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The electromagnetic performance of phased array antenna is greatly affected by the phased array antenna surface deformation. How to apply the strain measurement data of sparse fiber grating strain sensors to sense the shape of antenna array is the key to realize structural health monitoring and electromagnetic performance control. This paper proposes a virtual sensing method for structural deformation under complex experimental modes. In this method，the complex mode transformation is first used to process the complex mode data obtained from modal testing to obtain the corresponding real displacement modes，and then the full field expansion of finite real displacement modes is realized using mode expansion；Combining the extended real displacement modal and finite element modal data，two virtual sensing equations named CMT-SEREP（complex mode transformation-system equivalent reduction expansion process）and CMT-LC（complex mode transformation-local correspondence），which characterize the relationship between sparse measured strain information and the full field displacement of the structure，have been derived to achieve the real-time estimation of the deformation shape of the antenna structure from sparse measured strain information. Using the developed large phased array antenna array deformation experimental platform，experimental verification of different sensing methods was carried out under three deformation working conditions. Experimental results show that the proposed method can reconstruct the full field displacement of the antenna array structure using sparse strain measurement information，and the sensing accuracy of CMT-LC is higher than that of CMT-SEREP. Compared to the traditional modal method，the relative percentage error of deformation sensing using CMT-LC method has been reduced by at least 6.105%. This method is not only suitable for deformation sensing of non-proportional damping antenna structures，but also suitable for other complex engineering structures，and it has a great application potential.
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| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |
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