CABLE TENSION CALCULATION METHOD SIMULTANEOUSLY CONSIDERING SAG, INCLINATION ANGLE AND BENDING STIFFNESS

Abstract

A cable tension calculation method simultaneously considering the sag, inclination angle and bending stiffness includes: querying basic parameters of a stay cable according to design data and construction data; considering influences of the sag, the inclination angle θ and the bending stiffness EI, to calculate dimensionless parameters γ, ε and λ.sup.2; testing an acceleration response of the stay cable by an acceleration sensor, to identify a frequency ω of the acceleration response of the stay cable, further calculating a dimensionless frequency {circumflex over (ω)} of the stay cable and the dimensionless parameters γ, ε and λ.sup.2, and substituting the dimensionless frequency {circumflex over (ω)} of the stay cable into a vibration characteristic equation, to establish a function relation between the dimensionless frequency {circumflex over (ω)} and a cable tension H* of the stay cable; and solving a root of the vibration characteristic equation, and identifying the cable tension H* of the stay cable according to the root.

Claims

1. A cable tension calculation method simultaneously considering sag, inclination angle and bending stiffness, comprising: step 1, querying basic parameters of a stay cable according to design data or construction data; step 2, calculating dimensionless parameters γ, ε and λ.sup.2 of the stay cable according to the sag, inclination angle θ and bending stiffness EI of the stay cable, the parameter γ being a dimensionless parameter related to the bending stiffness EI, the parameter ε being a dimensionless parameter related to the inclination angle θ, and the parameter λ.sup.2 being a dimensionless parameter related to the sag; step 3, testing an acceleration response of the stay cable by an acceleration sensor, to identify a frequency ω of the acceleration response of the stay cable, and further calculating a dimensionless frequency {circumflex over (ω)} of the stay cable, a calculation equation of the dimensionless frequency being as follows:
{circumflex over (ω)}=ωl.sup.2√{square root over (m/EI)} m being mass per unit length of the stay cable, and l being a length of the stay cable; step 4, substituting the dimensionless parameters γ, ε and λ.sup.2 and the dimensionless frequency {circumflex over (ω)} of the stay cable into a vibration characteristic equation of the stay cable to establish a function relation between the dimensionless frequency {circumflex over (ω)} and a cable tension H* of the stay cable; and step 5, using the dimensionless frequency of each order to calculate the cable tension H*, solving a root of the vibration characteristic equation, and identifying the cable tension H* according to the root.

2. The cable tension calculation method simultaneously considering the sag, inclination angle and bending stiffness of claim 1, wherein the basic parameters of the stay cable in step 1 comprise: the cable length l, the mass per unit length m, the inclination angle θ and the bending stiffness EI.

3. The cable tension calculation method simultaneously considering the sag, inclination angle and bending stiffness of claim 2, wherein calculation equations of calculating the dimensionless parameters γ, ε and λ.sup.2 influenced by the stay cable are as follows:
γ=l√{square root over (H*/EI)},
ε=ξ sin θ,
λ.sup.2=δξ{circumflex over (L)}.sub.e, H*≈H/cos θ representing the cable tension of the stay cable, H representing a horizontal component of the cable tension of the stay cable, ξ=mgl/H* representing a dimensionless parameter of a ratio of an inertia force to the cable tension of the stay cable, g representing the acceleration of gravity, {circumflex over (L)}.sub.e=1/(1+⅛ξ.sup.2) representing a dimensionless parameter of a ratio of an original length to length after deformation, and δ=EA/H* representing a dimensionless parameter of a ratio of an axial tensile rigidity EA to the cable tension; and the dimensionless parameters γ, ε and λ.sup.2 are functions of the cable length l, the mass m per unit length, the cable tension H* of the stay cable, the tensile rigidity EA, the inclination angle θ and the bending stiffness EI respectively, wherein γ=γ(l,H*,EI), ε=ε(m,l,H*,θ) and λ=λ(EA,H*,m,l).

