Risk statistic is a critical factor not only for risk analysis but also for financial application. However, the traditional risk statistics may fail to describe the characteristics of regulator-based risk. In this paper, we consider the regulator-based risk statistics for portfolios. By further developing the properties related to regulator-based risk statistics, we are able to derive dual representation for such risk.
Hydroelectricity is a major source of renewable electricity originating from a turbine driven by dammed largevolume water via a penstock or a drop shaft. Shafts suffer from risks of collapse due to the pressure from exterior structures and the erosion from inner water flow. Vertical shafts are an important part of hydroelectric power generation systems, and detecting defects in shafts guarantees the stable operation of hydropower stations. However, shaft defect detection is a great challenge due to the poor conditions, large drop in height, limited entrance size, lack of light and damp air, where suitable technology and equipment are not available. Aiming at defect detection for vertical shafts, we have developed a defect-detecting system based on unmanned airships, integrated panoramic CCD cameras, 3D laser scanners, inertial measurement units, barometric altimeters, illumination sensors, and control modules. Shaft defect detection methods (SDDMs) are proposed by fusing the multi-modal image features to extract typical defects on concrete surfaces. Compared with machine learning methods, the proposed method achieves the highest overall accuracy of 90.90% for defect detection. Our system was validated by experiments in the shafts of the Nuozhadu hydropower station to be functional for defect detection, which demonstrates its capability of reducing the risk of collapse and improving safety.
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