JPH09113250A - Instrument for measuring displacement of long object - Google Patents

Abstract

PROBLEM TO BE SOLVED: To find the displacement of a long object with accuracy by simplifying an arithmetic means and shortening the measuring time by sticking strain gauges to the boundary between each section formed on the outer or inner periphery of the long object along the axial center of the body and performing arithmetic operation by using a specific formula. SOLUTION: The curvature at the boundary between each section formed on a long object along the axis center is measured with strain gauges 111 -11n-1 . For each section, the displacement yi indicated by a polynomial yi =Σkαi Xi α and a plurality of continuous formulae, yi = yi+1 |Xi+1 =0},..., dα<-1> yi / dXi α<-1> = (dα<-1> yi+1 /dXi+1 α<-1> )|Xi+1 =0} are obtained against the coordinate Xn in the direction of the axial center having an origin at one end and a degree having a maximum value of 5-7. Then a coefficient calculating means 13 solves simultaneous equations from the formulae and displacement, inclination, and curvatures at both ends of the long object, and a boundary condition formula indicating (α+1) pieces of variations of the variations of the displacement, inclination, and curvatures and a displacement calculating means 15 obtains the displacement yi .

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a long body displacement measurement for obtaining a displacement caused by an external force in a hollow body having a length larger than a thickness or a long body made of a solid body and a distribution of the displacement along the axial center. Regarding the device.

[0002]

BACKGROUND OF THE INVENTION In rocks, embankments and structures, in general,
Due to natural conditions such as artificial excavation, loading, and penetration of rainwater, the load acting on each part varies, and the absolute shape changes. In addition, for hills, mountains, and artificially formed terrain, in order to detect the danger of landslides and landslides due to such loads, for example, insert type inclinometers and installation type hole Although an inclinometer is applied, the former requires a driving device when performing automatic measurement and is expensive, and there are restrictions on weather resistance and durability, and the latter measures the angle of inclination with respect to the axial direction of the hole. None of them were suitable for such applications because they required a large number of expensive sensors.

Further, as another similar technique, conventionally,
There is a pipe strain gauge that was applied to detect slip surfaces such as landslides. For such pipe strain gauges, in recent years, it has become possible to apply strain gauges that offer high performance at low cost, and when performing automatic measurement, high reliability is obtained without including mechanically movable members. In order to ensure high accuracy over a relatively long period of time, research on application and practical application of quantitative measurement of landslide behavior based on beam theory is under way.

In the conventional example to which such a pipe strain gauge is applied, the displacement (deflection) in each section along which the strain gauge is individually attached along the axis is, for example, on the section in the direction of the axis. Is approximated by a quintic equation of length. Furthermore, among these sections, displacement, inclination (deflection angle), curvature (moment), conversion rate of that curvature (shear force), and rate of change of shear force (external force) under the quintic equation in adjacent sections. The simultaneous equations consisting of boundary condition equations indicating that is continuous are the actual values of curvature obtained by each strain gauge, the boundary conditions of four items preset for the upper end and the lower end of the pipe, and these It is solved by applying the transfer matrix method together with the actual measurement values obtained by the auxiliary strain gauges individually provided in the section including the upper end and the section including the lower end. Since the solution thus obtained is the coefficient of each term of the above-mentioned polynomial, the displacement for each section can be obtained by setting these coefficients in the polynomial.

[0005]

However, in such a conventional example, the arithmetic operation for applying the actual measurement values obtained by the above-mentioned auxiliary strain gauge is performed in the same manner as the boundary condition expression described above. Since the calculation is applied, the procedure may be complicated and an error may occur. Further, in particular, in the process of arithmetic operation based on the transfer matrix method, since such an error greatly affects the accuracy of the operation, it has been desired to suppress it to a value as small as possible.

It is an object of the present invention to provide a long displacement measuring apparatus for accurately calculating displacement while simplifying the calculation procedure and shortening the time required for calculation. FIG. 1 is a principle block diagram of the invention according to claims 1 and 3. FIG.
It is a principle block diagram of the invention of Claims 2 and 3.

