Sensors and level gauges for identifying the position of the interface

Abstract

An interface sensor is disclosed that has a well-balanced configuration in which the total number of conductors drawn from the interface sensor is less than the total number of observation points. The interface sensor 1 has a configuration determined by a coding system and its specific code words, and a) for the number e(k) of electrode pairs included in the kth (k∈[K]) sensor block included in the interface sensor 1, the maximum value max of the number e(k) in the set [K] is k∈[K] e(k) and minimum value min k∈[K] The difference between e(k) is smaller than that of the prior art, or b) the jth sensor (j∈[J]=[Σ k∈[K] c(k)], c(k) is the number of wires included in the kth (k∈[K]) sensor block), the maximum value max of the number t(j) on the set [J] of the number t(j). j∈[J] t(j) and minimum value min j∈[J] The difference in t(j) is smaller than that of the prior art.

Description

[Technical Field]

[0001] The present disclosure relates to a sensor for identifying the position of an interface between two types of substances (hereinafter referred to as an interface sensor), and a liquid level meter including the interface sensor. [Background technology]

[0002] The applicant of the present application is the applicant of Patent Document 1 (International Publication No. WO2023 / 203912A1), Patent Document 2 (International Publication No. WO2023 / 218744A1), Patent Document 3 (International Publication No. WO2023 / 248947A1), and Patent Document 4 (International Publication No. WO2024 / 024325A1).

[0003] Figure 1 is a copy of Figure 9 in Patent Document 1. Figure 2 is a copy of Figure 13 in Patent Document 2. Figure 3 is a copy of Figure 10 in Patent Document 3. Figure 4 is a copy of Figure 16 in Patent Document 4.

[0004] The interface sensor with the configuration shown in Figure 1 "An interface sensor 2 for identifying the position of an interface between a first substance and a second substance, K sensor blocks 3 are included, where K is a predetermined integer satisfying 2≦K; The k-th sensor block 3 among the K sensor blocks 3 includes M(k) electrode pairs 5 and n(k)+1 conducting wires 7, where k∈{x∈N:1≦x≦K}, N is a set of all positive integers, n(k) is a predetermined integer satisfying 2≦n(k), M(1)≧8, and for each k∈{x∈N:1≦x≦K},

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[0005] The interface sensor with the configuration shown in Figure 2 "An interface sensor 2 for identifying the position of an interface between a first substance and a second substance, a first electrical conductor 5a and K sensor blocks 3, where K is a predetermined integer satisfying 2≦K; The k-th sensor block 3 among the K sensor blocks 3 includes M(k) second electrical conductors 5b and n(k) conducting wires 7, where k∈{x∈N: 1≦x≦K}, N is a set of all positive integers, n(k) is a predetermined integer satisfying 2≦n(k), M(1)=4 or M(1)=6 or M(1)≧8, and for each k∈{x∈N: 1≦x≦K},

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[0006] The interface sensor with the configuration shown in Figure 3 "A sensor 200 for identifying the position of an interface between a first substance and a second substance, E electrode pairs 500, L conductors 700, and a conductor selector 800,

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[0007] The interface sensor with the configuration shown in Figure 4 "A sensor 200 for identifying the position of an interface between a first substance and a second substance, a first electrical conductor 500a, E second electrical conductors 500b, L conductors 700, and a conductor selector 800,

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[0008] [Patent Document 1] WO2023 / 203912A1 [Patent Document 2] WO2023 / 218744A1 [Patent Document 3] WO2023 / 248947A1 [Patent Document 4] WO2024 / 024325A1 Summary of the Invention [Problem to be solved by the invention]

[0009] The interface sensors disclosed in Patent Documents 1 to 4 all have an unbalanced configuration. The meaning of "unbalanced" will be mentioned in the "Analysis of Prior Art" section below.

[0010] We disclose an interface sensor having a well-balanced configuration in which the total number of wires drawn from the interface sensor is less than the total number of observation points, and a liquid level meter including the interface sensor. [Means for solving the problem]

[0011] The technical matters described herein are not intended to explicitly or implicitly limit the invention described in the claims, nor to enable anyone other than those who benefit from the invention (e.g., the applicant and the right holder) to limit the invention described in the claims, but are provided merely to facilitate understanding of the gist of the invention. The outline of the invention from other perspectives can be understood, for example, from the claims at the time of filing of this patent application.

[0012] The disclosed interface sensor is an interface sensor having a configuration determined by the adopted code system and its specific code words, a) Regarding the number e(k) of electrode pairs or electrical conductors included in the kth (k∈[K]) sensor block included in the interface sensor, the maximum value max of the number e(k) on the set [K] k∈[K] The difference between e(k) and the minimum value min k∈[K] e(k) is smaller than that of the prior art; or, b) The jth sensor included in the interface sensor (j∈[J]=[Σ k∈[K] c(k)], c(k) is the maximum value max of the number t(j) of electrode pairs or electrical conductors connected to the conductors (excluding the e(k) electrode pairs or electrical conductors connected to the kth (k∈[K]) sensor block) in the set [J] of the number t(j). j∈[J] t(j) and minimum value min j∈[J] The difference in t(j) is smaller than that of the prior art. holds true. [Effects of the Invention]

[0013] The interface sensor of the present disclosure has a well-balanced configuration in which the total number of conductors drawn out from the interface sensor is smaller than the total number of observation points. [Brief explanation of the drawings]

[0014] [Figure 1] Reproduction of Figure 9 of Patent Document 1. [Figure 2] Reproduction of Figure 13 of Patent Document 2. [Figure 3] Reproduction of Figure 10 of Patent Document 3. [Figure 4] Reproduction of Figure 16 of Patent Document 4. [Figure 5] FIG. 1 is a diagram for explaining code words in the configuration disclosed in Patent Document 1. [Figure 6] FIG. 10 is a diagram for explaining code words in the configuration disclosed in Patent Document 3. [Figure 7] 1 is a first example of the first embodiment. [Figure 8] 2 is a second example of the first embodiment. [Figure 9] 3 is a third example of the first embodiment. [Figure 10] 10 is another example of the first embodiment. [Figure 11] 10 is an example of a variation of the first embodiment. [Figure 12] 10 shows an equivalent configuration example 1 of the first embodiment. [Figure 13] 2 shows a second example of a configuration equivalent to the first embodiment. [Figure 14] 10 is an example of a second embodiment. [Figure 15] 10 shows an example of an equivalent configuration of the second embodiment. [Figure 16] 10 is an example of a third embodiment. [Figure 17] 10 shows an example of an equivalent configuration of the third embodiment. [Figure 18] 4 is an example of a fourth embodiment. [Figure 19] 13 shows an example of an equivalent configuration of the fourth embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0015] In the following, unless otherwise specified, N is the set of all positive integers. The symbol N is written in bold in mathematical formulas.

