Mathematical Model Of Measurement Research Articles

Photoelectric sensor array-based measurement method for the key motion parameters of the small flying object considering non-uniform curve trajectory

Purpose The paper aims to accurately measure the key motion parameters, such as velocity, azimuth and pitch angle, of the small flying object with a non-uniform curve trajectory. It proposes a measurement method and its calculation model of non-uniform curve trajectory using a photoelectric sensor array. Design/methodology/approach First, the basic composition of the measurement system and mechanism of photoelectric sensor array are described, respectively. Second, a non-uniform curve mathematical measurement model is constructed differently from the traditional linear trajectory, taking into account the influence of gravity and air resistance. Third, the measurement error of the system is analyzed through numerical simulation. Finally, the accuracy and feasibility of the approach are verified by live-ammunition experiments. Findings The results show that the systematic error of the hitting point coordinates can be reduced by 9% compared to the traditional linear measurement model. Consequently, this method can meet the higher measurement requirement for the key motion parameters of the small flying object under the non-uniform curve trajectory. Research limitations/implications (if applicable)- although the approach itself is generalizable, the method is unable to detect the motion parameters of multiple small flying objects. Research limitations/implications Although the approach itself is generalizable, the method is unable to detect the motion parameters of the multiple small flying objects. Practical implications It is evident that the proposed non-uniform curve measurement model is more precise in quantifying the essential characteristics of the small flying object, particularly in consideration of the environmental conditions. Social implications The precise measurement of the key motion parameters of the small flying object can facilitate the enhancement of the protective performance of protective materials. Originality/value A novel approach to measurement is proposed, which differs from the conventional uniform trajectory model. To this end, the space construction of the photoelectric sensor array is optimized. The number of the sensors is revised.

Using Machine Learning to Score Multidimensional Assessments of Students’ Skill Levels in Mathematics

This research aims to establish a mathematical skill measurement model to examine seventh-grade students’ mathematical skills in two aspects: their understanding of mathematical processes and the concept and structure. The researchers surveyed the mathematical skills of 521 seventh-grade students from the northeastern province of Thailand. Their test results were used to prototype a mathematical skill measurement model using machine learning. It involved a design-based approach that included four stages: a construct map, item design, a Wright Map, and outcome space, the so-called Multidimensional Random Coefficient Multinomial Logit Model, to verify its quality. The initial findings revealed the creation of a construct map consisting of five levels. The researchers determined the cut-off point in the form of the threshold level after considering the Wright Map criteria area for each aspect. Lastly, the measurement model was examined to provide adequate evidence of the internal structure’s validity and reliability. In conclusion, students’ skill levels can be measured accurately using multidimensional assessments, even though the levels of mathematical capabilities of the students varied from low to moderate to high. Therefore, it provides significant evidence of the mathematical skill measurement model to diagnose seventh-grade students’ learning. The significant implications contributed to educational measurement and evaluation are that machine learning algorithms can provide more accurate and consistent scoring of assessments compared to human graders. With accurate assessment using machine learning, teachers can gain deeper insights into individual students’ mathematical skills across multiple dimensions.

Research on Mathematical Measurement Model of Fair Value Based on Big Data and Cloud Computing

Research on Mathematical Measurement Model of Fair Value Based on Big Data and Cloud Computing

Investigation of Spatial Symmetry Error Measurement, Evaluation and Compensation Model for Herringbone Gears

In the machining process for herringbone gears manufactured by numerical control gear-shaping machines, out-of-tolerance problems of symmetry error generally exist. This paper proposed a high-precision control of spatial symmetry error in the one-time forming machining for herringbone gear. To improve the machining symmetry accuracy and quality of herringbone gear, a mathematical model of measurement, evaluation and compensation for spatial symmetry error was established based on the least square method. Meanwhile, a new shaping machining method based on spatial symmetry error detection and compensation was proposed. The test results indicated that the proposed method can maintain symmetry within 0.02 mm. This study provided a novel spatial symmetry error detection and compensation machining method for herringbone gear that has advantages compared to traditional methods in terms of machining accuracy, efficiency, and continuous machining type.