[0007]

Means for Solving the Problems The invention according to claim 1
Is a hollow body or solid body whose length is larger than its thickness.
On the outer or inner circumference of the elongated body along the axis of the elongated body.
Affixed individually to the boundaries of the created multiple n sections i (= 0 to (n-1))
And the curvature D at the boundaries of these sections_i Measure
Strain gauge 11₁~ 11_(n-1)For multiple sections
And coordinate X in the axial direction with one end as the origin_n And the maximum is
For order α that is either "5", "6", or "7"
The polynomial y_i= Σkα_iX_idisplacement y given by α_i Together with
Then, in the first-order to (α-1) th derivative of the polynomial
The values of each given expression are continuous at the boundary
That the length of the section L_i Multiple continuous expressions y shown below_i= {Y
_{i + 1}｜ X_{i + 1}= 0}, dy_i/ dX_i= {(Dy_{i + 1}/ dX_{i + 1}) ｜ X_{i + 1}= 0}
 , ..., dα^-1y_i/ dX_iα^-1＝ {(dα^-1y_{i + 1}/ dX_{i + 1} α^-1) ｜ X
_{i + 1}= 0} and the two outermost positions of these intervals
Each located at the end of the section and on the opposite side of the adjacent section
The variation given by these polynomials and their derivatives at one end
Position, inclination, curvature, and the rate of change of that curvature are predetermined
Boundary condition expression that shows (α + 1) combinations with known values
Coefficient kα_iMultiple simultaneous strain equations
11₁~ 11_(n-1)Curvature D individually measured by _i of
Half value is k_{2 (i + 1)}To solve the system of equations,
Coefficient calculating means 13 for obtaining these coefficients, k_{2 (i + 1)}of
Value and coefficient kα calculated by the coefficient calculation means 13_iWhen
Is applied to the polynomial, and the displacement y in the interval i_i To individually ask for
And a position calculating means 15.

According to a second aspect of the present invention, a plurality of sections i formed along the axis of the elongated body on the outer or inner circumference of the elongated body made of a hollow body or solid body having a length larger than the thickness. For the boundary of (= 0 to (n-1)), the database 21 in which the curvatures D _i measured individually beforehand are registered, and the coordinate X _n and the maximum value in the axial direction with one end as the origin for a plurality of sections. Where y is any one of “5”, “6”, and “7” and the displacement y _i given by the polynomial y _i = Σkα _i X _i α
In addition, a plurality of continuous expressions indicating under the interval length L _i that the values of the expressions respectively given by the first-order to (α−1) -th derivative of the polynomial are continuous at the boundary y _i
= {Y _{i + 1} | X _{i + 1} = 0}, dy _i / dX _i = {(dy _{i + 1} / dX _{i + 1} ) | X _{i + 1}
= 0}, ..., dα ^-1 y _i / dX _i α ^-1 = {(dα ^-1 y _{i + 1} / dX _{i + 1} α ^-1 )
| X _{i + 1} = 0} and given by these polynomials and their derivatives for the ends of the two outermost intervals of these intervals and the opposite ends of the adjacent intervals In the simultaneous equation of the coefficient kα _i consisting of displacement, inclination, curvature, and (α + 1) predetermined combinations of known values among the rates of change of the curvature
The half value of the curvature D _i registered in ₁ is substituted as k _{2 (i + 1)} , the simultaneous equations are solved, and coefficient calculating means 23 for obtaining these coefficients, and the value and coefficient of k _{2 (i + 1)} Displacement calculating means 25 is provided which applies the coefficient kα _i calculated by the calculating means 23 to a polynomial to individually obtain the displacement y _{i of the} section i.

According to a third aspect of the present invention, in the long-body displacement measuring apparatus according to the first or second aspect, the coefficient calculating means uses k ₂ for all possible values of i as a solution of simultaneous equations. It is characterized in that any one of the coefficients kα _i except _{(i + 1)} is deleted from the continuous conditional expression and the transfer matrix method is applied.

[0010]

Function: Long body displacement measurement according to the first aspect of the invention
The device is formed on the outer circumference of the elongated body along the axis of the elongated body.
Axial direction with one end as the origin for multiple sections i
Coordinate X_n And the order α and the polynomial y_i= Σkα_iX
_idisplacement y given by α _i And the first degree of the polynomial
To (α−1) th order derivative,
Rate, the rate of change of its curvature (shear force) and the change in shear force
If the conversion rate (external force) is continuous at the boundary,
Length L_i Shown below y_i= {Y_{i + 1}｜ X_{i + 1}= 0} dy_i/ dX_i= {(Dy_{i + 1}/ dX_{i + 1}) ｜ X_{i + 1}= 0} ・ ・ ・ dα^-1y_i/ dX_iα^-1＝ {(dα^-1y_{i + 1}/ dX_{i + 1}α^-1) ｜ X_{i + 1}= 0} α (n-1) continuous equations are calculated by the coefficient calculation means 13.
kα_iBe solved.