[0016] [Prior Art Analysis] According to a prior art interface sensor, M planes P(1),...,P(M) that are not coincident with each other and are parallel to each other are predetermined, and the position of the interface is identified as one of M+1 intervals I(1),...,I(M+1) defined by the M planes P(1),...,P(M). Interval I(1) is one of two half-spaces obtained by dividing space by plane P(1) that does not include planes P(2),...,P(M). Interval I(m) (m∈{x∈N:2≦x≦M}) is a spatial region between adjacent planes P(m−1) and P(m), and interval I(M+1) is one of two half-spaces obtained by dividing space by plane P(M) that does not include planes P(2),...,P(M). Being able to identify the position of the interface using the interface sensor means that it is possible to assign a mutually distinguishable codeword to each of the M+1 intervals I(1),...,I(M+1). Although there are no restrictions on the codeword, for ease of discussion, hereinafter, a codeword is represented as a concatenation of K non-negative integers. K is the total number of sensor blocks included in the interface sensor, and satisfies 2≦K.

[0017] In the interface sensor configuration disclosed in Patent Document 1 or Patent Document 2, M+1 code words are systematically assigned to M+1 sections I(1),...,I(M+1) as follows: When M is expressed as the product of K factors n(k) (see Equation (1)), the k-th sensor block is assigned to each of M planes P(1),...,P(M) that are different from each other. i=k K Pi located on n(i) planes i=k KSince it contains n(i) electrode pairs (or electrical conductors), the planes on which the electrode pairs (or electrical conductors) are located are used as boundaries, and one of n(k) non-negative integers determined by the number n(k) of conductors is systematically assigned to each of the spatial regions distinguished by these boundaries. Specifically, M+1 non-negative integers are assigned to M+1 sections I(1),...,I(M+1) in the k-th (k∈{x∈N:2≦x≦K-1}) sensor block according to equation (2). Equation (2) represents a sequence of non-negative integers, not a matrix. In equation (2), the index Π at the bottom right i=1 k-1 n(i) represents the number of repetitions of each non-negative integer, and the upper right index Π i=k+1 K n(i) represents the number of repetitions of a sequence of non-negative integers. The bottom right index for the first sensor block is set to 1, and the top right index for the Kth sensor block is set to 1. Therefore, the set of M+1 code words assigned to the M+1 intervals I(1),...,I(M+1) is expressed by equation (3). As is clear from equation (3), the code words for interval I(1) and interval I(M+1) are the same. However, the code words for interval I(1) and interval I(M+1) can be distinguished by measuring the capacitance of any one electrode pair (or electrical conductor) included in the Kth sensor block.

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[0018] 5 shows a specific example of the allocation of M+1 code words to M+1 sections I(1),...,I(M+1) in the configuration of the interface sensor disclosed in Patent Document 1. In this example, M=30, K=3, n(1)=3, n(2)=5, and n(3)=2. For example, when k=2, the value of the exponent in the upper right corner of equation (2) is 2 and the value of the exponent in the lower right corner is 3, so the sequence of non-negative integers in equation (2) is as follows: 0 4 4 4 3 3 3 2 2 2 1 1 1 0 0 0 4 4 4 3 3 3 2 2 2 1 1 1 0 0 0 Therefore, the code words for each interval according to equation (3) are as follows: I(31):000 I(30):142 I(29):141 I(28):140 I(27):132 I(26):131 I(25):130 I(24):122 I(23):121 I(22):120 I(21):112 I(20):111 I(19):110 I(18):102 I(17):101 I(16):100 I(15):042 I(14):041 I(13):040 I(12):032 I(11):031 I(10):030 I(9):022 I(8):021 I(7):020 I(6):012 I(5):011 I(4):010 I(3):002 I(2):001 I(1):000

[0019] The configuration of the interface sensor disclosed in Patent Document 3 or Patent Document 4 is based on the configuration of the interface sensor disclosed in Patent Document 1 or Patent Document 2. Therefore, in the configuration of the interface sensor disclosed in Patent Document 3 or Patent Document 4, the set of M+1 code words assigned to the M+1 sections I(1),...,I(M+1) is obtained by modifying the set of code words expressed in equation (3). Specifically, in the configuration of the interface sensor disclosed in Patent Document 3 or Patent Document 4, when M is expressed as the product of K factors n(k) (see equation (1)), the set of code words assigned to each of the M+1 sections I(1),...,I(M+1) is expressed by equation (4). G k R is a sequence of non-negative integers G k The k-th (k∈{x∈N:1≦x≦K-1}) sensor block alternately shows the upside-down k and G k R The total number of i=k+1 K n(i).

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[0020] FIG. 6 shows a specific example of the allocation of M+1 code words to M+1 sections I(1),...,I(M+1) in the interface sensor configuration disclosed in Patent Document 3. In this example, M=24, K=3, n(1)=3, n(2)=4, and n(3)=2. The interface sensor configuration conceivable from the disclosure of Patent Document 3 is shown on the left side of FIG. 6, and this configuration is equivalent to the circuit configuration shown on the right side of FIG. 6. For example, when k=2, the sequence of non-negative integers in the second sensor block is as follows: 0 0 0 0 1 1 1 2 2 2 3 3 3 3 3 3 2 2 2 1 1 1 0 0 0 Therefore, the code words for each section according to equation (4) are as follows: I(25):000 I(24):100 I(23):101 I(22):102 I(21):112 I(20):111 I(19):110 I(18):120 I(17):121 I(16):122 I(15):132 I(14):131 I(13):130 I(12):030 I(11):031 I(10):032 I(9):022 I(8):021 I(7):020 I(6):010 I(5):011 I(4):012 I(3):002 I(2):001 I(1):000

[0021] From the above explanation, it can be seen that the set of M+1 code words assigned to the M+1 intervals I(1),...,I(M+1) in the interface sensor configuration disclosed in Patent Document 1 or Patent Document 2 is a code based on the positional notation system.

[0022] From the above explanation, it can be seen that the set of M+1 code words assigned to the M+1 intervals I(1),...,I(M+1) in the configuration of the interface sensor disclosed in Patent Document 3 or Patent Document 4 is a reflected Gray code when n(K) is an even number, and is a reflected Gray code except for the interval I(M+1) when n(K) is an odd number.

[0023] This suggests that the configuration of the interface sensor is determined by the coding scheme and its specific code words.

