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In mathematical modeling, MATLAB plays an important role, especially for large amounts of data for analysis, handling, processing, which manual calculations is difficult to complete, people often uses MATLAB to achieve.
With powerful graphics capabilities, ease of data visualization, MATLAB can not only draw a variety of different two-dimensional coordinate system curve, but also to draw three-dimensional surface, reflecting the powerful graphics capabilities.
Data were analyzed to calculate, identify factors that play a major role, after the necessary refined, simplified, made ​​a number of assumptions in line with the objective reality.
There is error analysis of the results, the stability analysis of the data model; Model checking.
With the actual phenomenon, data comparison, reasonable test model applicability; Model application.

It can extract by learning an important characteristic of a set of data or a certain inherent law, according to the discrete time way to classify[2] .
Network can take any high dimension of input mapped to low dimensional space, and makes some similar nature of the input data internal performance for geometry on the characteristics of the adjacent mapping .
After get sample data vector, due to its various indices differ, the original sample of each vector in order of magnitude difference is very big, in order to easy calculation and prevent some neurons to supersaturated state, need to sample the input of the normalized processing, the data processing for the interval of data between [-1, 1].
SOM is a typical characteristic of the network can be formed on a two-dimensional array processing unit topological distribution features of the input signal, Therefore, in the integrated network, SOM network can be regarded as feature extraction network,  data after primary network formed the clustering results of failure mode.
Fig.3: Fault diagnosis results Conclusions SOM neural network compared with other network, the degree of dependence on the mathematical model of the controlled object is low, have self learning and adaptive, associative memory, strong fault tolerance and non-linear pattern recognition ability, having the advantages of high efficiency and solving quality, can the multidimensional input vector clustering and dimensionality reduction to two-dimensional plane, through the graphical visualization easily classify the failure mode.

The process tomography system basically consists of three parts: (1) a sensoring system to acquire the measurement data, (2) an electronic system for data acquisition, and (3) a computer system for measurement control, image reconstruction and displaying the result [1,2].
Like other process tomography systems, ECT has a fatal problem, and that is the tradeoff between the accuracy of the reconstructed image and the rate of the data acquisition.
Consequently, an increase in the number of the integral measurements would increase the data acquisition time, and thus would decrease the real time capability.
The issue raised is how to acquire reconstruction results with sufficient accuracy for process quantification from the limited experimental integral data without sacrificing the time resolution for reliable real time measurements.
Prior to data recording, the system requires calibration for the two extreme cases when the sensor area is filled with the higher permitivity material (which is coal ash in this case) and the lower permitivity material (which is air in this case).

For example, Jieshi Chen (2009) study Sheet metal forming limit prediction based on plastic deformation energy, the sheet metal forming limit is calculated by fitting curve from experimental data.
Calculated and plotted to FLD and Comparison of predicted forming limit strains with measured experimental data for 6061-T4 seamless extruded tubes.
The four strain paths are obtained from experimental data.
As the approximate trend lines, the strain paths at the pole of the forming tube for different strain ratios have a trend line of data as linear.
The critical strain from the experimental data and the analytical results, the FLD and forming limit curves (FLC) of STKM 11A tubes are constructed as shown in Fig. 4.

Fig. 1 show observed, calculated and difference pattern for Rietveld analysis from the XRD data using initial structure model of Ba4Ti12O27 [9].
Observed, calculated, and difference patterns for the Rietveld analysis using the powder X-ray diffraction data of Ba4Ti12O27.
In fact, the data successfully least-squares fit to the Mott-Davis VRH law with r2 = 0.9991 (r is the correlation coefficient).
The crystal structure of Ba4Ti12O27 was refined by Rietveld analysis using the powder X-ray diffraction data.
The magnetic susceptibility data showed Van Vleck Para magnetism in the range of 50 to 300K.

According to creep test data fitted in excel at 0oC with the rheological model to compared with actual measurement data as seen in Figure 3.
Table 2 Parameters for revised Burgers model at 0oC Category E1/104 MPa E2/ MPa /105 MPa.s A/ Pa.s B/10-2 Error/% Base asphalt mixture 1.949 196 2.593 2.789 1.304 1.727 MMT modified asphalt mixture 1.949 298 4.416 3.548 1.314 1.980 Summary The total deformation of MMT modified asphalt mixtures are decreased during loading period, and the elastic and retardant elastic deformations are increased, which lead to the reduction of permanent deformation for mixtures.

Introduction Poly(lactic acid) (PLA) has received attention for large scale industrial applications, with the building of big synthesis plants has allowed effective price reduction.
The historical data on soil temperature and moisture are shown in Fig. 1.
Fig.1 Historical data of soil burial analysis Results and Discussion Fig.2 Weight loss of PLA/PBS blend after soil burial Fig.3 Number-average molecular weight of PLA/PBS blend after soil burial Soil burial test was performed to investigate the effect of ambient environment on the samples.

Estimation method In plunge cylindrical grinding, the force model is most accurately obtained by performing an experiment for a given setup [1]: , (1) where a is the infeed distance per workpiece revolution, kc is the grinding force coefficient, is the rate of reduction of the workpiece radius and nw is the rotational speed of the workpiece.
(7) Eq.7 may be applied to grinding AE RMS data to periodically update the empirical values of τ and the AE coefficient Ks to maintain an accurate process monitoring.
While Ks was substituted into Eq. 7, the time constant τ may be calculated using the LMS of AE RMS data in real time.

Introduction With the increasing requirements of the huge information storage, higher density and higher data transfer rate become the trends of optical data storage.
The two isomers of diarylethenes differ from each other not only in their absorption spectra, but in many physical and chemical properties including geometry, refractive index, as well as oxidation/reduction potential, etc. [6, 1].

This negative effect could be restrained by two methods: 1) reduction of the tetragonal leucite grain size dispersed in the matrix below a critical leucite particle size as Mackert et al. published previously [2]; 2) stabilization of cubic leucite - Rasmussen at al. supposed possible transformation toughening which can occur in Cs2O stabilized leucite ceramic [3].
Data were scanned with an ultrafast detector X'Celerator over the angular range 5-60° (2θ) with a step size of 0.02° (2θ) and a counting time of 0.3 s step-1.
Data evaluation was performed in the software package HighScore Plus.