JP5820750B2 - Tomography apparatus and tomography measurement method - Google Patents

Description

  The present invention relates to a tomography apparatus and a tomography measurement method for measuring a distribution of electrical impedance in an internal cross section of an object to be measured, and in particular, a tomography apparatus and tomography for correcting a change in electrical impedance due to the shape of the object to be measured. It relates to the measurement method.

  Conventionally, an electrical impedance tomography method (Electrical Impedance Tomography) has been used as a method of measuring the distribution of electrical impedance in the internal cross section of the object to be measured (see, for example, Patent Documents 1 to 3). In the electrical impedance tomography method, all electrodes are arranged by arranging a plurality of electrodes on the outer periphery of the object to be measured and passing a current between a pair of adjacent electrodes to measure a potential difference between the other pair of adjacent electrodes. The electrical impedance distribution in the internal cross section of the object to be measured is calculated using a predetermined algorithm from the measured total potential difference.

  For example, as described in Patent Document 1 and the like, the electrical impedance tomography method diagnoses whether or not cancer cells are present inside a patient's thorax, and is configured from an electrically nonconductive material such as an acrylic resin. It is used to determine whether or not the contents in the tank or pipeline contain foreign matter. These utilize the difference in electrical impedance between cancer cells and normal cells, and contents and foreign substances.

Japanese Patent No. 3759606 Special table 2010-504781 gazette JP-T 9-510014

  By the way, the above-described electrical impedance tomography method derives the electrical impedance distribution in a cross section of the object to be measured. In order to reduce the influence of the electrical impedance other than the measurement cross section, the cross sectional area of the object to be measured is It was assumed that there was no significant change in the height direction or the direction perpendicular to the measurement cross section, or that current easily flows in the measurement cross section.

  For example, when the electrical impedance tomography method is applied to a cylindrical object to be measured, the current path passing through the vicinity of the wall surface of the object to be measured is the shortest path in the arc on the measurement section. On the other hand, when applying the electrical impedance tomography method to a measurement object whose cross-sectional area changes in the height direction of the measurement cross section or in the direction perpendicular to the measurement cross section, such as a conical shape with a reduced diameter downward, the measurement object The path of the current passing through the vicinity of the wall may not be an arc on the measurement section, but a curve passing below the measurement section may be the shortest path. As described above, when a current flows through a path that does not pass through the measurement section, the value of the measured potential difference becomes smaller than the actual value, and there is a problem that an error in the derived electrical impedance distribution becomes large.

  The present invention has been devised in view of the above-described problems, and it is possible to accurately measure the electrical impedance distribution in the measurement cross section of the measurement object whose cross-sectional area changes in the height direction or the direction perpendicular to the measurement cross section. An object is to provide a tomography apparatus and a tomography method.

According to the present invention, there is provided a tomography apparatus for measuring the electrical impedance distribution measuring section in an object to be measured using electrical impedance tomography, the object to be measured is, along a direction perpendicular to the measuring section shaped to change the size of the cross-sectional area Te, a plurality of electrodes disposed on the outer circumference of the measuring section, adjacent the power source for supplying a current to the pair of current load electrode is selected from the plurality of electrodes A voltmeter for measuring a potential difference between another pair of measurement target electrodes selected from the plurality of electrodes, and measuring a potential difference of all the measurement target electrodes with respect to the current load electrode, By selecting all combinations of the current load electrodes with respect to the electrodes and measuring all potential differences of the measurement target electrodes, all of the current load electrodes and the measurement target electrodes A calculation unit that obtains measurement data of a potential difference for the combination, performs calculation by the electrical impedance tomography method based on the measurement data, and derives the distribution of the electrical impedance of the object to be measured; The outer edge distance along the outer periphery of the measurement cross section between the intermediate point of the pair of current load electrodes and the intermediate point of the pair of measurement target electrodes, the intermediate point of the pair of current load electrodes, and the pair A tomography apparatus is provided, wherein the measurement data is corrected based on a ratio of a shortest distance along a wall surface of the object to be measured between an intermediate point of the measurement target electrode .

  The calculation unit may correct the measurement data by multiplying the measurement data by a correction coefficient obtained by dividing the outer edge distance by the shortest distance.

  For all combinations of the current load electrode and the measurement target electrode, the correction coefficient is calculated by obtaining the outer edge distance and the shortest distance, and the correction coefficient for each combination of the current load electrode and the measurement target electrode. May be stored in the database.

  The measured object has a wall surface made of, for example, a container having a conical surface or a pyramid surface or a curved or bent pipe.

  The measurement cross section may have a polygonal cross section, and the electrode may include an electrode disposed across two sides constituting each corner of the polygonal cross section. Furthermore, the electrodes may include electrodes arranged on each side of the polygonal cross section at equal intervals in the middle part of the electrodes arranged at the corners. The measurement cross section may have a polygonal cross section, and the electrode may include an electrode disposed at an intermediate portion of each side of the polygonal cross section.

Further, according to the present invention, there is provided a tomography measurement method for measuring an electrical impedance distribution of a measurement cross section in a measurement object using an electrical impedance tomography method, wherein the measurement object is perpendicular to the measurement cross section. A mesh creating step of arranging a plurality of electrodes on an outer periphery of the measurement cross section to divide the measurement cross section into a plurality of measurement regions, and a shape of the cross section area changing along a direction; A potential difference measuring step for supplying a current to a pair of adjacent current load electrodes selected from the plurality of electrodes and measuring a potential difference between another pair of measurement target electrodes selected from the plurality of electrodes; and the pair of current loads and the outer edge distance along the outer circumference of the measuring section between the midpoint of the intermediate point of the electrode and the pair of the measurement target electrodes, the pair of the measurement target conductive and the midpoint of the pair of current load electrode Of the shortest distance along the wall surface of the object to be measured between the middle point, and the potential difference correction step of correcting the potential difference based on the ratio of, by repeating the potential difference measuring step and the potential difference correction step, the current Obtain measurement data of potential differences corrected for all combinations of the load electrode and the measurement target electrode, perform calculation by the electrical impedance tomography method based on the measurement data, and distribute the electrical impedance of the measurement object A tomography measurement method comprising: an electrical impedance distribution deriving step for deriving.

  In the potential difference correction step, the potential difference may be corrected by multiplying the potential difference by a correction coefficient obtained by dividing the outer edge distance by the shortest distance.