[0024] In any of the interface sensors disclosed in Patent Documents 1 to 4, the number of electrode pairs (or electrical conductors) is greatest in the first sensor block and least in the Kth sensor block, and the difference between the number of electrode pairs (or electrical conductors) in the Kth sensor block and the number of electrode pairs (or electrical conductors) in the kth (k∈{x∈N:1≦x≦K−1}) sensor block increases multiplicatively as k decreases. In other words, any of the interface sensors disclosed in Patent Documents 1 to 4 have an unbalanced configuration in this respect. Considering that the factorization of M using Equation (1) is not necessarily uniquely determined, in the interface sensor disclosed in Patent Document 1 or Patent Document 2, the minimum difference between the number of electrode pairs (or electrical conductors) included in the first sensor block and the number of electrode pairs (or electrical conductors) included in the Kth sensor block is given by Equation (5). In the interface sensor disclosed in Patent Document 3 or Patent Document 4, the minimum difference between the number of electrode pairs (or electrical conductors) included in the first sensor block and the number of electrode pairs (or electrical conductors) included in the Kth sensor block is given by Equation (6). Hereinafter, unless otherwise noted, max represents the maximum element of a set, and min represents the minimum element of a set. Hereinafter, unless otherwise noted, the symbol [X] represents the set {x∈N:1≦x≦X} determined by positive integer X. Therefore, [K] is the set {x∈N:1≦x≦K}. Hereinafter, unless otherwise noted, symbols on either side of M / 2 represent floor functions. Hereinafter, unless otherwise noted, symbols resembling a backslash represent the difference set. For example, if M=24 and K=3, the factorization of M is M=2×2×6 or M=2×4×3 (note that the order of the factors is not taken into account). Therefore, F(M,K)={{2,6},{2,3,4}}. Therefore, the value of equation (5) is 18, and the value of equation (6) is 6.

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[0025] As is clear from equations (5) and (6), the value of equation (6) is always smaller than the value of equation (5). Therefore, for the number e(k) of electrode pairs (or electrical conductors) included in the kth (k∈[K]) sensor block included in the interface sensor, the maximum value max k∈[K] e(k)=max{e(1),...,e(K)} and the minimum value min k∈[K] If the difference between e(k)=min{e(1),...,e(K)} is smaller than the value of equation (6), the interface sensor can be said to have a well-balanced configuration compared to prior art interface sensors.

[0026] From another perspective, in any of the interface sensors disclosed in Patent Documents 1 to 4, the number of electrode pairs (or electrical conductors) connected to one conductor (excluding conductors connected to all electrode pairs or electrical conductors included in the sensor block to which this conductor belongs) is greatest in the first sensor block and least in the Kth sensor block, and the difference between the number of electrode pairs (or electrical conductors) connected to one conductor (excluding conductors connected to all electrode pairs or electrical conductors included in the first sensor block) in the first sensor block and the number of electrode pairs (or electrical conductors) connected to one conductor (excluding conductors connected to all electrode pairs or electrical conductors included in the kth sensor block) in the kth (k∈{x∈N:1≦x≦K−1}) sensor block increases multiplicatively as k decreases. In other words, any of the interface sensors disclosed in Patent Documents 1 to 4 have an unbalanced configuration in this respect. Considering that the factorization of M in equation (1) is not necessarily unique, in the interface sensors disclosed in any of Patent Documents 1 to 4, the minimum difference between the number of electrode pairs (or electrical conductors) connected to one conductor in the first sensor block (excluding the conductors connected to all electrode pairs or electrical conductors included in the first sensor block) and the number of electrode pairs (or electrical conductors) connected to one conductor in the Kth sensor block (excluding the conductors connected to all electrode pairs or electrical conductors included in the Kth sensor block) is given by equation (7). For example, when M = 24 and K = 3, the factorization of M is M = 2 × 2 × 6 or M = 2 × 4 × 3 (note that the order of the factors is not taken into account). Therefore, F(M, K) = {{2, 6}, {2, 3, 4}}. Therefore, the value of equation (7) is 3.

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[0027] Therefore, the jth sensor included in the interface sensor (j∈[J]=[Σ k∈[K]c(k)], c(k) is the maximum value max of the number t(j) of electrode pairs (or electrical conductors) connected to the conductors (excluding the e(k) electrode pairs or electrical conductors connected to the e(k) electrode pairs or electrical conductors contained in the kth (k∈[K]) sensor block) in the set [J] of the number t(j). j∈[J] t(j)=max{e(1),...,e(J)} and the minimum value min j∈[J] If the difference between t(j)=min{e(1),...,e(J)} is smaller than the value of equation (7), the interface sensor can be said to have a well-balanced configuration compared to prior art interface sensors.

[0028] In short, a sufficient condition for the interface sensor disclosed herein to have a well-balanced configuration compared to prior art interface sensors is that, in an interface sensor having a configuration determined by the adopted code system and its specific code words, a) Regarding the number e(k) of electrode pairs (or electrical conductors) included in the kth (k∈[K]) sensor block included in the interface sensor, the maximum value max of the number e(k) on the set [K] k∈[K] e(k) and minimum value min k∈[K] The difference in e(k) is smaller than the value of equation (6). or, b) The jth sensor included in the interface sensor (j∈[J]=[Σ k∈[K] c(k)], c(k) is the maximum value max of the number t(j) of electrode pairs (or electrical conductors) connected to the conductors (excluding the e(k) electrode pairs or electrical conductors connected to the e(k) electrode pairs or electrical conductors contained in the kth (k∈[K]) sensor block) in the set [J] of the number t(j). j∈[J] t(j) and minimum value min j∈[J] The difference between t(j) is smaller than the value of equation (7). Based on the results of such analysis of the prior art, an embodiment of the interface sensor disclosed herein will be described.

[0029] [First embodiment] The interface sensor 1 of the first embodiment is an interface sensor having a configuration determined by the adopted coding system and its specific code words, and satisfies the above-mentioned condition a) for the number e(k) of electrode pairs included in the k-th (k∈[K]) sensor block included in the interface sensor, the maximum value max k∈[K] e(k) and minimum value min k∈[K] The difference between e(k) is smaller than the value of equation (6).

