# Application of Neural Networks for Water Meter Body Assembly Process Optimization
## 2 Materials and Methods
### Artificial Neural Networks in Mechanical Assembly Problem
[PERSON] and [PERSON] in 1943 proposed the model of biological neurons, which is considered to be the first model of a neural network, with a given relationship:  
\[\text{Transfer function }\Rightarrow\ y=f(\sum_{i=1}^{k}x_{i}w_{i}+w_{0}) \tag{1}\]  
The typical signal route between neurons (processing units) is presented in Figure 3, where \(x_{i}\) are the input signals of the neurons (or external input data for system), \(w_{i}\) are the weights of the edge connections (synapses), \(w_{0}\) is the sensitivity threshold of the neuron (the so-called bias), and \(f\left(\cdot\right)\) is a simple non-linear function, for example, a sigmoid or a logistic function. Activation (transfer) functions (AF) are possible for each hidden and output layer. In this study logistic, exponential, linear, sine and tanh functions were tested, which were used to activate hidden and output layers. To activate a neuron, the sum of each signal multiplied by the corresponding weight has to be equal to or greater than the sensitivity threshold \(w_{0}\), otherwise it remains inactive. An input signal can be an excitatory or inhibitory type, depending on the positive or negative sign of the weight value [23]. Figure 3: Symbolic representation of the neuron’s model. The Concept of a System Supporting the Optimization of Radial Runout in the Assembly Process Based on Artificial Neutral Networks  
The presented tool, using ANN, aims to predict, due to the selected criteria, the magnitude of the radial runout parameter for a selected case in a production plant. During the assembly process of the water meter, the following parameters are taken into account:  
* The value of the clamping force for the first and second assembly steps;
* Number of cycles performed by presser (it is possible to replace it);
* Time of applied force in the second assembly operation;
* The type of used clamp;
* Sequence of assembly procedures. The selection of the presented criteria was preceded by a long-term analysis and testing of many other criteria. It was assumed that the hot-forged body with specific dimensional characteristics is delivered for assembly (the forging process also takes place in the discussed plant). Parameters and input characteristics that may have a significant impact on the final result of the radial runout value were determined. As a result, after hot forging and machining operations, the following parameters were measured (Figure 4). * The dimension of the main reference diameter;
* The roundness deviation of the main reference diameter;
* The dimension of the hole for the axle that is being assembled (averaged);
* The dimension in five planes of the hole for the axle that is being assembled, along its entire depth;
* The position of the hole for axle that is being assembled relative to the main reference diameter in the X axis;
* The position of the hole for axle that is being assembled relative to the main reference diameter in the Y axis;
* The body bottom wall thickness on the left and right sides of the symmetry axis;
* The average thickness of the body bottom. Figure 4: Parameters and input characteristics: 1—the dimension of the main reference diameter, 2—the roundness deviation of the main reference diameter, 3—the dimension of the hole for the axle that is being assembled (averaged), 4—the position of the hole for axle that is being assembled relative to the main reference diameter in the X axis, 5—the position of the hole for axle that is being assembled relative to the main reference diameter in the Y axis, 6, 7, 8, 9, 10—the dimension in five planes of the hole for the axle that is being assembled, along its entire depth, 11, 12—the body bottom wall thickness on the left and right sides of the symmetry axis. The measurements were carried out using the LH65 coordinate measuring machine by WENZEL with a measurement uncertainty MPEp of 1.5 \(\upmu\)m. The dimensions of the measured bodies were recorded by a Renishaw PH20 5-axis touch-trigger system with a ruby stylus.