CN105320596A - Bridge deflection test method based on inclinometers and system thereof - Google Patents

Abstract

The invention discloses a bridge deflection test method based on inclinometers. The bridge deflection test method comprises the following steps: an inclination measurement step for measuring the cross section corners of a bridge by setting the inclinometers at a plurality of cross section positions of the bridge so as to obtain the corner values of the inclinometers; a deflection test step for obtaining the combination coefficient of an n-order vibration type based on the difference of corner values collected by each inclinometer at the same moment and the initial corner value of each inclinometer and calculating to obtain bridge deflection based on the combination coefficient. The invention also discloses a bridge deflection test system based on the inclinometers.

Description

A kind of bridge deflection test method based on inclinator and system thereof

Technical field

The present invention relates to a kind of method of testing of deflection of bridge span, be applicable to the deflection test of any spanning length any position, belong to Bridge Inspection field, specifically relate to a kind of high precision in bridge machinery process and high efficiency bridge deflection test method.

Background technology

In Bridge Detection Experiment, need measure deflection of bridge span, the evaluation of the accuracy direct relation bridge state of its deflection metrology data, meanwhile, bridge machinery ageing requires high.Therefore, in bridge machinery process, high precision and high efficiency deflection of bridge span test macro seem most important.In prior art, the on-the-spot test of deflection of bridge span is generally adopted with the following method: 1, adopt the optical gauges such as spirit-leveling instrument to measure deflection of bridge span, although easy and simple to handle, but measuring accuracy is low, measurement result is comparatively large by man's activity interference, and cannot be applicable to the test of bridge dynamic deflection, error is larger.2, the displacement such as dial gauge, clock gauge measurement examination deflection of bridge span is adopted, framing scaffold need be set up below beam body, to install deflection test instrument on framing scaffold, but when setting up framing scaffold under bridge, there is complex procedures, waste time and energy, and there is larger potential safety hazard in higher framing scaffold, itself rock the test result that also can affect deflection of bridge span with bottom non-uniform settling.3, photoelectric image principle is used, by the picture signal gathered, adopt data processing method, draw the deflection value of bridge, as application number be 200710103777.0, publication number is CN101055218, name is called the Chinese invention patent application of " monitoring device of deflection of bridge span and displacement and monitoring method ", its principle of work is complicated, image data acquiring is subject to the restriction of the specified conditions such as weather, light, data processing complex, and cost is higher, precision is lower, actual poor operability.4, based on connecting pipe principle, change according to the liquid level in open communicating pipe directly measures deflection of bridge span, the method principle is simple, but due to the viscosity resistance between liquid and tube wall and the capillary action between water and tube wall, cause measuring accuracy not high, and the test of bridge dynamic deflection cannot be applicable to.5, based on connecting pipe principle, directly amount of deflection is converted into the pressure of liquid in pipe, pressure unit is adopted to change pressure change the change of amount of deflection into, if the patent No. is 200310108447.2, Authorization Notice No. is CN100385201C, name is called the Chinese invention patent of " Large Span Bridges deflection monitoring method ", its theoretical method has feasibility, but in actual mechanical process especially when bridge span is comparatively large or measuring point is more, viscosity resistance is produced due to the relative flowing between liquid in pipe with tube wall, the pressure of liquid has loss to a certain degree, cause measuring accuracy lower, the test of bridge dynamic deflection cannot be applicable to simultaneously.

Therefore, there is following defect in existing highway bridge deflection test device: 1, measuring accuracy is low, and error is larger; 2, proving installation is installed complicated, and data acquisition is more complicated, and cost of labor is high, inefficiency; 3, the detection of bridge dynamic deflection and deflection of bridge span such as leap great river and Grand Canyon etc. cannot be applicable to.

Summary of the invention

The object of the present invention is to provide a kind of bridge deflection test method based on inclinator and system thereof, low to solve prior art Bridge deflection test precision, error is large, and proving installation is installed complicated, the problem that data acquisition efficiency is low.

For reaching above-mentioned purpose, the present invention proposes a kind of bridge deflection test method based on inclinator, comprising:

Measurement of dip angle step: by arranging inclinator in multiple sectional positions of test bridge, carrying out the measurement of the sectional twisting angle of bridge, obtaining the corner numerical value of described inclinator;

Deflection test step: the difference of the corner numerical value collected at synchronization based on each described inclinator and the initial corner value of inclinator described in each obtains the combination coefficient of a n first order mode, and calculate based on described combination coefficient and obtain deflection of bridge span.