  According to the tomography apparatus and the tomography measurement method according to the present invention described above, by correcting the potential difference according to the ratio between the outer edge distance and the shortest distance, the cross-sectional area of the object to be measured is changed to the height direction or the measurement cross section. Even in the case of changing in the vertical direction, the electrical impedance distribution in the measurement cross section can be accurately measured using the same electrical impedance tomography method as in the prior art.

It is a figure for demonstrating the tomography apparatus which concerns on 1st embodiment of this invention, (a) is an external view of a to-be-measured object, (b) has shown the schematic block diagram of the apparatus. It is a figure which shows the flow of the electric current in the measurement cross section of a to-be-measured object, (a) has shown the case where electrical conductivity is uniform, (b) has shown the case where the electrical conductivity of a wall surface vicinity is high. It is a figure which shows the relationship between an outer edge distance and the shortest distance, (a) is an external view of a to-be-measured object, (b) is a top view of a measurement cross section, (c) has shown the expanded view of the to-be-measured object. . It is a flowchart which shows the tomography measuring method which concerns on this invention. It is a figure which shows the simulation result at the time of using the tomography measuring method which concerns on this invention with respect to the to-be-measured object which has a conical surface, (a) is the actual change of the electrical impedance in the wall surface of a to-be-measured object, (b ) Shows the actual change in the electrical impedance in the measurement section, and (c) shows the electrical impedance distribution after image reconstruction by the tomography method. It is a figure which shows the simulation result at the time of using the tomography measurement method of a prior art with respect to the to-be-measured object which has a conical surface, (a) is the actual change of the electrical impedance in the wall surface of a to-be-measured object, (b) Represents the actual change in the electrical impedance in the measurement section, and (c) represents the electrical impedance distribution after image reconstruction by the tomography method. It is a figure which shows the modification of a to-be-measured object, (a) is an external view of a 1st modification, (b) is an expanded view of a 1st modification, (c) is an external view of a 2nd modification. . It is a figure which shows the electrode arrangement | positioning in the tomography apparatus which concerns on 2nd embodiment of this invention, and the flow of an electric current, (a) is when an electric current is sent between E1 electrode and E2 electrode, (b) is E2 electrode (C) is a current between the E1 electrode and the E2 electrode of the comparative example, and (d) is a gap between the E2 electrode and the E3 electrode of the comparative example. When a current is passed through, is shown. It is a figure which shows the reconfigure | reconstructed electrical impedance distribution image, (a) is true distribution, (b) is a comparative example, (c) has shown 2nd embodiment. It is a figure which shows the modification of electrode arrangement | positioning, (a) is a 1st modification, (b) is a 2nd modification, (c) is a 3rd modification, (d) is a 4th modification, (e) The 5th modification is shown. It is a figure which shows the example of application of the tomography apparatus which concerns on embodiment of this invention.

  Hereinafter, a tomography apparatus and a tomography measurement method according to an embodiment of the present invention will be described with reference to FIGS. 1 to 11. Here, FIG. 1 is a diagram for explaining the tomography apparatus according to the first embodiment of the present invention, wherein (a) is an external view of an object to be measured, and (b) is a schematic configuration diagram of the apparatus. Show. 2A and 2B are diagrams showing the flow of current in the measurement cross section of the object to be measured, where FIG. 2A shows the case where the conductivity is uniform, and FIG. 2B shows the case where the conductivity near the wall surface is high. . 3A and 3B are diagrams showing the relationship between the outer edge distance and the shortest distance, wherein FIG. 3A is an external view of the object to be measured, FIG. 3B is a plan view of the measurement cross section, and FIG. Is shown. FIG. 4 is a flowchart showing a tomography measurement method according to the present invention.

  As shown in FIG. 1, the tomography apparatus 1 according to the first embodiment of the present invention uses an electrical impedance tomography method to form an arbitrary cross section of the object A whose cross-sectional area changes in the height direction. A tomography apparatus that measures an electrical impedance distribution of (measurement section B), and a plurality of electrodes 2 arranged on the outer periphery of the measurement section B and a pair of adjacent current load electrodes 2a selected from the plurality of electrodes 2 , 2a, a voltmeter 4 for measuring a potential difference between another pair of measurement target electrodes 2b, 2b selected from a plurality of electrodes 2, and a current load electrode 2a. By measuring the potential difference of the measurement target electrode 2b and selecting all combinations of the current load electrodes 2a for the plurality of electrodes 2 and measuring all the potential differences of the measurement target electrode 2b, An arithmetic unit that acquires potential difference measurement data for all combinations of 2a and measurement target electrode 2b, calculates an electrical impedance tomography method based on the measurement data, and derives an electrical impedance distribution of the object A to be measured The calculation unit 5 includes an outer edge distance L1 along the outer periphery of the measurement cross section B between the current load electrode 2a and the measurement target electrode 2b, and between the current load electrode 2a and the measurement target electrode 2b. The measurement data is corrected based on the ratio of the shortest distance L2 along the wall surface of the object A to be measured.

  As shown in FIG. 1A, the measurement object A has a substantially frustoconical outer shape and has a wall surface constituted by a conical surface whose diameter is reduced downward. The measurement section B is set, for example, on a plane perpendicular to the central axis of the measurement object A. That is, the measurement object A has a shape whose cross-sectional area changes in the height direction or in a direction perpendicular to the measurement cross section B.

  The m electrodes 2 are arranged at equal intervals along the outer periphery of the measurement section B. m is an arbitrary integer, and is set to 8, 12, 16, 32, for example (eight in the figure). Further, the electrode 2 is disposed so as to penetrate the wall surface of the measurement object A and allow current to flow through the internal contents. Further, the electrode 2 is disposed in a state where it is electrically insulated from the wall surface of the object A to be measured. When the wall surface of the measurement object A is made of an insulating material, the electrode 2 only needs to be inserted. However, when the wall surface of the measurement object A is made of a conductive material, the outer periphery of the electrode 2 is measured. You may make it arrange | position an insulating material to. If the electrode 2 and the wall surface of the measurement object A are not insulated, the current flowing from the electrode 2 flows to the wall surface of most measurement object A and does not flow into the measurement section B. is there.

