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This paper presents a novel low-cost, double-fiber model optical fiber sensor for distributed strain monitoring. The sensor is composed of two fibers: the active fiber and the passive fiber. Localized strain makes light couple from the active fiber to the passive fiber. The output of the active fiber is used for strain value sensing, whereas the double-ended outputs of the passive fiber are used for strain position sensing. Distributed sensing is realized based on the attenuation of the passive fiber, which has a greater attenuation coefficient than the active fiber. Since light emission and detection are performed by light-emitting diodes and photodiodes with a common preamp circuit, the entire system is realized with an extremely low cost, compared with other distributed optical fiber sensor systems. The theoretical model and limit parameter analysis, including the maximum length and the spatial resolution, are proposed with the experimental prototype model sensor that has been developed and tested. The performance of sensor is confirmed by a theoretical analysis and experimental results.