ON DYNAMIC SIMILARITY MODEL TEST OF DAMAGE DETECTION FOR TRANSMISSION TOWER

In order to explore the dynamic similarity model test method different from atmospheric boundary layer wind tunnel and shaking table model test, in accordance with dynamic similar theory, an elastic model of a transmission tower with 1/35 scale and 5.2m height has been designed and manufactured with thin-walled circular pipes of high-density polyethylene. The model has been tested in the laboratory for time and frequency domain responses under suddenly unloading, essential dynamic characteristic of the scale model is also analysed and compared with that of its prototype tower, the dynamic similarity of the two is confirmed. By the mathematical deduction of Wigner-Ville Distribution (WVD) signal terms of structural free vibration response, the new damage detection index with clear physical signification is forwarded for damage detection for transmission tower, the damage detection test of the scale model of transmission tower is then carried out, totally three damage cases, related with chord rod weakening, flank rods failure, different damage degrees and positions, are tested to validate the proposed damage detection index.


INTRODUCTION
Transmission tower is the main structure of the power transmission project, the safety of which is the basis of the large scale regional power system reliability, but the engineering failures of transmission tower at home and abroad occasionally have happened in recent decades.Existing research [1][2][3][4] indicates that the vibration of transmission tower with so much members is more complex than general civil engineering, and dynamic characteristics are influenced much by environment condition, incitation factor, tower-line coupling and stiffness changing point, which lead many present proposed damage detection methods and indexes difficult to be applied [5][6][7][8].As the two-dimensional function of time and frequency, the Wigner-Ville Distribution (WVD) has almost all the expected mathematical properties of damage detection, which has been successfully applied in the field of mechanical fault detection [9][10], it is also a very effective method for the damage detection of transmission tower.
Up to now, the researches of transmission tower are mainly focused on the structural dynamic response under wind load and earthquake.The few atmospheric boundary layer wind tunnel and shaking table model test of transmission tower are the application research, which regard the practical project as the research background, mainly measure the structural dynamic characteristics and response, in order to test the rationality of dynamic calculation model and its analysis method, https://doi.org/10.14311/CEJ.2016.03.0018 2 and ensure the safety and construction of the specific project [11][12].Meanwhile, the researches on damage detection for transmission tower are still at preliminary stage, even the research on model test of damage detection for transmission tower has not been reported yet.
Therefore, to explore the dynamic similarity model test method different from atmospheric boundary layer wind tunnel and shaking table model test, in accordance with dynamic similar theory, an elastic model of a transmission tower with 1/35 scale and 5.2m height has been designed and manufactured with thin-walled circular pipes of high-density polyethylene.The model has been tested in the laboratory for time and frequency domain responses under suddenly unloading, essential dynamic characteristic of the scale model is also analysed and compared with that of its prototype tower, the dynamic similarity of the two is confirmed.The damage detection test of the scale model of transmission tower is then carried out, totally three damage cases, related with chord rod weakening, flank rods failure, different damage degrees and positions, are tested to validate the proposed damage detection index.

DYNAMIC SIMILARITY CRITERION
The similarity of physical process or phenomenon is expressed by the similarity of various physical characteristics in physical process or phenomenon.There is a certain relationship between the various physical characteristics in the similar physical phenomena, which is the similarity condition of the two similar physical phenomena, is also the principle of the model test.Four similar conditions should be satisfying for general mechanic's phenomena: the similarity of material, the similarity of geometry, the similarity of kinematic and the similarity of dynamic.
The model test takes the transmission tower as the structure prototype, the dynamic characteristics and the free vibration response of the structural system is mainly simulated, and the free vibration equation of the whole quantity form can be expressed in a general manner: where, M , C and K is respectively mass, damping and stiffness matrix, a , v and y is respectively acceleration, velocity and displacement vector.Due to the structural damping theory is still not perfect, the damping mechanism is not fully reflected by the viscous damping and hysteretic damping theory, the structural damping parameter is difficult to be controlled in the design and manufacture of the model.Thus, the free vibration equation of the prototype of the n -degree structural system without quantitative damping is simplified as: To the model: where, subscript i is i th degree, subscript p and m is respectively prototype and model, By equation ( 4) and decoupling, the equation ( 2) is deformed as: Only: -
The essence of similarity index is to maintain the similarity between the elastic restoring force and the inertia force, according to the dimensional analysis method, the equation ( 6) is deformed as: where, is respectively similar coefficient of elastic modulus, density and time.The similarity conditions of the model are mainly derived from the similarity of geometry, elastic modulus and density, the similarity coefficient of time determines the similarity of velocity, acceleration, frequency and other physical variables.Thus, the selection of geometry and material of model is particularly important and key.