The above-mentioned bridge deflection test method based on inclinator, described multiple sectional position is: beam-ends, 1/4 across, span centre and 3/4 across.

The above-mentioned bridge deflection test method based on inclinator, described deflection of bridge span is calculated by following formula and obtains:

Wherein, A _ifor described combination coefficient, it is the i-th first order mode.

The above-mentioned bridge deflection test method based on inclinator, described combination coefficient A _icalculated by following formula and obtain:

$A_i=\frac{P_i}{{\mathrm{\ω}}_i^2{M}_i}$

Wherein, described P _iand M _ibe respectively the i-th first order mode power and vibration shape quality, described ω _ifor the i-th rank natural frequency of vibration of bridge structure;

Described P _icomputing formula be:

Described M _icomputing formula be:

Wherein, described p (x) is evenly load, and described m (x) is modal mass, it is the i-th first order mode.

The above-mentioned bridge deflection test method based on inclinator, described i-th first order mode can be by trigonometric series:

Wherein, described b _nfor constant coefficient, L is bridge span, and variable n is the maximum order of the i-th first order mode.

The above-mentioned bridge deflection test method based on inclinator, based on described combination coefficient A _iwith described i-th first order mode described in the bridge at distance beam-ends x place, the computing formula of amount of deflection is:

$u\left(x\right)=\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{c}_i\·\sin \frac{\mathrm{i\πx}}{L}(i=\mathrm{1,2},...4)$

Described c _icomputing formula be: $\underset{i=1}{\overset{4}{\mathrm{\Σ}}}\frac{\mathrm{i\π}{c}_i}{L}\·\cos \frac{\mathrm{i\πx}}{L}={\mathrm{\θ}}_i(i=\mathrm{1,2},...4),$ Wherein, described θ _i(i=1,2,3 ... 5) be the difference of the inclination value of being surveyed by described inclinator and initial reading.

The present invention also provides a kind of deflection of bridge span test macro based on inclinator, adopt as described in based on the bridge deflection test method of inclinator, comprising:

Measurement of dip angle module: by arranging inclinator in multiple sectional positions of test bridge, carrying out the measurement of the sectional twisting angle of bridge, obtaining the corner numerical value of described inclinator;

Deflection test module: the difference of the corner numerical value collected at synchronization based on each described inclinator and the initial corner value of inclinator described in each obtains the combination coefficient of a n first order mode, and calculate based on described combination coefficient and obtain deflection of bridge span.

The above-mentioned deflection of bridge span test macro based on inclinator, described multiple sectional position is: beam-ends, 1/4 across, span centre and 3/4 across.

The above-mentioned deflection of bridge span test macro based on inclinator, described deflection of bridge span is calculated by following formula and obtains:

Wherein, A _ifor described combination coefficient, it is the i-th first order mode.

The above-mentioned deflection of bridge span test macro based on inclinator, described combination coefficient A _icalculated by following formula and obtain:

$A_i=\frac{P_i}{{\mathrm{\ω}}_i^2{M}_i}$

Wherein, described P _iand M _ibe respectively the i-th first order mode power and vibration shape quality, described ω _ifor the i-th rank natural frequency of vibration of bridge structure;

Described P _icomputing formula be:

Described M _icomputing formula be:

Wherein, described p (x) is evenly load, and described m (x) is modal mass, it is the i-th first order mode.

The above-mentioned deflection of bridge span test macro based on inclinator, described i-th first order mode can be by trigonometric series:

Wherein, described b _nfor constant coefficient, L is bridge span, and variable n is the maximum order of the i-th first order mode.

The above-mentioned deflection of bridge span test macro based on inclinator, based on described combination coefficient A _iwith described i-th first order mode described in the bridge at distance beam-ends x place, the computing formula of amount of deflection is:

$u\left(x\right)=\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{c}_i\·\sin \frac{\mathrm{i\πx}}{L}(i=\mathrm{1,2},...4)$

Described c _icomputing formula be: $\underset{i=1}{\overset{4}{\mathrm{\Σ}}}\frac{\mathrm{i\π}{c}_i}{L}\·\cos \frac{\mathrm{i\πx}}{L}={\mathrm{\θ}}_i(i=\mathrm{1,2},...4),$ Wherein, described θ _i(i=1,2,3 ... 5) be the difference of the inclination value of being surveyed by described inclinator and initial reading.

