Search Results (26)

In a recent article in this journal, Nikolić et al. presented a mathematical model for computing the coordinates in the trimetric projection of a 3D object, in terms of the projections of unit areas on the three dihedral planes. We revisit this model and analytically formalize its geometric principles, noting that such projections amount to the direction cosines of the unit normal to the viewplane. Thus, we reinterpret their proposal as providing three direction numbers that define a scaled version of this unit normal. The model also derives formulas relating the trimetric parameters (i.e., trimetric angles and foreshortening ratios). We observe that these relationships, found in classical literature, admit more compact expressions through simpler derivations. Also, we compile and reexamine various methods for selecting the trimetric projection, making them more accessible. In particular, the turn and tilt rotations of interactive user interfaces provide an intuitive way to choose the direction cosines. Ultimately, any method defines the mathematical model through a transformation matrix that maps 3D world coordinates to viewplane coordinates in the viewing pipeline. Full article

Discrete cosine transforms (DCTs) are widely used in intelligent electronic systems for storing, processing, and transmitting data. Their popularity stems, on the one hand, from their unique properties and, on the other hand, from the availability of fast algorithms that minimize the computational and hardware complexity of their implementation. Until recently, the Type VIII DCT had been one of the least studied variants, with virtually no publications addressing fast algorithms for its implementation. However, this situation has changed, making the development of efficient implementation methods for this transform a timely and important research problem. In this paper, several algorithmic solutions for implementing the Type VIII DCT are proposed. A set of Type VIII DCT algorithms for small lengths N = 3, 4, 5, 6, 7 is presented. The effectiveness of the proposed solutions is due to the possibility of successful factorization of small-sized DCT-VIII matrices, leading to a reduction in the computational complexity of implementing transforms of this type. Compared with direct matrix–vector computation, the proposed algorithms achieve an approximate 53% reduction in the number of multiplications, at the cost of an increase of about 21% in the number of additions. This work continues a series of previously published studies aimed at creating a library of small-sized algorithms for discrete trigonometric transforms. Full article

This paper presents new fast algorithms for the type VII discrete cosine transform (DCT-VII) applied to input data sequences of lengths ranging from 3 to 8. Fast algorithms for small-sized trigonometric transforms enable the processing of small data blocks in image and video coding with low computational complexity. To process the information in image and video coding standards, the fast DCT-VII algorithms can be used, taking into account the relationships between the DCT-VII and the type II discrete cosine transform (DCT-II). Additionally, such algorithms can be used in other digital signal processing tasks as components for constructing algorithms for large-sized transforms, leading to reduced system complexity. Existing fast odd DCT algorithms have been designed using relationships among discrete cosine transforms (DCTs), discrete sine transforms (DSTs), and the discrete Fourier transform (DFT); among different types of DCTs and DSTs; and between the coefficients of the transform matrix. However, these algorithms require a relatively large number of multiplications and additions. The process of obtaining such algorithms is difficult to understand and implement. To overcome these shortcomings, this paper applies a structural approach to develop new fast DCT-VII algorithms. The process begins by expressing the DCT-VII as a matrix-vector multiplication, then reshaping the block structure of the DCT-VII matrix to align with matrix patterns known from the basic papers in which the structural approach was introduced. If the matrix block structure does not match any known pattern, rows and columns are reordered, and sign changes are applied as needed. If this is insufficient, the matrix is decomposed into the sum of two or more matrices, each analyzed separately and transformed similarly if required. As a result, factorizations of DCT-VII matrices for different input sequence lengths are obtained. Based on these factorizations, fast DCT-VII algorithms with reduced arithmetic complexity are constructed and presented with pseudocode. To illustrate the computational flow of the resulting algorithms and their modular design, which is suitable for VLSI implementation, data-flow graphs are provided. The new DCT-VII algorithms reduce the number of multiplications by approximately 66% compared to direct matrix-vector multiplication, although the number of additions decreases by only about 6%. Full article