Research on Mono-Pulse Beam Angle Tracking Algorithm of Phased Array Antenna Based on CKF

Phased array antenna beam tracking and communication system based on mono-pulse system is an alternative satellite-to-earth communication technology solution for future planetary spacecraft, which meets the mission requirements of agile scanning, multimode, wide field of view, and small size. This paper firstly outlines the technical scheme of mono-pulse angle tracking based on the planar phased array antenna. A simplified mathematical model of angle measurement is summarized. Secondly, the beam pointing of the spacecraft communication antenna is frequently affected by the attitude and presents a nonlinear dynamic change. A robust two-dimensional angular tracking filtering algorithm based on cubature Kalman filter (CKF) is proposed, in order to solve this complex high-order nonlinear dynamic estimation problem. Finally, the comprehensive performance of the proposed algorithm is simulated and analyzed under two conditions of stable flight and high dynamic flight of the spacecraft. When the angular velocity is within 4°/s, the tracking accuracy can be better than 0.65°, and the tracking accuracy will be better than 1° when the angular velocity is within 8°/s. Compared with the basic CKF algorithm, the robust CKF tracking accuracy is significantly improved, while the resource consumption is slightly reduced. The research results can provide reference for the engineering implementation of related fields in the future.

Measurement, Evaluation, and Model Construction of Mathematical Literacy Based on IoT and PISA

“Mathematics Curriculum Standard for Ordinary Senior High School” points out that mathematical modelling literacy is the literacy of abstracting real problems mathematically, expressing problems with mathematical language, and building models with mathematical methods to solve problems. It assesses the amount to which students who are about to finish compulsory schooling have the knowledge and aptitude to deal with future life issues, based on the notion of lifelong learning. The usage of a local integrated development environment requires a number of complex processes, including installation and setup, as well as the procurement of necessary hardware. In reality, in order to nurture students, the core literacy of mathematics is to completely execute quality education, further identify the training and development direction of talents, and infiltrate the core literacy material into junior high school mathematics classroom instruction. For such a large-scale international education measurement project, the research and development of test questions is very important. Therefore, detailed technical consideration has been carried out and test volumes have been designed that are relatively suitable for different countries. The test questions are closely related to life, while there are few questions related to real situational problems in the test, which are mathematically processed first. Due to the international background of evaluation, it is a great challenge for researchers to realize the localization of evaluation on the basis of adapting to the domestic situation. At the same time, there is no scientific and perfect mathematical modelling literacy evaluation system in China’s basic education research. How can middle school front-line teachers better evaluate students’ mathematical modelling literacy? As a result, it is critical to develop a scientific and quantitative mathematical literacy measurement model that will aid in the teaching and research of mathematical modelling by middle school front-line teachers, as well as contributing theoretically to the evaluation and research of mathematical modelling literacy in China. Therefore, based on mathematics literacy evaluation, this paper studies the hierarchy of the IoT and the measurement and evaluation model of mathematics literacy based on the IoT, as well as its enlightenment to the compilation of mathematics academic test questions in China.

EVALUATION OF SYSTEMATIC ERRORS OF STRIP ASYMMETRIC HUMIDITY SENSOR

The methodical estimation of the methodical component of the error arising at measurement of humidity of heterogeneous dispersed dielectrics by the band asymmetric sensor is carried out. In the process of evaluation it was shown that the most significant component of methodological error occurs due to changes in temperature and frequency of the information wave. Temperature-dependent values included in the mathematical model of the band asymmetric humidity sensor are: relative dielectric constant of the substrate dielectric and the object of control, length and width of the central conductor, substrate dielectric thickness. The dielectric constant of the dielectric of the object of control depends on the frequency of the information wave, and this parameter is directly included in the coefficients of the sensor conversion equation. The results of the research showed that in the process of measuring the conversion of humidity in the band asymmetric sensor there is a methodological component of the error associated with changes in temperature and instability of the frequency of the information wave. To ensure a frequency error at a level not exceeding 0.5%, the error of instability of the frequency of the information wave when converting humidity into the output amplitude of the information wave should not exceed ± 3 kHz, provided by existing RF generators. It is advisable to remove the temperature component of the error using the method of correction. The mathematical model of band asymmetric measurement of moisture conversion of heterogeneous dispersed dielectrics in the high-frequency region was also improved.