[0030] The interface sensor 1 of the first embodiment is a sensor for identifying the position of the interface between two types of substances (i.e., a first substance and a second substance that are different from each other). An "interface" is a contact boundary between a first substance as a homogeneous phase and a second substance as a homogeneous phase. A "homogeneous phase" is an entity of a material system which is uniform in chemical composition and physical state. In other words, any part V of a certain substance system entity s The physical and chemical properties of the part V of the substance system s Any part W different from s If the physical and chemical properties of the two planes are the same, the substance system is a "homogeneous phase." In order to accurately identify the position of the interface, the number of interfaces must be 1 or 0 in the range from plane P(1) to plane P(M), which will be described later. The interface sensor 1 detects the Σ k∈[K] e(k) electrode pairs 5 and K+Σ k∈[K] It contains c(k) conductors 7. Σ k∈[K]Each of the e(k) electrode pairs 5 is composed of two electrodes 5a and 5b. The identification of the position of the interface between the first substance and the second substance is achieved by using the physical quantity generated in the electrode pair 5 according to the properties of the first substance or the second substance existing between the two electrodes 5a and 5b that make up the electrode pair 5. Let C be the capacitance between two conductors with equal amounts of positive and negative charges, R be the electrical resistance between the two conductors, ε be the dielectric constant of the medium between the two conductors, and ρ be the electrical resistivity of the medium between the two conductors. Then, since the relationship RC = ερ holds, in the first embodiment, capacitance is adopted as the physical quantity generated in the electrode pair 5, and the description of the example of adopting electrical resistance as the physical quantity is omitted. A typical example of the interface sensor 1 is a sensor for identifying the position of the interface between a liquid (e.g., water) as the first substance and a gas (e.g., air) as the second substance.

[0031] The interface sensor 1 is a sensor having a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, 8, 9, or having a configuration equivalent thereto. First, the "configuration that satisfies all of conditions 1, 2, 3, 4, 5, 6, 7, 8, 9" and its specific example will be described, and then the "equivalent configuration" and its specific example will be described.

[0032] <Condition 1> The interface sensor 1 includes K sensor blocks {B k : k ∈ [K]}. K is a predetermined integer satisfying 2 ≤ K < M. K preferably satisfies Equation (8). Hereinafter, unless otherwise specified, the symbol sandwiching log2M represents the ceiling function. M is a predetermined integer satisfying 8 ≤ M except when K = 2, and is a predetermined odd number satisfying 9 ≤ M when K = 2. M determines the resolution of the interface sensor 1. That is, M corresponds to the total number of the above-mentioned "observation points".

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[0033] The K sensor blocks {B k{B: k ∈ [K]} are formed on Q substrates 9 each having a flat plate shape without being limited to the following examples. Q is a predetermined integer satisfying 1 ≤ Q ≤ K. When Q < K, there are substrates 9 having two or more sensor blocks. In each example shown later, Q = 1. When Q ≥ 2, the Q substrates 9 may be arranged on one plane, may be arranged like angle steel or channel steel, or may be arranged like triangular pipes or square pipes without being limited to the following examples.

[0034] <Condition 2> For any k ∈ [K], among the K sensor blocks {B k : k ∈ [K]}, the k-th sensor block B k includes e(k) electrode pairs 5 and c(k) + 1 conducting wires 7. e(k) is a predetermined integer satisfying 1 ≤ e(k) < M. c(k) is a predetermined integer satisfying 2 ≤ c(k) ≤ e(k) except when e(k) = 1, and is 1 when e(k) = 1.

[0035] When e(k) ≠ 1, among the K sensor blocks {B k : k ∈ [K]}, the k-th sensor block B k the e(k) electrode pairs 5 included in have the same capacitance C k with each other when the space between the electrodes 5a and 5b of each of the e(k) electrode pairs 5 is filled with, for example, a first substance. The capacitance C k of each of the e(k) electrode pairs 5 included in the k-th sensor block B k may be the same as or different from the capacitance C j of each of the e(j) electrode pairs 5 included in the j-th (j ≠ k) sensor block B j Each of the c(k) + 1 conducting wires 7 is a conducting wire drawn from any of the K sensor blocks {B k : k ∈ [K]}, and as will be described later in relation to Condition 5, the Σ that the interface sensor 1 has k∈[K]At least one of the e(k) electrode pairs 5 is connected to the electrode pair 5. The c(k)+1 conductors 7 are connected to a measurement circuit, which will be described later. In the drawing, for ease of viewing, only some of the electrode pairs and some of the conductors are labeled.

[0036] <Condition 3> Σ that interface sensor 1 has k∈[K] Each of the e(k) electrode pairs 5 is located in one of M planes P(1),...,P(M) that are mutually disjoint and parallel. k∈[K] At least one electrode pair 5 out of the e(k) electrode pairs 5 is located on the set P(1),...,P(M). In other words, there is no plane among the M planes P(1),...,P(M) on which an electrode pair 5 is not located. The M planes P(1),...,P(M) are arranged in space in an order according to the ordering relation of elements of the set [M]={x∈N:1≦x≦M} (i.e., a binary relation < on N (note that a binary relation < is a strict total order)). Specifically, between the first plane P(1) and the pth plane P(p) (p∈{x∈N:3≦x≦M}), the qth plane P(q) (q∈{x∈N:2≦x≦p-1}) exists. More simply, if the normal direction of the M parallel planes P(1),...,P(M) is called the first direction, the M planes P(1),...,P(M) are arranged in this order in the first direction. For any g∈{x∈N:1≦x≦M-2} and any h∈{x∈N:g+1≦x≦M-1}, the distance between the gth plane P(g) and the g+1th plane P(g+1) may or may not be equal to the distance between the hth plane P(h) and the h+1th plane P(h+1). For example, it is advisable to narrow the interval between adjacent planes in a measurement range where the position of the interface is desired to be more accurately identified. Note that when the first direction is the vertical direction, the term "plane" may be rephrased as, for example, "level."

[0037] <Condition 4> For any k∈[K], there are K sensor blocks {B k :k∈[K]}, the kth sensor block B kThe i-th electrode pair 5 of the e(k) electrode pairs 5 included in is p(1),...,P(M) of the M planes P(1),...,P(M). k,i The th plane P(p k,i ), equation (9) holds. Unless otherwise noted, the symbol "×" represents a Cartesian product, A×B={(a,b):a∈A∧b∈B}.

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[0038] <Condition 5> For any (k,i)∈[K]×[e(k)], there are K sensor blocks {B k :k∈[K]}, the kth sensor block B k In this case, one electrode 5a of the i-th electrode pair 5 among the e(k) electrode pairs 5 is connected to s of the c(k)+1 conducting wires 7. k,i The other electrode 5b is connected to the c(k)+1-th conductor 7 of the c(k)+1 conductors 7. k,i is expressed by equation (10). Unless otherwise specified, the symbol mod represents a modulo operation, and a mod b is the remainder obtained by Euclidean division of the dividend a by the divisor b. In equation (10), the dividend of the modulo operation is i-1. In this example, the electrode 5a and s of the i-th (i∈[e(k)]) electrode pair 5 k,i The i-th conductor 7 is connected to the c(k)+1-th conductor 7 via a branch line 7x, and the other electrode 5b of the i-th (i∈[e(k)]) electrode pair 5 and the c(k)+1-th conductor 7 are connected to each other via a branch line 7y.