Compared to method of the prior art, the main beneficial effect of the present invention is:

1, principle of work is simple, and theoretical foundation is reliable, is not subject to the impact of bridge structure form and bridge changes of section, is applicable to the deflection test of any span bridge any position.

2, use easy and simple to handle, test macro each several part composition in-site installation is convenient, and test job efficiency is high, and measuring accuracy is high, and data acquisition is convenient.

3, test macro is not subject to the restriction of span and field working conditions, can be applicable to the test of crossing over the deflection of bridge span such as great river and Grand Canyon.

Accompanying drawing explanation

Fig. 1 is the bridge deflection test method step schematic diagram that the present invention is based on inclinator;

Fig. 2 is the deflection of bridge span test system structure block diagram that the present invention is based on inclinator;

Fig. 3 is the deflection of bridge span test macro application schematic diagram that the present invention is based on inclinator.

Wherein, Reference numeral:

1 measurement of dip angle module 2 deflection test module

S1 ~ S2: the administration step of various embodiments of the present invention

Embodiment

Describe the present invention below in conjunction with the drawings and specific embodiments, but not as a limitation of the invention.

The invention provides a kind of bridge deflection test method based on corner, be the change of deflection of bridge span by the corner change transitions in bridge cross section, namely arrange that sectional twisting angle measured by inclinator in 5 cross sections of bridge, (electricity) signal of change of pitch angle is sent to acquisition system in time by signal cable, utilize cross section inclination value to extrapolate the mathematical relation formula of deflection of bridge span and corner, and then extrapolate the amount of deflection at any position place.The present invention is easy to operation and test data is accurate, measures efficiency high, and stable and reliable for performance, not by the impact of bridge structure form and bridge changes of section, can solve and cross over the deflection of bridge span such as great river and Grand Canyon and test the problems such as difficult, measure data precision is poor.

The inventive method obtains the combination coefficient of 4 first order modes by the system of equations solving synchronization and be made up of the difference of diverse location inclinator reading and initial reading, then calculates deflection of bridge span equation, finally determines the deflection value of spanning any position.

In order to eliminate the impact of bridge structure form and bridge changes of section, adopting the bridge Mode Equation in Structural Dynamics, simplifying and utilizing bridge sectional twisting angle to change the formula solving deflection equation.

As shown in Figure 1, a kind of bridge deflection test method based on inclinator provided by the invention, comprising:

Measurement of dip angle step S1: by arranging inclinator in multiple sectional positions of test bridge, carrying out the measurement of the sectional twisting angle of bridge, obtaining the corner numerical value of inclinator; Deflection test step S2: the difference of the corner numerical value collected at synchronization based on each inclinator and the initial corner value of each inclinator obtains the combination coefficient of a n first order mode, and calculate based on combination coefficient and obtain deflection of bridge span.

Below in conjunction with the drawings and specific embodiments, the specific embodiment of the invention is described in further detail:

In specific embodiment, the range of inclinator sensor is-3.00 × 10 ^-4rad ~ 3.00 × 10 ^-4rad, the measuring accuracy of inclinator chooses 10 ^-6rad can meet actual test request, and the displacement measurement precision of its correspondence is 0.01mm.

In inclinator bridge deflection test method, across sectional position mounted angle instrument, and be connected to deflection of bridge span test macro across, span centre and 3/4 at test bridge beam end, 1/4.

In inclinator bridge deflection test method, to be the mechanism of deflection of bridge span change be test bridge sectional twisting angle change transitions: for beam-ends, 1/4 across, span centre and 3/4 across inclinator initial reading, u (x) is the deflection of bridge span apart from beam-ends x place, for bridge is by after external load effect generation deflection deformation, beam-ends, 1/4 across, span centre and 3/4 across inclinator reading.When bridge is by external load generation deflection deformation:

${\mathrm{\θ}}_i={\mathrm{\θ}}_i^1-{\mathrm{\θ}}_i^0(i=\mathrm{1,2,3},...5)---\left(1\right)$

In above formula, θ _i(i=1,2,3 ... 5) for beam-ends before and after distortion, 1/4 across, span centre and 3/4 across the difference of inclinator reading.