  The power source 3 is, for example, an AC power source, and supplies current to the current load electrodes 2 a and 2 a selected from the plurality of electrodes 2. The current load electrode 2a is a pair of electrodes 2 adjacent to each other. As shown in FIG. 1 (b), when there are eight electrodes 2, the current load electrode 2a has eight combinations. Here, a case where current is supplied to one set of current load electrodes 2a is illustrated, but in reality, power distribution is performed so as to supply current to all eight sets of current load electrodes 2a. In order to supply current to each set of current load electrodes 2a, wiring may be performed so that current can be supplied from one power supply 3 to each set of current load electrodes 2a, or the number of power supplies 3 corresponding to each set. May be arranged. Note that the switching of the current load electrode 2 a that supplies current to the object A to be measured and the supply of current are processed based on a command from the calculation unit 5.

  The voltmeter 4 measures the potential difference between the measurement target electrodes 2 b and 2 b selected from the plurality of electrodes 2. The measurement target electrode 2b is a pair of adjacent electrodes 2 selected from the remaining electrodes 2 excluding the set of current load electrodes 2a. For example, as shown in FIG. 1 (b), when eight electrodes 2 are provided, the electrode is selected from six electrodes 2 excluding one set of current load electrodes 2a. Have. Here, the case of measuring the potential difference of one set of measurement target electrodes 2b is illustrated, but in actuality, wiring is performed so that the potential difference of all the five sets of measurement target electrodes 2b can be measured. Further, the voltmeter 4 has five sets of measurement target electrodes 2b for eight sets of current load electrodes 2a that can be selected, and is wired so that the potential difference can be measured for all combinations of the measurement target electrodes 2b. ing. In order to measure the potential difference of each set of measurement target electrodes 2b, wiring may be performed so that the potential difference of all the combination of measurement target electrodes 2b can be measured with one voltmeter 4, or the number of the corresponding number of sets. A voltmeter 4 may be arranged. Note that the switching of the measurement target electrode 2b for measuring the potential difference and the measurement of the potential difference are processed based on a command from the calculation unit 5.

  Here, the resolution of the measurement cross section B based on the number of electrodes 2 will be described. For example, as shown in FIG. 1B, when eight electrodes are arranged, five sets of measurement target electrodes 2b are provided for one set of current load electrodes 2a, and there are eight types of current load electrodes 2a. Therefore, the number of measurement points can be calculated as 8 × 5/2 = 20 in consideration of overlapping combinations. If this is generalized, the number of measurement points x when m electrodes are arranged can be obtained by a calculation formula of x = m (m−3) / 2. The resolution of the measurement section B is determined by the number of measurement points x, and has the same resolution as the number of measurement points x. Therefore, it is preferable to divide the measurement section B into elements (measurement regions U) that are equal to or greater than the number of measurement points x. For example, as shown in FIG. 1B, when eight electrodes are provided, a mesh of 20 measurement regions U1 to U20 can be created.

  The calculation unit 5 sets a measurement region U (for example, U1 to U20) in the measurement section B according to the number of electrodes 2 and controls the power source 3 and the voltmeter 4 to calculate the potential difference for the 20 measurement points. The measured measurement data is acquired, the electrical impedance is calculated for each measurement region U, and the distribution of the electrical impedance in the measurement section B is derived. Further, the calculation unit 5 corrects the measurement data when deriving the distribution of the electrical impedance in the measurement section B. Specific processing of the calculation unit 5 will be described later. The calculation unit 5 is configured by a so-called computer.

  By the way, when the conductivity in the measurement section B of the object A is uniform, the current supplied by the current load electrode 2a is a current in the measurement section B as shown in FIG. Will flow uniformly. On the other hand, when the conductivity in the vicinity of the wall surface in the measurement section B of the measurement object A is high, the current supplied by the current load electrode 2a is a current in the measurement section B as shown in FIG. Tends to flow along the vicinity of the wall. For example, when the measurement object A has a shape whose cross-sectional area changes in the height direction as shown in FIG. 1A, foreign matter such as sediment or sediment is deposited on the wall surface of the measurement object A or It tends to remain. When the foreign matter has conductivity, ideally, the current supplied by the current load electrode 2a is along the vicinity of the wall surface of the measurement object A in the measurement cross section B as shown in FIG. I want it to flow. This is because the accumulation amount or residual amount of foreign matter in the measurement cross section B can be grasped by such a current flowing.

  Now, as shown in FIGS. 3A and 3B, points a to d on the outer edge of the measurement cross section B when the measurement object A has a shape whose cross-sectional area changes in the height direction. Think about the relationship. Here, a point a indicates an intermediate point of the current load electrode 2a, and points b to d indicate intermediate points of the measurement target electrode 2b.

  As shown in FIG. 3C, when the conical surface of the measurement object A is flattened, the shortest distance between the points a and b is not the arc ab (the distance is the outer edge distance L1), A straight line ab (the distance is the shortest distance L2). Similarly, the shortest distance between the points a and c is not the arc ac (outer edge distance L1) but a straight line ac (shortest distance L2), and the shortest distance between the points a and d is the arc ad (outer edge distance L1). ), Not a straight line ad (shortest distance L2). Therefore, the current path when the object A has a shape whose cross-sectional area changes in the height direction is not an arc having the outer edge distance L1 on the measurement cross section B, but the shortest distance L2 passing below the measurement cross section B. A curve having と な っ て becomes the shortest path. As a result, when current is supplied from the power source 3 to the current load electrode 2a, most of the current flows through the path having the shortest distance L2, and the amount of current flowing through the measurement section B is reduced. The measured potential difference value becomes smaller than the actual value. This makes it impossible to measure an accurate electrical impedance distribution.

  Therefore, in the present embodiment, since the length of the current path and the amount of flowing current are inversely proportional, the outer edge distance L1 along the outer periphery of the measurement section B between the current load electrode 2a and the measurement target electrode 2b. The potential difference is corrected based on the ratio between the current load electrode 2a and the measurement target electrode 2b and the shortest distance L2 along the wall surface of the object A to be measured. Specifically, the potential difference is corrected by multiplying the measured potential difference by a correction coefficient α (α = L1 / L2) obtained by dividing the outer edge distance L1 by the shortest distance L2. Further, depending on the shape of the measurement object A and the properties of the foreign matter, the amount of foreign matter deposited or remaining in the height direction may change greatly, and the ease of current flow may change. In such a case, the measured potential difference may be corrected by calculating a correction coefficient based on the shape of the measurement object A, the amount of accumulated foreign matter, or the residual amount by simulation or experiment.

