Hull Theory Research Articles

A sub-convex similarity-based model updating method considering multivariate uncertainties

This paper proposes an innovative model updating technique that thoroughly considers the interrelations among multivariate output features. The approach involves developing a novel uncertainty quantification metric, termed Sub-Convex Similarity. A specialised data preprocessing operator is proposed to reveal the inherent distributional attributes of multivariate datasets through a sequencing pre-processing. To manage the inherent randomness associated with sample location dispersion, we propose a binning algorithm based on the equal-bin-datapoints principle. This method allows for the quantification of multidimensional stochastic data without the need to calculate the joint probability distribution function. Utilising convex hull theory, sub-regional boundaries are established within each bin to reveal multivariate dataset characteristics. Sub-Convex Similarity serves as a metric for quantifying both interval-based and stochastic uncertainties, measuring discrepancies between simulated and experimental datasets in the context of both interval and stochastic model updating. The proposed model updating framework employs the sparrow search algorithm, a swarm intelligence-based optimization mechanism. The effectiveness and broad applicability of this approach are demonstrated through case studies involving a three-degree-of-freedom mass-spring system and a finite element model of a satellite, addressing multivariate uncertainties.

A hierarchical LFFC control scheme for underactuated unmanned surface vessels based on unreliable communication interaction

This article investigates the leader-follower formation-containment (LFFC) control issue of underactuated unmanned surface vessels (USVs) system subject to unreliable communication interaction and the external disturbances. Firstly, an adaptive control scheme is established for the leaders to track the desired trajectory associated with preset formation configuration. Subsequently, by means of convex hull theory, a formation-containment control algorithm is developed to guide the followers into the specific area generated by the leaders. Nevertheless, the communication interaction among USVs is frequently unreliable, which is constrained by communication distance, equipment quality, and indeterminate cyber-attack. Worse still, this unreliability will magnify the unpredictable impact on system stability. Moreover, the signals generally undergo multilevel transmission from virtual leader to followers under LFFC structure, which will result in the amplification of unreliable ratio during the information transmissions. To address the aforementioned issues, an online-update auxiliary signal is constructed through the quasi-sliding mode manifold, which can suppress the impact of unreliable communication interaction. Theoretical analysis and numerical simulations are demonstrated to verify the feasibility and validity of the proposed control strategies.

Linearization Method for Large-Scale Hydro-Thermal Security-Constrained Unit Commitment

Security-constrained unit commitment (SCUC) is one of the most fundamental optimization problems in power systems. The objective of SCUC is to minimize the operating cost while respecting both system-wide and generator-specific constraints. It leads to a large-scale and mixed-integer programming (MIP) model with a large number of binary decision variables which is difficult to solve. This paper, based on the convex hull theory of single-unit, proposes a linearization method for the hydro-thermal SCUC problem with decoupled thermal units and variable-head hydro units. Then, the strategy of embedding two types of convex hulls in a multi-unit commitment and the heuristic method of constructing a feasible solution are designed, by which the multi-UC is approximated from large-scale mixed-integer programming to linear programming that can be solved in polynomial time. Finally, we theoretically prove that the optimal solution of the proposed LP model is always better than that of the Lagrangian Relaxation model. Numerical experiments on several large-scale test systems demonstrate the effectiveness and efficiency of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper proposes a linear programming model for the SCUC problem by lifting up to a higher-dimensional space. It realizes an important innovation in reducing the computational complexity of SCUC from the perspective of linearization. The proposed method can be well applied to large-scale long-term unit commitment problems. To better use this method, the following two properties should be highlighted: 1) the error of the proposed method is less than the Lagrangian relaxation method and decreases with the increasing system scales and 2) the computational efficiency of the proposed method is 10-100 times faster than that of the MIP model. We have tested many practical power systems and find that the error of the proposed LP model is usually very small compared with the precise MIP while the computational performance is significantly improved. In some practical cases, the decision makers usually do not want to find the precise optimal solution while only an approximation under a fast speed, because the boundary condition is imprecise. The proposed method is useful. Besides, for the cases that need the precise optimal solution, the proposed method can provide a high-quality initial solution for the MIP model to accelerate the convergence.