Although such a continuous expression is composed of only terms including coefficients kα _i which are unknowns, it is the end of the two outermost sections of the above-mentioned plurality of sections and the adjacent sections. Y ₁ = known value y _n = known value dy, which indicates the displacement, slope, curvature, and rate of change of that curvature given by these polynomials and derivatives at each end located on the opposite side of ₁ / dX ₁ = known value dy _n / dX _n = known value d ² y ₁ / dX ₁ ² = known value d ² y _n / dX _n ² = known value d ³ y ₁ / dX ₁ ³ = In the boundary condition formula of known value d ³ y _n / dX _n ³ = known value, the formula of the number of lines in which “1” is added to the predetermined order α is the measured value or the corresponding end Is established under the physical environment of, and in the interval i, in general, the constant term k _{2 (i + 1} ) on the left side of the continuous equation including the second derivative of the above continuous equation ₎ the double Of the strain gauge 11
_{1 to} 11 _(n-1) corresponds to the half value of the measured curvature D _i , and the maximum value of the order α is set to any of "5" to "7".

Therefore, the above α (n-1) continuous equations and (α + 1) boundary condition equations are simultaneous equations in which αn coefficients kα _i excluding the coefficient k _{2 (i + 1)} are unknowns. Therefore, the coefficient calculating means 13 solves these simultaneous equations to obtain the coefficients, and the displacement calculating means 15 obtains the coefficient kα _i (including k _{2 (i + 1))} thus obtained. By applying the above-mentioned polynomial, the displacement y _i of the section i can be individually obtained.

That is, among displacements, inclinations, curvatures and rates of change of the curvatures at both ends of a long body in which an error due to an external force is unlikely to occur, "1" is added to the degree α of a polynomial which gives the displacement in these sections. By setting the boundary conditions for a number of items, the displacement of each section can be calculated in a complicated and peculiar arithmetic operation with respect to the curvature obtained from the auxiliary strain gauge added to the position other than the boundary as in the conventional example. Asked without doing.

A long body displacement according to the invention as defined in claim 2.
In the measuring device, the shape is formed on the outer circumference of the elongated body along the axis of the elongated body.
With respect to the boundaries of the plurality of n intervals i (= 0 to (n-1)) formed,
Curvature D measured in advance_i Is registered in the database 21
Then, the coefficient calculation means 23 refers to the database.
Thereby, the long body displacement measuring device according to claim 1 is configured.
Perform the same arithmetic operation as the arithmetic operation performed by the coefficient calculation means
Therefore, the coefficient kα_iAsk for. Furthermore, displacement calculation means
25 is the coefficient kα obtained in this way_i(k _{2 (i + 1)}
including. ) Is applied to the polynomial and the displacement y of interval i_i Individual
Ask for.

Therefore, similarly to the elongated body displacement measuring apparatus according to the first aspect of the invention, the displacement of each section is
It can be obtained without performing a complicated arithmetic operation for the curvature obtained from the auxiliary strain gauge added to the position other than the boundary as in the conventional example. In the long body displacement measuring device according to the third aspect of the present invention, in the long body displacement measuring device according to the first or second aspect, the coefficient calculating means has k _{2 (i} ) for all possible values of _{i. The} simultaneous equations are solved by eliminating any one of the coefficients kα _i except ₊₁₎ from the continuous conditional expression and applying the transfer matrix method.

Under such a transfer matrix method, the coefficients k _{1i to} kα _i of the section i are determined by the constant coefficients given by the lengths of the sections 1 to (i-1) and the curvature D _i measured in advance. Since the coefficients are sequentially given, as long as the matrix formed by the coefficients and the boundary condition given by the boundary condition expression have sufficient accuracy, all the coefficients can be surely obtained with high accuracy by repeating similar arithmetic operations. Further, in the present invention, since the error amount due to the variation or fluctuation of the characteristics of the auxiliary strain gauge does not intervene in the process of calculating these coefficients, the error occurs in the process of multiplying the transfer matrix as compared with the conventional example. Is suppressed, and the accuracy is maintained high when the order α and the number n of sections are set large or the length of each section is set small.

[0017]

Embodiments of the present invention will be described below in detail with reference to the drawings. FIG. 3 is a diagram showing an embodiment corresponding to the invention described in claims 1 to 3. In the figure, a pipe strain gauge 31 includes a pipe material 32 such as an aluminum pipe, and strain gauges 33 ₁ to 33 attached to the outer periphery of the pipe material 32 at predetermined intervals along the axis of the pipe material.
It is composed of 33 _{n -1} and is buried in the ground at a predetermined angle (here, vertical for simplicity) with one end thereof coinciding with the ground surface. The outputs of the strain gauges 33 _{1 to} 33 _{n -1} are all connected to one end of a terminal board provided in the switch box 34, and the other terminal board provided opposite to the terminal board is connected via the data logger 35. Processing unit 3
6 connected to the corresponding inputs. In the switch box 34, a fixed or variable jumper ring is provided between the two opposing terminal boards, and the processing device 3
An input / output device having a man-machine interface is integrated with 6.

