of error limits.

Logical-semantic models and methods of knowledge representation: cases for energy management systems and SMR digital infrastructures

The subject of this article is the development of information technologies at the end of the 20th and the beginning of the 21st century for the Fourth Industrial Revolution in the form of Industry 4.0, i.e., Internet of Things (IoT) technologies. Successes in the implementation of this technology have led to the development of new applications in the energy sector, such as energy management systems, small modular reactor (SMR) management systems, and alternative power supply systems based on renewable energy sources. The digital infrastructure of these management systems is characterized by a high "density of knowledge", which requires clarification of fundamental concepts in information theory, namely the content of the concepts "data", "information", "knowledge" and "meaning of knowledge". Special attention was given to defining the role of knowledge. The aim of this study is to further develop methods and models of semiotic theory by determining the role and place of logical as well as eight- and four-factor logical-semantic models of knowledge bases in semiotic space. The tasks: comparing existing knowledge representation methods and models. Research results: We found that the logical models used in the development of knowledge bases are based on the principles of artificial intelligence theory, which relies on sign system hypotheses and formal logic theory. The main drawback is the complexity of practical implementation in the form of expert systems. For logical-semantic models in the form of eight-vector graphic models, it was found that there is currently no theoretical justification for defining the vectors that form the coordinate axes, making these models unique to specific subject areas. It was determined that the advantage of using these methods is that an expert can independently form such a knowledge model. For logical-semantic models in the form of four-factor graphic models, there is a theoretical justification for defining the factors of the model that form the coordinate axes, making these models universal for specific subject areas. It was established that the advantage of these models is that they can be developed by experts without the involvement of a knowledge engineer. Therefore, it is proposed to use four-factor logical-semantic knowledge representation models for further application. It is also proposed to split the element "logical-semantic models" into two elements in the semiotic spatial model in vector K8 "Knowledge Representation Models", namely: "logical-semantic eight-vector models" and "logical-semantic four-factor models". Additionally, it is proposed to add the element "post-Cartesian representation of meta-knowledge" to the element "geometric" in vector K5 "Ideal Models". Conclusions: The theoretical basis for developing eight-factor logical-semantic knowledge representation models is the form of connections between adjacent vectors in the form of Cartesian products on elements of the corresponding inter-coordinate matrices. The theoretical basis for the methodology of developing four-factor logical-semantic knowledge representation models is the form of connections between adjacent vectors in the form of Cartesian products for elements of the corresponding inter-coordinate matrices, as well as for diametrically opposite pairs of factors in the form of dialectical unity of the concepts "general" and "particular." The application of logical-semantic knowledge representation models for alternative energy-source management systems will ensure increased energy efficiency. Other cases related to the development of databases for SMR digital infrastructure are discussed.

CL&CD: Contrastive Learning and Cluster Description for Zero-Shot Relation Extraction

Zero-shot Relation Extraction (ZRE) is designed to identify new relations when the model is adapted to a new environment in a new domain. The majority of existing ZRE methods employ distant supervision for data labeling, which inevitably leads to incomplete annotations and noise. To handle this problem, we propose a ZRE framework based on Contrastive Learning and Cluster Description (CL&CD), a two-stage contrastive learning method is used to train labeled data which consists pseudo-labeled data and labeled data. The framework can effectively promote the model mapping the instances of the same relations to the adjacent vector space better. The module of clustering description reasonably optimizes the time of manual intervention and enormously reduces the consumption of human resources. Experimental results on Wiki-ZSL and FewRel show the superior performance of the CL&CD, which outperforms all baseline models including the state-of-the-art RCL. Furthermore, CL&CD improves F1-Score by up to 8% in both Wiki-ZSL and FewRel with 15 unseen relations.

An Angle-Based Virtual Vector Model Predictive Current Control for IPMSM Considering Overmodulation

The conventional model predictive control method suffers from large current and torque harmonics due to the limited voltage vectors. To increase the control performance, in many papers, the methods of extending the predictive control set by adding virtual vectors are proposed. However, constructing virtual vectors will bring extra computational burden for vector optimization. To solve this problem, this paper proposes an angle-based virtual vector model predictive current control (ABVV-MPCC) method for interior permanent magnet synchronous motor (IPMSM). In this method, a hexagonal coordinate system is introduced to define the virtual vectors. After obtaining the composite relationship between the reference voltage vector and the adjacent basic vector, the vector optimization range is reduced from six voltage sectors to one voltage sector. And the optimal voltage vector is directly obtained by searching for the closest candidate voltage vector. After adopting the proposed method, the exhaustive optimization is avoided and the calculation burden is independent from the virtual voltage vectors number. Therefore, virtual voltage vectors number can be set arbitrarily, which greatly reduces current harmonics. Besides, a simple overmodulation dealing method by finding the optimal reachable voltage vector is proposed. And the dynamic performance under overmodulation is increased without adding additional control module.