Objectives: Existing motor imagery electroencephalography (MI-EEG) decoding approaches are constrained by their reliance on sole representations of brain connectivity graphs, insufficient utilization of multi-scale information, and lack of adaptability. Methods: To address these constraints, we propose a novel Local–Partition–Global Graph learning Network (LPGGNet). The Local Learning module first constructs functional adjacency matrices using partial directed coherence (PDC), effectively capturing causal dynamic interactions among electrodes. It then employs two layers of temporal convolutions to capture high-level temporal features, followed by Graph Convolutional Networks (GCNs) to capture local topological features. In the Partition Learning module, EEG electrodes are divided into four partitions through a task-driven strategy. For each partition, a novel Gaussian median distance is used to construct adjacency matrices, and Gaussian graph filtering is applied to enhance feature consistency within each partition. After merging the local and partitioned features, the model proceeds to the Global Learning module. In this module, a global adjacency matrix is dynamically computed based on cosine similarity, and residual graph convolutions are then applied to extract highly task-relevant global representations. Finally, two fully connected layers perform the classification. Results: Experiments were conducted on both the BCI Competition IV-2a dataset and a laboratory-recorded dataset, achieving classification accuracies of 82.9% and 87.5%, respectively, which surpass several state-of-the-art models. The contribution of each module was further validated through ablation studies. Conclusions: This study demonstrates the superiority of integrating multi-view brain connectivities with dynamically constructed graph structures for MI-EEG decoding. Moreover, the proposed model offers a novel and efficient solution for EEG signal decoding. Full article

Traditional centralized modeling and fault detection methods for large-scale industrial processes have limitations, including a significant computational load and reduced performance. To address these issues, this paper proposes a distributed dynamic direct orthogonal decomposition method for quality-related fault detection in large-scale industrial processes. This method first decomposes the industrial process to several subunits based on its inherent mechanism. To fully consider the coupling relationship between subunits and improve the communication efficiency among them, the representative variables within each subunit are first selected based on the cosine function. On this basis, regression equations are established between the representative variables of each local subunit and those of its adjacent subunits using LASSO. Then, relevant adjacent unit variables are selected based on the regression coefficients to achieve effective information exchange between the local and adjacent subunits. For the reconstructed local subunits, a dynamic direct orthogonal decomposition method is proposed to achieve quality-related fault detection. In the proposed fault detection method at the subunit level, to better capture the dynamics within the data, the time-delay factor is first introduced to the process variables and the quality variables, and the load matrix of the process variables and the quality variables is obtained using standard partial least squares. Subsequently, the covariance matrix of the load matrix is decomposed based on singular value decomposition to construct an orthogonal decomposition matrix, thereby achieving orthogonal division of the process variables based on the quality variables within each subunit. To derive a more concise detection logic, the Bayesian fusion strategy is adopted to integrate the statistical indicators corresponding to the same type of faults detected in each subunit. Finally, the effectiveness of this method is verified through an industrial example. Full article

Low-cost MEMS sensors are widely utilized in UAV platforms to address attitude estimation problems due to their compact size, low power consumption, and cost-effectiveness. Diverse UAV payloads pose new challenges for attitude estimation, such as magnetic interference environments and high dynamic environments. In this paper, we propose a hierarchical decoupled attitude estimation algorithm, termed HDAEA. Initially, a novel hierarchical decoupling approach is introduced for the attitude and angle representation of the direction cosine matrix, enabling the representation of angles in a new manner. This method reduces the data dimensionality and nonlinearity of observation equations. Furthermore, a magnetic interference identification algorithm is proposed to compute the magnetic interference intensity accurately and quantitatively. Combining the quantified errors of estimated state variables, an error model for magnetic interference and attitude angles in high-dynamic environments is constructed. Subsequently, the proposed error model is employed to calibrate the hierarchical decoupled angles using accelerometer and magnetometer measurements, effectively mitigating the impact of magnetic interference on the calculation of pitch angles and roll angles. Moreover, the integration of the proposed hierarchical decoupled attitude estimation algorithm with the error-state extended Kalman filter reduces system nonlinearity and minimizes linearization errors. Experimental results demonstrate that HDAEA exhibits significantly improved attitude estimation accuracy of UAV payloads. Full article

