RU2303792C1 - Method for measuring of the magnetic moment of a large-sized body of an extended form - Google Patents

Abstract

FIELD: the invention refers to the field of measuring of a magnetic moment.

SUBSTANCE: the body is divided on longitudinal sections with unknown magnetic moments, the parameters of induction of the magnetic field of the body in external points and distance between the points and the center of the body including range or minimal distance between the sensor and the center are measured. According to the results of measuring a system of equations is compiled and decided relatively to the sections of the magnetic moments whose sum is equal to the body of the magnetic moments. A calculated model of the body with the given magnetic moments is compiled and the measuring on a computer for the given configuration of the points of measuring of the parameters of the field and the given average quadratic deviations of errors of the means of measuring of the parameters of the field and the distances. The magnetic moment of the body is measured at removal and the number of the sections chosen in the area of the minimal error in the modeled measurement.

EFFECT: increases accuracy of measuring of magnetic moments more then 1o times higher at the ratio of the range to the length of the body 0,35-0,5.

5 tbl, 1 dwg

Description

The invention relates to the field of measuring magnetic moment (MM), in particular a large body of an elongated shape (for example, a ship). Of course, we are talking about an indirect measurement of the MM body.

Known two-point magnetometric method for measuring MM [Semenov V.G. and Sonina V.E. Analysis of methods for measuring magnetic moments // Metrology, 1992, No. 8, p.7]. This method is used to measure the MM of large-sized bodies due to its simplicity and efficiency. However, as shown in the article [Semenov and Sonina, 1992, p.32, 35], the resulting error of the two-point method is quite large, especially for an elongated body (20-30%). Moreover, in the resulting error (16-23%), the methodical error or the error from the non-dipole nature of the body (10-16%) prevails.

Also known is the twelve-point magnetometric method for measuring MM [Semenov V.G. and Sonina V.E. Analysis of methods for measuring magnetic moments // Metrology, 1992, No. 8, p.10], which provides increased accuracy (2.7-3.4%) due to a significant reduction in the methodological component of the error (0.9-1.7%) . But due to the large number of points located in a special way around the test body, the method is not applicable for large bodies. For small bodies this method can be applied. An example of a small body is a magnetic model of a ship on a scale of 1 / 25-1 / 100.

There is also a known method for measuring the MM of ships and ships [V.I. Bolshakov et al. Assessment of the magnetic state of a ship by measuring its magnetic field // Transactions of the Second International Conference on Shipbuilding. Section E. Physical fields of ships and the ocean. 1998, vol. 2, p. 12-16. SPb.]. More precisely, this technique is aimed at monitoring the magnetic field of a ship in a plane at a depth equal to the half-width of the ship, and the determination of MM by this technique is obtained as a secondary result. It turned out that this method of measuring MM has poor accuracy. The reasons for the poor accuracy of MM measurements remained incomprehensible, but the authors of the methodology decided satisfactorily the main task - monitoring the field of the vessel on a given plane.

We quote an excerpt from the article [Bolshakov et al. 1998, p.14]:

"Studies [4] have shown that such a model at distances of the order of the half-width of a vessel adequately describes its magnetic field. This segment is divided into 8-10 sections of approximately equal length." In this passage, as will be shown below (see table 5), the key lies in the poor accuracy of MM measurements by the known method.

According to the set of essential features, as a closest analogue of the proposed method, a method for measuring the MM of an oversized elongated body is adopted [Bolshakov et al. 1998, p.14].

A known method of measuring the MM of a large body of an elongated shape [Bolshakov et al. 1998, p.14] includes measuring the parameters of the body’s magnetic field at points external to the body, measuring the distances between these points and the center of the body, dividing the body into longitudinal sections, designing and solving the system linear equations for MM sections and determining the result as the sum of MM sections.

The reason that impedes the achievement of the technical result indicated below when using the known method is the incorrect recommendations for choosing the distance and the number of sections of the partition of the body when measuring MM.

The task to which the invention is directed is to increase the accuracy of measuring the MM of a large body of an elongated shape.