Exploring the Influencing Factors of Students’ Fire Behavior Awareness Based on the Theory of Internal Drive Reduction

Abstract Here argued that human behavior is primarily governed by habit, not by biological drive. When the need is satisfied, the drive generated by the need will decrease. This process is also the stimulation and reinforcement of the connection between the problem-coping behaviors, that is, the enhancement of the strength of the habit. This paper applies Herner’s drive theory to explore the influencing factors of college students’ fire awareness to strengthen college students’ behavioral potential in the face of fire danger. Based on the current situation of fire education, this paper analyzes the three influencing factors of the driving force, inducement, and habit intensity through the theory of Hull drive reduction, and discusses how to strengthen the habit intensity of college students in the face of fire danger and strengthen the behavioral connection between fire risk and safety countermeasures, which is conducive to exploring the characteristic fire safety education mode of colleges and universities.

Research on Consensus of Multi-agent System Under Saturation Constrained Impulse Control

This paper mainly analyzes and studies the impulse consensus of nonlinear time-delay multi-agent systems under communication constraints. Firstly, considering the inherent attribute of the actuator -- each agent communication channel is finite, the control protocol design considers the global input saturation constraint and introduces the general case that the upper and lower bounds of saturation constraint are ±1. Secondly, due to the complexity of the real communication environment, it is often difficult for the agent to ensure real-time and continuous communication in the communication process, so this paper mainly considers the impulse control method in the discontinuous control. In addition, when the communication environment of the agent is complex, time delay is also a common phenomenon, so the nonlinear system with time delay is studied in this paper. Based on Lyapunov theory, convex hull theory and other theoretical methods, the sufficient conditions to ensure the lead-following consensus of multi-agent systems are given in view of the above saturated constraints. Finally, the correctness and effectiveness of the proposed method are verified by a simulation example.

A POIs Based Method for Location Optimization of Urban Fire Station: A Case Study in Zhengzhou City

In order to strengthen urban rescue capabilities, a new method is proposed to optimize the spatial distribution of fire stations in urban areas. Potential fire risk places are simplified into points of interest (POIs). Based on the Minimize Facilities Method and Maximize Coverage Algorithm, the number and location of fire stations are determined. In addition, the POIs assigned to the stations are also determined. Moreover, the service area of the fire station is identified according to topological convex hull theory. After that, the coverage rate of the POIs and the sensitivity of the accessible area to the driving time are discussed. At last, Zhongyuan District of Zhengzhou City is taken as an example to verify the effectiveness of the proposed method. The results reveal that current fire stations are insufficient for protecting fire safety. It is necessary to construct three new stations, which will significantly enhance firefighting capabilities. Thus, the areas capable of being timely reached by fire forces in 4.3 min reach 108.8 km2, covering more than 50% of the target district. About 94 percent of the area composed of the target district can be reached in 10 min. Good accessibility indicates the proposed method is capable of optimizing the location of the urban fire station.

Practical and comparative application of efficient data reduction - Multivariate curve resolution

The term 'Big Data' has recently attracted much attention in science. Working with big data sets can be both challenging and rewarding. The complexity and big data sets make the analysis difficult to deal with, and the increasing volume of data sets requires the development of new practical methods for their handling. In this contribution, we explored the efficient data reduction-multivariate curve resolution (EDR-MCR) strategy based on the convex hull theory for quantitative and qualitative analysis of large chemical data sets. For the quantitative example, the potential of the EDR-MCR method for selecting a representative calibration set was investigated, and the results were compared with the widely used Kennard–Stone (KS) algorithm. The EDR-MCR strategy strongly limits the number of calibration samples with a high potency of prediction performance. The priority of EDR-MCR over KS is its ability to find informative variables and eliminate redundant features.Moreover, the EDR-MCR strategy was also applied for the qualitative analysis of a large-scale metabolomic data set. The comparable analysis results of EDR-MCR with the region of interest (ROI) method confirmed the ability of this method for quantitative analysis of big mass spectrophotometer data sets.

To construction of Green matrices of edge problems of theory of flat hulls with cyclic periodicity

To construction of Green matrices of edge problems of theory of flat hulls with cyclic periodicity.

