Papers by Keyword: Data Fitting

Abstract: In order to find hyperelastic material model constants, data fitting technique is often used. For this task, the data is collected through different laboratory tests, namely, the uniaxial, the biaxial and the pure shear. However, due to the difficulty in getting biaxial data, often only uniaxial data was used for the fitting. Despite frequent use, it was established that this practice creates erroneous results. With a view to improve the data fitting results and at the same time to overcome the difficulty of collecting primary biaxial data, uniaxial data was used to generate a secondary biaxial data set. The data derived through this method was then tested with four common models as to examine the compatibility of the method. Subsequently, real biaxial data was used to compare with the data fitting results obtained through the proposed method. As results indicated combined data fitting for both instances were very much identical with respect to all tested models. Cases where somewhat higher deviation observed between experimental curves and data fitted curves for biaxial data, gave similar results for adjusted data driven data fitting too. However, such deviation could be attributed to mismatch between models with the particular material behaviour rather than the generated data.

Abstract: The risk of error in using only uniaxial data for fitting constitutive model curves is emphasized by many hyperelastic material researchers over the years. Unfortunately, despite these indications, often the method is utilized in finding material constants for mathematical models. The reason behind this erroneous practice is the difficulty in obtaining biaxial data. Therefore, as a remedial measure, in this research work we suggest a method of forecasting biaxial data from uniaxial data with a reasonable accuracy. Initially, a set of data is collected through standard uniaxial test. A predefined generalized function is then used to generate a set of values which subsequently used as multiplication factors in order to get biaxial tension data. Eventually, with availability of two data sets, Mooney-Rivlin two parameter model was used for combined data fitting. Material constants were then obtained through least squares approach and thereby theoretical load curves namely uniaxial, equi-biaxial tension and pure shear were drawn. The results of this work suggest a definite improvement related to three curves when compared with only uniaxial test data fitted outcomes. For validation of secondary biaxial data, separate eqi-biaxial test was done and resulting curves were compared. Biaxial primary data curve and forecasted data driven curve show identical data distribution pattern though there is a shift and therefore provide a basis for further research in this direction.

Abstract: This paper presents a new method, called data fitting method based on numerical results, to calculate the contact deformation between logarithmical crowned roller and raceway of rolling bearings. First, the contact deformations between logarithmically crowned roller and raceway are analyzed and numerically calculated according to influence coefficient method, and then a fitting formula based on the calculated contact deformations is obtained by means of multiple linear regression method. The formula includes the dimensions and logarithmic crowned parameters of bearing together with the load parameter, and can be used for fast calculation of contact deformation between logarithmical crowned roller and raceway in low and medium load conditions, so that the formula is suitable to efficiently analyze the dynamics characteristics of arbitrary logarithmic crowned rolling bearing.

Abstract: To select an appropriate relaxation kernel function is significant for shape memory polymers (SMPs) in their thermomechanical constitutive models. The relaxation modulus of SMPs are described by fractional-order viscoelastic (FOV) kernel and three other kinds of viscoelastic kernel, that is, Prony series, Kohlrausch-Williams-Watts (KWW) kernel and Cole-Cole Model (CCM) kernel. The data fitting result shows FOV kernel is a valuable tool to describe the relaxation response of SMPs. Compared with Prony series, KWW kernel and CCM kernel, the FOV kernel can give a comparative description of relaxation modulus of SMPs with fewer material parameters.

Abstract: According to the main characteristics of boiler operation process, part parameters of boiler and monitoring data, we not only can tease the relationship between various each physical quantity and the influence on the thermal efficiency of the boiler, but also be reasonable parameters and omit the complex on the minimal influence factors of heat loss, finally we use the counter balance calculation method to calculate heat loss, which is mainly aimed at the greatest effect of excess air coefficient, and we consider other major factors that affect the thermal efficiency of the boiler. According to the definition established physical model, the thermal efficiency of the boiler is optimized.

Abstract: In this paper, the influence of the soft magnetic particle content on the properties of MRFs is studied. Besides, the relationships between the shear stress of MRFs and the magnetic induction intensity, the soft magnetic particle content, and the shear rate are discussed. The curve equation that expresses the relationship between the shear stress, the magnetic induction intensity, and the soft magnetic particle content is established through the fitting of experimental data. The results show that the shear stress of MRFs increases with increasing magnetic induction intensity and that the shear stress will tend to stabilise when the magnetic induction intensity reaches a sufficient value. The validity of the Bingham model and the H-B model for describing the relationship between the shear stress and shear rate is established, and the phenomenon of shear thinning of MRFs can be better represented by the H-B model than by the Bingham model.

Abstract: Shanghai Expo, a global event, has enormous influence in a large scope in terms of space and contents. This thesis studies its influence in one aspectthe influence on economy. Based on cost-benefit theory, data fitting and the input-output table of the 2010 World Expo in Shanghai, the thesis has set up a complete mathematical model for quantitative assessment of costs and benefits to analyze the direct and indirect influence of the Expo on the economy of Shanghai. Through the cost-benefit assessment model, we can get the direct economic revenue of the Expo is RMB 1.691 billion Yuan. By data fitting analysis, because of the influence of the Expo, tourism income is 14.69 billion Yuan more than the natural growth and business volume of science and technology is 2.89 billion Yuan more than the natural growth.

Abstract: In the Inner Mongolia beef cattle feeding, barn temperature is an important parameter. Barn temperature has an important impact on cattle breeding and beef production. In order to ensure that there is appropriate temperatures barn, data recorded in the barn a month temperature monitoring points, the acquisition time for each temperature monitoring point for the one-hour time interval. Using MATLAB software barn temperature data were analyzed, the data fit (least squares) and plotted, and finally get a barn temperature prediction formula. And use this formula to predict the temperature of the barn, forecasting results show that the design is reasonable, the error is small, can be applied in practice.

Abstract: In the data processing of iron ore metallurgical properties, the polynomial least squares method or the assumed functions are usually employed to fit the performance curve. This is stuck at a high degree of the polynomial, where the equation group is prone to morbid problems. To solve this problem, the use of orthogonal functions as the least squares method may help draw out the reductioln metallurgical performance curves.

Abstract: In order to better observe the trend of small sample data, this paper based on that the least squares support vector machine (LS-SVM) algorithm has an outstanding performance in the data processing of small sample, presents a data fitting method for small sample. The quantum particle swarm optimization (QPSO) that has better global search ability is used to optimize the parameters of the least squares support vector machine, and establish the curve fitting model. According to error analysis, show that the method presented in this paper has a good application value.