## 3 Measurement Point Optimization Strategy of Long-Span Steel Beam Based on the IPSOARW
### Acquisition of Training Data for Bridge Decks Based on IPSOARW  
In order to optimize the modal test points of long-span steel beam structures, the modal data of the structure is needed, no matter the number optimization or position optimization. Therefore, the finite element model of the long-span steel beam structure was established in ANSYS (R19.2), and then modal analysis was carried out to obtain the frequencies and modes of the structure in the frequency band of interest. In the follow-upwork, the IPSOARW will take the modal shape data of the structure as the training data so as to optimize the position of the structure's modal test measuring points.  
Strategy for Optimizing the Number of Measurement Points for the Modal Test of Large-Span Steel Beams  
The number of measurement points is optimized by:  
(1) constructing a fitness function with the minimum value of the non-diagonal elements of the \(MAC\) matrix; (2) increasing the number of randomly selected measurement points and observing the change in the value of the fitness function. (3) The number of measurement points is determined by the relation curve between the number of measurement points and the fitness function value.  
The steps for optimizing the number of measurement points are as follows.  
* Construct the \(MAC\) matrix formula. \[MAC_{ij}=\frac{\left(\Phi_{i}^{T}\Phi_{j}\right)^{2}}{\left(\Phi_{i}^{J}\Phi_ {i}\right)\left(\Phi_{j}^{T}\Phi_{j}\right)}\]
* Set the maximum value of the non-diagonal elements of the \(MAC\) matrix to be the function \(f_{max}\).
* Select one node at random from all the nodes as a measurement point and calculate the relationship between the number of measurement points and \(f_{max}\), select one node at random from the remaining nodes to add a measurement point, calculate the number of measurement points at this moment as a function of \(f_{max}\) and repeat the superposition of measurement points.
* Using the above iterative method, the value of the function \(f_{max}\) can be derived under different numbers of measurement points.
* On this basis, the most reasonable number of measurement points is determined by plotting the value of the function \(f_{max}\) against the number of measurement points.  
Optimization Strategy for the Location of Measurement Points on Large-Span Steel Beams Based on the IPSOARW  
Based on the known data of the structural mode and the optimized number of measuring points, the fitness function is taken as the optimal number of measuring points in the particle dimension. The structural mode data are used as the training data of the optimization algorithm.  
The steps of measurement point position optimization are as follows:  
* Introduce the matrix \[MAC_{ij}=\frac{\left(\Phi_{i}^{T}\Phi_{j}\right)^{2}}{\left(\Phi_{i}^{J}\Phi_ {i}\right)\left(\Phi_{j}^{T}\Phi_{j}\right)}\]
* Construct the fitness function with the maximum value \(f_{max}\) of the off-diagonal elements of the matrix.
* Set IPSOARW parameters, such as population size, particle dimension, maximum number of iterations, learning factor, particle speed, etc.
* Calculate and obtain the modal shape data of the structure.
* Use the IPSOARW to optimize the position of the measurement point, calculate the current fitness value of each particle and determine the group extreme value and the individual extreme value of the particle. The loop iterates. When the maximum number of iterations is reached, the loop ends and the optimal value is output. The value is the node number of the optimal location of the measurement points.