An Analysis of the Effects of Torque, Engine Geometry, and Speed on Choosing an Engine Inertia Model to Minimize Prediction Errors

1996 ◽  
Vol 118 (1) ◽  
pp. 181-184 ◽  
Author(s):  
Chung-Hung Pan ◽  
John J. Moskwa
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Prediction Errors ◽  
Estimation Errors ◽  
Engine Operation ◽  
Model Simulations ◽  
Engine Model ◽  
Advantages And Disadvantages ◽  
Inertia Model ◽  
Selection Of

Constant inertia engine models have been used for years by control engineers to attain real-time engine simulations. The accuracy of the estimation largely depends on the selection of the constant engine inertia value used in these engine models. A methodology that uses the least squares method to calculate the engine inertia value for constant inertia engine model is developed. This methodology enables the constant inertia engine model simulations to have minimum acceleration estimation errors. The effects of net external torque, engine geometry, and speed on the inertia value computation are also investigated. Since most of the constant inertia engine models use the averaged engine inertia as the constant inertia value, comparisons of these two inertia values in engine operation simulations are presented. Discussions of the advantages and disadvantages of both methods are also included. Precautions and restrictions of using the methodology are discussed as well.

A Modified Algorithm for the Least Squares Identification

1983 ◽  
Vol 105 (1) ◽  
pp. 50-52
Author(s):  
C. Batur
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Mechanical Systems ◽  
Model Structure ◽  
Input Output ◽  
Unknown Parameters ◽  
Estimation Errors ◽  
Usual Practice ◽  
Unknown Disturbances ◽  
Modified Algorithm

To identify the dynamics of mechanical systems, the usual practice is to assume a certain model structure and try to estimate the unknown parameters of this model on the basis of input output observations. For mechanical systems operating under noisy industrial conditions, the number of unknowns of the problem exceeds the number of equations available. It is then inevitable that certain assumptions must be made on the unknown disturbances. This paper assumes that the only reliable feature of the disturbance is its independence of input. This yields a set of assumptions in excess of the minimal requirements and an endeavor has been made to exploit this excess to minimize the parameter estimation errors. Th resulting algorithm is similar to that of the Two Stage Least Squares method [1].

Study on Roundness Error Evaluation with Least-Squares Method Based on Nonlinear Optimization

2013 ◽  
Vol 765-767 ◽  
pp. 755-758 ◽  
Author(s):  
Zhen Tao Liu ◽  
Jian Xin Yang ◽  
Ben Zhao
Keyword(s):  
Least Squares ◽  
Nonlinear Optimization ◽  
Least Squares Method ◽  
Convergence Time ◽  
Error Evaluation ◽  
Nonlinear Constraint ◽  
Roundness Error ◽  
Advantages And Disadvantages ◽  
Derivative Free Optimization ◽  
Derivative Free

Roundness error evaluation software is developed based on two-dimensional circle fitting with least-squares method based on nonlinear optimization with constraints. The local derivative-free optimization algorithms of NLopt can solve nonlinear constraint problems by combining with augmented Lagrangian algorithm. The fitting precision and convergence time of each algorithm are analyzed by calculating the fitting results with same test data to find its advantages and disadvantages. It is shown that each algorithm has different behaviors from others on performance and stability. This work provides a good basis for choosing the appropriate algorithm for roundness error evaluation.

Incorporation of Neural Network State Estimator for GPS Attitude Determination

2004 ◽  
Vol 57 (1) ◽  
pp. 117-134 ◽  
Author(s):  
Dah-Jing Jwo ◽  
Chun-Fan Pai
Keyword(s):  
Neural Network ◽  
Kalman Filter ◽  
Least Squares ◽  
Kalman Filtering ◽  
Attitude Determination ◽  
Least Squares Method ◽  
State Estimator ◽  
Estimation Errors ◽  
Network State ◽  
The Neural Network

The Global Positioning System (GPS) can be employed as a free attitude determination interferometer when carrier phase measurements are utilized. Conventional approaches for the baseline vectors are essentially based on the least-squares or Kalman filtering methods. The raw attitude solutions are inherently noisy if the solutions of baseline vectors are obtained based on the least-squares method. The Kalman filter attempts to minimize the error variance of the estimation errors and will provide the optimal result while it is required that the complete a priori knowledge of both the process noise and measurement noise covariance matrices are available. In this article, a neural network state estimator, which replaces the Kalman filter, will be incorporated into the attitude determination mechanism for estimating the attitude angles from the noisy raw attitude solutions. Employing the neural network estimator improves robustness compared to the Kalman filtering method when uncertainty in noise statistical knowledge exists. Simulation is conducted and a comparative evaluation based on the neural network estimator and Kalman filter is provided.

scholarly journals Sustainable Development in the Digital Age of Entrepreneurship

2021 ◽  
Vol 13 (8) ◽  
pp. 4429
Author(s):  
Ewa Stawicka
Keyword(s):  
Sustainable Development ◽  
Knowledge Management ◽  
Least Squares ◽  
Business Models ◽  
Least Squares Method ◽  
Structural Equations ◽  
Development Model ◽  
Csr Communication ◽  
Advantages And Disadvantages ◽  
Csr Strategy

The purpose of this article is to present a research model that examines dependencies of how aspects of corporate social responsibility (CSR)—specifically, communication with stakeholders, knowledge management, and strategy—influence the building of a sustainable development model in enterprises. An instrument with four constructs (CSR-communication with stakeholders, CSR-knowledge management, CSR-strategy, and sustainable development) was prepared and served to entities from medium-sized enterprises. The collected data was analyzed by modeling the partial least squares structural equations using the least squares method. The results showed that all three constructs (CSR-communication with stakeholders, CSR-knowledge management, CSR-strategy) were positively and strongly associated with sustainable development model building in enterprises. The practical implications were intended to provide an understanding of behavior related to the development of business models oriented towards sustainable development in the small business sector. Research can help companies identify the advantages and disadvantages of retaining existing users and attracting new users by communicating with stakeholders, managing knowledge, and creating responsible strategies. This study enriches the literature by contributing to general knowledge about creating a model of sustainable development. Social reports on actions for sustainable development are of particular importance, and this topic is also important for the small and medium sized enterprises (SME) sector.