Regarding the correspondence between this embodiment and the block diagrams shown in FIGS. 1 and 2, the strain gauge 33 ₁
.About.33 _n-1 correspond to the strain gauges 11 _{1 to} 11 _n-1 , and the data logger 35 and the processing device 36 are the coefficient calculating means 13,
23, displacement calculating means 15 and 25, and database 21
Corresponding to FIG. 4 is a diagram illustrating the operation of the present embodiment.

Hereinafter, referring to FIG. 3 and FIG.
The operation of this embodiment corresponding to the invention described in claim 3 will be described. Tubing 32 and deflection some force in the ground where the pipe strain gauge 31 is embedded acts, curvature D _i is measured by the strain gauges 33 ₁ ~33 _n-1. Along with the data logger 35 through the switch box 34 were collected in association with such a curvature D _i sequentially strain gauge 33 ₁ ~33 _n-1, and the processing unit 36 takes in these curvatures D _i, the time series The strain gauges 33 _{1 to} 33 _n-1 are associated with the strain gauges in this order and recorded to generate a database. It should be noted that such a database is generated in a storage area of a hard disk (not shown) in which the processing device 36 is incorporated for simplicity.

By the way, the displacement y _i of the pipe material in the section bounded by the positions where the strain gauges 33 _{1 to} 33 _n-1 are attached along the axis of the pipe material 32 is the origin at the upper end of the corresponding section. Polynomial of coordinate X _{i in} the axial direction (here, α
= 5, and for simplification, the coefficients a _i , b _i corresponding to the section _i ,
In the formula of y _i = a _i X _i ⁵ + b _i X _i ⁴ + c _i X _i ³ + d _i X _i ² + e _i X _i + f _i (1) for c _i , d _i , e _i and f _i Suppose there is. ) Can be approximated.

Under such a coordinate system, the tilt,
The curvature, the rate of change of the curvature (hereinafter, referred to as “shear force” for simplicity) and the rate of change of the elastic force (hereinafter, referred to as “external force” for simplicity) are each once in X _i . It is given approximately by a formula obtained by differentiating the above formula (1) four times. Therefore, the displacement, tilt, and
If the curvature, the shear force, and the external force are continuous at the boundary between two sections that are adjacent to each other, the length L _{i of the} section _i
For a _i L _i ⁵ + b _i L _i ⁴ + c _i L _i ³ + d _i L _i ² + e _i L _i + f _i = f _{i + 1} (2) 5a _i L _i ⁴ + 4b _i L _i ³ + 3c _i L _i ² + 2d _i L _i + e _i = e _{i + 1} ... (3) 20a _i L _i ³ + 12b _i L _i ² + 6c _i L _i + 2d _i = 2d _{i + 1} ... (4) 60a _i L _i ² + 24b _i L _i + 6c _i = 6c _{i + 1} (5) 120a _i L _i + 24b _i = 24b _{i + 1} (6)

Further, the moment M _i acting on the section _i
Is generally a strain gauge 3 located at the top of the section.
The bending strain ε _i measured by 3 _i , the outer diameter 2r of the pipe 32, the Young's modulus E, and the second moment of area I are expressed by the formula M _i = EI ε _i / r. _{When i + 1} is “0”, M _i = −2d _{i + 1} EI / {1+ (dy / dX) ² | X _{i + 1} = by the curvature obtained by differentiating the above formula (1) twice. 0} ^3/2
It is also shown by the formula of / r. However, since the term of {(dy / dX) ² | X _{i + 1} = 0} is generally a small value and can be ignored, under these two expressions, 2d _{i + 1} = −ε _i / expression r is satisfied, the value 2d _{i + 1} of the left-hand, as represented by the formula _{D i = 2d i + 1 ···} (7), respectively the strain gauges 33 _{two or} three
Immediately given as the curvature D _i measured by 3 _n-1 .