From Structural Dynamics, under evenly load p (x) effect, bridge deflection curve can be expressed as the superposition of the multistage vibration shape, that is:

In above formula, and A _ibe respectively the i-th first order mode and its combination coefficient.A _ican be expressed as:

$A_i=\frac{P_i}{{\mathrm{\ω}}_i^2{M}_i}---\left(3\right)$

In above formula, L is bridge span, and m (x) is modal mass, ω _ifor the i-th rank natural frequency of vibration of structure; P _iand M _ibe respectively the i-th first order mode power and vibration shape quality.

The natural mode of vibration of beam body can be write as following trigonometric series form:

In above formula, b _nfor constant coefficient, L is bridge span, and variable n is the maximum order of the i-th first order mode.

By in formula (6) substitution formula can obtain in (4):

$P_i=\underset{0}{\overset{L}{\∫}}p\left(x\right)\underset{n}{\mathrm{\Σ}}{b}_n\·\sin \frac{\mathrm{n\πx}}{L}\mathrm{dx}=\underset{n}{\mathrm{\Σ}}{b}_n\·\underset{0}{\overset{L}{\∫}}p\left(x\right)\sin \frac{\mathrm{n\πx}}{L}\mathrm{dx}---\left(7\right)$

Within the unit interval, the expression formula of p (x) is fixing, and do not change with the position of acting force in time, therefore, formula (7) can be reduced to:

$P_i=\underset{n}{\mathrm{\Σ}}{b}_n\·p\left(x\right)\underset{0}{\overset{L}{\∫}}\sin \frac{\mathrm{n\πx}}{L}\mathrm{dx}=-\frac{\underset{n}{\mathrm{\Σ}}{b}_n\·\stackrel{\‾}{p}\·L}{\mathrm{n\π}}---\left(8\right)$

In above formula, for acting on the concentrated force equivalence value of beam body in the unit time, L is bridge span.

Each rank circular frequency ω of bridge structure _ibe generally constant, by formula (6) substitution formula can obtain in (5):

Simplified by modal mass, therefore, formula (9) can be reduced to:

$M_i=\underset{n}{\mathrm{\Σ}}{b}_n^2\underset{0}{\overset{L}{\∫}}m\left(x\right){\sin }^2\left(\frac{\mathrm{n\πx}}{L}\right)\mathrm{dx}=\frac{\underset{n}{\mathrm{\Σ}}{b}_n^2\stackrel{\‾}{m}L}{2}---\left(10\right)$

In above formula, for beam body linear mass.

By formula (6), formula (8), formula (10) and ω _iin substitution formula (2), can obtain:

$u\left(x\right)=\underset{i=1}{\overset{\∞}{\mathrm{\Σ}}}\frac{-\frac{\underset{n}{\mathrm{\Σ}}{b}_n\·\stackrel{\‾}{p}\·L}{\mathrm{n\π}}}{{\mathrm{\ω}}_i\·\frac{\underset{n}{\mathrm{\Σ}}{b}_n^2\stackrel{\‾}{m}L}{2}}\·(\underset{n}{\mathrm{\Σ}}{b}_n\·\sin \frac{\mathrm{n\πx}}{L})---\left(11\right)$

In above formula, except sin (n π x/L), for except x function, all the other are constant, with c _ireplace, therefore, formula (11) can be reduced to:

$u\left(x\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{c}_i\·\sin \frac{\mathrm{i\πx}}{L}---\left(14\right)$

The inclination angle equation of beam body section to be differentiated to x by formula (12) and is obtained:

$u^{\′}\left(x\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{\mathrm{i\π}{c}_i}{L}\cos \frac{\mathrm{i\πx}}{L}---\left(13\right)$

Specific embodiments of the invention only consider 4 rank mode, namely get n=4, and the present invention is not as limit.According to the inclination value of actual measurement and the difference θ of initial reading _i(i=1,2,3 ... 5) system of equations of 5 equation compositions can, be set up;

$\underset{i=1}{\overset{4}{\mathrm{\Σ}}}\frac{\mathrm{i\π}{c}_i}{L}\·\cos \frac{\mathrm{i\πx}}{L}={\mathrm{\θ}}_i(i=\mathrm{1,2},...4)---\left(14\right)$

Solving equation group, can obtain c _i(i=1,2 ... 4), by c _i(i=1,2 ... 4) substitute in formula (12), can apart from the deflection of bridge span equation at beam-ends x place.