The Risley prism system offers advantages such as compact structure and excellent dynamic performance, making it suitable for installation on static and motion platforms for target acquisition, aiming, and tracking. This paper presents a strapdown line-of-sight (LOS) stabilization method for the Risley prism system on motion platforms. The method establishes the coordinate transformation between the Risley prism and the motion platform. Real-time platform attitude angles from an inertial measurement unit (IMU) are used to compute the direction cosine matrix, which, combined with the coordinate transformation, determines the target’s actual guided position in the Risley prism’s coordinate. The Risley prism’s rotational angles are then calculated based on the target’s actual guided position to ensure LOS stability and capture the target. After LOS stabilization, an image-based closed-loop tracking cascade control system that integrates a Risley prism and a fast steering mirror with a single image detector (IBCLTCR-F), is used to enable fast and high-precision target tracking. Experimental results demonstrate that the proposed method achieves disturbance rejection of −32.8 dB, −28.8 dB, and −17.3 dB for platform disturbances at 0.05 Hz, 0.2 Hz, and 0.5 Hz, respectively. Furthermore, compared to the Risley prism system, the IBCLTCR-F system improves the dynamic response capability of target tracking in the nonlinear region by a factor of 10 and reduces the tracking error by 70%. Full article

The interface between old and new concrete is a critical component in many construction practices, including concrete pavements, bridge decks, hydraulic dams, and buildings undergoing rehabilitation. Despite various treatments to enhance bonding, this interface often remains a weak layer that compromises overall structural performance. Traditional design methods typically oversimplify the interface as a homogeneous or empirically adjusted factor, resulting in significant uncertainties. This paper introduces a novel framework for quantifying the anisotropic properties of old–new concrete interfaces using X-ray computed tomography (CT) and finite element-based numerical homogenization. The elastic coefficient matrix reveals that specimens away from the interface exhibit higher values in both normal and shear directions, with normal direction values averaging 33.15% higher and shear direction values 39.96% higher than those at the interface. A total of 10 sampling units along the interface were collected and analyzed to identify the “weakest vectors” in normal and shear directions. The “weakest vectors” at the interface show consistent orientations with an average cosine similarity of 0.62, compared with an average cosine similarity of 0.23 at the non-interface, which demonstrates directional features. Conversely, the result of average cosine similarity at the interface shows randomness that originates from the anisotropy of materials. The average angle between normal and shear stresses was found to be 88.64°, indicating a predominantly orthogonal relationship, though local stress distributions introduced slight deviations. These findings highlight the importance of understanding the anisotropic properties of old–new concrete interfaces to improve design and rehabilitation practices in concrete and structural engineering. Full article

Fast algorithms for type-five discrete cosine transform (DCT-V) for sequences of input data of short length in the range of two to eight are elaborated in the paper. A matrix–vector product representation of the DCT-V is the starting point for designing the algorithms. In each specific case, the DCT-V matrices have remarkable structural properties that follow from the localization of identical entries within the matrices. Each matrix of the DCT-V has only a few distinct entries that are repeated at different positions in its structure. Using simple transformations such as permutations of the rows and/or columns of this matrix or its favorable decomposition into two or more matrix components, it is possible to obtain efficient matrix structures that lead to useful factorization schemes. Based on the suitable factorization schemes we obtained, we developed fast algorithms that reduce the number of arithmetic operations when calculating the DCT-V. The correctness of the obtained algorithmic solutions was justified theoretically using a strict mathematical background of each of them. The developed algorithms were then further tested using MATLAB R2023b software to finally confirm their correctness. Finally, an evaluation of the computational complexity for each obtained solution is presented. The evaluation results were compared with the computational complexity of the direct calculation of matrix–vector products. The resulting factorizations of the matrices of the DCT-V reduce the average number of multiplications by 57% but increase the number of additions by 29%. Full article