The technical result obtained by carrying out the invention consists in choosing when measuring such a distance and such a number of sections of the partition that correspond to the increased accuracy of the measurement of MM. The accuracy is expected to increase by at least an order of magnitude at measurement distances of 0.35–0.5 of the body length L with the number of sections p = 4–12.

The specified technical result is achieved by the fact that in the inventive method of measuring the magnetic moment (MM) of an elongated large-sized body by measuring the parameters of the magnetic field of the body at external points and the distances between the points and the center of the body, including the removal or minimum distance between the field parameter sensor and the center of the body , by dividing the body into longitudinal sections, compiling and solving a system of linear equations for MM sections and determining the result as the sum of MM sections, in contrast to In the natural method, the measurement of MM is carried out when removing and the number of sections providing increased accuracy of measuring MM, for the determination of which they compose a calculated magnetic model for bodies of the same class with a given MM and simulate the measurement on a computer for a given configuration of the points of measurement of the parameters of the body’s magnetic field and the specified standard deviations of errors means of measuring the parameters of the magnetic field induction and distances, then the difference between the simulated and given values of MM is calculated, a number of statistical estimates of different Tei at different distances and numbers of regions and removing selected portions and the number corresponding to the lowest evaluation region.

The drawing shows one of the possible schemes for measuring MM body elongated according to the claimed method. The diagram in the drawing includes an elongated body 1, three-component measuring 2 and compensation 3 sensors of a differential magnetometer.

The inventive method is as follows. Body 1 is mentally divided into p sections of equal length. Each site is credited with its unknown MM X ₁ -X _p . Body 1 is uniformly moved under its own power, for example, along a straight path along the measuring 2 and compensation 3 sensors of a differential magnetometer, which measure m increments of the magnetic field induction of body 1 at spaced points 1, 2, 3 ... q ... m-1, m. Each section of the body 1 with MM Xs creates at point q its share of the increment of the magnetic induction between points 2 and 3, described by the relation [Semenov V.G. and Sonina V.E. 1992, p. 7]

where _{ΔB 23qs} is the column vector of the increment of magnetic induction between points 2 and 3, T;

n _2qs , n _2qs , n _3qs , n _3qs - dyads from unit direction vectors of radius vectors between points 2q and s and points 3q and s;

R _2qs , R _3qs - modules of radius vectors between points 1q and s and points 2q and s, m;

X _s is the column vector of the MM at the point s, Am ² ;

N _qs is a 3 × 3 matrix.

The entire increment of induction at q can be written as

where ΔB _q is the total increment of induction at point q between the measuring and compensation sensors - 3 × 1 matrix;

N _q is a 3 × 3p matrix,

X is a single-column matrix 3p × 1.

For m measuring points of increments of magnetic induction from (2) we obtain

where ΔB is a one-column matrix of increments of magnetic induction of size 3m × 1;

N is a 3m × 3p rectangular matrix called the coordinate matrix.

The system of 3m linear algebraic equations (3) can be solved with respect to 3p unknowns if m is equal to or greater than p. The least squares solution (3) is of the form

where N ^T is the transposed matrix N;

(N ^T · N) ^-1 is the inverse matrix from the square matrix (N ^T · N) of size 3p × 3p.

Solution (4) exists if there is an inverse matrix (N ^T · N) ^-1 . Then, using the one-column matrix X determined using (4), one finds the MM of the body

- результат (косвенного) измерения ММ тела.Where

- the result of an (indirect) measurement of the MM of the body.

Note. The inventive method is applicable not only to the differential magnetometer circuit with sensors 2 and 3 shown in the drawing. It is also applicable to the scheme of one sensor 2 (or several sensors 2) without a compensation sensor 3. In this case, in the sensor 2 in the absence of body 1, the Earth field is compensated and the zeros of the magnetometer are corrected, then the body 1 is brought closer and the magnetic field induction of the body is measured by background of the compensated constant part of the Earth’s field. Although in both cases the term “increment of magnetic field induction” is correct, it is not included in the normative documentation for magnetic measurements. The documentation recommends the term "measurement of magnetic field induction", which does not correspond to the diagram in the drawing. In order to cover both measurement schemes with and without compensation sensor 3, without contradicting the recommendations of the regulatory documentation, in the description of the proposed method, the term "measuring the magnetic field induction parameters" sometimes sometimes uses the equivalent term "measuring the magnetic field induction" . In the claims used the term "measurement of the parameters of the magnetic field.

