DISPLACEMENT RECONSTRUCTION METHOD FOR LATTICE TOWER STRUCTURE BASED ON IMPROVED MODE SUPERPOSITION

Abstract

The present invention belong to the technical field of lattice tower structure monitoring, and discloses a displacement reconstruction method for a lattice tower structure based on improved mode superposition. The method comprises: uniformly arranging D strain sensors on main member of a lattice tower along the height, processing collected strain data {ε}.sub.D×1 using a stochastic subspace identification (SSI) method to obtain a matrix [Ψ].sub.D×n.sup.T of first n-order strain modes;

calculating a function relation y(x) between a distance from a measuring point to a neutral layer and a height according to a lattice tower design drawing; performing polynomial fitting on the first n-order strain modes with a height coordinate x of the lattice tower respectively to obtain a strain mode function Ψ.sub.i(x), expanding a function

[00001]$\frac{{\Psi }_i\left(x\right)}{y\left(x\right)}$

according to a Taylor formula, performing double integration on the expansion result and substituting same into a boundary condition, to obtain a displacement mode function Φ.sub.i(x); evaluating a modal coordinate {q}.sub.n×1 by means of the least square method, substituting the height coordinate x of a displacement object point to be reconstructed, and multiplying the displacement mode function value Φ.sub.i(x) by the modal coordinate {q}.sub.n×1. The improved mode superposition method of the present invention has the advantages of a small number of sensors required, simple calculation process, accurate calculation result, and strong operability and practicality.

Claims

1. A displacement reconstruction method for a lattice tower structure based on improved mode superposition, characterized in that a lattice tower is simplified into a thin-walled variable cross-section cantilever beam, a neutral layer is assumed to be located between two main members, a stochastic subspace identification method is introduced to identify strain modes, judge order of participating modes, and reduce the amount of calculation, and an existing mode superposition method is improved into a method suitable for variable cross-section structures, comprising the following steps: (1) uniformly arranging D strain sensors on main member of a lattice tower along the height direction, the number of the strain sensors is at least four; (2) processing strain data {ε}.sub.D×1 collected by the strain sensors using a stochastic subspace identification method, drawing a stabilization diagram according to the processing result, judging order n of modes participating in vibration according to the obtained stabilization diagram, where n is a natural number and does not exceed D, and extracting a matrix [Ψ].sub.D×n.sup.T of first n-order strain modes; (3) calculating a function relation y(x) between a horizontal distance y from any point of the main member to the neutral layer and a height x from the point to the ground according to a lattice tower design drawing; (4) performing polynomial fitting on the first n-order strain modes with the height x from the strain sensor arrangement points to the ground respectively to obtain a strain mode function Ψ.sub.i(x), expanding a function $\frac{{\Psi }_i\left(x\right)}{y\left(x\right)}$ according to a Taylor formula, performing double integration on the expansion result and substituting same into a boundary condition fixedly connected to the bottom of the lattice tower structure, to obtain a displacement mode function Φ.sub.i(x); (5) in the case where the strain mode matrix [Ψ].sub.D×n.sup.T and the strain data {ε}.sub.D×1 of the lattice tower are known, evaluating a modal coordinate {q}.sub.n×1 of the lattice tower in the vibration process by means of the least square method; (6) substituting the height coordinate x of any point of the lattice tower into the displacement mode function Φ.sub.i(x), and multiplying the obtained displacement mode function value Φ.sub.i(x) by the modal coordinate {q}.sub.n×1 to obtain dynamic displacement of the point.

Description

DESCRIPTION OF DRAWINGS

[0018] FIG. 1 is a flow chart of implementation of the present invention;

[0019] FIG. 2 is an arrangement diagram of sensors of a lattice tower; FIG. (a) is a front view of a lattice tower, where circles represent strain sensors; and FIG. (b) is a side view of a lattice tower, where dotted line represents an imaginary neutral layer.

