# Application of Neural Networks for Water Meter Body Assembly Process Optimization
## 3 Results  
### Parameters and Operation of the Modeled Neural Network  
Artificial neural networks were modeled in the Statistica version 13.1 software. The network efficiency, defined by the minimum SOS prediction error, was considered the main quality criterion of the model. For this purpose, a number of neural networks characterized by unique parameter values were developed and then assessed in accordance with the previously adopted assumptions. A total of 1000 models were made, keeping 10 with the lowest prediction errors of the output value (Table 1). The following variable parameters of the neural network, modified in successive variants of the model were considered:  
* Network type (MLP--multilayer perceptron, RBF--radial basis functions network);
* Number of hidden neurons (integers in the range from 1 up to and including 30);
* Hidden and output neurons activation function--applies only to MLP (linear, logistic, hyperbolic tangent, exponential, sine). In addition to the variable parameters, in each developed neural network model, a number of specified invariant parameters occur:  
* The number of data conditioning the prediction task (18 inputs and 1 output);
* The type of prediction algorithm of the modeled output variable (regression algorithm for one variable assuming continuous values);
* Data categorization (quantified, defined numerically);
* Percentage share of data in groups performing the task of learning (70%), testing (15%) and validating the neural network (15%). The #7 MLP 18-3-1 network was considered the best neural network and it was selected for further analysis (Table 1). The selected neural network consists of three layers: input (18 neurons), hidden (3 neurons) and output (1 neuron) layers. The accuracy of the network operation during the model validation stage was 93%, and the error value of the SOS was 0.007. Figure 5 shows a diagram of the relationship between the actual and predicted values of the axle runout. The correlation model allows you to determine the expected values of one random variable on the basis of unit representations of another random variable with features of mutual correlation. The validation was performed using the set of input and output data, that were not used before. From the diagram, one can deduce the direction and strength of the correlation relationship. The points of the studied dependence are grouped along a hypothetical straight regression, indicating the strength of the correlation. One of the most significant thing in the process of modeling the structure of an artificial neural network is assigning weights to interneuronal connections. The efficiency of the prediction of the output value is inextricably linked with the values of weights assigned to individual units of the network layer, where negative values weaken and positive values strengthen the transmitted signals. Table 2 shows the weight values generated for the analyzed MLP 18-3-1 network. On the basis of the generated values of the weights of interneuronal connections, the most important input parameters creating the structure of the neural network can be identified. Values greater than neutral zero indicate greater importance from the point of view of prediction of the output value. Analyzing the example of predicting the value of radial runout in the assembly operation of machine parts, the greatest significance of the parameters was observed: the dimension of the main reference diameter; the position of the hole for the axle that is being assembled, relative to the main reference diameter in the Y axis; the position of the hole for axle that is being assembled relative to the main reference diameter in the X axis; body bottom wall thickness on the left side of the symmetry axis; the dimension in five planes of the hole for the axle that is being assembled, along its entire depth (V plane).