###### Abstract  
This paper proposes a new type of solar trough collector with a spliced cylindrical mirror and develops a new ray-tracing method to predict and optimize its performance. The mirrors of this system are composed of multiple cylindrical mirrors whose centers are on a parabola, and the normal vector of the centers of each cylindrical mirror is consistent with the normal vector of the parabola point where it is located. The new ray-tracing method is based on the transverse distribution of solar radiation, and it has been validated with Soltrace, with the maximum intercept factor error in the calculations being less  
Solar trough collector systems with cylindrical trough collectors have been studied for a long time. [PERSON] and [PERSON] [7] examined a cylindrical parabolic solar collector, defining their ideal performance as a benchmark for intermediate-temperature reflectors. It identified optimal target widths for maximizing the energy concentration in different solar collector configurations, observing a continuous energy increase for the backside solar collector. [PERSON] [8] provided an integral expression to calculate the concentration ratios of flat receivers with cylindrical parabolic solar collectors by incorporating rim angles, solar models, and mirror reflectivity. [PERSON] [9] compared five line-focusing solar trough collectors and found that the cylindrical parabolic solar collector attained the best-focusing factor. Further studies by [PERSON] evaluated four solar-disk models (square, uniform, real, and Gaussian) and found that the real model was the most accurate, and significant differences in local concentration factors only appeared when solar concentrator imperfections were small and non-concentrators were also considered. For practical applications, all models were sufficient for concentration calculations with typical imperfections, but precise local calculations required careful model selection [10]. [PERSON] [11] presented an optimized design for a cylindrical solar collector, designed at a rim angle of 45\({}^{\circ}\), which offered a good balance between cost and performance less sensitivity to solar ray deviations and provided consistent efficiency for thermal application. The other focusing solar collectors, such as the dish solar concentrators, use segmented mirrors instead of complete parabolic mirrors. Previously, we proposed a composite dish concentrator comprising 249 spherical mirrors with a concentration ratio of approximately 2000, which achieved a net thermal efficiency of 85.87% and an intercept factor of 98.60% [12]. In 2003, the Australian National University (ANU) proposed a dish concentrator that employed an array of equilateral triangular spherical mirrors. The 400 m\({}^{2}\) composite spherical mirrors were configured in a parabolic shape to assess their optical performance and feasibility as paraboloidal dish concentrators and compared with conventional multi-facet solar collectors. The study suggested that utilizing identical spherical reflector sub-components oriented paraboloidal on a space frame structure could simplify the manufacturing process and lower the costs, with optical performance similar to traditional designs, while simplifying mirror panel production [13]. The Australian National University subsequently designed and built a 500 m\({}^{2}\) composite dish solar system with 390 spherical mirrors, each measuring 1.17 m \(\times\) 1.17 m [14]. Furthermore, [PERSON] [15], in 2012, proposed a dish solar collector as a model for a parabolic surface using square flat facets supported by a parabolic frame and optimized it to achieve specific flux characteristics at the focal plane through Monte Carlo ray-tracing analysis. Key findings included the design and optimization of a 164-facet concentrator delivering up to 8.15 kW of radiative power over a 15 cm radius disk, achieving an average concentration ratio exceeding 100. This design offered a cost-effective alternative to traditional parabolic dish concentrators for industrial applications.