PENERAPAN TEORI CLARK LEONARD HULL DALAM PEMBELAJARAN MATEMATIKA

This study aims to assist teachers in identifying the application of Clark Leonard Hull's theory in mathematics learning. Clark Leonard Hull's theory suggests that biological needs (drive) and the satisfaction of biological needs (drive reduction) are in a central position in all human activities, so that the stimulus ) what happens in learning is almost always associated with biological needs, although the response that comes may take various forms. This theory argues that the learning process occurs due to the Stimulus-Response (SR) interaction. In Hull's theory, the most famous of which is the drive reduction theory which has 4 principles, namely (1) drive, (2) stimulus and response, (3) response, (4) reinforcement. If the Hull theory is applied to mathematics learning activities, it will make students more interested in learning and easily understand the material to be taught by the teacher. In its implementation there are six processes, namely (1) Determination of learning objectives to be achieved, (2) preparation in the process of achieving goals, (3) understanding the environmental situation of the subject to be taught, (4) interpreting the environmental situation based on the understanding obtained, (5) implementation of activities in achieving the goals to be achieved, (6) reflection.

О некоторых классах корректных задач мембранной теории выпуклых оболочек

On the basis of the theory of the modified Riemann-Hilbert problem for generalized analytic functions, a geometric description is given of a fairly wide family of correct by I. N. Vekua of boundary value problems of the membrane theory of convex hulls with a piecewise smooth boundary. Solutions to the corresponding Riemann-Hilbert problem for an elliptic system of equilibrium equations are found in the classes of N.I. Muskhelishvili and realize a state of tense equilibrium under the condition of stress concentration in corner points. An effective formula is given for calculating the index of the boundary condition, which allows us to formulate the results in a visible form. Families of shells are found for which the solvability picture of the main boundary-value problem coincides with the solvability picture of the Vekua problem for shells with a smooth border.

Water takeoff performance calculation method for amphibious aircraft based on digital virtual flight

Owing to the strong coupling among the hydrodynamic forces, aerodynamic forces and motion of amphibious aircraft during the water takeoff process, the water takeoff performance is difficult to calculate accurately and quickly. Based on an analysis of the dynamics and kinematics characteristics of amphibious aircraft and the hydrodynamic theory of high-speed planing hulls, a suitable mathematical model is established for calculating the hydrodynamics of aircraft during water takeoff. A pilot model is designed to illustrate how pilots are affected by the lack of visual reference and the necessity to simultaneously control the pitch angle, flight velocity and other parameters during water takeoff. Combined with the aerodynamic model, engine thrust model and aircraft motion model, a digital virtual flight simulation model is developed for amphibious aircraft during water takeoff, and a calculation method for the water takeoff performance of amphibious aircraft is proposed based on digital virtual flight. Typical performance indicators, such as the liftoff time and liftoff distance, can be obtained via digital virtual flight calculations. A comparison of the measured flight test data and the calculation results shows that the calculation error is less than 10%, which verifies the correctness and accuracy of the proposed method. This method can be used for the preliminary evaluation of airworthiness compliance of amphibious aircraft design schemes, and the relevant calculation results can also provide a theoretical reference for the formulation of flight test plans for airworthiness certification.

Precision measurement and evaluation of flatness error for the aero-engine rotor connection surface based on convex hull theory and an improved PSO algorithm

The precision measurement and evaluation of the geometry form error for high-end precision components is one of the most important tasks for metrologists. In this paper, a novel hybrid flatness error evaluation method is proposed to measure and evaluate the flatness error for large-scale point cloud data. This method is based on the convex hull algorithm and the improved particle swarm optimization (IPSO) algorithm. Not only are a large number of redundant measurement data points effectively removed through the convex hull algorithm, but also this operation does not lose any valuable information for flatness error evaluation. Then an accurate mathematical model for flatness error evaluation is established based on the minimum zone criteria recommended by ISO, and then the IPSO algorithm is adopted to solve this complex non-linear optimization problem. In particular, the non-linear dynamic inertia weights w and learning factors c1, c2 are introduced to improve the calculation accuracy. Finally, the proposed method is verified through an experiment measuring and evaluating the flatness error of an aero-engine rotor connection surface. The effective measurement data points are reduced from 18 000 to 856, or 4.76%, which is significant compared to the original data points. The flatness error evaluation result is 369 µm according to the IPSO method that we propose. Last but not least, we compare our method with the traditional least squares method and unmodified particle swarm optimization algorithm. The calculation results indicate that the evaluation accuracy is increased by 21 µm and 44 µm, respectively.