Fusing DCN and BBAV for Remote Sensing Image Object Detection

At the oriented object detection in aerial remote sensing images, the perceptual field boundaries of ordinary convolutional kernels are often not parallel to the boundaries of the objects to be detected, affecting the model precision. Therefore, an object detection model (DCN-BBAV) that fuses deformable convolution networks (DCNs) and box boundary-aware vectors (BBAVs) is proposed. Firstly, a BBAV is used as the baseline, replacing the normal convolution kernels in the backbone network with deformable convolution kernels. Then, the spatial attention module (SAM) and channel attention mechanism (CAM) are used to enhance the feature extraction ability for a DCN. Finally, the dot product of the included angles of four adjacent vectors are added to the loss function of the rotation frame parameter, improving the regression precision of the boundary vector. The DCN-BBAV model demonstrates notable performance with a 77.30% mean average precision (mAP) on the DOTA dataset. Additionally, it outperforms other advanced rotating frame object detection methods, achieving impressive results of 90.52% mAP on VOC07 and 96.67% mAP on VOC12 for HRSC2016.

Three-Dimension Space Vector Modulation for Three-Phase Series-End Winding Voltage-Source Inverters

Series-end winding voltage-source inverters (SEW-VSIs) can effectively improve the dc-link voltage utilization and provide the capabilities to handle the zero-sequence loop. However, the existing modulation schemes for SEW-VSIs cannot fully utilize the output capability of SEW-VSIs while guaranteeing simple implementation. To this end, a three-dimensional space vector modulation (3D-SVM) scheme is proposed for driving three-phase SEW-VSIs in this paper. The modulation is conducted in the 3D-space made up of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α-β</i> plane and the zero-sequence-axis, and the reference voltage vector in the 3D-space is synthesized by three adjacent basic voltage vectors and the null voltage vector, which can fully utilize the output capability of three-phase SEW-VSI. Then, a convenient implementation method based on a look-up table is developed to find three basic voltage vectors adjacent to the reference voltage vector. Moreover, in the 3D-space, the feasible region and the linear modulation region of the proposed 3D-SVM are investigated. Accordingly, intuitive overmodulation between different subspaces and the switching sequence generation are developed. A series of simulation and experimental results are presented to validate the effectiveness of the proposed 3D-SVM for three-phase SEW-VSI drives.

Conditional-Extreme-Point Based Fault-Tolerant Predictive Control of Five-Phase PMSM With Low Switching Frequency

The virtual voltage vector (VVV) based fault-tolerant control has been widely concerned, but suffering from the increased switching frequency and the reduced bus voltage utilization at the faulty operation. Also, the harmonic space is uncontrollable. This paper proposes a conditional-extreme-point based fault-tolerant model predictive control for a five-phase permanent magnet synchronous motor. The conditional extreme point is used to predict the optimal reference voltage vector. Firstly, to suppress the harmonics, dual control sets are established without the sacrifice of bus voltage utilization. Then, the unconditional extreme point and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</i> -axis voltage are predicted to select the appropriate control set, and two adjacent vectors are pre-selected for generating the optimal reference voltage vector. Subsequently, the conditional extreme point of the cost function is calculated to obtain the optimal reference voltage vector. Due to the unemployment of the null vector, the switching frequency is greatly reduced. Finally, the experimental results are presented to verify the proposed control scheme.

Current fluctuations reduction strategy based on optimal three‐space‐vector pulse‐width modulation for service‐life improvement of DC‐link electrolytic capacitors in three‐phase voltage‐source inverter system

AbstractThe authors propose a current fluctuation reduction strategy based on optimal three‐space‐vector pulse‐width modulation (TSVPWM), which is used to improve the service‐life of the dc‐link electrolytic capacitors in two‐level three‐phase voltage‐source inverter (VSI) system. Differing from the typical SVPWM‐based method that employs two adjacent active voltage vectors and zero voltage vectors to synthesise the reference voltage, the proposed strategy selects the required voltage vectors based on the minimum dc‐link electrolytic capacitor current fluctuation. With the proposed strategy, an objective function for the root‐mean‐square value of dc‐link electrolytic capacitor current is first constructed under the constraint of eight permissible voltage vectors. And then, by solving the minimum of the objective function through the piecewise linear programming, the optimal three voltage vectors under the different modulation ratios and load power factors are obtained accordingly, so as to achieve the minimum dc‐link electrolytic capacitor current fluctuations during each switching period. Meanwhile, a PWM implementation scheme based on positive–negative double carrier signals is presented, which not only simplifies the implementation process but also effectively reduces the switching losses of power devices. Finally, the experimental results demonstrate that the proposed strategy can minimise the dc‐link electrolytic capacitor current fluctuation under different working conditions.