  The correction coefficient α is stored in, for example, a storage device such as the database 6. That is, the tomography apparatus 1 calculates the correction coefficient α by obtaining the outer edge distance L1 and the shortest distance L2 for all combinations of the current load electrode 2a and the measurement target electrode 2b as shown in FIG. The database 6 stores the correction coefficient α for each combination of the current load electrode 2a and the measurement target electrode 2b. As shown in FIG. 1B, when eight electrodes 2 are provided, the measurement pattern is geometrically determined by all combinations of the current load electrode 2a and the measurement target electrode 2b, as shown in FIG. Are summarized in the three patterns shown in FIG. Therefore, in the above-described embodiment, the correction coefficient α is the length of the arc ab / the length of the straight line ab, the length of the arc ac / the length of the straight line ac, the length of the arc ad / the length of the straight line ad. One of three types is set.

  Here, the tomography measurement method according to the embodiment of the present invention using the tomography apparatus 1 described above will be described with reference to the flowchart shown in FIG.

  The tomography measurement method according to the embodiment of the present invention uses an electrical impedance tomography method to measure the electrical impedance distribution of the measurement section B in the measurement object A whose cross-sectional area changes in the height direction. A method of creating a mesh (SP101) in which a plurality of electrodes 2 are arranged on the outer periphery of a measurement section B and the measurement section B is divided into a plurality of measurement regions U, and a pair of adjacent ones selected from the plurality of electrodes 2 A potential difference measuring step (SP104) of supplying a current to the current load electrode 2a and measuring a potential difference between another pair of adjacent measurement target electrodes 2b selected from the plurality of electrodes 2, and the current load electrode 2a and the measurement target The outer edge distance L1 along the outer periphery of the measurement cross section B between the electrode 2b and the outermost distance along the wall surface of the measurement object A between the current load electrode 2a and the measurement target electrode 2b. The potential difference correcting step (SP105) for correcting the potential difference measured based on the ratio of the distance L2 and the potential difference measuring step (SP104) and the potential difference correcting step (SP105) are repeated to repeat the current load electrode 2a and the measurement target electrode 2b. Electrical impedance distribution deriving step of obtaining potential difference measurement data corrected for all combinations of the above, performing calculation by the electrical impedance tomography method based on the measurement data, and deriving the electrical impedance distribution of the object A to be measured ( SP106 to SP107).

  In the mesh creation step (SP101), as shown in FIG. 1B, the measurement cross section B is divided into a plurality of measurement regions U1 to U20 and measured so that a resolution corresponding to the number of electrodes 2 can be obtained. This is a step of creating a mesh for use.

  Next, the potential difference V (n) fir at the measurement number n when all the measurement regions U are low resistance and the potential difference V (n) obj at the measurement number n when all the measurement regions U are high resistance. Using the finite element method, the potential difference V (e, n) at the measurement number n when only the e-th measurement region U is high resistance is obtained (SP102).

Next, the potential difference V (n) fir, the potential difference V (n) obj, and the potential difference V (e, n) are substituted into the following equation (Equation 1) to obtain the sensitivity matrix S (e, n) (SP103 ). However, β (e) = D (e) / Dall, D (e) is the area of the e-th measurement region U, and Dall is the sum of the areas of all the measurement regions U.

  The potential difference measuring step (SP104) is a step of supplying a current to the current load electrode 2a by the power source 3 and measuring the potential difference of the measurement target electrode 2b by the voltmeter 4. This step may move to the next step (potential difference correction step) for each potential difference measurement, or move to the next step (potential difference correction step) after measuring the potential difference for all measurement points x. May be. The potential difference measured by the voltmeter 4 is defined as V (n) measured. In addition, the process from the mesh creation process (SP101) to the potential difference measurement process (SP104) described above is a process of performing the same processing as the tomography measurement method in the prior art.

  The potential difference correcting step (SP105) is a step of correcting the potential difference V (n) measured measured by the voltmeter 4 based on the ratio between the outer edge distance L1 and the shortest distance L2. Specifically, the potential difference is corrected by multiplying the measured potential difference V (n) measured by a correction coefficient α (α = L1 / L2) obtained by dividing the outer edge distance L1 by the shortest distance L2, and measurement data Get. Such processing is performed by the calculation unit 5 using the database 6. Note that the correction coefficient α is merely an example, and a correction coefficient that takes into account the shape of the measurement object A, the properties of the foreign matter, and the like may be used together or substituted.

  The electrical impedance distribution derivation step is divided into an electrical impedance calculation step (SP106) and an impedance image reconstruction step (SP107). In the electrical impedance distribution derivation step, processes other than the use of the corrected measurement data are the same as the tomography measurement method in the prior art.

The electrical impedance calculation step (SP106) is a step of calculating electrical impedance based on the corrected measurement data. First, it is made dimensionless by substituting the corrected potential difference V (n) measured into the following equation (Equation 2). By using this dimensionless potential difference, the maximum value of resistance becomes 1 and the minimum value becomes 0, which is convenient for imaging.

Thereafter, the impedance matrix value P (e) is calculated by substituting the sensitivity matrix S (e, n) and the dimensionless potential difference into the following equation (Equation 3).

  The impedance image reconstruction step (SP107) is a step of reconstructing an electrical impedance distribution image based on the calculated impedance equivalent value P (e). In this process, the electrical impedance distribution image is reconstructed with a maximum value of 1 and a minimum value of 0 for a plurality of impedance equivalent values P (e) obtained from a single measurement result in the measurement section B.

  Next, it is determined whether or not the measurement has been performed for a predetermined time or a predetermined number of times (SP108). This step is a step of determining whether or not the electrical impedance distribution derivation step has been repeated a required number of times based on time or the number of times. The required number of times is determined based on whether or not all measurement points x (for example, 20 patterns) have been measured in the measurement cross section B when the potential difference is corrected by the correction coefficient α every time the potential difference is measured. Further, when the potential difference is corrected by the correction coefficient α after measuring the potential difference at all the measurement points x, the required number of times may be set to one time, or an average value of a plurality of times may be calculated. In some cases, the necessary number of times may be set to two or more.

  If the measurement in the electrical impedance distribution deriving step does not satisfy the predetermined condition (time or number of times), the process returns to the potential difference measuring step (SP104) and repeats the electric impedance distribution deriving step, and the predetermined condition (time or time) If the number of times is satisfied, the process is terminated.

