## 1 Introduction  
In chemical industry production, chemical reactions, heating, cooling, mixing, or other processes often take place in process equipment and, therefore, it must be possible to precisely measure the mass of internal materials. The total mass of the materials inside process equipment and its real-time change are important parameters, which are of great significance to the mass balance, energy balance, and device scaling-up design of chemical process [1, 2, 3, 4]. At present, the mass measurement methods of materials inside vessels mainly include: measuring the flow of inlet and outlet, and calculating by the law of conservation of mass [5]; tracking and measuring the internal materials inside vessels using radioactive materials, and calculating according to each phase holdup and density [6]; installing the pressure sensor at the opening of the outer wall and calculating according to the pressure difference signal [7]. However, due to the complex operation state of chemical processes, the above mass measurement methods have many limitations, such as destroying the continuity of the device and operation process, large measurement error of complex phase change processes, high test cost and difficult maintenance and update, etc. Weighing method refers to installing a weighing device directly on the equipment to obtain the total weight of the equipment and its internal materials. In the dynamic process of continuous feeding and discharging, the change of material mass inside the equipment is converted into electrical signals, and the real-time dynamic mass of the internal materials is measured [8]. As a high-precision detection method that can obtain real-time data during operation without interfering with process operation, the weighing method is not only widely used in continuous chemical production processes, but also becomes a common method to obtain process characteristic parameters in scientific research [9; 10; 11; 12; 13; 14]. For example, in the fuming furnace smelting process of a nonferrous metallurgy system, the real-time mass change of pulverized coal is an important parameter in the smelting process. Weighing method obtains more reliable data than a capacitive potentiometer and other material level gauges. The dynamic mass data were obtained by on-line continuous weighing of the two-phase flow reactor, and the dynamic liquid holdup of the reactor was obtained by subtracting the dry column mass [15; 16]. However, in most industrial plants there are a number of pressure vessels, or other equipment (reactors, towers, etc. ), connected by a piping system used to convey fluids from one stage of the process to the next [17; 18]. Evaluating the influence of attached piping on the weighing result is a bottleneck in the application of the weighing method to measure the internal material mass of equipment [19]. When the equipment moves downward under the internal material weight load, the pipe moves downward the same distance that the equipment deflects. The pipe acts like a cantilever beam, exerting a vertical force on the unit equipment. This force, together with the material weight load, acts on the weighing cell and has a significant effect on the weighing accuracy, especially when many pipes are connected to equipment with a relatively low capacity [20]. In past applications, flexible connection structures, such as PTFE pipes, corrugated expansion joints, and metal hoses, are used to minimize unwanted forces exerted by piping when the vessel deflects [21]. The angle, length, and other flexible connection parameters are demanding, but most are still based on experience. In the reaction process with phase change, high pressure will lead to the Bourdon tube effect [22], so it is necessary to fill the soft joint with flexible materials to improve its bearing capacity, but the operation is difficult.