# Condition Monitoring of Industrial Equipment Based on Multi-Variables State Estimate Technique
## 4 Modeling Description
### Vector Selection for Memory Matrix  
While the MSET was first proposed, the \(\mathbf{D}\) is constructed by the extreme vectors for each parameter, and the boarder of normal state envelope space is defined by the extreme vectors. In latest works, vectors of normal condition are added to memory matrix according to constant interval and access criteria, indeed, the method improved the memory matrix \(\mathbf{D}\) and enhanced the ability for describing normal conditions. However, special normal condition vector might be omitted in sample process,  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Remark** & **Gray Relational Degree** \\ \hline t\({}_{2}\) & Temperature of End-Side Bearings & 0.913 \\ Vol & Current Air Volume of Unit & 0.844 \\ \(f\) & Operation Frequency of Driving Motor & 0.819 \\ I & Current of Driving Motor & 0.789 \\ Load & Current Load of The Unit & 0.595 \\ p\({}_{2}\) & Furnace Pressure & 0.549 \\ P & Power of Driving Motor & 0.417 \\ t\({}_{1}\) & Temperature of Bearings & 0.355 \\ P\({}_{1}\) & Inlet Air Pressure & 0.191 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Results of grey relational analysis for horizontal vibration.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Remark** & **Gray Relational Degree** \\ \hline \(f\) & Operation Frequency of Driving Motor & 0.847 \\ I & Current of Driving Motor & 0.739 \\ t\({}_{2}\) & Temperature of End-Side Bearings & 0.733 \\ P & Power of Driving Motor & 0.719 \\ Vol & Current Air Volume of Unit & 0.627 \\ P\({}_{1}\) & Inlet Air Pressure & 0.514 \\ t\({}_{1}\) & Temperature of Bearings & 0.419 \\ Load & Current Load of The Unit & 0.261 \\ P\({}_{2}\) & Furnace Pressure & 0.167 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Results of grey relational analysis for vertical vibration.  
which would seriously affect the prediction performance. Thus, a novel normal vectors selection method using self-adaption access criteria is proposed. After standardization, the deviation degree is reflected by the distance between normal vector with origin point in hyperplane. Because the vectors for memory matrix is selected in normal condition, the vectors are relatively intensive in the area that is close to the origin point in hyperplane, and in the area relatively far from the origin point, vectors are sparse and special normal condition often appears. The special normal condition vector might not be selected by using the constant interval and access criteria sampling method.  
In order to select representative normal vector and retain some special normal vector, the sample access criteria change with probability density function, while the value of function is small, which means the vector is located in sparse area in hyperplane, the access criteria is relatively loose for introducing more special normal vectors. As shown in Figure 2, the maximum of probability density function is 0.62. The number of vector in memory matrix \(\mathbf{D}\) is set as 200. The procedure for constructing memory matrix \(\mathbf{D}\) is formulated in Figure 3.  
Figure 2: Fitting for probability density function.  
Where,  
\[\varepsilon=\frac{k}{\varphi(j)} \tag{16}\]  
\(k\) is an empirical parameter, and is set as 0.0015 in our simulation.