Towards automatic classification of diffuse reflectance image cubes from paintings collected with hyperspectral cameras

Knowledge of pigments and their distribution in paintings can inform conservators and scholars to better understand, and conserve these objects. In recent years, a variety of macro-scale non-contact imaging modalities have been applied to paintings to create classification/material maps. One modality, reflectance imaging spectroscopy (RIS) captures the diffuse reflectance spectral signatures of the artists’ materials present in the objects which can be used for classification (by defining regions of the image cube that have the same spectral reflectance signature). In Cultural Heritage Science the ENVI spectral hourglass wizard (ENVI-SHW) has been used to create classification maps from RIS. This method is slow and requires an expert user input during the processing in order to find the reflectance spectra that define the spectral classes (spectral endmembers or exemplars). The pigments are then deduced from spectral features in endmember spectra and from other non-invasive analytical chemical analysis of sites defined by the RIS maps. This paper explores the potential of more automated algorithms, such as maximum distance (MaxD), that are based on the theory of convex hulls for doing these classifications as well as spectral matching algorithms to an optimal spectral library. While all of these algorithms were developed for Remote Sensing community, MaxD and the library matching examine all the spectra in the reflectance image cube, require little user input, and are reproducible and fast. The results from the analysis of reflectance image cubes (400 to 950 nm) of three paintings with MaxD and a spectral library matching algorithm are presented and compared to those obtained with the ENVI-SHW algorithm. The three paintings analyzed are the central panels from illuminated leafs, two from the Laudario of Sant’Agnese (c. 1340) painted by the Master of the Dominican Effigies, namely The Nativity with the Annunciation to the Shepherds and, Christ and the Virgin Enthroned with Forty Saints, and one cutting from a leaf from a Choir book, Saint Francis Receiving the Stigmata, painted by Cosmè Tura (c. 1470s). Specifically, the results include the spectral endmembers recovered from each method as well as the associated classification maps. The findings from this study show that the MaxD algorithm was able to find the majority of the reflectance spectral endmembers with little user input.

On the Hirzebruch–Kobayashi–Ono proportionality principle and the non-existence of compact solvable Clifford–Klein forms of certain homogeneous spaces

Abstract This article continues a line of research aimed at solving an important problem of T. Kobayashi of the existence of compact Clifford–Klein forms of reductive homogeneous spaces. We contribute to this topic by showing that almost all symmetric spaces and 3-symmetric spaces do not admit solvable compact Clifford–Klein forms (with several possible exceptions). Our basic tool is a combination of the Hirzebruch–Kobayashi–Ono proportionality principle with the theory of syndetic hulls. Using this, we prove a general theorem which yields a sufficient condition for the non-existence of compact solvable Clifford–Klein forms.

Reducing Redundancy of Musculoskeletal Robot With Convex Hull Vertexes Selection

It has been a long-term dream of roboticist to create a robot that has similar behavior and appearance to human. With highly redundant joints and actuators, the musculoskeletal system of human can fulfill movement and operation with high precision, flexibility, and reliability. However, the redundancy of the musculoskeletal system also brings great difficulties to the control and fabrication of a human-like robot. Therefore, we propose an algorithm based on the convex hull theory to effectively reduce the number of redundant muscles. Specifically, taking the strength limitation and state-dependent characteristics of muscles into consideration, by analyzing the torque contribution of muscles for the discrete motion of joints, each muscle can be represented by a feature vector, and the convex hulls are formed by these vectors in high-dimensional space. By applying the proposed algorithm, the muscles corresponding to the vertexes of the convex hull are reserved while the redundant muscles within the convex hull are deleted, and a simplified model can be obtained. Sets of motion experiments demonstrate that the simplified model can achieve high-precision movement as a complete model. Based on the simplified model, a hardware platform of a robotic arm is constructed, which consists of six degrees of freedom and 11 pneumatic muscles.

Dynamics of an N-Species Gilpin–Ayala Impulsive Competition System

Abstract In this paper, we consider an N-species Gilpin–Ayala impulsive competition system. By using comparison theorem, Lyapunov functional, and almost periodic functional hull theory of the impulsive differential equations, this paper gives some new sufficient conditions for the permanence, global asymptotical stability, and almost periodic solution of the model. Our results extend some previously known results. The method used in this paper provides a possible method to study the permanence, global asymptotical stability, and almost periodic solution of the models with impulsive perturbations in biological populations.