Application of adaptive Monte Carlo method to evaluate pose uncertainty in monocular vision system

Due to the influence of many factors in monocular vision pose measurement, the reliability of pose measurement results needs to be evaluated by uncertainty. The difficulties of the traditional guide to the expression of uncertainty in measurement (GUM) method in actual pose evaluation are analyzed, and the adaptive Monte Carlo method (AMCM) is used to evaluate the uncertainty of pose results. According to the mathematical model of pose measurement, the factors affecting pose results are analyzed in detail. The uncertainty evaluation model is established by the error traceability method and the distribution of uncertainty components is analyzed reasonably. Both the Monte Carlo method (MCM) and AMCM are used to evaluate the uncertainty of pose results. The feasibility and effectiveness of the AMCM evaluation method are verified. The experimental results show that MCM and AMCM, as the supplement of the GUM method, can well solve the problem of pose evaluation in the actual measurement system. However, AMCM is more convenient and efficient than MCM to solve the problem of too large or too small sampling times.

Validation of a Method for Measuring the Position of Pick Holders on a Robotically Assisted Mining Machine’s Working Unit

For effective mining, it is essential to ensure that the picks are positioned correctly on the working unit of a mining machine. This is due to the fact that the design of roadheader cutting heads/drums using computer-aided tools is based on the operating conditions of the roadheader/shearer/milling machine. The geometry of the cutting head is optimized for selected criteria by simulating the mining process using a computer. The reclaimed cutting head bodies that are utilized in production are manufactured again in the overhaul process. Ensuring that the dimensions of the cutting head bodies match the rated dimensions is labor-intensive and involves high production costs. For dimensional deviations of the cutting head bodies, it is necessary to control the position of the pick holders relative to the cutting head side surface in real time during robotic-assisted assembly. This article discusses the possibility of utilizing a stereovision system for calculating the distance between the pick holder base and the roadheader cutting head side surface at the point where the pick holder is mounted. The proposed measurement method was tested on a robotic measurement station constructed for the purpose of the study. A mathematical measurement model and procedures that allow automatic positioning of the camera system to the photographed objects, as well as acquisition and analysis of the measurement images, were developed. The proposed method was validated by using it for measuring the position of the pick holders relative to the side surface of the working unit of a mining excavating machine, focusing on its application in robotic technology. The article also includes the results observed in laboratory tests performed on the developed measurement method with an aim of determining its suitability for the metrology task under consideration.

Restoration of Hardware Function of Spectral Colorimeters Using Regularization Methods

The problem of determining the spectral characteristic of a controlled sample under conditions of limited a priori information using regularization methods is considered in the paper. A change in the state of the surface of optical elements significantly increases the light scattering, so it is necessary regularly to take into account the amount of scattered light in the light flux reflected from the surface and the measured and comparative samples. The conversion of the light flux into the electrical signal of the photodetector can also occur non-linearly. This requires the development of such measurement method that considers both the scattered light and various non-linearities of the measuring circuit. It is known that the mathematical model of measurement is described by the Fredholm integral equation of the first kind, its solution under the accepted assumptions is recommended to be sought in the form of a matrix equation using a recurring procedure. With regard to the fact that the estimation of the initial data errors in the equation is associated with certain difficulties, in the case under consideration, it is advisable to determine the regularization parameter based on the method of quasi-optimality. A characteristic disadvantage of the known analytical and experimental methods for determining the hardware function of a spectral device is that they do not take into account its change during operation. Since the actual hardware function of the device usually differs from the Gaussian curve, the use of hardware functions in the form of analytical dependencies does not always give the desired result, and for experimental methods, special equipment with a quasi-monochromatic radiation source is required. An algorithm for restoring the hardware function of a spectral device based on regular methods for solving ill-posed problems is proposed. The estimation of the matrix operator of the hardware function is proposed to be obtained on the basis of explicit least squares estimation algorithms. The expediency of choosing a value of the regularization parameter that minimizes the accepted characteristic of the accuracy of the solution is indicated.

