Tested to reduce the order of the equation to improve the speed of calculation

Applying reasonable calculation methods can significantly improve both the speed and accuracy of the computation. One effective approach is to reduce the order of the system of equations. While, in theory, the current in each bar and the induced potential in the detection coil are related to the induced potential of every bar, in practice, the potential from bars that are several positions away from the excitation magnet is negligible and can be considered zero. This simplification allows us to focus only on the nearby bars, thereby reducing computational complexity.

Specifically, we only need to analyze the GB1 and eB1 waveforms within a range of m guide bars around the magnet in the circumferential direction. This reduces the value of p, which in turn lowers the order of the equations and accelerates the calculation. However, if we still use a cubic spline function to fit GB1 and eB1, the endpoints of the interval no longer align. To address this, an additional constraint is applied: G''sB1(tm) = 0, where tm represents the time when the -m and m bars pass the detection coil.

At this point, the number of unknowns becomes , instead of the original (n+2p+4). Moreover, the value of p can be smaller than before, further lowering the equation's order. By carefully selecting the interpolation points, we can take advantage of the symmetry of the GB1 waveform about the vertical axis. This allows us to consider only the values at half of the interpolation points, effectively halving the value of p. However, since the eB1 waveform is affected by the current in the guide bars and loses its symmetry, it cannot be treated in the same way.

When testing a large batch of products on the assembly line, especially when inspecting many rotors, statistical analysis of the test data can help obtain the best-fit curves for GB1 and eB1. Based on these curves, the interpolation points can be more reasonably chosen, reducing their number and improving both the speed and accuracy of the calculations. This approach not only enhances efficiency but also ensures more reliable results in practical applications.

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