# Development of Ground Special Vehicle PHM with Case-Based Reason Model
## 2 Framework Description
### Case Representation  
In case-based reasoning, the problem that is to be solved is usually referred to as the target case, the historical data or experience is called the source case, and each case is collected and stored in the database to form a case library. How to describe cases in a proper form is the premise of case-based reasoning. By using PHM structure, historical operating conditions of fault and health maintenance solutions are stored in a database. It is a raw knowledge base. The record in the knowledge base is either a text-based description or a sensor value and in the form of discrete format or numerical format. In order to establish the CBR model, the corresponding relationship between the operating conditions of the health maintenance solution must be extracted and converted into a case for storage to form a case base. That is to say, the method of case presentation is the premise. Some methods of case presentation, such as frame representation, the semantic network method, and the object-oriented method, can be found in the literature [28]. The simplest way to represent a case is by using attribute-value pairs, which is the property characteristic value description method. This way of representation is also beneficial for database storage.  
In order to make the CBR method more practical and feasible for the mentioned PHM structure, the key indexes in the raw knowledge base are extracted to form a case attribute. In this paper, a single case contains condition attributes and solution attributes, condition attributes correspond to operational behaviors (problem description of the operational parameters), solution attributes correspond to health maintenance assessments (normal/abnormal, the degree of health status).  
The general structure for the case base can be represented as \(C=\{C_{1},C_{2},\ldots,C_{n}\}\), a single case \(C_{i}\) in the case base can be expressed in two-tuples:  
\[C_{i}:\ \langle X_{i},Y_{i}\rangle,i=1,2,\ \ldots\,n \tag{1}\]  
Figure 6: A snapshot of the CBR process.  
In the above representation, \(n\) is the total number of cases, \(X_{i}\) is condition attributes, and \(Y_{i}\) is solution attributes. The representation of \(X_{i}\) and \(Y_{i}\) are expressed as follows:  
\[X_{i} =(x_{i1},x_{i2},\dots,x_{im}) \tag{2}\] \[Y_{i} =\big{(}y_{i1},y_{i2},\dots,y_{ip}) \tag{3}\]  
where \(m\) and \(p\) is the total number of condition attributes for \(X_{i}\) and solution attributes for \(Y_{i}\), respectively.  
The value of the condition attribute is continuously varying real numbers, or the value of attribute is discrete varying numbers. Therefore, different similarity calculation formulas need to be used. The calculation method of similarity is given in Section 2.3. The solution attribute can be a conclusion, which is used to indicate the positive (normal state) or negative (abnormal state). It can also be a probability of occurrence, which is used to describe the degree of health performance. As s result, the solution attribute will be reduced to \(Y_{i}=(y_{i1})\), namely, one attribute is defined for \(Y_{i}\).