DAMAGE DETECTION INDEX
Under initial displacement condition, the acceleration response of free vibration at position k of non-damping structural system with n degrees of freedom is: Where, Can be seen from analytic expression, the signalterms in WVD of free vibration response are as follows: If frequency parameter i f of a signal term is determined, while the i th natural frequency i  is easy to be acquired by frequency spectrum or time-frequency analysis, then the time-decaying amplitude can be determined, the response function of i th mode shape at test point k also can be acquired, by analogy with , the response function of i th mode shape at one time point ( 0 t t  ) can be obtained at any test point, finally the i th mode shape can be acquired: The positive and negative relations between mode shape components can be determined by the phase relationship of cross-power spectrum at test points, with same direction as positive and different direction as negative.
The structural damage generally will bring changes in physical parameters (such as mass, stiffness and so on), and then results in that structural vibration mode also will change, so the damage massage is inevitably contained in the change of mode shape.Meanwhile, the response function relation between WVD signal terms amplitude of free vibration response and mode shape has been revealed.To determine the specific position of structural damage, the key features of damage information can be extracted by WVD signal terms amplitude.Therefore, based on the principle that https://doi.org/10.14311/CEJ.2016.03.0018 4 quadratic index is more sensitive to small change in mode shape and can find the mutation of damage position, the index WAC is proposed for damage detection for transmission tower: where, is respectively amplitude curvature of signalterms in WVD at test point i before and after damage , which can be calculated by central difference method: where, i l is the space between test points.

MODEL DESIGN, MANUFACTURE AND TEST
At present, there are two kinds of transmission tower model design and manufacture methods, which are concentrated stiffness method and discrete stiffness method.The concentrated stiffness method is that the stiffness distribution of prototype is simulated by stiffness distribution along height of the mandrel made with appropriate elastomer, although the design and manufacture of model is simplified, this method has some obvious deficiencies, such as structure stress transmitting path distortion and so on.The discrete stiffness method requires all the members of model to be stiffness similar, the main difficulty of this method is the material and manufacture, because thin-wall steel tubes and angles of transmission tower prototype are scaled down, according to the geometric similar coefficient, the wall of members is very small, which cannot be finished in the actual manufacture.
However, according to the mechanic characteristics of transmission tower, the tower structure can be regarded as the spatial truss structure composed of two force bars by ignoring local bending of the bar, so the simulation of stiffness is only required to meet the similarity of tensile stiffness.The model regards a transmission tower with 181.8m height as structural prototype, the members of model are manufactured with thin-wall circular pipes of high-density polyethylene, a small amount of thin-wall steel angles are replaced according to the principle of equal section area, the density and elastic modulus are respectively 0.958g/cm 3 and 0.7GPa.The model similar coefficients are shown in Table 1, Figure 1 is the photo of transmission tower model in laboratory, and Figure 2 is the position of acceleration sensors and simulated damages.The suddenly unloading incitation is exerted by cutting the tensile wire (diameter 0.2mm) along the horizontal direction, incentive point is located at the bottom of tower head and middle of crossarm, which is respectively load case (1) and ( 2), the incentive amplitude is the weight (500g) hanged to the wire through the pulley.

RESULTS AND DISCUSSIONS
Figure 4 and Figure 5 are respectively the model typical acceleration response of x and y direction under suddenly unloading incitation, it is shown that the vibration response of the model fade very fast because of the damping effect, the acceleration responses of the model are mainly the low frequency components.Figure 6 and Figure 7 are the model typical acceleration spectrum of x and y direction under suddenly unloading incitation, it is shown that the first order modal response is absolutely dominant in the dynamic response for high rise structures such as transmission tower, and the structural dynamic analysis of the first three order modal components is sufficiently accurate.

CONCLUSIONS
To explore the dynamic similarity model test method different from atmospheric boundary layer wind tunnel and shaking table model test, in accordance with dynamic similar theory, an elastic model of a transmission tower with 1/35 scale and 5.2m height has been designed and manufactured with thin-walled circular pipes of high-density polyethylene.
The model has been tested in the laboratory for time and frequency domain responses under suddenly unloading, essential dynamic characteristic of the scale model is also analysized and compared with that of its prototype tower, the dynamic similarity of the two is confirmed.

C
is respectively similar coefficient of mass, stiffness, acceleration and geometry.

Fig. 3 .
Fig. 3. -Damage simulation: (a) flank rod failure (b) chord rod cross-section weakening of tower body (c) chord rod cross-section weakening of tower head

Figure 9
Figure 8 is the detection result of index WAC for simulated damage (1), it is seen that the value of WAC is as a single peak at test point No.6 under two load cases, accurately showing the position of local damage from flank rod failure.The WAC small peak values at junction of tower body and head (test point No.8), middle of tower head (test point No.10) as well as crossarm (test point No.13) are caused by structural itself stiffness mutation.Figure9is the detection result of index WAC for simulated damage (2), it is seen that the value (a) Load case (1) (b) Load case (2) Fig.9.-Detection result of simulated damage (2) (a) Load case (1) (b) Load case (2) Fig.10.-Detection result of simulated damage (3) By the mathematical deduction of Wigner-Ville Distribution (WVD) signal terms of structural free https://doi.org/10.14311/CEJ.2016.03.0018 9 vibration response, the new damage detection index with clear physical signification is forwarded for damage detection for transmission tower, the damage detection test of the scale model of transmission tower is then carried out, totally three damage cases, related with chord rod weakening, flank rods failure, different damage degrees and positions, are tested to validate the proposed damage detection index.
, and k can be deducted as:

Table 2
is the natural frequency of transmission tower model; the model expectation valve comes from prototype theory valve according to the frequency similar coefficient.It can be seen that the model test valve is well identical with the expectation valve, indicating that the design and manufacture of transmission tower model based on dynamic similarity criterion is successful.Tab.2.-Natural frequency of transmission tower model