Decision tree classification of regions of operation

In the majority of cases, the operators of the technology look for the co-occurrence of certain alarm messages as a fingerprint-based primary symptom of process mal-functions. The present work follows this simple cognitive model of fault detection of the human mind.

Let us assume there are n_C types of operations (n_C −1 malfunctions and normal operating conditions) in the analysed system that should be identifiable. Although the normal region of operation and the different faulty conditions should be sep-arable according to the alarm messages that occur, the definition of informative alarm thresholds for a complex, multivariate process is a highly labor-intensive process and the consideration of every possible scenario cannot be guaranteed even with the systematic work of the process experts. Therefore, as learning from examples is one of the most important features of machine learning techniques and

the bottleneck of expert system development, such techniques are widely available for the identification of process models. The historical data of the process is re-quired to learn the process model using the historical scenarios. In the present context, the considered information is the matrix of the measured process vari-ables, which is logged in most of the modern DCS or SCADA process control systems and a logged list of historical fault types and occurrence time stamps.

Let us assume an n×m measurement matrix X, where n denotes the number of samples (sampled from the measurements from an arbitrary sampling time base) and m represents the number of measured process variables. Therefore, X is composed of X = [x¹. . .x^m] variable vectors with the dimensions n ×1.

Moreover, the vector X_i is the vector of the measured variables at sample point i (X_i = [x¹_i . . . x^m_i ]). The aim of fault detection and diagnosis is to classify the process into the Cj class (j = 1. . . nC) based on the arbitrary feature vectorSi at time stamp i, and indicate the presence of either the normal state orn_C−1types of malfunctions. Mathematically, the functionf in Equation 3.1 is constructed as:

y_i =f(S_i) (3.1)

where y_i ∈ C = [C₁. . . C_j. . . C_nC] and S_i is the feature vector of arbitrary size, where the features are composed of the information available at time stamp i in the measurement matrix X. This information can be of various source of the technology utilized by the general classification-based fault detection function f. In the present chapter, the classification functionf is constructed using the binary decision tree classifier. The tool is not just suitable for the classification of the measurements into different classes describing the state of the process, but for forming informative alarm thresholds as well using the defined decision boundaries.

Moreover, an advantage of the decision tree classifiers is that the m_a variables to alarm and their respective alarm limits (even with multiple alarm limits for a single variable) can be chosen in a single step.

For a simple and didactic example of the proposed methodology, consider the explanatory case study presented in Figure 3.2. The operators of the technology monitor the occurrence of alarm messages to detect the presence of abnormalities.

Hence, the aim of alarm messages is to distinguish normal operating conditions from two faults of the reactor: an increased temperature can be caused by the temporarily increased temperature of the reactor coolant (Fault 1), however, if it

Figure 3.2: (a) An example of a time series data of process variables concern-ing temperature (top) and concentration (bottom). By applyconcern-ing the proposed methodology, the alarm limits can be determined, denoted by red dashed lines.

The input data of the decision tree can be formed of the minimum and maximum values of the process variables during the malfunctions, denoted by red and blue crosses, respectively, and in this case, for the online application of the generated classification algorithm, the minimum and maximum values of process variables in a sliding window are used. (b) Example of a binary decision tree. (c) The

decomposed feature space.

is not just temporary, e.g., the cooling cycle underperforms due to the problems of the heat-exchanger network, then the product can be degraded as well which is reflected in the decreased concentration of the product (Fault 2). An arbitrary number of faults can be collected based on the expert knowledge of the process and once a historical (or simulated) database of the recorded process variables of each malfunction is available, like presented for the variables of temperature and concentration in part a) of Figure 3.2, a binary decision tree can be trained to classify the process variables as presented in part b) of Figure 3.2. As the decision trees determine the most informative features of every step following a greedy approach as well as the respective decision limits on these variables, these

decision functions can be analogously transformed into alarm limits. Moreover, the decision tree for alarm-based fault identification is ready to be used by the process operators and the feature space of the multivariate decision-tree model can be visualized as well as presented in partc) of Figure 3.2.

The question is how to define the input dataset of the decision tree classifier.

The application of the directly measured process data can be counteractive as the process may not contain enough information for the correct classification of every time sample. Another approach is the application of the characteristics with regard to the extrema of the variables in case of malfunctions as denoted by the red and blue crosses of Figure 3.2 for Faults 1 and 2. However, the classification may be more accurate since the online application of the trained classification algorithm requires a sliding window in which the extrema form the input of the decision tree classifier. The generation of the training data is discussed in detail in the following section.