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[0039] <Condition 6> non-negative integer g m,k is defined by equation (11), and the codeword h(m) is defined as K non-negative integers g m,kWhen the sequence of (k∈[K]) is determined by equation (12), equation (13) or equation (14) holds. m,k is given as a sequence arranged in ascending order of the ordering relation of k∈[K]. That is, h(m)=(g m,1 g m,2 ...g m,K ) In equation (13) or (14), h(m1) ≠ h(m2) means that two code words h(m1) and h(m2) do not match. The mismatch between two code words is defined by equation (15). Although the code word is not limited to a concatenation of K non-negative integers, there is no loss of generality if the code word is expressed as a concatenation of K non-negative integers.

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[0040] Let I(1) be the half-space that does not include the plane P(2),...,P(M) of the two half-spaces obtained by dividing space by the plane P(1), and let I(m) (m∈{x∈N:2≦x≦M}) be the spatial region between the adjacent planes P(m-1) and P(m). Let I(M+1) be the half-space that does not include the plane P(2),...,P(M) of the two half-spaces obtained by dividing space by the plane P(M). Clearly, there exists a bijection between the M+1 codewords h(m) (m∈[M+1]) and the M+1 intervals I(m) (m∈[M+1]). However, the bijective image of h(m) is I(m) (m∈[M+1]). That is, in the interface sensor 1, a one-to-one correspondence is established between the M+1 code words h(m) (m∈[M+1]) and the M+1 intervals I(m) (m∈[M+1]). Therefore, specifying the position of the interface using the interface sensor 1 is equivalent to specifying the interval, and specifying the interval is nothing more than determining a K-digit code word based on the physical quantity occurring in the electrode pair 5. In other words, by determining a K-digit code word based on the physical quantity occurring in the electrode pair 5, the interval in which the interface exists can be specified. This will be described in detail as a method for specifying the position of the interface.

[0041] If equation (14) holds, the code words for interval I(1) and interval I(M+1) are the same. In this case, the code words for interval I(1) and interval I(M+1) can be distinguished by measuring the capacitance of any one electrode pair included in any sensor block.

[0042] For r(k) (k∈[K]) defined in condition 6, if equation (13) holds, then equation (16) holds, and if equation (14) holds, then equation (17) holds.

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[0043] <Condition 7> max({d H (h(m),h(m+1)):∀m∈[M]})=1 holds, where d H (h(m), h(m+1)) is the Hamming distance between codeword h(m) and codeword h(m+1). In other words, the coding system in the first embodiment is a Gray code.

[0044] <Condition 8> From condition 2, the kth (k∈[K]) sensor block B k contains c(k)+1 conducting wires 7. Therefore, in order for the total number of conducting wires 7 drawn from the interface sensor 1 to be less than the total number of observation points, i.e., the number of planes M, it is sufficient that the formula (18) is established. Meanwhile, according to the condition 5, the kth (k∈[K]) sensor block B k In the kth (k∈[K]) sensor block B, the c(k)+1th conductor 7 is connected to the e(k) electrode pairs 5. In other words, the c(k)+1th conductor 7 provides a reference potential to the e(k) electrode pairs 5. Therefore, the kth (k∈[K]) sensor block B k The c(k)+1th conductor 7 and the jth (j∈[K], j≠k) sensor block B j In the extreme case, the k-th (k∈[K]) sensor block B kThe c(k)+1th group of conducting wires 7 in can be replaced with a single conducting wire. Therefore, it is sufficient that equation (19) holds.

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[0045] <Condition 9> Equation (20) is established. Equation (20) corresponds to the above-mentioned condition a). The left side of the inequality in equation (20) is the kth (k∈[K]) sensor block B k Regarding the number e(k) of electrode pairs 5 included in k∈[K] e(k) and minimum value min k∈[K] This represents the difference between e(k). The right-hand side of the inequality in equation (20) is the same as equation (6). The value of K on the right-hand side of the inequality in equation (20) is the same as the value of K on the left-hand side of the inequality in equation (20). The set F(M,K) is a set whose elements are the union of singletons, each of which has K factors n(k) (k∈[K]) of M excluding 1 as its elements. Again, note that the factorization of M is not necessarily unique. For example, if M=24 and K=3, the factorization of M using K factors excluding 1 is M=2×2×6 or M=2×4×3 (note that the order of the factors is not taken into account). Therefore, F(M,K)={{2,6},{2,3,4}}. The symbol F for the set F(M,K) is written in calligraphy in mathematical formulas. An element F of a set F(M,K) is written in German letters in mathematical formulas. If M cannot be expressed as a product of K factors excluding 1, then the inequality in formula (20) holds (vacuous truth).

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[0046] [Example of coding system] As an example, M=2 K-1 holds, the coding system that gives the codeword h(m)(m∈[M+1]) is a K-digit max({r(k):k∈[K]})-ary counting sequence. As another example, if r(k)=2 for any k∈[K] in condition 6, the coding system that gives the codeword h(m)(m∈[M+1]) is a K-digit binary Gray code. Furthermore, d H A coding system that gives a codeword h(m) (m∈[M+1]) is cyclic if (h(M+1),h(1))=1 holds. For more information on such coding systems, see Reference A. (Literature A) I Nengah SUPARTA, "Counting Sequences, Gray Codes and Lexicodes", Dissertation at Delft University of Technology, 2006, ISBN 90-8559-176-7

[0047] [design] An example of the design of the interface sensor 1 will be briefly described. The essence (groundwork) of the design of the interface sensor 1 is to determine the code word h(m) (m∈[M+1]). When the coding system that gives the code word h(m) (m∈[M+1]) is, for example, balanced Gray codes or uniform counting sequences, the process of determining the code word h(m) (m∈[M+1]) is disclosed in Document A (Document A discloses several examples of balanced Gray codes or uniform counting sequences as transition sequences (see, for example, Example 3.2.6)). Once the balanced Gray codes or uniform counting sequences are determined, it is easy to design the interface sensor 1 that satisfies conditions 1 to 9. For example, when a code word h(m) (m∈[M+1]) having three or more predetermined digits is determined as a balanced Gray code, K is the number of digits of the code word h(m) (m∈[M+1]), and M=2K -1 and condition 7 are naturally determined, and e(k)(k∈[K]) is determined from the transition counts (i.e., the sum of the number of transitions from 0 to 1 and the number of transitions from 1 to 0) of the k-th digit of the codeword h(m)(m∈[M+1]), and the plane P(p k,i )(i∈[e(k)]) is defined as the position of the transition (i.e., a change from 0 to 1 or a change from 1 to 0) in the kth digit of the codeword h(m)(m∈[M+1]), and furthermore, c(k)=r(k)=1+max({g m,k By adopting {:m∈[M+1]})=2(k∈[K]), it is possible to easily design an interface sensor 1 that satisfies conditions 1 to 9. If the set of all configurations of the interface sensor 1 that satisfy conditions 1 to 9 is denoted as X1, and the set of all configurations of the interface sensor 1 determined by the balanced Gray codes or uniform counting sequences disclosed in Document A is denoted as X2, then X2 ⊂ X1 holds, but the reverse does not hold. Therefore, the configuration of the interface sensor 1 that satisfies conditions 1 to 9 is not limited to the configuration of the interface sensor 1 determined by the balanced Gray codes or uniform counting sequences disclosed in Document A.

