###### Abstract
They solved the balance matrix by using the Gaussian elimination method, which solved the problem of finding the rank deficiency of the node balance matrix in the force density method, and took the lead in applying the force density method to the form finding research of the tensegrity structure [13]. Based on the research of [PERSON] and [PERSON], [PERSON] and [PERSON] (2006) proposed the self-adaptive density method based on eigenvalue analysis and spectral decomposition of the force density matrix. In an iterative calculation, the force density matrix was automatically adjusted to constantly find the required rank deficiency value, which solved the problem of difficulty in applying the force density method to structures with massive cable and strut elements [14]. Based on the self-adaptive density method, [PERSON] et al. (2010) adjusted the iterative strategy, presented an iterative calculation method that could be applied to a super-stable structure, and successfully carried out form finding analysis of the cable system and tensegrity structures [15; 16]. Recently, [PERSON] et al. (2022) proposed a force density informed neural network method by utilizing a fully connected neural network, which can obtain the feasible pre-stress design of multiple tensegrity models without depending on the amount of data samples and considers the structural symmetric property effectively [17]. [PERSON] (1966) first put forward the concept of the dynamic relaxation method, which is essentially applied to the numerical solution of a series of nonlinear equations [18]. [PERSON] and [PERSON] (1970) first applied the dynamic relaxation method to the analysis of cable structures [19]. [PERSON] (1984) used the dynamic relaxation method to solve the static response of cable truss and other pre-tension cable structures [20]. Recently, [PERSON] et al. compared nine schemes of dynamic relaxation methods and summarized the most efficient and stable method [21]. [PERSON] et al. (2015) introduced the operation principle of the nonlinear force method into the dynamic relaxation method and proposed the nonlinear dynamic finite element theory [22]. In addition, the research on applying the idea of optimization algorithm to form finding analysis increase gradually, such as the genetic algorithm [23; 24], evolutionary algorithm [25] and so on, which could realize the optimization of the form finding results of numerical solutions through intelligent algorithms. At present, it is used in various types of long-span space structures, such as reticulated shell structure [26; 27], cable dome [28], cable membrane structure [29] and so on. In terms of construction methods, the traditional tower erection method is still applicable to the cable supported grid structure, which generally includes erecting a supporting tower, hoisting the upper grid structure on the tower, lifting and installing a high-altitude cable net, and ensuring cable tension. Recently, based on a typical cable supported grid structure composed of a rigid saddle-shaped, single-layer grid structure at the top chord, 68 radial cables at the bottom chord, one tension ring, and a vertical brace, [PERSON] et al. (2021) successfully applied the traditional tower erection construction method and simulated the whole construction process using ANSYS finite element software to verify the accuracy and rationality of the method [30]. However, the erection of the supporting tower is bound to have some problems, such as the time it takes during the construction period, the lack of flexibility in arranging the construction process due to site occupation, and large expenditure on temporary construction measures. Therefore, it is of great research value to improve the traditional method of constructing a cable supported grid structure and put forward a method that does not require the set of brackets. In fact, in the research of cable strut tension structures of other systems, some non-bracket methods have already been proposed and applied in practice. With regard to cable domes, [PERSON] et al.