Until now, the inventive method has been repeated known. Then the differences begin. To begin with, the MM measurement result determined by relation (5) will not be accurate even with absolutely accurate measurements of induction increments and distances, i.e. for absolutely exact elements of the matrix N and the column vector ΔB. The accuracy of the measurement result of MM extremely strongly depends on the choice of the removal of the body R (see figure 1) and the choice of the number of partition zones. In the claimed method, the choice of R was dictated by the need to control the magnetic fields of the vessel in a given horizontal plane under the vessel at a vertical distance from the waterline of the order of the half-width of the vessel [Bolshakov et al. 1998, p.14]. Such a measurement distance close to the body (half-width or width) is disadvantageous in terms of the accuracy of measuring the body’s MM (see table 5). To select the removal and the number of sites favorable for measuring MM, the claimed method uses a calculated magnetic model of the body with a known exact value of the MM model and with the distribution of MM along the length close to the distribution of the full-scale body. In a first approximation, this can be a uniformly magnetized ellipsoid oriented in a geomagnetic field similarly to the orientation of a natural body. For example, it is known that some body with a longitudinal axis in the North-South direction has an MM equal to M = [M _x ; M _y ; M _z ]. If the body is approximated by a uniformly magnetized ellipsoid of revolution with the semi-axes L / 2, B / 2, N / 2, where L is the length, B is the width, H is the height of the body, and divide the body, for example, into 11 sections, then MM sections will be by the following:

When the ellipsoid is divided into sections of equal length, the volumes of the sections increase from the ends to the center of the ellipsoid, and the coefficients in the numerators of the MM sections change proportionally to the volumes (6). Note that the sum of the MM of all sites is equal to the MM of the body, i.e. M, since 31 + 85 + 127 + 157 + 175 + 181 + 175 + 157 + 127 + 85 + 31 = 11 ³ .

Having the known MM sections (6), according to relation (1) using a computer program, for example, MatLab, the increments of the magnetic field induction created by the model of body 1 in a given set of measurement points of increments are calculated. The increments using MatLab add random variables with a zero mean and standard deviation σ _B equal to the standard deviation of the additive instrumental error of a differential magnetometer with measuring 2 and compensation 3 sensors. For typical magnetometers, when the sensors are removed at a distance of at least 8 km from the DC electric traction lines, σ _V ranges from 0.1 to 0.5 nT, depending on the identity of the measuring and compensation sensors and the accuracy of the angular matching of their magnetically sensitive axes. In addition, to the given distances over which the coordinate matrix N is calculated, random errors with zero mean and standard deviation σ _R corresponding to the standard deviation of distance measuring instruments are added. For typical distance measuring instruments, σ _R ≤1 m. Then, system (4) is solved and the MM models of the body (5) are calculated, weighed down by the methodological (systematic) and two random instrumental errors in computer simulation of the MM measurement from the errors in measuring magnetic field parameters and distances. MatLab repeats the solution procedure 30-10 ³ times, processes the entire set of results and finds the components and the resulting error estimates of the (simulated) MM measurement. It is important that MatLab not only models the errors themselves, but also finds statistical estimates of these errors. The difference between the error and its estimate is that the error contains a random (indefinite) value, and the estimate of this error (if it is sufficiently representative) is a deterministic (definite or nonrandom) value.

We write the average component of the relative (systematic) methodological error in the form

where X _MIx X _MIy , X _MIz are the components of the result of the (simulated) measurement of the MM model according to equations (4) - (5) for the exact column vector of the induction increments ΔВ and the coordinate matrix N;

M _x, M _y, M _z - MM model components;

| M | - module MM model.

(In the claimed method, the components and module of the MM model are known).