  Here, the simulation result when the tomography measurement method according to the present embodiment described above is used will be described in comparison with the simulation result when the conventional tomography measurement method is used. FIG. 5 is a diagram showing a simulation result when the tomography measurement method according to the present invention is used for an object having a conical surface, and (a) shows an actual electric impedance of the wall surface of the object to be measured. The change, (b) shows the actual change of the electrical impedance in the measurement section, and (c) shows the electrical impedance distribution after image reconstruction by the tomography method. FIG. 6 is a diagram showing a simulation result when the tomography measurement method of the prior art is used for an object to be measured having a conical surface, and (a) shows an actual change in electrical impedance on the wall surface of the object to be measured. (B) shows the actual change of the electrical impedance in the measurement section, and (c) shows the electrical impedance distribution after image reconstruction by the tomography method. In each figure, the figures arranged side by side represent the states at the same time.

  The above-described simulation shows that the object to be measured A has a substantially frustoconical outer shape as shown in FIG. 1A and has a wall surface constituted by a conical surface whose diameter is reduced downward. Filled with a conductive fluid, a highly conductive substance (for example, metal particles) is uniformly distributed on the top surface, creating a state where it settles over time, and the temporal change in electrical impedance was measured. Is. Further, as an index indicating time, a numerical value obtained by dividing the measurement time t by the time ts at which the concentration of the highly conductive substance peaks in the measurement cross section B is used. 5A to 5B and FIGS. 6A to 6B, the darker the color, the higher the concentration of the highly conductive material, the lower the electrical impedance, and the easier the current flows. 5 (c) and 6 (c), the darker the color, the lower the electrical impedance.

  As shown in FIG. 5A, a highly conductive material is applied to the wall surface of the object A to be measured every time t / ts = 0.6, 1.0, 1.4, 1.6. It can be easily understood that it is deposited or remains. Note that the nodes in FIG. 5A are based on the accuracy of the simulation and do not affect the results. Similarly, in FIG. 5B showing the measurement cross section B, it is possible to grasp how the highly conductive substance is deposited or remains on the wall surface of the measurement object A.

  When the tomography measurement method according to the present embodiment described above is used, as shown in FIG. 5C, the electrical impedance of the measurement region U of the outer edge portion in the measurement cross section B in all time zones. Can be grasped. A low electrical impedance means that the resistance value is low, and a low resistance value means that it contains a large amount of highly conductive material. Therefore, as shown in FIG. 5C, the low electrical impedance of the outer edge portion in the measurement cross section B means that the wall surface of the object A to be measured as shown in FIGS. 5A and 5B. It means that the state where the highly conductive substance is deposited or remains is accurately measured.

  On the other hand, as shown in FIG. 6, when the tomography measurement method of the prior art is used, in the time zone of t / ts = 0.6, 1.0, 1.4, the case of the present embodiment. Similarly, the electrical impedance of the outer edge portion in the measurement cross section B is measured low. However, in the time zone of t / ts = 1.6, the electrical impedance at the center of the measurement cross section B is measured low. This is presumed that a large amount of highly conductive material is accumulated or remains on the wall surface of the object A to be measured, and a large amount of current at the time of potential difference measurement flows through the path having the shortest distance L2 instead of the outer edge distance L1. . This is easily understood from the object A having a conical surface because the current passing through the shortest distance L2 flows near the center of the object A as shown in FIG. can do. Accordingly, when the tomography measurement method of the prior art is used, as shown in FIG. 6C, the fact that the electrical impedance of the central portion in the measurement cross section B is low indicates that FIGS. This means that the state in which a highly conductive substance is deposited or remains on the wall surface of the measurement object A as shown in FIG.

  As described above, according to the tomography apparatus 1 and the tomography measurement method according to this embodiment described above, the potential difference is corrected according to the ratio between the outer edge distance L1 and the shortest distance L2, so that the cross-sectional area of the measurement object A is increased. Even in the case of changing in the height direction or the direction perpendicular to the measurement cross section B, the electrical impedance distribution in the measurement cross section B can be accurately measured using the same electrical impedance tomography method as in the prior art.

  Next, a modified example of the measurement object A will be described with reference to FIG. Here, FIG. 7 is a figure which shows the modification of a to-be-measured object, (a) is an external view of a 1st modification, (b) is an expanded view of a 1st modification, (c) is a 2nd modification. It is an external view of an example.

  The first modification shown in FIGS. 7A and 7B represents a case where the measured object A is constituted by a container having a quadrangular pyramid surface. As shown in FIG. 7A, the measurement object A has a substantially quadrangular pyramid shaped outer shape, and has a wall surface constituted by a quadrangular pyramid surface whose sectional area decreases downward. The measurement cross section B is set, for example, on a plane perpendicular to the central axis of the measurement object A, and has a square shape. That is, the measurement object A has a shape whose cross-sectional area changes in the height direction or in a direction perpendicular to the measurement cross section B. In addition, although the case where the to-be-measured object A has a quadrangular pyramid surface is illustrated here, the to-be-measured object A may have a triangular pyramid surface or a polygonal pyramid surface that is greater than a pentagonal pyramid surface. Also good.

  As shown in FIGS. 7A and 7B, the relationship between points a to c on the outer edge of the measurement cross section B will be considered. As shown in FIG. 7B, when the quadrangular pyramid surface of the object A to be measured is flattened, the shortest distance between the points a and b is not the path acb (outer edge distance L1) but the straight line ab (shortest). Distance L2). Therefore, as in the above-described embodiment, the potential difference measured by the correction coefficient α is corrected. The shortest distance between the points a and c is a straight line ac, and the outer edge distance L1 and the shortest distance L2 are equal. As described above, when the relationship of the outer edge distance L1 = the shortest distance L2 is satisfied, it is not necessary to perform correction using the correction coefficient α.

  The second modified example shown in FIG. 7C represents a case where the measured object A has a wall surface formed by a bent pipe. When the object A to be measured is a curved or bent pipe, the pipe may be arranged obliquely as illustrated. In this case, since the surface of the contents forms a horizontal plane, the measurement cross section B is not in a direction perpendicular to the pipe but in a direction parallel to the horizontal plane. And when the electroconductive substance has adhered to the inner surface of piping, it will become easy to flow into the shortest distance L2 shown with the broken line of the figure at the time of potential difference measurement. For example, when considering the relationship between the points a and b on the outer edge of the measurement section B, the shortest distance between the points a and b is not the route ab (outer edge distance L1) but the route ab ′ (shortest distance L2). Become. Therefore, as in the above-described embodiment, the potential difference measured by the correction coefficient α is corrected. In this case, the correction coefficient α is determined by, for example, the length of the arc ab (outer edge distance L1) / the length of the arc ab ′ (shortest distance L2).