The above equation (4) is solved for a _i to obtain the above equation
By substituting into (2), (3), (5), and (6) to eliminate the a _i , and matrix display,

(Equation 1) Is obtained. However, these elements K _{i11 to} K
_i55 is K _i11 = 1 K _i21 = (D _i −D _i-1 ) / 4L _i ² , K _i22 = −2, K _i23 = −1.5 / L _i K _i31 = (D _i −D _i-1) ) / 2L _i , K _i32 = -2L _i , K _i33 = -2 K _i41 = (D _i + 3D _i-1 ) L _i / 4, K _i42 = L _i ³ , K _i43 = 1.5L _i ² , K _{i44 = 1 K i51 = (D i} + 9D i-1) L i 2/20, K i52 = 0.4L i 4, K i53 = 0.7L i 3 K i54 = L i, is given by the equation K _i55 = 1.

Further, when the transfer matrix method is applied, the value of i in the above equation (8) is "1" to "n-".
Obtained by applying the 1 "(n-1) factor when this formula is synthesized _{b n, c n, e n} , f n _{is, b n = SK 21 + SK} 22 b 1 + SK 23 c 1 + SK 24 e 1 _{+ SK 25 f 1 ··· (9} ) c n = SK 31 + SK 32 b 1 + SK 33 c 1 + SK 34 e 1 + SK 35 f 1 e n = SK 41 + SK 42 b 1 + SK 43 c 1 + SK 44 e 1 + SK 45 f ₁ f _n = SK ₅₁ + SK ₅₂ b ₁ + SK ₅₃ c ₁ + SK ₅₄ e ₁ + SK ₅₅ f ₁ are given as functions of b ₁ , c ₁ , e ₁ , and f ₁ as shown in the equations. However, for SK _{21 to} SK ₅₅ ,
For the matrix [K _i ] including the elements K _{i11 to} K _i55 in the above formula (8), it is defined by the formula of [SK] = [K _n-1 ] ... [K ₂ ] [K ₁ ]. Elements of the composite matrix, and the first and second subscripts in each case indicate the row number and the column number of the composite matrix.

The relational expressions that are satisfied under the boundary conditions relating to both ends of the pipe 32 will be described below. Regarding displacement y ₀ , inclination, curvature, and shear force at one end of the pipe member 32, the above equation (1) is sequentially differentiated and “0” is applied as the subscript i, and the equation of X _i = 0 is substituted. Therefore, when the formula of f ₁ = y ₀ (10) is satisfied and these inclinations, curvatures, and shear forces are “0”, e ₁ = 0. (11) d ₁ = 0 ... (12) c ₁ = 0 ... (13)

Regarding the displacement, inclination, curvature, and shearing force at the other end of the pipe 32, the above equation (1) is sequentially differentiated, and "n" is applied as a subscript i,
It is obtained by substituting the length L _{n of the} section including the other end as X _i . Therefore, the displacement in such other end, if inclined, the curvature, the shear force are each ^{_{"0", a n L n 5 + b}} n L n 4 + c n L n 3 + d n L n 2 + e n L _n + f _n = 0 ... (14) 5a _n L _n ⁴ + 4b _n L _n ³ + 3c _n L _n ² + 2d _n L _n + e _n = 0 (15) 20a _n L _n ³ + 12b _n L _n ² + 6c _n L _n + 2d _n = 0 (16) 60a _n L _n ² + 24b _n L _n + 6c _n = 0 (17)

When the processor 36 completes the generation of the above-mentioned database, the boundary condition set in advance (here, by referring to the curvature D _i recorded in the database).
For simplicity, the displacement, curvature and shear force at one end of the pipe 32 are y ₀ , “0” and “0” respectively, and the displacement, curvature and shear force at the other end are all “0”.
It is. ), The following arithmetic operations are performed.

Under the above boundary conditions, the above equations (10) and (1
2) to (14), (16), and (17) are established. However, equations (14), (1
6), (a 17), not included in the above equation (9) a _n, because it contains the term of d _n, for example, a _n = obtained equation (17) is solved for a _n - (24b _n L _n + 6c _n ) / 60L _n ² (18) and the above expression (7) are substituted into expressions (14) and (16) to eliminate these terms, and b _n and c _n, e _n, 3L _n ⁴ is obtained by organizing the _{f n b n / 5 + 9L} n 3 c n / 10 + D n L n 2/2 + e n L n + f n = 0 ··· (14 ') 4L n 2 b _n + 4L _n c _n + D _n = 0 (16 ′) is substituted into each of the above equations (9) to obtain equations (14 ′), (1
Two linear expressions of b ₁ , c ₁ , e ₁ and f ₁ (not shown here for simplicity) are obtained corresponding to 6 ′).