4. The cable tension calculation method simultaneously considering the sag, inclination angle and bending stiffness of claim 3, wherein a function relation between the dimensionless frequency {circumflex over (ω)} and the cable tension H* of the stay cable is established as follows: $P\left(\hat{\omega },\lambda ,\gamma ,\epsilon \right)=\frac{\frac{1}{2{\lambda }^2{\gamma }^4}\left({\lambda }^2{\gamma }^2-{\hat{\omega }}^2\right)}{\frac{{\beta }_2\tan \left[\frac{{\beta }_1}{2}\right]-{\beta }_1\tanh \left[\frac{{\beta }_2}{2}\right]}{{\beta }_1{\beta }_2\left({\beta }_1^2+{\beta }_2^2\right)}+\frac{\tanh \left[\frac{\gamma }{2}\right]}{{\gamma }^3}-{\epsilon }^2\frac{\Omega \left(\gamma ,\hat{\omega }\right)}{2{\gamma }^2}}1=0,$ ${\beta }_1=\sqrt{-\frac{{\gamma }^2}{2}+\sqrt{\frac{{\gamma }^4}{4}+\widehat{{\omega }^2}}}\mathrm{and}{\beta }_2=\sqrt{\frac{{\gamma }^2}{2}+\sqrt{\frac{{\gamma }^4}{4}+\widehat{{\omega }^2}}}$ being characteristic roots of a horizontal stay cable frequency equation, Ω(γ,{circumflex over (ω)}) being a high-order nonlinear term, and Ω(γ,{circumflex over (ω)}) being a function of the dimensionless parameter γ and the dimensionless frequency {circumflex over (ω)}, and a specific calculation equation of Ω(γ,{circumflex over (ω)}) being as follows: $\Omega \left(\gamma ,\hat{\omega }\right)=\left\{\frac{1}{3}+\frac{2{\gamma }^2\left(-2+{\beta }_1\cot \left[\frac{{\beta }_1}{2}\right]\right)}{{\beta }_1^2\left({\beta }_1^2+{\beta }_2^2\right)}+\frac{2{\gamma }^2\left(-2+{\beta }_2\coth \left[\frac{{\beta }_2}{2}\right]\right)}{{\beta }_2^2\left({\beta }_1^2+{\beta }_2^2\right)}-\frac{3\left(-2+\mathrm{\gamma cot}\left[\frac{\gamma }{2}\right]\right)}{{\gamma }^2}+\frac{4\gamma \left(\gamma -2\tanh \left[\frac{\gamma }{2}\right]\right)}{{\hat{\omega }}^2}+\frac{\left(-4\gamma +\left(8+{\gamma }^2\right)\tanh \left[\frac{\gamma }{2}\right]\right)}{{\gamma }^3}+\frac{4{\beta }_2^2{\gamma }^3\left(-2+{\beta }_1\cot \left[\frac{{\beta }_1}{2}\right]\right)\tanh \left[\frac{\gamma }{2}\right]-4{\gamma }^5\left(-2+{\beta }_1\cot \left[\frac{{\beta }_1}{2}\right]\right)\tanh \left[\frac{\gamma }{2}\right]}{{\beta }_1^2\left({\beta }_1^2+{\beta }_2^2\right){\hat{\omega }}^2}-\frac{4\gamma \left(-2+{\beta }_1\cot \left[\frac{{\beta }_1}{2}\right]\right)\tanh \left[\frac{\gamma }{2}\right]}{{\beta }_1^2\left({\beta }_1^2+{\beta }_2^2\right)}-\frac{4{\beta }_1^2{\gamma }^3\left(-2+{\beta }_2\coth \left[\frac{{\beta }_2}{2}\right]\right)\tanh \left[\frac{\gamma }{2}\right]}{{\beta }_2^2\left({\beta }_1^2+{\beta }_2^2\right){\hat{\omega }}^2}-\frac{4{\gamma }^5\left(-2+{\beta }_2\coth \left[\frac{{\beta }_2}{2}\right]\right)\tanh \left[\frac{\gamma }{2}\right]}{{\beta }_2^2\left({\beta }_1^2+{\beta }_2^2\right){\hat{\omega }}^2}-\frac{4\gamma \left(-2+{\beta }_2\coth \left[\frac{{\beta }_2}{2}\right]\right)\tanh \left[\frac{\gamma }{2}\right]}{{\beta }_2^2\left({\beta }_1^2+{\beta }_2^2\right)}\right\},$ and therefore a frequency characteristic equation establishes the function relation between the cable tension H* and the dimensionless frequency {circumflex over (ω)} of the stay cable, wherein P=P({circumflex over (ω)}, H*, EA, m, l, EI, θ).