Designing Standards-Setting for Levels of Mathematical Proficiency in Measurement and Geometry: Multidimensional Item Response Model

This study intends to design and verify the quality of a model that measures mathematical proficiency and aims to set the standards in measuring levels of proficiency in the subjects of measurement and geometry. Construct modeling was employed to design a mathematical proficiency measurement model which consists of the mathematical process and the dimensions of a conceptual structure. A total of 517 Secondary Year 1 students were selected from the big data to participate as test-takers. Design-based research encompassing four phases was used to verify the quality of the mathematical proficiency measurement model. A Multidimensional Random Coefficient Multinomial Logit model was used to examine the standards-setting of the mathematical proficiency measurement model. The results indicated that the two dimensions of mathematical proficiency can be further divided into five levels, from non-response/irrelevance to strategic/extended thinking and extended abstract structure for mathematical process and conceptual structural dimensions, respectively. The assessment tool covers 18 items with 15 multiple-choice items and three subjective items in measurement and geometry. Moreover, the results also demonstrated that the validity evidence associated with the internal structure of the multidimensional model is fit. Besides, reliability evidence, as well as item fit, is compliance with the quality of the mathematical proficiency measurement model as illustrated in analysis of the standard error of measurement and infit and outfit of the items. Finally, the researchers managed to set standards for the mathematical proficiency measurement model based on the assessment criterion results from the Wright Map. In conclusion, the standards-setting of the mathematical proficiency measurement model provides substantial information, particularly for measuring those students who are above the lowest level of mathematical proficiency because the error for estimating proficiency was low.

Measurement of respirable crystalline silica concentration by X-ray diffraction: Evaluation of metrological performances

Worker exposure to Respirable Crystalline Silica (RCS) is related with increased risk for lung cancer, so it is important to correctly assess it, through measurements of RCS. There are several methods for the uncertainty evaluation of the concentration of RCS measured by X-ray diffraction, however, none involves the calculation of the sensitivity coefficients of the mathematical measurement model. Hence, the aim of this research work is to propose an improved method, in which the sensitivity coefficients are calculated as partial derivatives of the model. The method was applied to four measurements campaigns in a factory, and the results seem to be comparable with those published in literature. It arose that for low concentrations the major contribution of uncertainty is due to the X-ray diffraction calibration line. This may mean that the minimum number of six calibration test filters, as suggested by the standards, is not sufficient, especially for low concentrations.

Mathematical modeling of errors for determining time of death based on the Newton’s–Richman’s cooling law

Background: A mandatory factor in the development and implementation of diagnostic technologies for determining the time of death by the thermal method is the assessment of possible errors. For equations of cadaver cooling that have a deterministic character, error estimation is possible using a mathematical model of indirect measurement. Here, a mathematical model has been proposed for estimating the maximum absolute error in determining death on the basis of the Newton'sRichman's cooling law under conditions of constant and changing ambient temperature. Aim: Using a mathematical model of indirect measurement, this study developed a method for estimating errors in determining the prescription of death according to the Newton'sRichman's cooling law. Material and methods: Mathematical modeling of errors in determining the time of death in conditions of constant and changing ambient temperature was conducted according to the Newton'sRichman's law. The computer program code was drafted in the C# programming language using the Microsoft Visual Studio 2019 application. Results: Based on the indirect measurement model, a method for estimating the maximum absolute errors for determining the time of death during cooling according to the Newton'sRichman's law under conditions of constant and changing ambient temperature was developed. The results obtained allowed us to analytically determine errors in time the prescription of death in the early postmortem period. Conclusions: We developed a mathematical model for estimating maximum absolute errors while determining the time of death according to the Newton'sRichman's cooling law under conditions of constant and changing ambient temperature. The developed mathematical model was implemented as an application program Warm Bodies NRN. The proposed method might be used in forensic medical expert practice for determining the time of death.

Music genre influence and artist similarity based on data analysis

Based on related data and cluster analysis, this paper creates a mathematical model of similarity measurement based on the data set, and finally obtains the influence of different music genres on their followers and the similarity of artists of different musical genres. Here, since the study is about the similarity of music, it is divided into 2 categories according to the provided music characteristics and related indicators of music type. The data is standardized and normalized. Because there is no clear indicator to measure the similarity of music, we use spss to perform K-means clustering analysis. Here, since the similarity of music is studied, it is built on the music characteristics and music provided. Types of related indicators divide it into two categories for analysis. In order to determine the reliability of the model, this article uses meaningful learning to train 70% of the previous data, 30% to test, and finally establishes a complete mathematical model.

Estimation of optical speed measurement error for traffic monitoring systems

This article is devoted to the problem of accurate vehicle speed measurement from video images. The analysis of existing methods of optical speed measurement is carried out, and the need to estimate the measurement error is justified. An idealized mathematical model of speed measurement based on binding to the size of the license plate is studied and the influence of various factors on the measurement accuracy is shown: the influence of the intrinsic and extrinsic camera parameters, the influence of license plate size in images, influence of data averaging. A comparison of the obtained results with the accuracy of widely used in practice radar technologies is shown.