Denote:

σ _MB - standard deviation or estimation of MM measurement errors from measurement errors of magnetic induction increments;

σ _MR - standard deviation or estimation of MM measurement errors from errors in measuring distances between the center of the body and the points of increment measurement.

Then the estimate of the relative resulting error with a confidence probability of 0.95 can be represented as

[A.N. Seidel. Errors of measurement of physical quantities. Science, 1985, pp. 61-66].

An estimate of the resulting error could be chosen differently, for example, with a confidence probability of 0.99

or with a confidence level of 0.997

[Guide to the expression of uncertainty in measurement ISO Geneva. Guidance on the expression of measurement uncertainty. VNIIM, St. Petersburg, 1999, p. 71].

Examples of calculating the estimates of measurement errors MM are given in tables 1-5. The results are presented in the function of removing a body related to its length at σ _B = 0.5 nT, σ _R = 1 m for the body model (6), the number of sections of the body partition p = 1, 2, 4, 6, 8, 10, 12 at 32 measuring points of increments uniformly distributed over a straight line segment 1.25 L. long

Table 1
The methodological component of the error δM _met R / L 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 p = 1 .52 .fifty .46 .41 .36 .32 .28 .24 .22 .19 p = 2 .52 .47 .43 .39 .34 .thirty .26 .22 .19 .fifteen p = 4 .fifty .45 .38 .29 .twenty .13 .07 .03 .016 .008 p = 6 .46 .42 .27 .12 .026 .006 .003 .0014 .0007 .0004 p = 8 .48 .37 .12 .009 .0012 .0002 .0001 .0000 .0000 .0000 p = 10 .60 .33 .013 .0003 .0000 .0000 .0000 .0000 .0000 .0000 p = 12 .63 .25 .0004 .0001 .0000 .0000 .0000 .0000 .0000 .0000

The methodological error δM _{met is} not a random value, therefore, it coincides with its estimate. As can be seen from table 1, δM _met is large near the body, but with distance it decreases the faster, the greater the number of sections of the partition p.

table 2
Estimation (RMS) of the instrumental error σ _MV / | M | R / L 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 p = 1 .0001 .0001 .0002 .0003 .0005 .0007 .0009 .0011 .0015 .0018 p = 2 .0001 .0002 .0003 .0005 .0008 .0012 .0016 .0022 .0029 .0039 p = 4 .0002 .0005 .0012 .0023 .0035 .0053 .0073 .0099 .0128 .0163 p = 6 .0007 .0015 .0024 .0034 .0050 .0066 .0091 .0130 .0179 .0265 p = 8 .0011 .0019 .0029 .0043 .0058 .0083 .0130 .0191 .0298 .0488 p = 10 .0013 .0021 .0032 .0047 .0075 .0117 .0195 .0327 .0.554 .1093 p = 12 .0014 .0023 .0036 .0058 .0104 .0192 .0365 .0678 .1384 .2712

In contrast to the methodological error, the estimate σ _MV / | M | grows with distance from the body the earlier and steeper, the more p.

Table 3
Estimation (RMS) of the instrumental error σ _MR / | M | R / L 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 p = 1 .0111 .0105 .0103 .0094 .0092 .0086 .0083 .0088 .0076 .0072 p = 2 .0145 .0127 .0112 .0101 .0096 .0082 .0078 .0074 .0065 .0062 p = 4 .0162 .0144 .0122 .0105 .0104 .0112 .0100 .0103 .0089 .0089 p = 6 .0208 .0219 .0178 .0146 .0124 .0115 .0104 .0091 .0088 .0081 p = 8 .0310 .0229 .0196 .0140 .0128 .0106 .0102 .0087 .0084 .0080 p = 10 .0331 .0209 .0149 .0140 .0122 .0102 .0102 .0085 .0076 .0068 p = 12 .0323 .0200 .0150 .0137 .0117 .0098 .0088 .0085 .0077 .0063

As can be seen from table 3, the estimate σ _MR / | M | monotonously decreases with distance from the body.

Close to the body, the larger it is, the larger p, the dependence on p disappears with distance from the body. Some deviations from this rule among the table data are apparently explained by the insufficient representativeness of the estimates due to the small sample size (100).