[0048] Several examples of the interface sensor 1 according to the first embodiment will be described with reference to the drawings. In each drawing, in consideration of ease of viewing the drawing, when two or more identical components are present, one or more, but not all, of the two or more identical components are given reference numerals.

[0049] FIG. 7 shows a first example of the first embodiment. In the first example, K=4 M=15 e(1)=4, e(2)=3, e(3)=4, e(4)=4, Σ k∈[K] e(k)=15 c(1)=2, c(2)=2, c(3)=2, c(4)=2 p 1,1 =4, p 1,2 =9, p 1,3 =11, p 1,4 =14 p 2,1 =3、p 2,2 =5、p 2,3 =10 p 3,1 =2、p 3,2 =6、p 3,3 =8、p 3,4 =12 p 4,1 =1、p 4,2 =7、p 4,3 =13、p 4,4 =15 s 1,1 =1、s 1,2 =2、s 1,3 =1、s 1,4 =2 s 2,1 =1、s 2,2 =2、s 2,3 =1 s 3,1 =1、s 3,2 =2、s 3,3 =1、s 3,4 =2 s 4,1 =1、s 4,2 =2、s 4,3 =1、s 4,4 =2 r(1)=2、r(2)=2、r(3)=2、r(4)=2 h(16)=0100 h(15)=0101 h(14)=1101 h(13)=1100 h(12)=1110 h(11)=0110 h(10)=0010 h(9) =1010 h(8) =1000 h(7) =1001 h(6) =1011 h(5) =1111 h(4) =0111 h(3) =0011 h(2) =0001 h(1) =0000 max({d H (h(m),h(m+1)):∀m∈[M]})=1 It is easy to verify that equations (13), (16), and (19) hold. Since M cannot be expressed as a product of K factors excluding 1, equation (20) holds (vacuous truth). The coding system in the first example is cyclic 4-digit binary Gray codes.

[0050] FIG. 8 shows a second example of the first embodiment. In the second example, K=3 M=23 e(1)=8, e(2)=8, e(3)=7, Σ k∈[K] e(k)=23 c(1)=3, c(2)=2, c(3)=4 p 1,1 =5, p 1,2 =8, p 1,3 =10, p 1,4 =11, p 1,5 =14, p 1,6 =16, p 1,7 =18, p 1,8 =20 p 2,1 =4, p 2,2 =6, p 2,3 =9, p 2,4 =13, p 2,5 =15, p 2,6 =19, p 2,7 =21, p 2,8 =23 p 3,1 =1, p 3,2 =2, p 3,3 =3, p 3,4 =7, p 3,5 =12, p 3,6 =17, p 3,7 =22 s 1,1 =1, s 1,2 =2, s 1,3 =3, s 1,4 =1, s 1,5 =2, s 1,6 =3, s 1,7 =1, s 1,8 =2 s 2,1 =1, s 2,2 =2, s 2,3 =1, s 2,4 =2, s 2,5 =1, s2,6 =2, s 2,7 =1, s 2,8 =2 s 3,1 =1, s 3,2 =2, s 3,3 =3, s 3,4 =4, s 3,5 =1, s 3,6 =2, s 3,7 =3 r(1)=3, r(2)=2, r(3)=4 h(24)=203 h(23)=213 h(22)=212 h(21)=202 h(20)=102 h(19)=112 h(18)=012 h(17)=011 h(16)=211 h(15)=201 h(14)=101 h(13)=111 h(12)=110 h(11)=010 h(10)=210 h(9) = 200 h(8) =100 h(7) = 103 h(6) = 113 h(5) =013 h(4) =003 h(3) =002 h(2) =001 h(1) =000 max({d H (h(m),h(m+1)):∀m∈[M]})=1 It is easy to confirm that equations (13), (16), and (19) hold. Since M cannot be expressed as a product of K factors excluding 1, equation (20) holds (vacuous truth). The coding system in the second example is a 3-digit maximum quaternary code.

[0051] FIG. 9 shows a third example of the first embodiment. In the third example, K=5 M=32 e(1)=6、e(2)=6、e(3)=6、e(4)=6、e(5)=8、Σ k∈[K] e(k)=32 c(1)=2、c(2)=2、c(3)=2、c(2)=2、c(3)=2 p 1,1 =2、p 1,2 =8、p 1,3 =12、p 1,4 =17、p 1,5 =27、p 1,6 =32 p 2,1 =6、p 2,2 =14、p 2,3 =20、p 2,4 =22、p 2,5 =25、p 2,6 =31 p 3,1 =3、p 3,2 =9、p 3,3 =16、p 3,4 =18、p 3,5 =21、p 3,6 =29 p 4,1 =5、p 4,2 =7、p 4,3 =11、p 4,4 =23、p 4,5 =26、p 4,6 =28 p 5,1 =1、p 5,2 =4、p 5,3 =10、p 5,4 =13、p 5,5 =15、p 5,6 =19、p 5,7 =24、p 5,8 =30 s 1,1 =1、s 1,2 =2、s 1,3 =1、s 1,4 =2、s 1,5 =1、s 1,6 =2 s 2,1 =1、s 2,2 =2、s 2,3 =1、s 2,4 =2、s 2,5 =1、s 2,6 =2 s3,1 =1、s 3,2 =2、s 3,3 =1、s 3,4 =2、s 3,5 =1、s 3,6 =2 s 4,1 =1、s 4,2 =2、s 4,3 =1、s 4,4 =2、s 4,5 =1、s 4,6 =2 s 5,1 =1、s 5,2 =2、s 5,3 =1、s 5,4 =2、s 5,5 =1、s 5,6 =2、s 5,7 =1、s 5,8 =2 r(1)=2、r(2)=2、r(3)=2 h(33)=00000=h(1) h(32)=10000 h(31)=11000 h(30)=11001 h(29)=11101 h(28)=11111 h(27)=01111 h(26)=01101 h(25)=00101 h(24)=00100 h(23)=00110 h(22)=01110 h(21)=01010 h(20)=00010 h(19)=00011 h(18)=00111 h(17)=10111 h(16)=10011 h(15)=10010 h(14)=11010 h(13)=11011 h(12)=01011 h(11)=01001 h(10)=01000 h(9) =01100 h(8) = 11100 h(7) =11110 h(6) = 10110 h(5) = 10100 h(4) = 10101 h(3) = 10001 h(2) =00001 h(1) =00000 max({d H (h(m),h(m+1)):∀m∈[M]})=1 It is easy to verify that equations (14), (17), and (19) hold. The only factorization of M using K factors excluding 1 is M=2×2×2×2×2, so F(M,K)={{2}}. Therefore, equation (20) holds. The coding system in the third example is 5-digit binary balanced Gray codes.