A Color Image Segmentation Method Based on Region Salient Color and Fuzzy C-Means Algorithm

This paper proposes a color image segmentation method based on region salient color and the fuzzy C-means (FCM) algorithm. The method first uses the convex hull theory based on Harris corner detection to detect the object of the image. Thus, the object and the background can be separated. Then, the quantized color histogram can be studied in the HSV color space. By calculating the number of the peak values of both the object and the background histograms, the quantity of the regional salient colors can be obtained. The quantity is the number of the clustering centroids of FCM algorithm. Finally, the FCM algorithm and the noise correction algorithm can be used in the object and the background, respectively. The obtained segmented image consists of the object and the background segmentation. It proves that the method in this paper is an effective segmentation method based on the experiments made by use of Berkeley segmentation dataset. According to the experimental results, it can be concluded that the proposed algorithm has the highest segmentation accuracy and the shortest computing time among the algorithms mentioned in this paper. The algorithm can achieve high-quality, stable and accurate color image segmentation results.

ICFS Clustering With Multiple Representatives for Large Data

With the prevailing development of Cyber-physical-social systems and Internet of Things, large-scale data have been collected consistently. Mining large data effectively and efficiently becomes increasingly important to promote the development and improve the service quality of these applications. Clustering, a popular data mining technique, aims to identify underlying patterns hidden in the data. Most clustering methods assume the static data, thus they are unfavorable for analyzing large, unbalanced dynamic data. In this paper, to address this concern, we focus on incremental clustering by extending the novel [clustering by fast search (CFS) and find of density peaks] method to incrementally handle large-scale dynamic data. Specifically, we first discuss two challenges, i.e., assignment of new arriving objects and dynamic adjustment of clusters, in incremental CFS (ICFS) clustering. We then propose two ICFS clustering algorithms, ICFS with multiple representatives (ICFSMR) and the enhanced ICFSMR (E_ICFSMR) to tackle the two challenges. In ICFSMR, we explore the convex hull theory to modify the representatives identified for each cluster. E_ICFSMR improves the generality and effectiveness of ICFSMR by exploring one-time cluster adjustment strategy after integration of each data chunk. We evaluate the proposed methods with extensive experiments on four benchmark data sets, as well as the air quality and traffic monitoring time series, with comparisons to CFS and other three state-of-the-art incremental clustering methods. Experimental results demonstrate that the proposed methods outperform the compared methods in terms of both effectiveness and efficiency.

Recognition of the position of Chinese wolfberry branches under the artificial background

Chinese wolfberry is one of the important economic crops in Northwest china. Wolfberry harvest is seasonal and labor intensive, and, the existing various types of Chinese wolfberry harvesting equipment cannot meet the operation requirements. Thus the development of low damage and intelligent equipment is important to guarantee the healthy development of the industry. Many kinds of intelligent recovery equipment need accurate location information of branches of Chinese wolfberry. However, the color of the branches is close to the natural background, and the occlusion is serious, resulting in difficulties in identifying the branches. Aiming at solving these problems, a method of identifying branches of wolfberry based on mathematical morphology and convex hull theory is proposed in this paper. Compared with artificial recognition, the success recognition rate is more than 60%.

An Automatic Measurement Method for Absolute Depth of Objects in Two Monocular Images Based on SIFT Feature

Recovering depth information of objects from two-dimensional images is one of the very important and basic problems in the field of computer vision. In view of the shortcomings of existing methods of depth estimation, a novel approach based on SIFT (the Scale Invariant Feature Transform) is presented in this paper. The approach can estimate the depths of objects in two images which are captured by an un-calibrated ordinary monocular camera. In this approach, above all, the first image is captured. All of the camera parameters remain unchanged, and the second image is acquired after moving the camera a distance d along the optical axis. Then image segmentation and SIFT feature extraction are implemented on the two images separately, and objects in the images are matched. Lastly, an object’s depth can be computed by the lengths of a pair of straight line segments. In order to ensure that the most appropriate pair of straight line segments are chosen, and also reduce computation, convex hull theory and knowledge of triangle similarity are employed. The experimental results show our approach is effective and practical.