Table 4
Estimates of the resulting errors δM _0.95 R / L 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 p = 1 .3831 .3374 .2959 .2620 .2330 .2096 .1897 .1729 .1585 .1465 p-2 .3677 .3210 .2791 .2434 .2110 .1848 .1626 .1429 .1273 .1143 p = 4 .2308 .1500 .0905 .0562 .0408 .0317 .0326 .0335 .0388 .0441 p = 6 .0696 .0418 .0329 .0311 .0251 .0272 .0318 .0400 .0554 .0787 p = 8 .0473 .0398 .0293 .0281 .0270 , 0329 .0421 .0619 .0988 .1659 p = 10 .0420 .0304 .0293 .0272 .0321 .0440 .0676 .1118 .2190 .4027 p = 12 .0402 .0310 .0298 .0313 .0431 .0752 .1367 .2774 .5434 1.148

As can be seen from table 4, for some R / L estimates of δM _0.95 for p = 4-12 turn into minima (marked in bold), for p = 1-2 the minima did not fit. They are presented below in table 5.

The optimal removal of R / L, the number of sections p and the corresponding minima of the estimates δM _0.95 and δM _0.997 by the _present method in comparison with similar estimates with the recommendations of the known method (R / L = 0.1 and p = 8-10).

Table 5 R / L 0.1 0.35 0.4 0.45 0.5 0.95 1.3 p-1 .088 p-2 .086 p = 4 .032 p = 6 .025 p = 8 .025 p = 10 .027 p = 12 .030 by a known method (δM _0.95 ) p = 8 .44 p = 10 .42 according to the claimed method (δM _0.997 ) p = 4 .046 p = 6 .042 p = 8 .039 p = 10 .041 p = 12 .042 by a known method (δM _0.997 ) p = 8 .47 p = 10 .47

As can be seen from table 5, at the existing level of measuring instruments for the increments of induction and distances (σ _B = 0.5 nT, σ _R = 1 m), the inventive method provides an increase in the accuracy of measuring MM not less than 10 times in comparison with the known method. In addition, the inventive method provides greater freedom of choice of removals and the number of sections p due to the control of the behavior of the estimates in the region of the minimum. For example, as shown in table 5, in this case, the best measurement mode is R / L = 0.4 and p = 8. Let us assume a regime, for example, R / L = 0.35 and p = 10 or R / L = 0.5 and p = 6, since the corresponding estimates of 0.041 and 0.042 differ little from the minimum of 0.039.

As can be seen from tables 1-5, in the inventive method, the proportion of the methodological component in the overall error estimation is extremely small. In the known method, it prevails. This means that if you increase the accuracy of the means of measuring the parameters of the magnetic field and distance, for example, 5 times (σ _B = 0.1 nT, σ _R = 0.2 m), then the inventive method will provide almost five-fold increase in the accuracy of measuring MM, and in the known method, the accuracy MM measurements will not change.

Since the fraction of the methodological error in the claimed method is small, deviations of the calculated model from nature do not lead to a significant loss in the accuracy of MM measurements. This is another important feature of the proposed method.

Claims (1)

A method for measuring the magnetic moment (MM) of an elongated large-sized body by measuring the parameters of the magnetic field induction of the body at external points and the distances between the points and the center of the body, including removing or minimizing the distance between the field parameter sensor and the center of the body, by dividing the body into longitudinal sections and solving a system of linear equations with respect to the MM sites and determining the result as the sum of the MM sites, characterized in that the measurement of MM is performed when removing and the number of sites, ensuring which increase the measurement accuracy of MM, for the determination of which they compose for the bodies of one class a calculated magnetic model with a given MM and simulate the measurement on a computer for a given configuration of the measurement points of the magnetic field parameters of the body and the given standard deviations of the errors of the means of measuring the magnetic induction parameters and distances, then calculate the difference between the simulated and given values of MM, a number of statistical estimates of the differences are found for different distances and the number of sections and rayut removal and the number of portions corresponding to the lower field evaluation.