Mathematical Model Of Measurement Research Articles

Accuracy and Resolution of Kinect Depth Data for Indoor Mapping Applications

Consumer-grade range cameras such as the Kinect sensor have the potential to be used in mapping applications where accuracy requirements are less strict. To realize this potential insight into the geometric quality of the data acquired by the sensor is essential. In this paper we discuss the calibration of the Kinect sensor, and provide an analysis of the accuracy and resolution of its depth data. Based on a mathematical model of depth measurement from disparity a theoretical error analysis is presented, which provides an insight into the factors influencing the accuracy of the data. Experimental results show that the random error of depth measurement increases with increasing distance to the sensor, and ranges from a few millimeters up to about 4 cm at the maximum range of the sensor. The quality of the data is also found to be influenced by the low resolution of the depth measurements.

Spectrum Absorption Methane Gas Sensor with Optical Fiber Based on Frequency Harmonic Detection Mechanism

Methane is an easily burning and exploding gas. It is the primary component of many gas fuels such as mine gas and natural gas and so on. In the coal mine accidences of our country, the casualties caused by gas explosion covers over 50% in all great casualties, and it becomes the largest obstruction of safe production. Incident online detecting methane gas density has important significance for mine and plant safe production and personal safety. Based on the near infrared spectral absorption of methane, a system using absorption type optical fiber for high sensitivity methane detection is demonstrated in this paper. DFB LD is adopted as light source in this paper. Modulating the light source, methane gas is detected by second harmonic. The ratio of the fundamental and second harmonic signal can be used for eliminating the interference owing to light power changing. The mathematical model of gas concentration harmonic measurement is built up. The result of methane concentration is also shown. The system overcomes the defect of great interference of available instruments by light route. It has advantages such as high sensitivity, quick response speed, large dynamic range, preventing electromagnetic interference, preventing burning and explosion, not easily being poisoned and so on. The probe can be put in condition of easily burning and exploding, being poisonous being high temperature and so on that man and instrument can not easily enter. It can realize online continuous telecontrol and telemeter.

Study on wet gas online flow rate measurement based on dual slotted orifice plate

According to the current technical problems existing in gas and liquid flow measurement for wet gas production, the slotted orifice-couple flow meter was developed and the basic measurement principles for gas and liquid flow was presented. A new wet gas flow meter was developed based on the dual slotted orifice transducer. The flow characteristics of liquid flow through dual slotted orifice plate, the relationship of differential pressure between the dual slotted orifice plate, pressure, temperature, and flow rate of gas/liquid of different aperture ratio were studied. A mathematical measurement model was established to be applied in the flow meter measurement system with dual slotted orifice plate. The model was tested and calibrated by on-site field experiments in the China National Center of Metrology at Daqing Oil field. The results showed that the maximum measurement error of the gas and liquid flow was less than 10% and 15% respectively, when the Gas Volume Fraction (GVF) was greater than 90 vol%. The measurement accuracy of this industrial prototype can meet the requirements of well fluids.

A Model of Time

Abstract: Based on a mathematical model of quantum measurement we derive some proper-ties of intuitive time.Keywords: Quantum Entropy, Energy, Measurement, Time.MSC 2000 Codes: 94A17, 81P151. IntroductionIn [7 ; 8] we present a model of quantum measurement which bases on the notions of decoherence andcollapse. Given an apparatus or register A , a system S and the environment E at temperature T , themeasurement process M can be thought of as being represented by the following sequence: M := A›S ! d tr E ( A›S ) ! p A ¶ ›S ¶ , ¶ 2 I: (1)The first step, d; is the decoherence of the entangled AS system and the creation of classical alterna-tives, mathematically expressed by a density matrix ‰ AS . The second step, p , is the projection or collapseto one of the eigenstates and a definite outcome. There is a fluctuation of entropy S ‰ AS connected to M .The fluctuation of entropy creates a pulse of energy whose average satisfies E 1 kTS ‰ AS where k de-notes the Boltzmann constant. The term ”measurement” is somewhat misleading in this context and wewant to replace it by ”realization” because what happenes in

Evaluation of uncertainty in a vortex flowmeter measurement

Measurement results of all quantities are inevitably subject to uncertainties. Proper estimation and expression of uncertainties are important to every domain of scientific and engineering researches. In this paper, the uncertainty of a vortex flowmeter was evaluated based on a novel mathematical measurement model and airflow experiment results. The proposed model was featured by regarding the vortex flowmeter and its calibration equipment as an entire measurement system, on which the uncertainty evaluation was carried out. The experiments were conducted in a 50-mm-diameter pipe with the Reynolds numbers from 9.42×103 to 8.48×104, and vortex frequencies were calculated by spectrum analysis of the differential pressures obtained on the pipe wall. The uncertainty analysis procedure followed the recommendations in the ISO Guide to the Expression of Uncertainty in Measurement. The results show that in the flowrates studied, the maximal uncertainty of the tested vortex flowmeter is less than 6.0% of the base value. Besides, higher measurement uncertainty takes place at lower flowrates, and the uncertainty appears to be constant when the flowrate is greater than a certain value. Among the relevant uncertainty sources, frequency resolution causes the biggest contribution to the total uncertainty especially at lower flowrates, and the uncertainty arose from the calibration system is less minor compared with uncertainties associated with the vortex frequency. It indicates that an effective strategy of reducing the uncertainty caused by the vortex frequency is improving its resolution, accordingly reducing the total uncertainty of a vortex flowmeter measurement.