  Next, a tomography apparatus according to a second embodiment of the present invention will be described with reference to FIGS. Here, FIG. 8 is a diagram showing an electrode arrangement and a current flow in the tomography apparatus according to the second embodiment of the present invention. FIG. 8A shows a case where a current is passed between the E1 electrode and the E2 electrode. (B) shows the case where a current is passed between the E2 electrode and the E3 electrode, (c) shows the case where a current is passed between the E1 electrode and the E2 electrode of the comparative example, and (d) shows the E2 of the comparative example. In the case where a current is passed between the electrode and the E3 electrode, FIG. FIG. 9 is a diagram showing a reconstructed electrical impedance distribution image, where (a) shows a true distribution, (b) shows a comparative example, and (c) shows a second embodiment. In addition, about the same component as the tomography apparatus 1 which concerns on 1st embodiment mentioned above, the same code | symbol is attached | subjected and the overlapping description is abbreviate | omitted.

  The second embodiment shown in FIGS. 8 and 9 shows a case where the measurement cross section B has a rectangular cross section (for example, a square cross section). When the measurement cross section B has a circular shape as in the first embodiment described above, a plurality of electrodes 2 can be arranged at equal intervals along the outer periphery thereof. Moreover, in 1st embodiment mentioned above, when the electrical conductivity in the measurement cross section B is uniform no matter how the current load electrode 2a is selected among the plurality of electrodes 2, the current in the measurement cross section B is Are substantially in the same state (for example, the state shown in FIG. 2A), and the equipotential line distribution at the time of each measurement has a substantially matching shape. Therefore, since each measurement condition of the potential difference in the measurement cross section B is substantially the same condition, the error in the case where the electrical impedance distribution is derived from the measurement data and the electrical impedance distribution image is reconstructed after the temperature correction is small. A highly accurate electrical impedance distribution image can be obtained.

  On the other hand, when the measurement cross section B has a rectangular cross section, the equipotential line distributions at the time of each measurement do not always coincide with each other simply by arranging the electrodes 2 at equal intervals along the outer periphery. For example, the comparative example shown in FIGS. 8C and 8D shows a case where two electrodes 2 (E1 electrode to E8 electrode) are arranged at equal intervals on each side of the measurement cross section B having a rectangular cross section. Show. Further, FIG. 8C shows a case where a current is passed between the E1 electrode and the E2 electrode, and FIG. 8D is a case where a current is passed between the E2 electrode and the E3 electrode. Is illustrated. In addition, the equipotential line distribution shown in each figure of FIG. 8 has shown the case where the electrical conductivity in the measurement cross section B is uniform.

  As shown in FIG. 8C and FIG. 8D, the case where a current is passed through the electrodes 2 (E1 electrode and E2 electrode) arranged on the same side and the electrodes 2 arranged on different sides. When the current is passed through (E2 electrode and E3 electrode), the current flows, that is, the equipotential line distribution has a different shape. Therefore, each measurement condition of the potential difference in the measurement cross section B has two types of conditions (when the electrode 2 on the same side is selected and when the electrode 2 on a different side is selected). Since the sensitivity given to the reconstructed image is different, the accuracy when the electrical impedance distribution image is reconstructed is lowered, and the error is increased.

  Here, FIG. 9A shows the true electrical impedance distribution in the measurement section B, and FIG. 9B shows the electrical impedance distribution image of the comparative example shown in FIGS. 8C and 8D. Is shown. In each drawing of FIG. 9, the lighter the color, the higher the impedance (resistance), and the darker the color, the lower the impedance (resistance). In the true distribution shown in FIG. 9A, the impedance of the central portion of the measurement cross section B is high and the impedance of the peripheral portion is low. On the other hand, in the distribution of the comparative example shown in FIG. 9B, the impedance of the middle part of each side of the measurement cross section B is the highest, and then the impedance of the center part and the corner part is displayed in a state of increasing. . According to the simulation result, when the electrode 2 is arranged in the measurement cross section B as in the comparative example, the accuracy when the electrical impedance distribution image is reconstructed is lowered, and the error is easily increased. Understandable.

  On the other hand, in the electrode arrangement in the second embodiment shown in FIGS. 8A and 8B, the measurement cross section B has a polygonal cross section (for example, a rectangular cross section), and the electrode 2 has each rectangular cross section. Including electrodes (E1 electrode, E3 electrode, E5 electrode, E7 electrode) arranged across the two sides constituting the corner, and electrodes (E1 electrode, E3 electrode, E5 electrode) arranged at each corner , E7 electrode) includes electrodes (E2 electrode, E4 electrode, E6 electrode, E8 electrode) arranged on each side of the rectangular cross section at equal intervals. Therefore, the electrode 2 (E1 electrode, E3 electrode, E5 electrode, and E7 electrode) disposed in the corner portion has an L-shaped cross section, and the electrode 2 (E2 electrode, E4 electrode, E6 electrode, and E8 electrode) has a flat plate shape.

  According to this electrode arrangement, when the adjacent electrode 2 is selected as the current load electrode 2a, the electrode 2 (for example, the E1, E3, E5, and E7 electrodes) arranged at the corners is always on the side. As shown in FIG. 8 (a) and FIG. 8 (b), the current flows as shown in FIG. 8 (a) and FIG. 8 (b). That is, the equipotential line distribution has a symmetrical shape. Therefore, in the vicinity of the center portion in the measurement cross section B, the equipotential line distribution has substantially the same shape, and there is little error when the electrical impedance distribution image is reconstructed, and a highly accurate electrical impedance distribution image can be obtained. it can.

  Here, FIG.9 (c) has shown the electrical impedance distribution image of 2nd embodiment shown to Fig.8 (a) and (b). As shown in the figure, in the distribution of the second embodiment shown in FIG. 9C, the impedance of the central portion of the measurement cross section B is high and the impedance of the peripheral portion is low. It can be easily understood that it has the same tendency as the true distribution shown. Therefore, the electrode arrangement in the second embodiment has less error when the electrical impedance distribution image is reconstructed than the electrode arrangement of the comparative example shown in FIG. Can be obtained.