$u\left(x\right)=\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{c}_i\·\sin \frac{\mathrm{i\πx}}{L}(i=\mathrm{1,2},...4)---\left(15\right)$

Said process shows, in test process, utilizes deflection testing system record not sectional twisting angle in the same time, namely obtains the deflection of bridge span equation apart from beam-ends x place by solving equation group.

This method of testing can be used for deflection test in bridge machinery and the long-term amount of deflection of bridge health monitoring process Bridge and linear monitoring and test.The present invention can also have other embodiment, and the technical scheme that all employings are replaced on an equal basis or equivalent transformation is formed, all drops within the scope of protection of present invention.

The present invention also provides a kind of deflection of bridge span test macro based on inclinator, adopt as described in based on the bridge deflection test method of inclinator, as shown in Figure 2, comprising:

Measurement of dip angle module 10: inclinator is set in multiple sectional positions of test bridge, carries out the measurement of the sectional twisting angle of bridge, obtain the corner numerical value of inclinator;

Deflection test module 20: the difference of the corner numerical value collected at synchronization based on each inclinator and the initial corner value of each inclinator obtains the combination coefficient of a n first order mode, obtains deflection of bridge span based on combination coefficient.

Specific embodiment of the invention systematic difference as shown in Figure 3, comprises multiple inclinator 1, connects wire 2 and deflection of bridge span test 3.Wherein multiple inclinator 1 is arranged at the beam-ends a1,1/4 of bridge across b, span centre c and 3/4 cross-location d, beam-ends a2, when bridge generation deflection deformation, the change of bridge sectional twisting angle is reflected in the change of inclinator 1 reading, and is input in deflection of bridge span test macro 3 by wire 2.The system of equations be made up of the difference of diverse location inclinator reading and initial reading by solving synchronization obtains the combination coefficient of 4 first order modes, and then calculates deflection of bridge span equation.

In sum, the object of this invention is to provide a kind of high precision, high-level efficiency and the strong bridge deflection test method of applicability and system thereof, the method overcome the deficiency that existing deflection test method cannot be applicable to cross over the detection of the deflection of bridge span such as great river and Grand Canyon, by arranging that sectional twisting angle measured by inclinator in 5 cross sections of bridge, the electric signal of inclinator collection is sent to deflection testing system in time by signal cable, utilize cross section inclination value change to extrapolate the mathematical relation formula of deflection of bridge span and corner, and then extrapolate the amount of deflection at diverse location place.This method not only measuring accuracy is high, and applicability is strong, easy to operate, is not subject to the impact of bridge structure form and bridge changes of section, has higher practical value.

Certainly; the present invention also can have other various embodiments; when not deviating from the present invention's spirit and essence thereof; those of ordinary skill in the art are when making various corresponding change and distortion according to the present invention, but these change accordingly and are out of shape the protection domain that all should belong to the claim appended by the present invention.

Claims (12)

1. based on a bridge deflection test method for inclinator, it is characterized in that, comprising:

Measurement of dip angle step: by arranging inclinator in multiple sectional positions of test bridge, carrying out the measurement of the sectional twisting angle of bridge, obtaining the corner numerical value of described inclinator;

Deflection test step: the difference of the corner numerical value collected at synchronization based on each described inclinator and the initial corner value of inclinator described in each obtains the combination coefficient of a n first order mode, and calculate based on described combination coefficient and obtain deflection of bridge span.

2. according to claim 1 based on the bridge deflection test method of inclinator, it is characterized in that, described multiple sectional position is: beam-ends, 1/4 across, span centre and 3/4 across.

3. according to claim 1 based on the bridge deflection test method of inclinator, it is characterized in that, described deflection of bridge span is calculated by following formula and obtains:

Wherein, A _ifor described combination coefficient, it is the i-th first order mode.

