Train Deceleration Speed-Limit Calculation Using Dichotomy Search
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Solution Overview
Problem
Existing methods for calculating calculation mode velocity limit values in train operations are inefficient and complex, particularly in deceleration zones, due to the need to traverse all velocities between the starting and end points of the deceleration zone.
Innovation Solution
A dichotomy-based algorithm and system that initializes intermediate variables to reduce the number of velocities to be calculated by using a dichotomy approach, determining braking conditions to efficiently find the calculation mode velocity limit value.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the traditional method traverses all velocities between starting point and end point of deceleration zone to calculate braking distance, then the calculation mode velocity limit value can be obtained, but the calculation efficiency is low and algorithm complexity is high
Solution Approach 1:
The velocity range is segmented into multiple intervals using dichotomy. The algorithm divides the search space for velocity into upper and lower halves, systematically narrowing down the range where the braking distance equals the target position distance. This segmentation reduces the number of velocities to traverse from O(n) to O(log n), significantly improving calculation efficiency while maintaining accuracy.
Solution Approach 2:
The algorithm incorporates feedback mechanisms by comparing the calculated braking distance with the target position distance at each iteration. Based on this comparison, the algorithm adjusts the velocity search range dynamically - if the braking distance is too long, it reduces the velocity range; if too short, it increases the velocity range. This feedback-driven adjustment efficiently converges on the correct velocity limit value.
2Measurement precision
If the algorithm traverses all velocities in sequence to find the velocity at which braking distance equals target position distance, then the calculation mode velocity limit value is obtained with sufficient accuracy, but the calculation time increases significantly
Solution Approach 1:
The algorithm transforms the one-dimensional sequential search through velocities into a two-dimensional search space defined by upper and lower velocity bounds. By operating in this dimensional space and systematically halving the search interval, the algorithm achieves the same accuracy as exhaustive search but with logarithmic time complexity, dramatically reducing calculation time while maintaining precision.
Data Source
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AI summary
Disclosed is a dichotomy-based algorithm and system for calculating a calculation mode velocity limit value. The algorithm includes the following steps: acquiring calculating parameters: a velocity Vs of a train at a starting point of a deceleration zone, a velocity Ve of the train at an end point of the deceleration zone, and a distance Sd between the starting point of the deceleration zone and a target position; setting intermediate variables: Vst, Vet, and Vt, where Vst tk is an upper limit of a velocity search range, Vet is a lower limit of the velocity search range, and Vt is an intermediate value of the current velocity search range between Vst and Vet; initializing the intermediate values: letting Vt=Vs+Ve2, Vst= Vs, and Vet= Ve; determining an initial braking velocity and a final braking velocity of the train, and calculating and obtaining a braking distance Sb, where the velocity Vs of the train at the starting point of the deceleration zone is taken as the initial braking velocity, and the intermediate variable Vt is taken as the final braking velocity; and judging whether a braking condition is met, where if the braking condition is met, the calculation mode velocity limit value is obtained; and the braking condition is as follows: whether Sb is equal to Sd; or, whether a difference value between Vst and Vet is less than or equal to 1. The above algorithm reduces the complexity of the algorithm for calculating the calculation mode velocity limit value and improves the efficiency and accuracy of the calculation mode velocity limit value.