V̇o2, V̇co2, and RQ in a respiratory chamber: accurate estimation based on a new mathematical model using the Kalman-Bucy method

2004 ◽  
Vol 96 (3) ◽  
pp. 1045-1054 ◽  
Author(s):  
L. Granato ◽  
A. Brandes ◽  
C. Bruni ◽  
A. V. Greco ◽  
G. Mingrone
Keyword(s):  
Mathematical Model ◽  
Measurement Errors ◽  
Estimation Method ◽  
Accurate Estimation ◽  
Production Rates ◽  
Estimation Errors ◽  
Respiratory Chamber ◽  
Residual Noise ◽  
Proposed Model

A respiratory chamber is used for monitoring O2 consumption (V̇o2), CO2 production (V̇co2), and respiratory quotient (RQ) in humans, enabling long term (24-h) observation under free-living conditions. Computation of V̇o2 and V̇co2 is currently done by inversion of a mass balance equation, with no consideration of measurement errors and other uncertainties. To improve the accuracy of the results, a new mathematical model is suggested in the present study explicitly accounting for the presence of such uncertainties and error sources and enabling the use of optimal filtering methods. Experiments have been realized, injecting known gas quantities and estimating them using the proposed mathematical model and the Kalman-Bucy (KB) estimation method. The estimates obtained reproduce the known production rates much better than standard methods; in particular, the mean error when fitting the known production rates is 15.6 ± 0.9 vs. 186 ± 36 ml/min obtained using a conventional method. Experiments with 11 humans were carried out as well, where V̇o2 and V̇co2 were estimated. The variance of the estimation errors, produced by the KB method, appears relatively small and rapidly convergent. Spectral analysis is performed to assess the residual noise content in the estimates, revealing large improvement: 2.9 ± 0.8 vs. 3,440 ± 824 (ml/min)2 and 1.8 ± 0.5 vs. 2,057 ± 532 (ml/min)2, respectively, for V̇o2 and V̇co2 estimates. Consequently, the accuracy of the computed RQ is also highly improved (0.3 × 10-4 vs. 800 × 10-4). The presented study demonstrates the validity of the proposed model and the improvement in the results when using a KB estimation method to resolve it.

A Mixture Price Trend Model for Long-Term Risk Management

2010 ◽  
pp. 157-173
Author(s):  
Eric S. Fung ◽  
Wai-Ki Ching ◽  
Tak-Kuen Siu
Keyword(s):  
Risk Management ◽  
Financial Risk ◽  
Estimation Method ◽  
Real Data ◽  
Price Trend ◽  
Trend Model ◽  
Proposed Model ◽  
Price Trends ◽  
Long Term Forecasting

In financial forecasting, a long-standing challenging issue is to develop an appropriate model for forecasting long-term risk management of enterprises. In this chapter, using financial markets as an example, we introduce a mixture price trend model for long-term forecasts of financial asset prices with a view to applying it for long-term financial risk management. The key idea of the mixture price trend model is to provide a general and flexible way to incorporate various price trend behaviors and to extract information from price trends for long-term forecasting. Indeed, the mixture price trend model can incorporate model uncertainty in the price trend model, which is a key element for risk management and is overlooked in some of the current literatures. The mixture price trend model also allows the incorporation of users’ subjective views on long-term price trends. An efficient estimation method is introduced. Statistical analysis of the proposed model based on real data will be conducted to illustrate the performance of the model.

scholarly journals Optical Enhancement of Exoskeleton-Based Estimation of Glenohumeral Angles

2016 ◽  
Vol 2016 ◽  
pp. 1-20 ◽  
Author(s):  
Camilo Cortés ◽  
Luis Unzueta ◽  
Ana de los Reyes-Guzmán ◽  
Oscar E. Ruiz ◽  
Julián Flórez
Keyword(s):  
Estimation Method ◽  
Position Estimation ◽  
Accurate Estimation ◽  
Joint Angles ◽  
Estimation Errors ◽  
Marker Position ◽  
Human Movements ◽  
Posture Estimation ◽  
Kinematic Models ◽  
Method Accuracy

