While solving the problems of technical diagnostics with machinery learning involvement, there is binary classification of an object state performed: the objects are subdivided into “good” and “bad” with the help of models, received as per learning samples. The quality of classification, which specifies the efficiency of machine learning, depends on several factors, such as: the scope of original sample, method of machine learning, method of dividing the sample into learning and validating parts, selection of value indicators, etc. Sometimes it is reasonable to use aggregate methods of classification, which are, in fact, the joined results of classification basic methods. To search the best aggregate method, one iterates over all possible basis sets.
1 1 ez . (4)
Data Science / V.N. Klyachkin, Yu.E. Kuvayskova, D.А. Zhukov
To identify parameters q0 ,..., qn , as a rule, maximum likelihood method is applied . This method is aim edat likelihood function maximization with the help of gradient descend method, Newton Raphson method and others.
With the time, while new data are received, the earlier found parameters can become out-dated. Toup-date them, different procedures can be used, e.g. those based on pseudogradient use [9].
The short coming of the logistic model is its sensitivity to factors correlation, that is why, the presence of strongly correlated input variables is unacceptable in the model.
The advantage of them odel is the possibility to take in to consideration the limitations of probability value, which cannot be out of frame 0 and 1, the possibility of conducting investigation and assessment of the factors, affecting the result.
While using another widely applied model – discriminant mining– to determine the object m class, linear discriminant functions are used: o1 (x) q01 q11 x1 ... q1n xn , o2 ( x) q02 q12 x1 ... qn2 xn , (5) ...
om (x) q0m q1m x1 ... qnm xn , Where o(x) is «counting», as per which this or that class is identified. In result, that class is chosen, which counting is the highest. The model parameters are assessed with the help of learning sample. In case of two classes, there sultcoincides with the result of linear regression.
The point is, that, in advance, one cannot say, which method, out of those mentioned above, will ensure the correct solution of the problem, that is why several methods or combination of methods are used. The decision is taken, based on the results of the performance functional for the validation set.
Aggregating methods (combined application of several methods) is of special interest, indeed, as this way compensates the disadvantages of one model with the help of the others, thus improving the forecasted accuracy. Now we will consider the follow in gset, let us say, of base 7 models [10,11]: neural network, logistic regression, discriminate mining, Bayesian classifier, Support Vector machine method, decision trees, bagging trees etc.
Let’s make all possible combinations of base models, consisting of two, three… etc. models. In case of seven models taken, the total amount of all the combinations, starting from two and finishing with all seven models, will make: С72 С73 С74 С75 С76 С77 120 models.
Let Y jm be the result of serviceability assessment of j-object. The result was determined with m base model, j 1,...,l and m 1,..., M , where М – the number of base models in combination. Now let us see the following ways of base models aggregating (joining).
This works as follows: if the majority of the models consider the object is “good”, then the result of aggregate classifier is a mean value of the results of the models, voting for the serviceable class. In opposite case, the object is “bad” (unserviceable) (Y=0). a. Aggregating ,based on mean value
In this case
M Yjm
YjAK _ mean mM1 , where Y jAK _ mean is the result of aggregate classifier based on mean value. b. Aggregation as per median value
M 1 Y AK _ median Y 2 ,
j j where Y jAK _ medianis the result of aggregate classifier as per median value. c. Aggregation as per voting
Firstly, we will grade the row, containing the results of the base models in combination Y jm . If the number of base models is odd: (6) (7)
The accuracy of classification is assessed with the help of performance functional, i.e. validations set classification mean error can be used.
When the results are presented in the terms of object “good’ or “bad” class probability, to assess the methods quality it is possible to find error dispersion σ2, which indicates the deviation of forecasted value from actual ones: 2 1 l (P(Yr ) Pˆ ( X r ))2 , (8) l r1 where P(Yr) is actual probability of serviceability class of r object (P(Yr)= 0, if the object is “bad” or P(Yr)= 1 for the “good” object), Pˆ ( X r ) is actual probability of serviceability class of r object, l is number of objects.
The performance functional mainly depends on the way of validation set constructing. If necessary, check the influence of the way of validation set constructing on the error dispersion.
In order to optimize the diagnostic of technical object functioning, the algorithm of serviceability forecasting is offered. This is the use of machine learning models combination and generating optimum decision on their basis.
The algorithm main stages: 1. Generating and preliminary processing of the original data, dividing them into learning and validation set. 2. Constructing the base classification model on a learning set. 3. Building all the possible models combination on the same learning set in addition to all base models with three mentioned above methods aggregation. 4. On the validation set, through all the constructed models, new (monitored) objects serviceability is forecasted. 5. For each model or model combination, the forecasted mean square root error is calculated, and the best model, providing the error minimum, is selected.
The computational investigation was done based on the example of St. Petersburg sewage plant operation [12].The parameters of the water supply source and the dosage of chemical agent, used for purifying, were monitored. At least one parameter of potable water quality, found out beyond the acceptable limitations, was considered to be the system malfunction. Seven base methods of binary classification were used, and the best result was shown by the method of support vector machines (SVM); mean classification error was equal to 0,238. Mean value aggregation had an error equal to 0,196 (combination of SVM with discriminate mining and neural network). While using the selection of tangible value parameters through the method of stepwise regression, the results deteriorated a little, but even that, minimum mean error of aggregation was 0,207. The set of base classification changed: the logistic regression method was added to those three available.
The performance quality of classification is determined by the scope of the original sample , selected by machine learning method (one of base or aggregate ), by the method of dividing the original sample into learning and validation one (either by random selection, or by taking a certain part of original sample for validation one; sometimes the procedure of sliding exam is reasonable, evidently, the scope of validation sample plays a certain role hereto ), method of tangible value ( e.g. stepwise regression ) and some other factors.
To provide the efficiency of machine learning for the technical object diagnostic, it is necessary to work out the system in order to investigate the influence of these factors on the performance quality of classification with original sample, which could ensure the optimum approaches.
The given above investigation showed, that the methods of machine learning could be used for solving the problems of technical diagnostics, i. e. identifying the state of serviceability of the investigated object. Here some problems may arise. The problems are those connected with generating a rather big scope original sample, with dividing the sample into learning and validating, with assessment of this or that method efficiency , with possibility to use aggregate classifiers .
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