Two‐stage deadbeat‐based predictive torque control strategy for modular multilevel converter‐fed three‐phase induction motors

AbstractRecently, Modular Multilevel Converters (MMC) are considered to be extensively used in medium‐voltage AC drives A two‐stage deadbeat‐based strategy is developed by the authors to make the implementation of Predictive Torque Control (PTC) technique for an induction motor that is fed by a three‐phase MMC possible . Despite various benefits of PTC strategy, it has not been widely employed for multilevel topologies due to the huge number of switching states of these converters, and the complex internal dynamics of topologies such as MMC. The proposed control scheme results in significant reduction of the computational burden, using an initial reference voltage that is determined at the first stage of the strategy by the deadbeat technique. Next, the predictive evaluation process is conducted at the second stage to simultaneously control the stator flux, electromagnetic torque and circulating current. The number of admissible vectors that should be evaluated in the cost function is effectively limited by only considering some adjacent vectors of the reference voltage in the first stage. Moreover, the circulating current control capability, which is necessary for effective operation of MMC, is also considered in the developed scheme. Finally, the satisfactory performance of the proposed strategy is validated through various experimental tests.

Cumulative Diversity Pattern Entropy (CDEn): A High-Performance, Almost-Parameter-Free Complexity Estimator for Nonstationary Time Series

Tedious parameter settings and poor performances seriously affect the entropy estimation's effectiveness in time series analysis. To solve these limits, we propose a conceptually novel definition, cumulative diversity pattern entropy (CDEn), focusing on eliminating parameter selections and improving quantization accuracy, stability, and robustness. The CDEn algorithm consists of three steps: (1) improved phase-space reconstruction (IPSR) with constant embedding dimension <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\bm{m\ }} = {\bm{\ }}2$</tex-math></inline-formula> and time delay <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\bm{\tau \ }} = {\bm{\ }}1$</tex-math></inline-formula> ; (2) diversity pattern partition generated by the cosine similarity between adjacent vectors; and (3) entropy calculation based on the normalized cumulative probability distribution. Numerical experiments are performed using 7 synthetic datasets and 15 baseline entropy methods for comparative validation. The results confirm CDEn's best description of chaotic/stochastic dynamics with the highest quantization accuracy and the lowest error rate of 2.04%. The coefficient of variation (CV) results also verify CDEn's excellent quantization stability with CV lower than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> . The relative change rate (RCR) results demonstrate that CDEn achieves the best robustness to data length and noise. Finally, the entropy algorithms are applied to a real-world dataset, i.e., neonatal sleep EEG analysis. The results further confirm that suggested CDEn outperforms the state-of-the-art entropy methods, with the minimum outliers and best statistical significance (highest mean of effect size, 1.22) in characterizing the neurodynamics of different sleep stages.

Optimized GICP registration algorithm based on principal component analysis for point cloud edge extraction

For iterative closest point (ICP) algorithm, the initial position and the number of iterations are needed in registration. At the same time, the ICP algorithm is easy to fall into local convergence and convergence speed is slow. By constructing K-D tree to search neighborhood points and artificially set threshold, plane fitting is carried out, the on-time point cloud to be deployed is separated from the complex background, and statistical analysis is used to calculate the distance between the point cloud and the neighborhood point to quickly remove the invalid point cloud. The surface equation is set to calculate the tangent plane of point cloud normal vector and each normal vector, and the local coordinate system is constructed. The angle between adjacent vectors and the local coordinate system is calculated to determine the feature point set of edge contour. According to the covariance matrix of the feature points set, the principal feature component is obtained, the principal axis direction of the two sets of point clouds is found, and the rotation matrix and the displacement vector are obtained. Finally, GICP precise registration of point cloud is carried out according to initial pose parameters and rigid body transformation matrix obtained by maximum likelihood estimation method. The results show that the optimized algorithm can effectively avoid local convergence. Compared with the traditional ICP algorithm, when the algorithm achieves the same registration accuracy in the public dataset experiment, the registration speed is on average 44.82% faster and the overlap rate is on average 15.26% higher. In the real dataset experiment, the registration speed is on average 59.04% faster, the registration accuracy is on average 30.24% higher and the overlap rate is on average 10.61% higher. This shows that the optimization algorithm is superior to the traditional ICP algorithm in registration accuracy and convergence speed.