In Robot-Assisted Rehabilitation (RAR) the accurate estimation of the patient limb joint angles is critical for assessing therapy efficacy. In RAR, the use of classic motion capture systems (MOCAPs) (e.g., optical and electromagnetic) to estimate the Glenohumeral (GH) joint angles is hindered by the exoskeleton body, which causes occlusions and magnetic disturbances. Moreover, the exoskeleton posture does not accurately reflect limb posture, as their kinematic models differ. To address the said limitations in posture estimation, we propose installing the cameras of an optical marker-based MOCAP in the rehabilitation exoskeleton. Then, the GH joint angles are estimated by combining the estimated marker poses and exoskeleton Forward Kinematics. Such hybrid system prevents problems related to marker occlusions, reduced camera detection volume, and imprecise joint angle estimation due to the kinematic mismatch of the patient and exoskeleton models. This paper presents the formulation, simulation, and accuracy quantification of the proposed method with simulated human movements. In addition, a sensitivity analysis of the method accuracy to marker position estimation errors, due to system calibration errors and marker drifts, has been carried out. The results show that, even with significant errors in the marker position estimation, method accuracy is adequate for RAR.

A robust regression analysis of recruitment in fisheries

1995 ◽  
Vol 52 (5) ◽  
pp. 993-1006 ◽  
Author(s):  
Y. Chen ◽  
J. E. Paloheimo
Keyword(s):  
Environmental Variables ◽  
Measurement Errors ◽  
Robust Regression ◽  
Estimation Method ◽  
Fish Stock ◽  
Estimation Errors ◽  
Ricker Model ◽  
Stock Recruitment ◽  
Atypical Values ◽  
Special Studies

Variations in environmental variables and (or) errors in measuring stock and recruitment often result in large and heterogeneous variations in fitting fish stock–recruitment (SR) data to a regression model. This makes the commonly used least squares (LS) method inappropriate in estimating the SR relationship. Hence, we propose the following procedure: (i) identify possible outliers in fitting data to a given SR model using the least median of the squared orthogonal distance that is not sensitive to atypical values and requires no assumption on distribution of errors and (ii) apply the LS method to the SR data with defined outliers being down weighted. We showed by simulation that the SR parameters of the Ricker model could be estimated with smaller estimation errors and biases using the proposed procedures than with the traditional LS approach. Examination of four sets of published field data leads us to suggest fitting fish SR data to suitable models using the proposed estimation method and interpreting the results with the assistance of knowledge on the relevant environmental variables and measurement errors. However, our interpretation should be viewed as a working hypothesis requiring special studies to clarify the causal links between environmental variables and recruitment.

scholarly journals Problems of Estimating the Resources of Accompanying Elements: A Case Study from the Cu-Ag Rudna Deposit (Legnica-Głogów Copper District, Poland)

Minerals ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 1431
Author(s):  
Justyna Auguścik-Górajek ◽  
Jacek Mucha ◽  
Monika Wasilewska-Błaszczyk ◽  
Wojciech Kaczmarek
Keyword(s):  
Estimation Method ◽  
Recovery Process ◽  
Ore Deposits ◽  
Economic Consequences ◽  
Main Element ◽  
Accurate Estimation ◽  
Estimation Errors ◽  
Reliable Assessment ◽  
One Year ◽  
Sampling Pattern

As a result of the exploitation of ore deposits, in addition to the main elements, the accompanying elements are also partially recovered. Some of them increase the profitability of exploitation, while others reduce it because they hinder the recovery of the main elements and thus increase the costs of the recovery process. A comprehensive economic calculation to assess the profitability of ore mining depends on an appropriately accurate estimation of the resources of both the main and associated elements. This issue was analyzed with the example of the Cu-Ag Rudna ore deposit (LGCD, Poland). The subject of the assessment was the resources prediction accuracy of the main element (Cu) and four (4) accompanying elements (Co, Ni, Pb, and V) using geostatistical estimation method, in particular the ordinary kriging after the estimation of the relative variograms for describing the spatial variability structures of elements abundance. It was found that the standard kriging errors (deviations) in accompanying elements resources that are scheduled for exploitation within a one-year period in some parts of deposits are drastically greater (2 to 5 times) than the estimation errors of the main element resources. This is due to the sparse sampling pattern for their determinations and/or the high variability (among others nugget effect) of their abundance. In this situation, without additional sampling and a denser sampling pattern, the possibilities of a reliable assessment of the influence of accompanying elements on the economic consequences of exploitation are very limited.