CALIBRATION OF OPTICAL DISPLACEMENT SENSOR SYSTEM

The optical displacement sensor was selected for accurate length measurement. The aim of this article is to determine the mathematical measurement model for displacement measurement using an assembled measuring chain by calibration. The uncertainty balance for the assembled measuring chain is determined in the next part of this article.

Flexibility measurement model of multi-agent systems

Flexibility is considered as one of the key objectives of agent-based technology. Despite this, we still lack a fundamental understanding of just what “flexibility in multi-agent system (MAS)” really is. Two main questions must be asked. First, how do agents and MAS achieve a high degree of flexibility? Second, what makes one agent or one MAS more flexible than others agents or others MASs? This paper addresses the answer to these two questions by proposing an ontology of the flexibility property and a mathematical measurement model for this property. The proposed ontology gives a comprehensive view of the flexibility by decomposing it on several characteristics and presents several techniques for implementing each characteristic. In addition, it relates these characteristics to MAS components. The proposed model presents a set of metrics for measuring the different characteristics of the flexibility property. The proposed metrics have been applied to JADE applications using a tool developed for this purpose.

Проблема адекватности метода анализа иерархий

The Analytic hierarchy process (AHP) is a popular method for solving multi-criteria problems. However, the problem of the adequacy of the AHP method is not solved. Opponents of the Analytic hierarchy process believe that the AHP as a whole is erroneous and cannot be applied in practice. Proponents of the method believe that the disadvantages of the method are compensated by a simple measurement procedure. In this paper, a modification of the AHP method is proposed. A mathematical model of measurement is formulated, which contains a built-in mechanism for checking adequacy. moreover, the measurement method is preserved, and the calculation algorithm becomes even simpler. The fact is that the Analytic hierarchy process is based on the assumption that the scale of relations can be obtained by pairwise comparison using numerical judgments based on the absolute scale of numbers. Fechner’s psychophysical law is considered as a justification for the existence of the scale of relations. But there are not one, but two psychophysical laws. The existence of two psychophysical laws is a problem of psychophysics. This problem can be solved by the rating method. To overcome the disadvantages of the Analytic hierarchy process, it is also proposed to use the rating method. The use of the rating method makes it possible to use the fundamental scale of the AHP method. As an example, the problem is solved using the traditional AHP scale.

Research on security trust measure model based on fuzzy mathematics

Abstract The existing safety measurement model has the disadvantages of poor reliability and stability. In order to improve the reliability of the security trust measurement structure, a fuzzy trust-based security trust measurement model is proposed. The hierarchical fuzzy transmission network is used to establish the mathematical model of the controlled object, and the control objective function is analyzed. The regression analysis model is combined with the convergence constraint function, and the fuzzy adaptive learning is performed according to the security trusted computing output weight, and the parameter analysis is performed. And adjust; on this basis, establish a mathematical model of safety confidence measurement, and perform parameter feedback adjustment and reliability control to improve the reliability of the security trust measurement structure. The simulation results show that the proposed method has good reliability and steady-state convergence, and can effectively improve the reliability calculation ability of the safety confidence measure. It has strong application advantages.

A one-dimensional mathematical simulation to salinity control in a river with a barrage dam using an unconditionally stable explicit finite difference method

Salinity refers to the amount of salt in rivers, where the salt can be in many different forms. There are two main methods of defining the concentration of salt in water such as the total dissolved solid measurement (TDS) and the electrical conductivity measurement (EC). The salinity is measured by evaporating water to dryness and weighing the solid residue. The electrical conductivity measurement is measured by passing an electric current through the water and measuring how readily the current flows. The total amount of salt in the water can affect the taste of water. The World Health Organization’s guideline on water palatability is that water with a salinity level of less than about 0.50–0.60 g/L is generally considered to be of a standard level. The drinking-water becomes significantly and increasingly unpalatable at salinity levels greater than about 1.0 g/L. In this research, a one-dimensional mathematical model of salinity measurement in a river is proposed. A modified model of salinity control in a river with a barrage dam is also introduced. An unconditionally stable explicit finite difference technique is used to approximate the salinity level under several conditions from the proposed model. The proposed computational technique gives good agreement results in realistic scenarios for water supply processes.