Double voltage vector model predictive control for grid-connected cascade H-bridge multilevel inverter with fixed switching frequency

Model predictive control (MPC) is an outstanding control method which can achieve superior dynamic response, nonlinear control and multi-objective collaborative control. However, because of unfixed switching frequency, the harmonic spectrum of the output current is dispersed, which would make it difficult to design the output filter. In this work, a double voltage vector model predictive control (DVV-MPC) algorithm for grid-connected cascade H-bridge (CHB) multilevel inverter is presented. The algorithm not only has the advantages of MPC but also produces fixed the switching frequency of the inverter. It is realized by a modulation stage with two adjacent voltage vectors in one switching cycle. And the duty cycle of the associated voltage level is obtained by minimizing an additional cost function. This method is suitable for the cascades of n cells inverter. For reducing the computation burden and eliminating the computation delay, adjacent regions prediction method and time-delay compensation method are applied to the inverter. Finally, in this paper, the proposed strategy is applied to a single-phase grid-connected 7-level CHB inverter. Simulation and experiment are executed to show the advantages of the proposed control algorithm in dynamic state and steady state.

3-D SVM for Three-Phase Open-End Winding Drives With Common DC Bus

Existing modulation strategies for three-phase open-end winding drives (OWDs) with common dc bus usually conduct the modulations for α-β subspace and zero-sequence loop (ZSL) separately, which cannot reflect the relationship between α-β subspace and ZSL and fully utilize the dc bus voltage. To this end, this paper proposes a three-dimensional space vector modulation (3-D SVM) strategy for three-phase OWDs with common dc bus, which can be conducted in both a-b-c and α-β- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</i> coordinates, leading to full utilization of dc bus voltage and convenient overmodulation adjustment. Voltage vector distributions of OWD in the 3-D spaces with a-b-c and α-β- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</i> coordinates are revealed at first. Subsequently, the three adjacent voltage vectors for reference voltage vector synthesis are selected based on the relationship between leg-voltage potentials, avoiding the complex tetrahedron identification in existing 3-D SVMs for other drive topologies. In addition, overmodulation in different coordinates is also investigated. Experimental results are presented to validate the feasibility of the proposed 3-D SVM for OWDs with common dc bus.

Calculation of water flow discharge using the truncated triangular prisms method

The article describes the calculating method for the water flow discharge. This method is based on the “velocity-area” proportion. In the proposed method, the flow of water passing through the cross section of the channel is represented as a body, the volume of which consists of a set of elements in the form of truncated triangular prisms. The side edges of the prism are the velocity vectors measured at the corresponding points. The bases of these prisms are the areas of triangles, the vertices of which are the points of measurement of the corresponding velocities. The volume of every element is determined by the formula for calculating the volume of a truncated prism. As a reference body, as a model of the diagram of flow velocities, one fourth of a sphere with a unit radius is taken, the volume of which can be calculated with the high accuracy. There are 15 speed verticals (they are also taken as measurement verticals) with five speed measurement points on every vertical: “surface”, 0.2h, 0.6h, 0.8h, “bottom”. The velocity value is represented by the length of the vector directed perpendicularly from the velocity vertical, from the point of velocity measurement to the surface of the sphere. Three adjacent velocity vectors are the side edges of the prism. The method of calculating the flow rate according to the approved measurement procedure is chosen for comparison. The results obtained by both methods are compared. As a result, the volume of the model, as one fourth of a sphere with the unit radius, was 1.0472; the volume calculated by the standard method was 1.0279; and by the method of prisms - 1.0124. Despite the absence of correction factors, the volume obtained by the prism method is only 1.55% less than one with the standard method. To smooth the results obtained by the method of truncated triangular prisms, the range of correction factors of 1.03…1.07 was determined, depending on the number of velocity verticals.

Altered Region Identification in Image Files using Copy-Move Forgery Detection Technique

Nowadays, digital images and videos have high importance because they have become the primary carriers of information. However, the easy availability of powerful image editing software has made it possible to manipulate and edit digital images and videos, leading to a loss of trust in their authenticity. It is possible to add or remove important features from an image without leaving any obvious traces of tampering. To detect this such type of forgeries, the proposed method involves dividing the image into overlapping blocks of the same size, extracting a feature for each block, and representing it as a vector. The vectors are then sorted using radix sort, and the difference in the positions of adjacent feature vectors in the sorted list is computed to obtain a shift vector. This method can even identify tampered parts of an image that have been enhanced or retouched to merge with the background or saved in a lossy format like JPEG. Several forged images were tested to demonstrate the effectiveness of this proposed method. Its application has significant implications in fields like forensics, journalism, and medical imaging to ensure the authenticity of digital images and videos.