First, the processing unit 36 calculates the values of c ₁ and f ₁ by the above equation (1) which is satisfied under the boundary condition as described above.
Obtained as a known value based on 3) and (10) (). Further, the processing device 36 determines the c ₁ , thus obtained,
By substituting the value of f ₁ into the two linear equations described above, a simultaneous equation involving b ₁ and e ₁ is generated, the simultaneous system is solved, and the values of b ₁ and e ₁ are obtained ().

Further, the processing device 36 has the above equation (4).
20a _i L _i ³ + 12b _i L _i ² + 6c _i L _i + 2d _i = D _i (19) is obtained by substituting (7) for a ₁ when the value of n is “1” obtained by solving a ₁ = - in formula _{(D 1 (12b 1 L 1} 2 + 6c 1 L 1 + 2d 1)) / 20L 1 3 ··· (4 '), determined in the preceding as described above B ₁ , c ₁ ,
The value of a ₁ is obtained by substituting d ₁ (= 0) ().

Further, processor 36, for d ₂ to d _n, as shown in the above equation (7), strain gauges 33 ₁ ~33 _n-1
The curvature values D _{1 to} D _n individually measured by are divided by “2” to sequentially obtain (). Further, the processing unit 36 uses the b ₁ , c ₁ , e ₁ , and f ₁ thus obtained.
By substituting the value of n into the equation (9) shown by i instead of n, b _i , c _i , e _i , and f _i of the sections in which the subscript i is “2” to “n” are sequentially calculated. Find the value ().

Further, the processing device 36 obtains by solving the above equation (19) for a _i : a _i = (D _i − (12 b _i L _i ² + 6c _i L _i + 2d _i )) / 20L _i ³ · By sequentially substituting the values of b _i , c _i , and d _i obtained in advance and the actual measurement value D _i into the equation (4 ″), the subscript i becomes “2” to “n”. Then, the value of a _i is calculated for each section ().

Further, in the processing device 36, the section i in which the strain gauges 33 _{1 to} 33 _n-1 are individually attached in this way is described.
When the values of a _i , b _i , c _i , d _i , e _i , and f _i are obtained for (= 1 to n), these values are substituted into the above equation (1) and X _i is set in the equation. The displacement is obtained by substituting the length in the corresponding section (). As described above, according to the present embodiment, the pipe material is not provided with the auxiliary strain gauge as in the conventional example, and the pipe material 32 is measured on the both ends of the pipe material 32 with high accuracy based on the boundary condition formed of a combination of the values. The generated displacement and the distribution of the displacement along the axis are efficiently and accurately obtained.

In the above embodiment, the displacement, inclination, curvature, shearing force, etc. at one end of the pipe 32 are set as boundary conditions.
It may be obtained by any method as long as the desired accuracy is ensured. For example, in the case where it can change with time, FIG.
Alternatively, as shown by the dotted line, a dedicated displacement measuring device may be applied for actual measurement, and if there is no such change and the value can be theoretically obtained, the value may be applied.

Further, in the above-described embodiment, the processing device 3
6 captures and stores the curvature D _i measured by the strain gauges 33 _{1 to} 33 _n-1 through the switch box 34, the present invention is not limited to such a configuration, and, for example, a processing device. If the processing power of 36 is high enough,
The processor may directly take in these curvatures and perform the arithmetic operations shown in steps 1 to 3 above in real time.

Further, in the case where such real-time arithmetic operation is required, for example, as the processing device 36, a processing device including a coprocessor such as an arithmetic unit that can obtain a desired arithmetic precision is applied, or For a part or all of the arithmetic operation process, a table is provided that stores the operation result obtained in advance corresponding to the boundary condition or the value obtained by the variable obtained as the result of the preceding operation in association with the variable. The calculation processing time may be shortened by appropriately referring to the table.

Further, in the above-described embodiment, the boundary condition given by the displacement, the curvature and the shearing force at both ends of the pipe 32 is applied, but the present invention is not limited to such boundary condition, and the both ends thereof are not limited. Among the displacement, inclination, curvature and shear force, the coefficients a _i , b _i shown in the above equation (1),
Boundary conditions of any combination may be applied as long as six combinations equal to the number “6” of c _i , d _i , e _i , and f _i are accurately given as constants.

Further, regarding the procedure of the arithmetic operation when such a boundary condition is applied, the above equations (10) to (1
Among 7), six equations corresponding to the items included in the boundary condition are specified to eliminate the coefficient a _n, and the simultaneous equations obtained by substituting the equation (9) are solved to obtain the coefficient b ₁ ,
The determination of c ₁ , e ₁ , f ₁ and a ₁ is possible in the same way because the number of specified equations and the number of coefficients to be determined are the same.