5. The cable tension calculation method simultaneously considering the sag, inclination angle and bending stiffness of claim 4, wherein a root of P=P({circumflex over (ω)}, H*, EA, m, l, EI, θ) is solved by a trust region dogleg method, to identify the dimensionless frequency {circumflex over (ω)}, such that the cable tension H* of the stay cable is solved.

6. The cable tension calculation method simultaneously considering the sag, inclination angle and bending stiffness of claim 4, wherein for a specific stay cable, the tensile rigidity EA, the mass per unit length m, the cable length l, the bending stiffness EI and the inclination angle θ in the frequency characteristic equation in step 4 are all constants, and therefore the cable tension H* of the stay cable is uniquely determined by the dimensionless frequency {circumflex over (ω)}.

7. The cable tension calculation method simultaneously considering the sag, inclination angle and bending stiffness of claim 1, wherein testing the acceleration response of the stay cable by the acceleration sensor in step 3 comprises: arranging a vibration string type acceleration response sensor near a middle span of the stay cable to test the acceleration response of the stay cable under excitation of an environment, converting an acceleration signal into an electric signal to be transmitted, transmitting, by a network cable, the electric signal to an external working station through a data acquisition instrument, and. summarizing, by the external working station, data to remotely transmit a data file back to a database for storage.

8. The cable tension calculation method simultaneously considering the sag, inclination angle and bending stiffness of claim 7, wherein the vibration string type acceleration response sensor uses a DH610J type voltage output type acceleration sensor.

9. The cable tension calculation method simultaneously considering the sag, inclination angle and bending stiffness of claim I, wherein the dimensionless frequency of each order of the stay cable in step 5 is identified by Fourier transform.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0027] FIG. 1 is a schematic diagram of implementation steps of proposed cable tension calculation method simultaneously considering the sag, inclination angle and bending stiffness provided in the present invention.

[0028] FIG. 2 is a layout diagram of an acceleration sensor for a stay cable provided in an example of the present invention.

[0029] FIG. 3 is a schematic diagram of an actual measurement of an acceleration response of a stay cable provided in an example of the present invention.

[0030] FIG. 4 is a schematic diagram of a frequency identification result of an acceleration response of a stay cable provided in an example of the present invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0031] A particular embodiment of the present invention is described in detail below in combination with FIGS. 1-4, but it should be understood that the scope of protection of the present invention is not limited by the particular embodiment.

[0032] In a long-term service process, under a coupling action of internal and external factors, performance deterioration and resistance attenuation of the stay cables are inevitably generated. According to display of replacement cases, most of the stay cables will have common problems such as corrosion fatigue and damage of anchor devices, seriously threatening safety of bridges. As shown in FIG. 1, the present invention provides a cable tension calculation method synchronously considering the sag, inclination angle and bending stiffness. The method can calculate the cable tension of stay cables with high accuracy, and feed back to the bridge management department by means of a diagnosis and evaluation subsystem, thereby effectively serving maintenance and management work of bridges.

[0033] One end of the stay cable is fixed to a bearing plate in an anchorage area of a girder of the bridge, and one end of the stay cable is fixed in an anchor box of a tower. There is a certain inclination angle between the two ends. Generally, a long stay cable has an inclination angle between 20° and 40°, and a short stay cable may have a larger inclination angle. Moreover, under the action of gravity, an equilibrium position of stay cables is no longer like a straight line in an ideal state, but there is a certain sag, and a configuration of the stay cable in a static state is a catenary. Vibration of the stay cable is a small oscillation near the vibration equilibrium position. The bending stiffness of the stay cable has some influence on a motion state, especially in a boundary area of an anchorage end. Therefore, it is necessary to synchronously consider influences of the sag, inclination angle and bending stiffness to normally calculate the cable tension of stay cables.