scholarly journals Compensation of Positioning Errors Caused by Tropospheric Wave Propagation in Wide-Area Multilateration Systems

2020 ◽  
Vol 23 (6) ◽  
pp. 59-69
Author(s):  
A. A. Monakov ◽  
A. M. Mirolubov
Keyword(s):  
Mathematical Model ◽  
Wave Propagation ◽  
Traffic Control ◽  
Wide Area ◽  
Navigation Systems ◽  
Estimation Errors ◽  
Positioning Errors ◽  
Proposed Model ◽  
Spatially Distributed ◽  
Tropospheric Refraction

Introduction. Wide area multilateration (WAM) systems are the main competitors of secondary surveillance radar (SSR) systems used in air traffic control (ATC). The general principle of WAM operation is based on the assessment of pseudoranges between a signal source (an aircraft airborne transponder) and the ground receivers with precisely known geographical coordinates deployed over the ATC area. The aircraft position is estimated by measuring pseudoranges. A significant factor affecting the accuracy of aircraft positioning is tropospheric refraction, a phenomenon caused by the inhomogeneity of the earth's atmosphere and manifested in a deviation in the direction of the rays along which the signal of an aircraft transponder propagates. Refraction increases the lengths of ray paths, thus increasing the corresponding pseudoranges. As a result, the estimate of the aircraft position receives an additional bias. Altitude estimates produce unreasonably large errors.Aim. To develop a mathematical model for the signals received by a WAM system, which accounts for tropospheric wave propagation, as well as to derive an algorithm for aircraft positioning with compensated tropospheric errors.Materials and methods. Equations for the pseudorange estimation errors caused by wave propagation in a spherically stratified atmosphere were derived using the method of geometrical optics.Results. This paper proposed a mathematical model for pseudorange estimates in WAM systems, which accounts for the bias associated with the phenomenon of tropospheric refraction. An analysis of the proposed model showed that pseudorange errors depend linearly on the distance between the aircraft transponder and the receiver. This conclusion allowed an algorithm for aircraft positioning with compensated tropospheric errors to be developed. The proposed algorithm yields an unbiased estimate of the aircraft position. The standard deviation of altitude estimates increases by 60%, although remaining within the limits permissible for WAM systems.Conclusions. The developed mathematical model of WAM signals, which considers tropospheric propagation errors in pseudorange estimation, as well as the algorithm for aircraft positioning with compensated tropospheric errors, can be used in the development of spatially distributed navigation systems.

THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

Application of the method of mathematical modeling for forecasting channel deformations at the underwater crossing of the main pipeline

2020 ◽  
Vol 10 (6) ◽  
pp. 599-609
Author(s):  
Valery А. Gruzdev ◽  
◽  
Georgy V. Mosolov ◽  
Ekaterina A. Sabayda ◽  
◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Roughness Coefficient ◽  
Computational Domain ◽  
Channel Deformations ◽  
Geological Surveys ◽  
Kuban River ◽  
The Stability ◽  
Protective Structures

In order to determine the possibility of using the method of mathematical modeling for making long-term forecasts of channel deformations of trunk line underwater crossing (TLUC) through water obstacles, a methodology for performing and analyzing the results of mathematical modeling of channel deformations in the TLUC zone across the Kuban River is considered. Within the framework of the work, the following tasks were solved: 1) the format and composition of the initial data necessary for mathematical modeling were determined; 2) the procedure for assigning the boundaries of the computational domain of the model was considered, the computational domain was broken down into the computational grid, the zoning of the computational domain was performed by the value of the roughness coefficient; 3) the analysis of the results of modeling the water flow was carried out without taking the bottom deformations into account, as well as modeling the bottom deformations, the specifics of the verification and calibration calculations were determined to build a reliable mathematical model; 4) considered the possibility of using the method of mathematical modeling to check the stability of the bottom in the area of TLUC in the presence of man-made dumping or protective structure. It has been established that modeling the flow hydraulics and structure of currents, making short-term forecasts of local high-altitude reshaping of the bottom, determining the tendencies of erosion and accumulation of sediments upstream and downstream of protective structures are applicable for predicting channel deformations in the zone of the TLUC. In all these cases, it is mandatory to have materials from engineering-hydro-meteorological and engineering-geological surveys in an amount sufficient to compile a reliable mathematical model.