For i = 2 to n, b _i , c _i ,
Regarding the procedure for obtaining e _i , f _i, and a _i , once the above-mentioned coefficients b ₁ , c ₁ , e ₁ , f ₁ , a _1, and d ₁ have been obtained, regardless of boundary conditions, Since the value of is substituted into the above equation (8) and the above equation (4 ″) is applied, the description thereof will be omitted here. Further, in the above-described embodiment, the above equation (1 ), The displacement y _i is given by a quintic equation of X _i , but the present invention is not limited to such a quintic equation.
When given as a combination of arbitrary 7 or 8 displacements, inclinations, curvatures and shear forces at both ends of 2, as long as the error occurring in the process of multiplication of the transfer matrix is acceptably small, It may be given by a 6th order expression or a 7th order expression of X _i . It should be noted that the above formulas (1) to (6) and (14) to (17) in such a case can be easily obtained by applying an expansion adapted to the increase of the order,
Moreover, regarding the above formulas (10) to (13) and (14) to (17), those corresponding to the items included in the boundary conditions can be appropriately selected and applied.

In the above-described embodiment, although the auxiliary strain gauge is not used, for example, the displacement y _i is X _i.
In the case of using a polynomial of 9th order or higher, if one or both of the sections including both ends of the pipe 32 are provided in the same manner as in the conventional example, if the error generated in the process of calculation of the transfer matrix is suppressed to an acceptable level. By providing an auxiliary strain gauge at, it is possible to ensure a number of equations equal to the coefficients of the polynomial.

Further, although the transfer matrix method is applied in the above-described embodiment, for example, the value of i (= 1 to 1)
n)) corresponding to the above equations (1) to (7) and the boundary condition equations (combinations of the above equations (10) to (13) and (14) to (17)). It is also possible to perform an operation that directly solves the equation. Further, in the above embodiment, coefficients obtained _{a i, b i, c i} , d i, e i, the displacement obtained by performing the arithmetic operation shown in the above equation (1) under f _i y _i However, the present invention is not limited to such a structure. For example, as shown in FIGS. When applied for the purpose of detecting or monitoring the displacement of a tunnel ground, embankment, etc., the displacement y _i and the slope calculated under these coefficients are set as thresholds that are set as allowable upper limit values in advance. It is also possible to perform a process of discriminating the magnitude relationship between the above and the above, and a process of discriminating the magnitude relationship between the rate of change along the time series and the threshold value similarly set.

Further, in the above-described embodiment, an aluminum pipe is used as the elongated pipe member 32, but the present invention is not limited to such a pipe member, and a strain gauge can be attached. If the member has a cross-sectional shape (for example, a polygon, a circle, an ellipse) for which sufficient curvature measurement accuracy is obtained, a solid body such as a steel bar or a steel plate or stainless steel,
It is also possible to apply a pipe material formed of vinyl chloride or the like.

[0043]

As described above, according to the first and second aspects of the invention, the displacement of these sections among the displacement, inclination, curvature and shearing force at both ends of the elongated body in which an error due to an external force is unlikely to occur is determined. By setting the boundary condition for an arbitrary number of items equal to the degree α of the polynomial given, the displacement of each section is set to the curvature obtained from the auxiliary strain gauge added to the position other than the boundary as in the conventional example. On the other hand, it is required without complicated and peculiar arithmetic operations.

In the long body displacement measuring apparatus according to the third aspect of the present invention, the coefficients k _{11 to} kα ₁ are obtained in advance based on the boundary condition formula under the transfer matrix method, and these coefficients are also obtained. since the coefficient k _1i ~kα _i of each interval i the subsequent based on the linear combination expression are sequentially calculated, as long as a high enough their length accuracy of a given boundary conditions and each section at the boundary condition, By repeating the same arithmetic operation, all the coefficients are surely calculated with high accuracy. Furthermore, in the present invention, since the error amount due to the variation or fluctuation of the characteristics of the auxiliary strain gauge cannot be included in the process of calculating these coefficients, the number n of sections is set to be larger than that in the conventional example. Even if this is done, the occurrence of errors due to multiplication of the transfer matrix is suppressed, and the accuracy is maintained high.

That is, since the hardware configuration and the calculation procedure can be simplified, and the displacement occurring in the elongated body and the distribution of the displacement can be accurately obtained, the displacement measurement of the elongated body to which these inventions are applied. In the device, cost reduction can be achieved, responsiveness and real-time performance can be achieved, and reliability can be improved.

[Brief description of the drawings]

FIG. 1 is a block diagram of the principle of the invention described in claims 1 and 3.