[0052] [Methods and algorithms for identifying interface locations] Next, an example of a method for identifying the position of an interface using the interface sensor 1 will be described. In the following example, for any k∈[K], 2≦e(k) and 2≦c(k). The kth sensor block B k (k∈[K]), a measurement circuit (not shown) for measuring capacitance is k (s k The composite of physical quantities (for example, composite capacitance) C(s k ) and s k + The composite of the physical quantities (for example, composite capacitance) C(s k +1) and measure the difference C(s k )-C(s k +1) is compared with the threshold value δ. The threshold value δ is determined in advance taking into consideration the relative permittivity of the first material, the relative permittivity of the second material, measurement error, the number of electrode pairs 5 connected to one conductor 7, etc. As a result of the comparison, C(s k )-C(s k +1) ≥ δ, the k-th non-negative integer in the codeword h(m) (m∈[M+1]) is s kIt is determined as follows: k ∈[c(k)-1], C(s k )-C(s k +1) ≥ δ does not hold, the k-th non-negative integer of the codeword h(m) (m∈[M+1]) is determined to be 0. k By performing such a measurement process for (k∈[K]), a K-digit code word is uniquely determined. Among the M+1 code words h(m) (m∈[M+1]), the interface exists in the interval corresponding to the uniquely determined K-digit code word h(m). For example, in the interface sensor 1 shown in FIG. 7, if the K-digit code word is determined to be 1010 as a result of the measurement process, the interface exists in interval I(9) (i.e., between planes P(8) and P(9)). Note that if the K-digit code word is 0000, the interface exists in interval I(1) and has not reached plane P(1); if the K-digit code word is 0100, the interface exists in interval I(16) and has exceeded plane P(15). The one-to-one correspondence between the M+1 code words h(m) (m∈[M+1]) and the M+1 intervals I(m) (m∈[M+1]) is stored in a memory (not shown) as a lookup table, and an arithmetic circuit (not shown) refers to the lookup table to identify the interval corresponding to the K-digit code word obtained by the measurement process of the measurement circuit.

[0053] The measurement circuit may be a component of the interface sensor 1 or may be a physical entity separate from the interface sensor 1. In the latter case, the measurement circuit may be a component of a level meter that includes the interface sensor 1. The measurement circuit is k ∈[c(k)], C(s k ) and a measuring instrument to measure each s k ∈[c(k)-1], the difference C(s k )-C(s kThe measurement circuit is not limited to a measurement circuit including a comparator that compares c(k)+1) with a threshold δ, but may further include an AC signal generator that generates an AC signal to be applied to the c(k)+1-th conductor 7 for each k∈[K], or may be a prior art measurement circuit or a measurement circuit including a programmable logic device (PLD). Examples of PLDs include a field-programmable gate array (FPGA).

[0054] Table 1 shows an algorithm for identifying the position of an interface using the interface sensor 1. The illustrated algorithm corresponds to the above-mentioned position identification method. In the algorithm, h="" indicates setting h to an empty string, and h=h+g indicates obtaining a new code word h by concatenating code word h with a non-negative integer g as a character. LOOKUP(h,TABLE) indicates the process of determining the interval corresponding to code word h by referring to the TABLE. This algorithm identifies the interval, i.e., the position of the interface. The illustrated TABLE is based on the example shown in Figure 7. [Table 1]

[0055] [Variation 1] In the case of a cyclic coding system or when h(1)=h(M+1) is satisfied, a method for easily creating variations from one embodiment will be explained.

[0056] Step A) In the case of a cyclic coding system, to make the explanation more concrete, the first example shown in FIG. 7 is adopted as one embodiment. In the first example shown in FIG. 7, M=15. The first example shown in FIG. 7 has a cyclic coding system. In the case of a cyclic coding system, one new electrode pair 5 is added to the (M+1)th plane P(M+1). As a result, a code word h(M+2) is also added. The added code word h(M+2) is the same as the code word h(1). The sensor block to which one new electrode is added is the kth sensor block B, which is determined by k in equation (21) under the condition that h(1)=h(M+2). k In this example, since k=2, one new electrode is added to the second sensor block B2 (see FIG. 10). The configuration shown in FIG. 10 is also an example of the first embodiment.

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[0057] Step B) In the configuration obtained by adding one new electrode pair 5 to the (M+1)th plane P(M+1), the M+1 code words h(m) (m∈[M+1]) except for the code word h(M+2) are shifted by a∈N. In other words, the M+1 code words in the variation configuration are shifted by h v Let (m)(m∈[M+1]), then h v (m)=h(1+((M+ma) mod (M+1)))(m∈[M+1]) h v (M+2)=h(1) Specifically, when a=5, h v (17) =h(1) =0000 h v (16) =h(11)=0110 h v (15) =h(10)=0010 h v (14) = h(9) = 1010 h v (13) = h(8) = 1000 h v(12) = h(7) = 1001 h v (11) = h(6) = 1011 h v (10) =h(5) =1111 h v (9) =h(4) =0111 h v (8) =h(3) =0011 h v (7) =h(2) =0001 h v (6) =h(1) =0000 h v (5) =h(16)=0100 h v (4) =h(15)=0101 h v (3) =h(14)=1101 h v (2) =h(13)=1100 h v (1) =h(12)=1110 is.