A Mathematical Model for the Anaerobic Digestion Process Applied to a Mixture of Night Soil and Septic Tank Sludge

1986 ◽  
Vol 18 (7-8) ◽  
pp. 239-248 ◽  
Author(s):  
Sung Ryong Ha ◽  
Dwang Ho Lee ◽  
Sang Eun Lee
Keyword(s):  
Mathematical Model ◽  
Anaerobic Digestion ◽  
Biomass Concentration ◽  
Gas Production ◽  
Septic Tank ◽  
Volatile Acid ◽  
Hydraulic Residence Time ◽  
Anaerobic Digestion Process ◽  
Digestion Process ◽  
Proposed Model

Laboratory scale experiments were conducted to develop a mathematical model for the anaerobic digestion of a mixture of night soil and septic tank sludge. The optimum mixing ratio by volume between night soil and septic tank sludge was found to be 7:3. Due to the high solids content in the influent waste, mixed-liquor volatile suspended solids (MLVSS) was not considered to be a proper parameter for biomass concentration, therefore, the active biomass concentration was estimated based on deoxyribonucleic acid (DNA) concentration in the reactor. The weight ratio between acidogenic bacteria and methanogenic bacteria in the mixed culture of a well-operated anaerobic digester was approximately 3:2. The proposed model indicates that the amount of volatile acid produced and the gas production rate can be expressed as a function of hydraulic residence time (HRT). The kinetic constants of the two phases of the anaerobic digestion process were determined, and a computer was used to simulate results using the proposed model for the various operating parameters, such as BOD5 and volatile acid concentrations in effluent, biomass concentrations and gas production rates. These were consistent with the experimental data.

Modeling of unforced demand response programs

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Hassan Jalili ◽  
Pierluigi Siano
Keyword(s):  
Demand Response ◽  
Load Shifting ◽  
Response Models ◽  
Temperature Changes ◽  
Proposed Model ◽  
Equipment Failures ◽  
Demand Response Programs ◽  
Simultaneous Implementation ◽  
Long Term Studies

Abstract Demand response programs are useful options in reducing electricity price, congestion relief, load shifting, peak clipping, valley filling and resource adequacy from the system operator’s viewpoint. For this purpose, many models of these programs have been developed. However, the availability of these resources has not been properly modeled in demand response models making them not practical for long-term studies such as in the resource adequacy problem where considering the providers’ responding uncertainties is necessary for long-term studies. In this paper, a model considering providers’ unavailability for unforced demand response programs has been developed. Temperature changes, equipment failures, simultaneous implementation of demand side management resources, popular TV programs and family visits are the main reasons that may affect the availability of the demand response providers to fulfill their commitments. The effectiveness of the proposed model has been demonstrated by numerical simulation.

scholarly journals On the Dragging Trajectory of Anchors in Clay for Merchant Ships

2021 ◽  
Vol 9 (2) ◽  
pp. 118
Author(s):  
Xinqing Zhuang ◽  
Keliang Yan ◽  
Pan Gao ◽  
Yihua Liu
Keyword(s):  
Mathematical Model ◽  
Structural Integrity ◽  
Indirect Measurement ◽  
Test System ◽  
Flow Rule ◽  
Burial Depth ◽  
Proposed Model ◽  
Depth Increase ◽  
Two Parameters ◽  
The Mathematical Model

Anchor dragging is a major threat to the structural integrity of submarine pipelines. A mathematical model in which the mechanical model of chain and the bearing model of anchor were coupled together. Based on the associated flow rule, an incremental procedure was proposed to solve the spatial state of anchor until it reaches the ultimate embedding depth. With an indirect measurement method for the anchor trajectory, a model test system was established. The mathematical model was validated against some model tests, and the effects of two parameters were studied. It was found that both the ultimate embedding depth of a dragging anchor and the distance it takes to reach the ultimate depth increase with the shank-fluke pivot angle, but decrease as the undrained shear strength of clay increases. The proposed model is supposed to be useful for the embedding depth calculation and guiding the design of the pipeline burial depth.

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