To address the issues of low efficiency and poor noise immunity in traditional active distribution network (ADN) fault location methods based on swarm intelligent optimization algorithms, this paper proposes a two-stage fault location method utilizing the COA-SVM model and cosine similarity. First, this paper constructs the fault signature database for the target distribution network by randomly simulating single- and multi-point faults using the fault current state equation. Next, this paper introduces the COA-SVM classification model, establishing the high-dimensional mapping relationship between the fault current direction matrix and the fault zones through model training. The well-trained COA-SVM classification model is used to identify the fault zones, which include the fault line segments. Finally, for each identified fault zone, this paper calculates the cosine similarity of the fault current direction information of adjacent line segments, accurately pinpointing the fault line segments by identifying mutation points of the cosine similarity. Using the modified IEEE 33 node test distribution network as an example, simulation results demonstrate that the proposed two-stage fault location method offers higher accuracy and resistance to signal interference compared to fault location methods based on swarm intelligence optimization algorithms. The COA-SVM classification model surpasses conventional models, achieving high accuracy and excellent noise resilience. It accurately identifies fault segments within the test distribution network with a remarkable 100% precision. Moreover, the accuracy of fault localization remains above 83% when the FTU encounters fewer than three abnormal signals. Full article

Attitude determination based on a micro-electro-mechanical system inertial measurement unit (MEMS-IMU) has attracted extensive attention. The non-gravitational components of the MEMS-IMU have a significant effect on the accuracy of attitude estimation. To improve the attitude estimation of low-dynamic vehicles under uneven soil conditions or vibrations, a robust Kalman filter (RKF) was developed and tested in this paper, where the noise covariance was adaptively changed to compensate for the external acceleration of the vehicle. The state model for MEMS-IMU attitude estimation was initially constructed using a simplified direction cosine matrix. Subsequently, the variance of unmodeled external acceleration was estimated online based on filtering innovations of different window lengths, where the acceleration disturbance was addressed by tradeoffs in time-delay and prescribed computation cost. The effectiveness of the RKF was validated through experiments using a three-axis turntable, an automatic vehicle, and a tractor tillage test. The turntable experiment demonstrated that the angle result of the RKF was 0.051° in terms of root mean square error (RMSE), showing improvements of 65.5% and 29.2% over a conventional KF and MTi-300, respectively. The dynamic attitude estimation of the automatic vehicle showed that the RKF achieves smoother pitch angles than the KF when the vehicle passes over speed bumps at different speeds; the RMSE of pitch was reduced from 0.875° to 0.460° and presented a similar attitude trend to the MTi-300. The tractor tillage test indicated that the RMSE of plough pitch was improved from 0.493° with the KF to 0.259° with the RKF, an enhancement of approximately 47.5%, illustrating the superiority of the RKF in suppressing the external acceleration disturbances of IMU-based attitude estimation. Full article

Investigating aircraft flight dynamics often requires dynamic wind tunnel testing. This paper proposes a non-contact, off-board instrumentation method using vision-based techniques. The method utilises a sequential process of Harris corner detection, Kanade–Lucas–Tomasi tracking, and quaternions to identify the Euler angles from a pair of cameras, one with a side view and the other with a top view. The method validation involves simulating a 3D CAD model for rotational motion with a single degree-of-freedom. The numerical analysis quantifies the results, while the proposed approach is analysed analytically. This approach results in a 45.41% enhancement in accuracy over an earlier direction cosine matrix method. Specifically, the quaternion-based method achieves root mean square errors of 0.0101 rad/s, 0.0361 rad/s, and 0.0036 rad/s for the dynamic measurements of roll rate, pitch rate, and yaw rate, respectively. Notably, the method exhibits a 98.08% accuracy for the pitch rate. These results highlight the performance of quaternion-based attitude estimation in dynamic wind tunnel testing. Furthermore, an extended Kalman filter is applied to integrate the generated on-board instrumentation data (inertial measurement unit, potentiometer gimbal) and the results of the proposed vision-based method. The extended Kalman filter state estimation achieves root mean square errors of 0.0090 rad/s, 0.0262 rad/s, and 0.0034 rad/s for the dynamic measurements of roll rate, pitch rate, and yaw rate, respectively. This method exhibits an improved accuracy of 98.61% for the estimation of pitch rate, indicating its higher efficiency over the standalone implementation of the direction cosine method for dynamic wind tunnel testing. Full article

