Pulse Source Location in Dispersive Media Using Phase Diagram Norms
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Solution Overview
Problem
Existing methods for locating pulse sources in dispersive media, such as electric cables, are prone to errors due to synchronization delays between sensors, leading to incorrect positioning of faults and repeated maintenance operations.
Innovation Solution
A method using at least one pair of sensors to detect pulses and construct phase diagrams, calculating the ratio of distances to the pulse source based on the norms of vectors from the phase diagrams, eliminating the need for synchronization between sensors by determining distance ratios from the shape differences of pulses rather than time differences.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If time-based pulse propagation measurement is used to locate pulse sources, then the location can be determined using simple sensor timing, but synchronization delays between sensors cause large positioning errors
Solution Approach 1:
The patent changes the measurement parameter from time-based (Δt) to shape-based (phase diagram norms). Instead of measuring the time difference of arrival which requires synchronization, the method uses the ratio of pulse shape characteristics (norms of phase diagram vectors) which are invariant to synchronization delays. This parameter transformation eliminates the synchronization problem while achieving accurate location.
Solution Approach 2:
Instead of using the conventional approach of measuring time differences to calculate position, the patent inverts the approach by using pulse shape characteristics. The location is determined from the ratio of norms of phase diagram vectors constructed from pulse amplitudes at successive sampling times, rather than from time delays. This inversion makes the measurement independent of synchronization.
2Loss of time
If GPS or radio modem synchronization systems are used between sensors, then time measurement can be performed, but synchronization delays still cause errors in source position calculation
Solution Approach 1:
The patent extracts the essential information needed for location (pulse shape characteristics) while discarding the problematic aspect (absolute timing). By using only the relative shape information encoded in the phase diagram norms and ignoring the absolute time stamps, the method achieves location accuracy without being affected by synchronization delays introduced by GPS or radio modem systems.
3Ease of manufacture
If pulse propagation speed is assumed constant for location calculation, then simple distance estimation is possible, but dispersive media cause pulse speed variation leading to positioning errors
Solution Approach 1:
Instead of trying to measure and compensate for variable pulse speeds in dispersive media, the patent inverts the approach by using pulse shape characteristics that are inherently affected by dispersion in a predictable way. The phase diagram norms capture the cumulative effect of dispersion over different path lengths, and their ratio provides location information that automatically accounts for speed variations without requiring explicit speed measurement or compensation.
Data Source
AI summary
The invention relates to a method of locating in a dispersive medium (5) a source (7) of pulses (s1, s2) by at least one pair of sensors (1, 2), the method comprising the following steps: at the level of each sensor (1, 2), detecting a pulse (s1, s2) originating from the source (7); for each of said pulses, constructing a phase diagram on the basis of N vectors of which the co-ordinates correspond to the amplitude of the pulse (s1, s2) at successive sampling instants ti; and for each pair of sensors, calculating the ratio between the distances L1 and L2 of each sensor from the source through the formula (I) where (II) and (III) are the norms of the vectors (IV) and (V) of the phase diagrams corresponding to the pulses detected by the sensors (1, 2).L1L2=∑i=1Nr1(ti)→/∑i=1Nr2(ti)→(I)r1(ti)→(II)r2(ti)→(III)r1(ti)→(IV)r2(ti)→(V)