FIG. 2 is a principle block diagram of the invention according to claims 2 and 3;

FIG. 3 is a diagram showing an embodiment corresponding to the invention described in claims 1 to 3.

FIG. 4 is a diagram illustrating the operation of the present embodiment.

FIG. 5 is a diagram showing an application example of the present embodiment.

[Explanation of symbols]

 11 Strain gauge 13,23 Coefficient calculation means 15,25 Displacement calculation means 21 Database 31 Pipe strain gauge 32 Tubular material 33 Strain gauge 34 Switch box 35 Data logger 36 Processing device

Claims (3)

[Claims] 1. A plurality of sections i (= 0 to (n-which are formed in the outer circumference or inner circumference of a hollow body having a length larger than the thickness or a solid body) along the axial center of the long body. The curvature D at the boundary of these sections is attached individually to the boundary of 1)).
Strain gauges 11 _{1 to} 11 _(n-1) that measure _i, and coordinate values X _{n in the} axial direction with one end as the origin and maximum values of “5”, “6”, and “7” for the plurality of sections. In addition to the displacement y _i given by the polynomial y _i = Σkα _i X _i α with respect to any degree α, the equations given by the first-order to (α-1) -th order derivatives of the polynomial A plurality of continuous expressions y _i = {y _{i + 1} | X _{i + 1} = 0}, dy _i / dX _i = {(, which indicate that all values are continuous at the boundary, under the length L _i of the interval. dy _{i + 1} / dX _{i + 1} )
│X _{i + 1} = 0}, ..., dα ^-1 y _i / dX _i α ^-1 = {(dα ^-1 y _{i + 1} / dX _{i + 1}
α ^-1 ) | X _{i + 1} = 0} and these polynomials and their derivatives for each end of the two outermost sections that are on the opposite side of the adjacent section Among the displacements, inclinations, curvatures, and rates of change of the curvatures given by and, in the simultaneous equations of the coefficient kα _i consisting of a boundary condition expression that shows a predetermined value of (α + 1) combinations, The half value of the curvature D _i individually measured by the plurality of strain gauges 11 _{1 to} 11 _(n-1) is substituted as k _{2 (i + 1)} , the simultaneous equations are solved, and the coefficients are calculated. Means 13
And the value of k _{2 (i + 1)} and the coefficient kα _i calculated by the coefficient calculating means 13 are applied to the polynomial, and the section i
And a displacement calculating means 15 for individually calculating the displacement y _i of the elongated body displacement measuring device. 2. A plurality of n sections i (= 0 to (n-which are formed along the axis of the elongated body on the outer or inner circumference of the elongated body composed of a hollow body or solid body having a length larger than the thickness). Regarding the boundary of 1)), the database 21 in which the curvatures D _i measured individually beforehand are registered, and the coordinate X _{n in the} axial direction with one end as the origin and the maximum value of “5”, “ 6 ”or“ 7 ”and the displacement y _i given by the polynomial y _i = Σkα _i X _i α with respect to the degree α and the derivative of the first to (α−1) th order of the polynomial. A plurality of continuous expressions y _i = {y _{i + 1} │X _{i + 1} = 0}, dy indicating that the values of the expressions given by the functions are continuous at the boundary under the interval length L _{i i} / dX _i = ((dy _{i + 1} / dX _{i + 1} )
│X _{i + 1} = 0}, ..., dα ^-1 y _i / dX _i α ^-1 = {(dα ^-1 y _{i + 1} / dX _{i + 1}
α ^-1 ) | X _{i + 1} = 0} and their polynomials and their derivatives for each end of the two outermost sections that are opposite to the adjacent section Among the displacements, inclinations, curvatures, and rates of change of the curvatures given by and, in the simultaneous equations of the coefficient kα _i consisting of a boundary condition expression that shows a predetermined value of (α + 1) combinations, The half value of the curvature D _i registered in the database 21 is substituted as k _{2 (i + 1)} to solve the simultaneous equations, and coefficient calculating means 23 for obtaining these coefficients, and k _{2 (i + 1)} The value and the coefficient kα _i calculated by the coefficient calculating means 23 are applied to the polynomial to obtain the section i
And a displacement calculating means 25 for individually calculating the displacement y _i of the elongated body displacement measuring device. 3. The long body displacement measuring device according to claim 1 or 2, wherein the coefficient calculating means excludes k _{2 (i + 1)} for all possible values of i as a solution of the simultaneous equations. An elongated body displacement measuring apparatus, characterized in that any one of the coefficients kα _i is deleted from the continuous conditional expression and the transfer matrix method is applied.