4. according to claim 1 or 3 based on the bridge deflection test method of inclinator, it is characterized in that, described combination coefficient A _icalculated by following formula and obtain:

$A_i=\frac{P_i}{{\mathrm{\ω}}_i^2{M}_i}$

Wherein, described P _iand M _ibe respectively the i-th first order mode power and vibration shape quality, described ω _ifor the i-th rank natural frequency of vibration of bridge structure;

Described P _icomputing formula be:

Described M _icomputing formula be:

Wherein, described p (x) is evenly load, and described m (x) is modal mass, it is the i-th first order mode.

5. according to claim 3 based on the bridge deflection test method of inclinator, it is characterized in that, described i-th first order mode can be by trigonometric series:

Wherein, described b _nfor constant coefficient, L is bridge span, and variable n is the maximum order of the i-th first order mode.

6. according to claim 5 based on the bridge deflection test method of inclinator, it is characterized in that, based on described combination coefficient A _iwith described i-th first order mode described in the bridge at distance beam-ends x place, the computing formula of amount of deflection is:

$u\left(x\right)=\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{c}_i\·\sin \frac{\mathrm{i\πx}}{L}(i=\mathrm{1,2},...4)$

Described c _icomputing formula be: $\underset{i=1}{\overset{4}{\mathrm{\Σ}}}\frac{\mathrm{i\π}{c}_i}{L}\·\cos \frac{\mathrm{i\πx}}{L}={\mathrm{\θ}}_i(i=\mathrm{1,2},...4),$ Wherein, described θ _i(i=1,2,3 ... 5) be the difference of the inclination value of being surveyed by described inclinator and initial reading.

7., based on a deflection of bridge span test macro for inclinator, employing based on the bridge deflection test method of inclinator, is characterized in that, comprising according to any one of claim 1-6:

Measurement of dip angle module: by arranging inclinator in multiple sectional positions of test bridge, carrying out the measurement of the sectional twisting angle of bridge, obtaining the corner numerical value of described inclinator;

Deflection test module: the difference of the corner numerical value collected at synchronization based on each described inclinator and the initial corner value of inclinator described in each obtains the combination coefficient of a n first order mode, and calculate based on described combination coefficient and obtain deflection of bridge span.

8. according to claim 7 based on the deflection of bridge span test macro of inclinator, it is characterized in that, described multiple sectional position is: beam-ends, 1/4 across, span centre and 3/4 across.

9. according to claim 7 based on the deflection of bridge span test macro of inclinator, it is characterized in that, described deflection of bridge span is calculated by following formula and obtains:

Wherein, A _ifor described combination coefficient, it is the i-th first order mode.

10. according to claim 7 or 9 based on the deflection of bridge span test macro of inclinator, it is characterized in that, described combination coefficient A _icalculated by following formula and obtain:

$A_i=\frac{P_i}{{\mathrm{\ω}}_i^2{M}_i}$

Wherein, described P _iand M _ibe respectively the i-th first order mode power and vibration shape quality, described ω _ifor the i-th rank natural frequency of vibration of bridge structure;

Described P _icomputing formula be:

Described M _icomputing formula be:

Wherein, described p (x) is evenly load, and described m (x) is modal mass, it is the i-th first order mode.

11., according to claim 9 based on the deflection of bridge span test macro of inclinator, is characterized in that, described i-th first order mode can be by trigonometric series:

Wherein, described bn is constant coefficient, and L is bridge span, and variable n is the maximum order of the i-th first order mode.

12., according to the deflection of bridge span test macro based on inclinator described in claim 11, is characterized in that, based on described combination coefficient A _iwith described i-th first order mode described in the bridge at distance beam-ends x place, the computing formula of amount of deflection is:

$u\left(x\right)=\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{c}_i\·\sin \frac{\mathrm{i\πx}}{L}(i=\mathrm{1,2},...4)$

The computing formula of described ci is: $\underset{i=1}{\overset{4}{\mathrm{\Σ}}}\frac{\mathrm{i\π}{c}_i}{L}\·\cos \frac{\mathrm{i\πx}}{L}={\mathrm{\θ}}_i(i=\mathrm{1,2},...4),$ Wherein, described θ _i(i=1,2,3 ... 5) be the difference of the inclination value of being surveyed by described inclinator and initial reading.