A New Method to Improve the Precision of SO2Measurement in Atmosphere

The thesis discusses the status quo and existent problems of SO2 measurement, explores sensor mechanism of measurement precision of SO2, and deduces the mathematical measurement model of SO2 according to Lambert-Beer Law. Aiming at the nonlinearity problem existing in the mathematical model, it employs Taylor's series expansion to resolve the problem. In addition, it designs the gas room of double optical paths to measure SO2 by infrared, which utilizes four detectors to eliminate the impact of CO2 and disturbed noise by receiving signals. Finally, through the analysis of the experimental data, it proves that this method has such features as easy implementation, high precision, strong anti-jamming capability, and real-time and on-line measurement of SO2required in the industry field.

Design of fan beam optical sensor and its application in mass flow rate measurement of pneumatically conveyed solids

The fan-beam optical sensor is made up of many semiconductor lasers and detectors fixed around the wall alternately at a cross section of pneumatically conveying pipe. When the sensor works, a scanning light source emits a 50° lamellar fan-beam through the gas-solid two phase flow, and the projection data resulting extinction effect of solid particles are detected at the same time. With the projection data, the flow rate mass can be calculated, and then the flow image can be reconstructed. In this paper, the design of the sensor including spatial arrangement of the structural parts, basic principle and measurement sensitivity distribution are introduced. The mathematical measurement model of solid mass flow rate is presented together with the testing results.

Estimation of uncertainty in routine pH measurement

A procedure for estimation of measurement uncertainty of routine pH measurement (pH meter with two-point calibration, with or without automatic temperature compensation, combination glass electrode) based on the ISO method is presented. It is based on a mathematical model of pH measurement that involves nine input parameters. Altogether 14 components of uncertainty are identified and quantified. No single uncertainty estimate can be ascribed to a pH measurement procedure: the uncertainty of pH strongly depends on changes in experimental details and on the pH value itself. The uncertainty is the lowest near the isopotential point and in the center of the calibration line and can increase by a factor of 2 (depending on the details of the measurement procedure) when moving from around pH 7 to around pH 2 or 11. Therefore it is necessary to estimate the uncertainty separately for each measurement. For routine pH measurement the uncertainty cannot be significantly reduced by using more accurate standard solutions than ±0.02 pH units – the uncertainty improvement is small. A major problem in estimating the uncertainty of pH is the residual junction potential, which is almost impossible to take rigorously into account in the framework of a routine pH measurement.1

Thirty Years of Nonparametric Item Response Theory

Relationships between a mathematical measurement model and its real-world applications are discussed. A distinction is made between large data matrices commonly found in educational measurement and smaller matrices found in attitude and personality measurement. Nonparametric methods are evaluated for estimating item response functions and (unconditional and conditional) inter-item covariances.

A computerized adaptive testing system for speech discrimination measurement: the Speech Sound Pattern Discrimination Test.

A computerized, adaptive test-delivery system for the measurement of speech discrimination, the Speech Sound Pattern Discrimination Test, is described and evaluated. Using a modified discrimination task, the testing system draws on a pool of 130 items spanning a broad range of difficulty to estimate an examinee's location along an underlying continuum of speech processing ability, yet does not require the examinee to possess a high level of English language proficiency. The system is driven by a mathematical measurement model which selects only test items which are appropriate in difficulty level for a given examinee, thereby individualizing the testing experience. Test items were administered to a sample of young deaf adults, and the adaptive testing system evaluated in terms of respondents' sensory and perceptual capabilities, acoustic and phonetic dimensions of speech, and theories of speech perception. Data obtained in this study support the validity, reliability, and efficiency of this test as a measure of speech processing ability.

A mathematical model of measurement of thermal conductivity by the nonsteady hot-wire method

Developpement d'un modele mathematique de la methode du fil chaud ainsi que de l'algorithme et du programme correspondant rendant possible l'evaluation de l'erreur theorique liee a la non-linearite du probleme

Attitude Measurement and Estimation of Solar Observation Satellites

A concept of applying scanning type earth horizon sensors has been proposed to solve the problem how do measure the attitude error angles of a pointing-to-sun satellite during the eclipse part in the orbit, and also the rotation angle of the satellite about the pointing axis. The concept is primarily an attitude estimation method which involves the mathematical model of horizon sensor measurement and the extended kalman filter algorithm with computer simulation results to show the usefulness of the method.

A formalization of measurement scale forms

The general measurement scale hierarchy developed by S. S. Stevens has had widespread use and discussion, but has suffered from various criticisms, many of which may be traced to the informal descriptions and minimal mathematical formulations used in the original definitions and claims. In this paper, a mathematical model of measurement and specific scale forms is developed, using the minimum mathematical structure necessary to define each scale type. Measurement is defined, and a series of restrictions are applied to measurements to yield a precisely specified hierarchy of measurement scale forms including nominal, ordinal, interval, and ratio scales, as well as several others. Equivalences are mathematically denned for each scale form, and theorems are presented specifying the sets of transformations under which equivalence is preserved, thus yielding the scale form invariances discussed by Stevens. The hierarchy of measurement scale forms is summarized in a pictorial ‘spectrum’ diagram. The development...