DETAILED DESCRIPTION

[0020] To make the purpose, features and advantages of the present invention more clear and legible, the technical solution in the embodiments of the present invention will be clearly and fully described below in combination with the drawings in the embodiments of the present invention. Apparently, the described embodiments are merely part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by those ordinary skilled in the art without contributing creative labor will belong to the protection scope of the present invention.

[0021] Referring to FIG. 1 to FIG. 2, embodiments of the present invention propose a displacement reconstruction method for a lattice tower structure.

[0022] For implementation case data source, see ZHANG Q, FU X, REN L, et al. Modal parameters of a transmission tower considering the coupling effects between the tower and lines [J]. Eng Struct, 2020, 220(110947) for details.

[0023] In an embodiment of the present invention, self-compiled programs or related commercial software may be used for building and transient analysis of a numerical model of the lattice tower. In this embodiment, by taking the widely-used finite element analysis software ANSYS as an example, the application of the improved mode superposition method to the lattice tower structure is achieved, which is specifically described with reference to the flow shown in FIG. 1 and the technical solution of the present invention: [0024] (1) The lattice tower in the embodiment is a self-supporting tower with a total height of 34 m, and is made of Q235 equal-leg angle steel. For tower structure information, see “FIG. 6” in “ZHANG Q, FU X, REN L, et al. Modal parameters of a transmission tower considering the coupling effects between the tower and lines [J]. Eng Struct, 2020, 220(110947)”for details. A finite element model of the tower is built using the software ANSYS, a beam 188 element is selected to simulate a lattice tower pole, connection between members is simplified using rigid nodes, and an ideal elastic-plastic model is used as a constitutive model for steel.

[0025] Since the first three-order modes need to be considered in the improved mode superposition method, eight strain measuring points are arranged in this embodiment. The above numerical model of the lattice tower is built according to the design drawing. [0026] (2) For horizontal load applied in this embodiment, see “FIG. 6”in “ZHANG Q, FU X, REN L, et al. Modal parameters of a transmission tower considering the coupling effects between the tower and lines [J]. Eng Struct, 2020, 220(110947)”for details. The solution type analyzed by software ANSYS is “antype,trans”, and the strain response of a strain measuring point can be extracted after the applied load is evaluated. Then, the strain response obtained is processed using the SSI method, assuming that the order is set to 100, the identified strain modes and corresponding height coordinates are extracted. [0027] (3) A function relation between a distance from a point of the main material to the neutral layer and a height coordinate is calculated according to a dimension of a lattice tower design drawing, which is a linear function relation in this embodiment. [0028] (4) Performing polynomial fitting on the strain modes with the height coordinate of the lattice tower respectively to obtain a strain mode function, expanding a function

[00004]$\frac{{\Psi }_i\left(x\right)}{y\left(x\right)}$

according to a Taylor formula, performing double integration on the expansion result and substituting same into a boundary condition, to obtain a displacement mode function Φ.sub.i(x) . [0029] (5) Evaluating a mode coordinate by means of the strain response and strain mode using the least square method. [0030] (6) Substituting the height coordinate at the object point into the displacement mode function to evaluate a function value, and multiplying the displacement mode function value by the mode coordinate to obtain dynamic displacement.

[0031] Attention shall be paid during the use of the present invention: firstly, the number of strain measuring points of the lattice tower is at least four; and secondly, transient analysis technique is a mature and well-known technique in the art, and self-compiled programs or related commercial software may be used for building and transient analysis of a numerical model of the lattice tower.

[0032] The above embodiments are only used for describing the technical solution of the present invention rather than limiting the same. Although the present invention is described in detail by referring to the above embodiments, those ordinary skilled in the art should understand that the technical solution recorded in each of the above embodiments can be still amended, or some technical features therein can be replaced equivalently. However, these amendments or replacements do not enable the essence of the corresponding technical solutions to depart from the spirit and the scope of the technical solutions of various embodiments of the present invention.