  The electrode arrangement in the second embodiment described above is not limited to the arrangement shown in the figure. For example, the measurement cross section B may be a polygonal cross section other than a rectangular cross section, or two sides constituting a corner portion. You may be comprised only by the electrode 2 arrange | positioned ranging. Here, FIG. 10 is a figure which shows the modification of electrode arrangement | positioning, (a) is a 1st modification, (b) is a 2nd modification, (c) is a 3rd modification, (d) is a 1st modification. 4 shows a modification, (e) a fifth modification. In addition, in each figure of FIG. 10, the broken line in the measurement cross section B has shown an example of the measurement area | region divided | segmented into plurality.

  In the first modification shown in FIG. 10A, the measurement cross section B has a rectangular cross section (for example, a square cross section), and all the electrodes 2 (E1, E2, E3, and E4 electrodes) have a rectangular cross section. Are arranged across two sides constituting each corner. According to such an electrode arrangement, when adjacent electrodes 2 are selected as the current load electrodes 2a, they are always combined by the electrodes 2 arranged at the corners, so that a current flows, that is, an equipotential line distribution. Have substantially the same shape, and an electrical impedance distribution image with high accuracy can be obtained.

  In the second modification shown in FIG. 10B, the measurement cross section B has a rectangular cross section (for example, a square cross section), and the electrode 2 extends over two sides constituting each corner of the rectangular cross section. Including the electrodes (E1 electrode, E4 electrode, E7 electrode, E10 electrode) arranged at equal intervals in the middle of the electrodes (E1 electrode, E4 electrode, E7 electrode, E10 electrode) arranged at each corner It includes electrodes (E2 electrode, E3 electrode, E5 electrode, E6 electrode, E8 electrode, E9 electrode, E11 electrode, E12 electrode) arranged on each side of the rectangular cross section.

  According to this electrode arrangement, when the adjacent electrode 2 is selected as the current load electrode 2a, not only the combination of the electrode 2 arranged at the corner and the electrode 2 arranged on the side, but also on the side A combination of only the arranged electrodes 2 also exists. However, the former combination has a larger number than the latter combination (in this case, twice), and the equipotential line distribution when two electrodes 2 arranged on the side are selected is shown in FIG. In view of the fact that it has a substantially bilaterally symmetric shape as shown and less distortion at the center of the measurement cross section B, it is possible to obtain a highly accurate electrical impedance distribution image with fewer errors than the comparative example described above. Can do.

  In the third modified example shown in FIG. 10C, the measurement cross section B has a regular hexagonal cross section, and all the electrodes 2 (E1, E2, E3, E4, E5, and E6 electrodes) are regular six. It arrange | positions ranging over two sides which comprise each corner | angular part of a square cross section. According to such an electrode arrangement, when adjacent electrodes 2 are selected as the current load electrodes 2a, they are always combined by the electrodes 2 arranged at the corners, so that the current flow distribution, that is, the equipotential lines The distribution has substantially the same shape, and a highly accurate electrical impedance distribution image can be obtained.

  In the fourth modification shown in FIG. 10 (d), the measurement section B has a regular hexagonal section, and the electrode 2 is an electrode arranged across two sides constituting each corner of the regular hexagonal section. (E1 electrode, E3 electrode, E5 electrode, E7 electrode, E9 electrode, E11 electrode) and electrodes arranged at each corner (E1 electrode, E3 electrode, E5 electrode, E7 electrode, E9 electrode, E11 electrode) The electrodes (E2 electrode, E4 electrode, E6 electrode, E8 electrode, E10 electrode, E12 electrode) arranged on each side of the regular hexagonal cross section at equal intervals are included in the middle portion of the.

  According to such an electrode arrangement, when the adjacent electrode 2 is selected as the current load electrode 2a, it is always a combination of the electrode 2 arranged at the corner and the electrode 2 arranged on the side. As in the case of the second embodiment, an equipotential distribution having symmetry can be obtained, and a highly accurate electrical impedance distribution image can be obtained.

  In the fifth modification shown in FIG. 10E, the measurement cross section B has a regular hexagonal cross section, and all the electrodes 2 (E1 electrode, E2 electrode, E3 electrode, E4 electrode, E5 electrode, and E6 electrode) are regular hexagons. It arrange | positions in the intermediate part of each edge | side of a square cross section. In this electrode arrangement, electrodes are arranged at equal intervals on the sides constituting the measurement section B. According to such an electrode arrangement, when adjacent electrodes 2 are selected as the current load electrodes 2a, they are always combined by the electrodes 2 arranged on the side, so that the current flow distribution, that is, the equipotential line The distribution has substantially the same shape, and a highly accurate electrical impedance distribution image can be obtained.

  The measurement section B is not limited to the above-described section shape, and may have a regular polygonal section such as a regular triangle, a regular pentagon, a regular octagon, or the like within an allowable error range. For example, it may have a polygonal cross section approximating a regular polygon.

  Further, in the first embodiment and the second embodiment (including the modifications) described above, the combination of the current load electrodes 2a does not necessarily need to be a combination of the adjacent electrodes 2. That is, instead of the pair of adjacent current load electrodes 2a, the pair of electrodes 2 is selected so that the equipotential line distribution in the vicinity of the central portion in the measurement cross section B has substantially the same shape to be the current load electrode 2a. May be. For example, if the equipotential line distribution is a combination of the electrodes 2 having substantially the same shape, the electrodes 2 located on the diagonal line, the electrodes 2 arranged alternately, etc. may be selected as the current load electrode 2a. Good. Specifically, in the measurement cross section B having the circular cross section shown in the first embodiment, a pair of electrodes 2 located on a diagonal line may be used as the current load electrodes 2a, or a second modification of the second embodiment. In the measurement cross section B shown, a combination of the E1 electrode and the E3 electrode, the E2 electrode and the E4 electrode, or the like may be selected as the current load electrode 2a.

  Finally, the case where the tomography apparatus 1 of the above-described embodiment is applied to the glass melting furnace 10 will be described with reference to FIG. Here, FIG. 11 is a diagram illustrating an application example of the tomography apparatus according to the embodiment of the present invention.