[0034] In view of the above problem, the present invention provides a cable tension calculation method synchronously considering the sag, inclination angle and bending stiffness. The present invention is further described in detail below in combination with accompanying drawings and examples. It should be understood that the specific example described herein is merely illustrative of the present invention and is not intended to limit the present invention. A specific implementation process includes:

[0035] Step 1. query basic parameters of a stay cable according to design data or construction data, such as the cable length l, the mass per unit length m, the inclination angle θ and the bending stiffness EI. As shown in FIG. 2, the present invention selects 5 stay cables of a cable-supported bridge, Poyanghu Bridge. The basic parameters of the stay cables are as follows:

TABLE-US-00001 TABLE 1 Basic parameters of stay cables of bridge bending mass per Inclination As-built Serial Length stiffness unit length angle cable tension number (m) (N .Math. m.sup.2) (kg/m) (°) (kN) A22 201.117 1.84 × 10.sup.6 85.5 26.51 5630 B20 184.251 1.84 × 10.sup.6 85.5 27.31 5290 C14 131.148 1.84 × 10.sup.6 85.5 28.29 5120 C16 146.701 1.84 × 10.sup.6 85.5 26.23 4190 D08 86.711 9.10 × 10.sup.5 60.1 39.06 3510

[0036] Step 2, consider influences of sag, inclination angle and bending stiffness, to calculate three dimensionless parameters γ, εand λ.sup.2 influenced by the stay cable, the parameter γ being a dimensionless parameter related to the bending stiffness, the parameter ε being a dimensionless parameter related to the inclination angle, and the parameter λ.sup.2 being a dimensionless parameter related to the sag. Calculation methods of the three dimensionless parameters are as follows:

γ=l√{square root over (H*/EI)}

ε=ξ sin θ

λ.sup.2=δξ{circumflex over (L)}.sub.e

[0037] In the example, the dimensionless parameters are functions of the cable length l, the cable tension H*, the tensile rigidity EA, the inclination angle θ and the bending stiffness EI respectively, i.e., γ=γ(l,H*,EI), ε=ε(m,l,H*,θ) and λ=λ(EA,H*,m,l). A specific calculation result is as shown in Table 2:

TABLE-US-00002 TABLE 2 Dimensionless parameter calculation result Serial Dimensionless Dimensionless Dimensionless number parameter γ parameter ε parameter λ.sup.2 A22 354.18 0.0132 0.3244 B20 314.53 0.0132 0.3282 C14 219.88 0.0101 0.1852 C16 222.83 0.0128 0.4193 D08 171.08 0.0091 0.0876

[0038] Step 3, test the acceleration response of the stay cable by means of an acceleration sensor. The frequency ω can be identified by the acceleration response, and further calculate a dimensionless frequency {circumflex over (ω)} of the stay cable as follows:

{circumflex over (ω)}=ωl.sup.2√{square root over (m/EI)}

[0039] A specific implementation process for this example is as follows: an acceleration response sensor is arranged near the middle span of the stay cable, and the acceleration response of the stay cable is tested under excitation of an environment, an acceleration signal is converted into an electrical signal to be transmitted, the electric signal is transmitted to an external working station by a network cable through a data acquisition instrument, and the external working station summarizes data and then transmits a data file back to a database for storage. The specifications of the acceleration sensor is a DH610J voltage output type acceleration sensor. This sensor is suitable for occasions having low frequency and low-amplitude vibration measurement. A typical measurement result is shown in FIG. 3. In the example, the stay cable A22 is used as an example, Fourier transform is used for identifying the frequency of the stay cable. The frequency identification result of each order is shown in FIG. 4,

[0040] Step 4, substitute the above parameters into a vibration characteristic equation of the stay cable to establish a function relation between the dimensionless frequency {circumflex over (ω)} and a cable tension H* of the stay cable:

[00004]$P\left(\hat{\omega },\lambda ,\gamma ,\epsilon \right)=\frac{\frac{1}{2{\lambda }^2{\gamma }^4}\left({\lambda }^2{\gamma }^2-{\hat{\omega }}^2\right)}{\frac{{\beta }_2\tan \left[\frac{{\beta }_1}{2}\right]-{\beta }_1\tanh \left[\frac{{\beta }_2}{2}\right]}{{\beta }_1{\beta }_2\left({\beta }_1^2+{\beta }_2^2\right)}+\frac{\tanh \left[\frac{\gamma }{2}\right]}{{\gamma }^3}-{\epsilon }^2\frac{\Omega \left(\gamma ,\hat{\omega }\right)}{2{\gamma }^2}}1=0$

[00005]${\beta }_1=\sqrt{-\frac{{\gamma }^2}{2}+\sqrt{\frac{{\gamma }^4}{4}+\widehat{{\omega }^2}}},\mathrm{and}{\beta }_2=\sqrt{\frac{{\gamma }^2}{2}+\sqrt{\frac{{\gamma }^4}{4}+\widehat{{\omega }^2}}}.$