Comparison of various inversion techniques as applied to the determination of a geophysical deformation model for the 1983 Borah Peak earthquake

1992 ◽  
Vol 82 (4) ◽  
pp. 1840-1866
Author(s):  
Yijun Du ◽  
Atilla Aydin ◽  
Paul Segall
Keyword(s):  
Least Squares ◽  
Penalty Function ◽  
Least Squares Method ◽  
Slip Distribution ◽  
Deformation Model ◽  
Long Wavelength ◽  
Inversion Technique ◽  
Elevation Changes ◽  
Damped Least Squares ◽  
Selection Of

Abstract A number of techniques are employed to overcome nonuniqueness and instability inherent in linear inverse problems. To test the factors that enter into the selection of an inversion technique for fault slip distribution, we used a penalty function with smoothness (PF + S), a damped least-squares method (DLS), damped least-squares method with a positivity constraint (DLS + P), and a penalty function with smoothness and a positivity constraint (PF + S + P) for inverting the elevation changes for slip associated with the 1983 Borah Peak earthquake. Unlike solving an ill-posed inverse problem using a gradient technique (Ward and Barrientos, 1986), we have restored the well-posed character between the elevation changes and normal slip distribution. Studies showed that the constraints based on sound understanding of the physical nature of the problem are crucial in the derivation of a meaningful solution and dictates primarily the selection of a particular inversion technique. All available geological and geophysical information were used to determine a geophysical deformation model for the earthquake. It is suggested that the PF + S + P solution for a fault length of 75 km is the preferred model. The long wavelength features in the estimated slip distribution are similar to those obtained by Ward and Barrientos (1986), whereas the shorter wavelength features differ between two solutions. The fault dips 49° to the southwest. The slipped zones deepen from the surface at the northwest to about 20-km downdip depth at the southeast. The fault extends to the southeast beyond the epicenter of the mainshock. It is also shown that only the long wavelength features of the slip distribution are well resolved. The resolution is better at shallower levels than at deeper levels. The resolution deteriorates when the deformation sources are away from the leveling lines. Smoothness constraints provide better resolution than damping does at depth. The addition of a positivity constraint significantly improves the model resolution.

Some Observations Regarding the Statistical Determination of Stress Rupture Regression Lines

1979 ◽  
Vol 101 (4) ◽  
pp. 286-291
Author(s):  
P. P. Pizzo
Keyword(s):  
Least Squares ◽  
Curve Fitting ◽  
Statistical Evaluation ◽  
Least Squares Method ◽  
Stress Rupture ◽  
Anomalous Behavior ◽  
Creep Data ◽  
Statistical Determination ◽  
Selection Of

Observations concerning the statistical evaluation of creep data are presented. Methods currently employed in the determination of stress rupture regression lines can result in conflicting and necessarily invalid results. Anomalous behavior is principally associated with the selection of the dependent variable. However, it is the least squares method of curve fitting which introduces regression bias. Methods to improve the validity of least squares regressions are suggested.

scholarly journals Creation of a Program for Finding an Approximating Function of the Obtained Experimental Results by the Method of Least Squares

2021 ◽  
Vol 7 (12) ◽  
pp. 367-372
Author(s):  
N. Kadyrkulova ◽  
V. Zhulev
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Measurement Data ◽  
Point Of View ◽  
Main Task ◽  
Method Of Least Squares ◽  
Empirical Formulas ◽  
Physical Experiments ◽  
Mathematical Relationships ◽  
Selection Of

When solving engineering and economic problems, it is often necessary to obtain mathematical relationships between various parameters characteristic of a given problem. As a rule, all physical experiments are reduced to measuring the dependence of a certain quantity u on one or several other quantities z1, z2,…, zn. The main task of using the least squares method as an approximation method from the point of view of approximate recovery of a function from its known values at a number of points is the selection of empirical formulas that allow an analytical presentation of the obtained experimental measurement data. This article discusses the problems of obtaining data and approximating a function by the least squares method using OOP.

Research on the Calculation Model of Signal Intersection Delay

2014 ◽  
Vol 587-589 ◽  
pp. 2096-2099
Author(s):  
Zhen Ying Yan ◽  
Zhi Hui Song ◽  
Shuang Chun Lv
Keyword(s):  
Least Squares ◽  
Theoretical Basis ◽  
Field Data ◽  
Least Squares Method ◽  
Calculation Model ◽  
Analysis And Evaluation ◽  
Advantages And Disadvantages ◽  
Delay Models ◽  
Sample Method ◽  
Road System

The researched object of this paper is the main intersections in Hohhot. The HCM model is chosen to estimate the delay of signal intersection after comparing the advantages and disadvantages of various delay models. Use the spotting sample method to collect field data, then compare the results with the results caculated by the HCM model, and modify the model by using the least squares method. So the delay calculation model consistent with intersection in Hohhot can be built, and it can provide a theoretical basis for the analysis and evaluation of intersections and road system in Hohhot .

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