  Conventionally, a glass melting furnace 10 is used to vitrify radioactive waste discharged from a nuclear power plant. In a general glass melting furnace 10 in Japan, radioactive waste 11 and glass raw material 12 are introduced into the furnace from the top, and heated using a main electrode 13, a bottom electrode 14 and an indirect heating device 15, The molten glass containing the radioactive waste is flowed down from the flow-down nozzle 16 and is solidified in a canister 17 installed under the furnace. In addition, the outer wall of the glass melting furnace 10 is comprised with the heat insulating materials 18, such as a refractory brick. The furnace bottom side of the glass melting furnace 10 has a conical surface or a pyramid surface, and has a shape whose cross-sectional area changes in the height direction.

  And the tomography apparatus 1 of this embodiment is used in order to grasp | ascertain the deposition or residual condition in the furnace of platinum group contained in a radioactive waste. Specifically, the bottom of the glass melting furnace 10 is the object A to be measured, and the measurement cross section B is formed by disposing a plurality of electrodes 2 at a place where it is desired to grasp the deposition or residual state of the platinum group. Although not shown, the power source 3, the voltmeter 4, the calculation unit 5, and the database 6 are arranged outside the furnace. Here, the measurement cross section B is arranged at one place, but a plurality of measurement cross sections B may be formed in the height direction.

  Since the platinum group has higher conductivity than molten glass and easily deposits or remains on the wall surface, the platinum group is suitable for using the tomography measurement method according to the above-described embodiment. By measuring the electrical impedance of the platinum group, the concentration distribution of the platinum group can be grasped, and the deposition or residual state of the platinum group in the furnace can be grasped.

  The tomography apparatus 1 and the tomography measurement method according to the embodiment described above are not limited to the case where the tomography apparatus 1 and the tomography measurement method are applied to the glass melting furnace 10, and the cross-sectional area is perpendicular to the height direction or the measurement cross section B. When it is desired to measure the electrical impedance in a portion having a changing shape, it can be applied to various melting furnaces and incinerators. For example, the present invention can be applied to a fluidized bed furnace in which gas and sand are mixed, and a piping system such as an evaporation pipe constituting a gas-liquid two-phase flow.

  The present invention is not limited to the above-described embodiment, and various changes can be made without departing from the spirit of the present invention, such as using an electric signal system such as a capacitor type instead of the electric resistance type for measuring the potential difference. Of course.

DESCRIPTION OF SYMBOLS 1 Tomography apparatus 2 Electrode 2a Current load electrode 2b Measuring object electrode 3 Power supply 4 Voltmeter 5 Calculation part 6 Database

Claims (9)

A tomography apparatus for measuring an electrical impedance distribution of a measurement cross section of an object to be measured using an electrical impedance tomography method,
The object to be measured has a shape in which the size of a cross-sectional area changes along a direction perpendicular to the measurement cross section,
A plurality of electrodes disposed on the outer periphery of the measurement cross section;
A power supply for supplying current to a pair of adjacent current load electrodes selected from the plurality of electrodes;
A voltmeter for measuring a potential difference between another pair of measurement target electrodes selected from the plurality of electrodes;
Measure potential differences of all the measurement target electrodes with respect to the current load electrode, and measure all potential differences of the measurement target electrodes by selecting all combinations of the current load electrodes with respect to the plurality of electrodes. Thus, potential difference measurement data is acquired for all combinations of the current load electrode and the measurement target electrode, and calculation is performed by the electrical impedance tomography method based on the measurement data, and the electrical impedance of the object to be measured An arithmetic unit for deriving a distribution of
The computing unit includes an outer edge distance along an outer periphery of the measurement cross section between an intermediate point of the pair of current load electrodes and an intermediate point of the pair of measurement target electrodes, and an intermediate point of the pair of current load electrodes. Correcting the measurement data based on the ratio of the shortest distance along the wall surface of the object to be measured between the intermediate points of the pair of measurement target electrodes ,
A tomography apparatus characterized by that.   The tomography apparatus according to claim 1, wherein the calculation unit corrects the measurement data by multiplying the measurement data by a correction coefficient obtained by dividing the outer edge distance by the shortest distance. .   For all combinations of the current load electrode and the measurement target electrode, the correction coefficient is calculated by obtaining the outer edge distance and the shortest distance, and the correction coefficient for each combination of the current load electrode and the measurement target electrode. The tomography apparatus according to claim 2, further comprising a database that stores therein.   The tomography apparatus according to claim 1, wherein the object to be measured has a wall surface constituted by a container having a conical surface or a pyramid surface or a curved or bent pipe.   The said measurement cross section has a polygonal cross section, and the said electrode contains the electrode arrange | positioned ranging over two sides which comprise each corner | angular part of the said polygonal cross section. Tomography device.   The tomography apparatus according to claim 5, wherein the electrodes include electrodes arranged on each side of the polygonal cross section at equal intervals in an intermediate portion of the electrodes arranged at the corners. .   The tomography apparatus according to claim 1, wherein the measurement cross section has a polygonal cross section, and the electrode includes an electrode disposed at an intermediate portion of each side of the polygonal cross section. A tomography measurement method for measuring an electrical impedance distribution of a measurement cross section of an object to be measured using an electrical impedance tomography method,
The object to be measured has a shape in which the size of a cross-sectional area changes along a direction perpendicular to the measurement cross section,
A mesh creation step of arranging a plurality of electrodes on the outer periphery of the measurement cross section and dividing the measurement cross section into a plurality of measurement regions;
A potential difference measuring step of supplying a current to a pair of adjacent current load electrodes selected from the plurality of electrodes and measuring a potential difference between another pair of adjacent measurement target electrodes selected from the plurality of electrodes;
The outer edge distance along the outer periphery of the measurement cross section between the intermediate point of the pair of current load electrodes and the intermediate point of the pair of measurement target electrodes, the intermediate point of the pair of current load electrodes, and the pair of measurement targets A potential difference correction step of correcting the potential difference based on a ratio of the shortest distance along the wall surface of the object to be measured between the intermediate point of the electrodes ;
The potential difference measurement step and the potential difference correction step are repeated to acquire potential difference measurement data corrected for all combinations of the current load electrode and the measurement target electrode, and the electrical impedance tomography is based on the measurement data. An electrical impedance distribution deriving step of performing an arithmetic operation and deriving an electrical impedance distribution of the object to be measured.
A tomography measurement method characterized by this. The tomography measurement method according to claim 8 , wherein the potential difference correction step corrects the potential difference by multiplying the potential difference by a correction coefficient obtained by dividing the outer edge distance by the shortest distance. .