Ω(γ,{circumflex over (ω)}) is a high-order nonlinear term, which is a function of the dimensionless parameters γ, the dimensionless frequency {circumflex over (ω)}. A specific calculation equation of Ω(γ,{circumflex over (ω)}) is as follows:

[00006]$\Omega \left(\gamma ,\hat{\omega }\right)=\left\{\frac{1}{3}+\frac{2{\gamma }^2\left(-2+{\beta }_1\cot \left[\frac{{\beta }_1}{2}\right]\right)}{{\beta }_1^2\left({\beta }_1^2+{\beta }_2^2\right)}+\frac{2{\gamma }^2\left(-2+{\beta }_2\coth \left[\frac{{\beta }_2}{2}\right]\right)}{{\beta }_2^2\left({\beta }_1^2+{\beta }_2^2\right)}-\frac{3\left(-2+\mathrm{\gamma cot}\left[\frac{\gamma }{2}\right]\right)}{{\gamma }^2}+\frac{4\gamma \left(\gamma -2\tanh \left[\frac{\gamma }{2}\right]\right)}{{\hat{\omega }}^2}+\frac{\left(-4\gamma +\left(8+{\gamma }^2\right)\tanh \left[\frac{\gamma }{2}\right]\right)}{{\gamma }^3}+\frac{4{\beta }_2^2{\gamma }^3\left(-2+{\beta }_1\cot \left[\frac{{\beta }_1}{2}\right]\right)\tanh \left[\frac{\gamma }{2}\right]-4{\gamma }^5\left(-2+{\beta }_1\cot \left[\frac{{\beta }_1}{2}\right]\right)\tanh \left[\frac{\gamma }{2}\right]}{{\beta }_1^2\left({\beta }_1^2+{\beta }_2^2\right){\hat{\omega }}^2}-\frac{4\gamma \left(-2+{\beta }_1\cot \left[\frac{{\beta }_1}{2}\right]\right)\tanh \left[\frac{\gamma }{2}\right]}{{\beta }_1^2\left({\beta }_1^2+{\beta }_2^2\right)}-\frac{4{\beta }_1^2{\gamma }^3\left(-2+{\beta }_2\coth \left[\frac{{\beta }_2}{2}\right]\right)\tanh \left[\frac{\gamma }{2}\right]}{{\beta }_2^2\left({\beta }_1^2+{\beta }_2^2\right){\hat{\omega }}^2}-\frac{4{\gamma }^5\left(-2+{\beta }_2\coth \left[\frac{{\beta }_2}{2}\right]\right)\tanh \left[\frac{\gamma }{2}\right]}{{\beta }_2^2\left({\beta }_1^2+{\beta }_2^2\right){\hat{\omega }}^2}-\frac{4\gamma \left(-2+{\beta }_2\coth \left[\frac{{\beta }_2}{2}\right]\right)\tanh \left[\frac{\gamma }{2}\right]}{{\beta }_2^2\left({\beta }_1^2+{\beta }_2^2\right)}\right\}$ [0041] therefore a frequency characteristic equation establishes the function relation between the cable tension H* and the dimensionless frequency {circumflex over (ω)} of the stay cable, i.e.,

P=P({circumflex over (ω)},H*,EA,m,l,EI,θ)

[0042] Step 5, solve the root of the vibration characteristic equation, and identify the cable tension of the stay cable according to the root: For a specific stay cable, the tensile rigidity EA, the mass m per unit length, the cable length l, the bending stiffness EI and the inclination angle θ in the frequency characteristic equation in step 4 are all constants, and therefore the cable tension H* of the stay cable is uniquely determined by the dimensionless frequency {circumflex over (ω)}. a trust region dogleg method is used for identifying a root of P=0 in the present invention. Since the stay cable has an infinite-order natural vibration frequency, the dimensionless frequency of each order of the stay cable may be used for calculating the cable tension. In practice, a first-order frequency is generally selected to calculate the cable tension. The first-order frequency of each stay cable test and a result of calculating the cable tension of the stay cable are shown in Table 3. The calculated error are shown in the corresponding brackets:

TABLE-US-00003 TABLE 3 Cable tension identification result of the present invention and string vibration theory identification result (errors in brackets, %) Cable tension String vibration Tested calculation result and theory cable first-order error of the method of tension calculation Serial frequency the present invention result and error number (Hz) (kN) (kN) A22 0.656 5728 (1.74) 5953 (5.73) B20 0.701 5498 (3.93) 5705 (7.84) C14 0.963 5328 (4.06) 5459 (6.62) C16 0.779 4269 (1.88) 4465 (6.56) D08 1.403 3499 (0.31) 3558 (1.37)

[0043] The result shows that the method of the present invention has higher identification accuracy, a maximum error is 4.06%, may be controlled within 5%, and satisfies engineering requirements compared with the string theory method. The calculated error of the string theory is generally greater than 5% of error. The maximum error is 7.84%. The calculation result influences the bridge management department to correctly evaluate the working state of the stay cable.

[0044] Another feature of the present invention is that for the same stay cable, the accuracy of calculating the cable tension by the high-order frequency has been greatly improved. As shown in Table 4, the result of calculating the cable tension by each order frequency of the No. A22 cable have higher accuracy than that of a traditional string theory. The calculated error is less than 5%. An error of calculating the cable tension by the string vibration theory is generally 5% or above, and the higher the frequency order is, the greater the error is.

TABLE-US-00004 TABLE 4 Calculation result of cable tension at each order frequency of stay cable No. A22 (error in brackets, %) Cable tension String vibration Tested calculation result and theory cable each order error of the method of tension calculation Frequency frequency the present invention result and error order (Hz) (kN) (kN) 1 0.656 5728 (1.74) 5953 (5.73) 2 1.304 5787 (2.79) 5863 (4.14) 3 1.961 5834 (3.63) 5917 (5.10) 4 2.619 5859 (4.07) 5944 (5.58) 5 3.275 5824 (3.45) 5913 (5.03) 6 3.934 5862 (4.12) 5956 (5.79) 7 4.595 5843 (3.78) 5943 (5.56) 8 5.244 5874 (4.33) 5980 (6.22) 9 5.922 5855 (4.00) 5969 (6.02) 10 6.279 5867 (4.21) 5989 (6.38) 11 7.249 5867 (4.21) 5999 (6.55) 12 7.910 5866 (4.19) 6008 (6.71) 13 8.575 5860 (4.09) 6013 (6.80) 14 9.239 5884 (4.51) 6049 (7.44) Average 5846.20 (3.84) 5970.53 (6.05)

[0045] The present invention discloses the cable tension calculation method simultaneously considering triple effects of the sag, inclination angle and bending stiffness, The method specifically includes: query the basic parameters of the stay cable according to the design data or the construction data; consider the influences of the sag, inclination angle and bending stiffness, to calculate the three dimensionless parameters influenced by the stay cable; test the acceleration response of the stay cable by acceleration sensors, to identify the frequency of the acceleration response of the stay cable, and further calculate the dimensionless frequency of the stay cable; substitute the above parameters into the vibration characteristic equation of the stay cable, to establish the function relation between the dimensionless frequency and the cable tension of the stay cable; and solve the root of the vibration characteristic equation, and identify the cable tension of the stay cable according to the root. Compared with a traditional cable tension calculation method, the method has higher calculation accuracy since the present invention simultaneously considers the influences of the sag, the inclination angle and the bending stiffness, and an error may be controlled within 5%, and satisfies actual engineering requirements, thereby providing a reliable method for accurate calculation of the cable tension of the stay cable. The calculation result may provide a reference basis for a bridge management department to manage and maintain the stay cable.

[0046] The present invention provides the cable tension calculation method simultaneously considering the sag, inclination angle and bending stiffness, which solves the problem of an error and insufficient accuracy in cable tension calculation of the stay cable. Compared with an existing method, the method breaks through limitations to calculate the cable tension in the prior art, which not only improves accuracy of calculating the cable tension by using a fundamental frequency, but also improves accuracy of calculating the cable tension by using the high-order frequencies, thereby creating conditions for identification of an actual cable tension of the stay cable in bridge engineering.

[0047] The embodiment of the present invention is described in detail above in combination with the accompanying drawings, but the present invention is not limited to the above embodiment, various changes can further be made within the scope of knowledge possessed by those of ordinary skill in the art without departing from the spirit of the present invention, and any changes that can be conceived by those skilled in the art shall fall within the scope of protection of the present invention.