Aeromagnetic surveys are widely used in geological exploration, mineral resource assessment, environmental monitoring, military reconnaissance, and other areas. It is necessary to perform magnetic compensation for interference in these fields. In recent years, large unmanned aerial vehicles (UAVs) have been more suitable for magnetic detection missions because of the greater loads they can carry. This article proposes some methods for the magnetic compensation of large multiload UAVs. Because of the interference of the large platform and instrument noise, the standard deviations (stds) of the compensation data used in this paper are larger. At the beginning of this article, using the traditional T-L model, we avoid the shortcomings of the anti-magnetic interference ability of triaxial magnetic gate magnetometers. The direction cosine information is obtained by using an inertial navigation system, the global positioning system, and a triaxial magnetic gate magnetometer. Then, we increase the amplitude of the maneuvers in the compensation process; this reduces the multicollinearity problems in the compensation matrix to a certain extent, but it also results in greater magnetic field interference. Lastly, we employ the method of Lasso regularization Newton iteration (LRNM). Compared to the traditional methods of least squares (LS) and singular value decomposition (SVD), LRNM provides improvements of 34% and 27%, respectively. In summary, this series of schemes can be used to perform effective compensation for large multi-load UAVs and improve the actual use of large UAVs, making them more accurate in the measurement of aeromagnetic survey data. Full article

Direct yaw moment control (DYC) can effectively improve the yaw stability of four-wheel distributed drive electric vehicles (4W-DDEVs) under extreme conditions, which has become an indispensable part of active safety control for 4W-DDEVs. This study proposes a novel hierarchical DYC architecture for 4W-DDEVs to enhance vehicle stability during ever-changing road conditions. Firstly, a vehicle dynamics model is established, including a two-degree-of-freedom (2DOF) vehicle model for calculating the desired yaw rate and sideslip angle as the control target of the upper layer controller, a DDEV model composed of a seven-degree-of-freedom (7DOF) vehicle model, a tire model, a motor model and a driver model. Secondly, a hierarchical DYC is designed combining the upper layer yaw moment calculation and low layer torque distribution. Specifically, based on Matlab/Simulink, improved linear quadratic regulator (LQR) with weight matrix optimization based on inertia weight cosine-adjustment particle swarm optimization (IWCPSO) is employed to compute the required additional yaw moment in the upper-layer controller, while quadratic programming (QP) is used to allocate four motors’ torque with the optimization objective of minimizing the tire utilization rate. Finally, a comparative test with double-lane-change and sinusoidal conditions under a low and high adhesion road surface is conducted on Carsim and Matlab/Simulink joint simulation platform. With IWCPSO-LQR under double-lane-change (DLC) condition on a low adhesion road surface, the yaw rate and sideslip angle of the DDEV exhibits improvements of 95.2%, 96.8% in the integral sum of errors, 94.9%, 95.1% in the root mean squared error, and 78.8%, 98.5% in the peak value compared to those without control. Simulation results indicate the proposed hierarchical control method has a remarkable control effect on the yaw rate and sideslip angle, which effectively strengthens the driving stability of 4W-DDEVs. Full article

In response to the COVID-19 pandemic and its strain on healthcare resources, this study presents a comprehensive review of various techniques that can be used to integrate image compression techniques and statistical texture analysis to optimize the storage of Digital Imaging and Communications in Medicine (DICOM) files. In evaluating four predominant image compression algorithms, i.e., discrete cosine transform (DCT), discrete wavelet transform (DWT), the fractal compression algorithm (FCA), and the vector quantization algorithm (VQA), this study focuses on their ability to compress data while preserving essential texture features such as contrast, correlation, angular second moment (ASM), and inverse difference moment (IDM). A pivotal observation concerns the direction-independent Grey Level Co-occurrence Matrix (GLCM) in DICOM analysis, which reveals intriguing variations between two intermediate scans measured with texture characteristics. Performance-wise, the DCT, DWT, FCA, and VQA algorithms achieved minimum compression ratios (CRs) of 27.87, 37.91, 33.26, and 27.39, respectively, with maximum CRs at 34.48, 68.96, 60.60, and 38.74. This study also undertook a statistical analysis of distinct CT chest scans from COVID-19 patients, highlighting evolving texture patterns. Finally, this work underscores the potential of coupling image compression and texture feature quantification for monitoring changes related to human chest conditions, offering a promising avenue for efficient storage and diagnostic assessment of critical medical imaging. Full article