[0058] Regarding condition 6), h(1) is always a concatenation of K zeros, but the codeword h v (1) is not a concatenation of K zeros. However, the codeword h v The codeword h is obtained by applying the remainder operation of the divisor r(k) to each digit of (m) (m∈[M+1]). v (m)(m∈[M+1]) is a codeword h that satisfies condition 6). r (m)(m∈[M+1]). Specifically, the m-th codeword h v (m) is the kth non-negative integer of g v m,k Then, the codeword h is obtained by equation (22). r (m)(m∈[M+1]) is obtained. Specifically, in this example, r(1)=2, r(2)=2, r(3)=2, r(4)=2, g v 1,1 = 1, g v 1,2 = 1, g v 1,3 = 1, g v1,4 =0, so h r (17)=0000 h r (16)=1000 h r (15)=1100 h r (14)=0100 h r (13)=0110 h r (12)=0111 h r (11)=0101 h r (10)=0001 h r (9) =1001 h r (8) =1101 h r (7) =1111 h r (6) =1110 h r (5) = 1010 h r (4) =1011 h r (3) =0011 h r (2) =0010 h r (1) =0000 These codewords are shown in FIG.

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[0059] The construction of this variation is shown in Figure 11. The codeword h r Since (m)(m∈[M+2]) is determined, as mentioned above, e(k)(k∈[K]) is the codeword h r (m)(m∈[M+2])) is determined by the k-th digit transition counts (i.e., the total number of non-negative integer changes), and the plane P(p k,i )(i∈[e(k)]) is the codeword h r(m) (m∈[M+2]) and the position of the transition (i.e., a non-negative integer change) in the k-th digit of (m) (m∈[M+2]), and furthermore, c(k) = r(k) = 1 + max({g m,k :m∈[M+2]})(k∈[K]), it is possible to easily design an interface sensor 1 that satisfies conditions 1 to 9. In the configuration of the variation shown in FIG. K=4 M=16 e(1)=4, e(2)=4, e(3)=4, e(4)=4, Σ k∈[K] e(k)=16 c(1)=2, c(2)=2, c(3)=2, c(4)=2 p 1,1 =3, p 1,2 =9, p 1,3 =14, p 1,4 =16 p 2,1 =5, p 2,2 =8, p 2,3 =10, p 2,4 =15 p 3,1 =1, p 3,2 =7, p 3,3 =11, p 3,4 =13 p 4,1 =2, p 4,2 =4, p 4,3 =6, p 4,4 =12 s 1,1 =1, s 1,2 =2, s 1,3 =1, s 1,4 =2 s 2,1 =1, s 2,2 =2, s 2,3 =1, s 2,4 =2 s 3,1 =1, s 3,2 =2, s 3,3 =1, s 3,4 =2 s 4,1 =1, s 4,2 =2, s 4,3 =1, s 4,4 =2 r(1)=2, r(2)=2, r(3)=2 max({d H (h(m),h(m+1)):∀m∈[M]})=1 The total number of variations using this method is M+1, since it matches the possible values ​​of the shift number. It is easy to verify that equations (14), (17), and (19) hold in the configuration shown in Figure 11. Note that in this example, M appearing in equations (14), (17), and (19) is M+1 (i.e., M+1=15+1=16). The only way to factorize M+1 using K factors excluding 1 is M+1=2×2×2×2×2, so F(M,K)={{2}}. Therefore, equation (20) holds. The coding system in this example is 4-digit binary balanced Gray codes.

[0060] A configuration example obtained by removing the electrode pair 5 located on the plane P(16) from the configuration example shown in FIG. 11 is also an example of the first embodiment.

[0061] To obtain the configuration of variations when h(1) = h(M+1), only step B) needs to be performed. Specifically, M codewords h(m) (m∈[M]) excluding codeword h(M+1) are shifted by a∈N. In other words, M codewords in the configuration of variations are shifted by h v Let (m)(m∈[M]), then h v (m)=h(1+((M+ma-1) mod (M)))(m∈[M]) h v (M+1)=h(1) The codeword h v (m)(m∈[M]) to codeword h r The transformation to (m)(m∈[M]) follows equation (22).

[0062] [Variation 2] Another method for easily creating variations from one embodiment will be described. In a second direction perpendicular to the first direction, K sensor blocks {B k Variations can be obtained by permuting {B :k∈[K]}.k :k∈[K]}, the total number of possible placement patterns is K!, that is, Π k=1 K k.

[0063] [Equivalent structure to the first embodiment] Next, a "configuration equivalent to a configuration satisfying all of conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9" and specific examples thereof will be described. A "configuration equivalent to a configuration satisfying all of conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9" is a configuration that has a different configuration from a "configuration satisfying all of conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9" but has the same function from the perspective of an electrical circuit. Because it is impossible to list all "equivalent configurations," and because a person skilled in the art can easily implement various equivalent configurations, only a few examples of "equivalent configurations" of the first example of the first embodiment will be described.

[0064] max({d H If (h(m),h(m+1)):∀m∈[M]}) is less than K, the electrode pairs 5 can be arranged in Y columns. Y is the sum of max({d H (h(m),h(m+1)):∀m∈[M]})≦Y≦K−1. In the first example of the first embodiment, max({d H Since (h(m),h(m+1)):∀m∈[M]})=1, 1≦Y≦K−1=3. Therefore, the electrode pairs 5 can be arranged in a single column. This configuration is shown in Figure 12.

[0065] Furthermore, as explained in <Condition 8>, the sensor block B of the kth (k∈[K]) conductor 7 k 12 may be changed to the configuration shown in FIG. 13, since the c(k)+1th group of conducting wires 7 in the above-mentioned configuration can be replaced with one conducting wire.

[0066] [Second embodiment] The interface sensor 2 of the second embodiment is an interface sensor having a configuration determined by the adopted coding system and its specific code words, and satisfies the above-mentioned condition b) the jth (j∈[J]=[Σ k∈[K] Regarding the number t(j) of electrode pairs connected to the conductors of the kth (k∈[K]) sensor block (excluding the e(k) electrode pairs or conductors connected to the electrical conductors), the maximum value max on the set [J] of the number t(j) is j∈[J] t(j) and minimum value min j∈[J] The difference between t(j) is smaller than the value of equation (7). In this respect, the second embodiment differs from the first embodiment.

[0067] Here, the substantial differences between the first embodiment and the second embodiment will be described, and for other technical matters, the description of the first embodiment will be applied mutatis mutandis to the description of the second embodiment. Therefore, the description of the first embodiment, excluding the substantial differences, is expressly incorporated mutatis mutandis herein. By applying the description of the first embodiment to the description of the second embodiment, for example, "interface sensor 1" can be rephrased as "interface sensor 2."

[0068] The interface sensor 2 of the second embodiment is a sensor having a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, and 8, or a configuration equivalent to said configuration. First, the "configuration that satisfies all of conditions 1, 2, 3, 4, 5, 6, 7, and 8" and specific examples thereof will be explained, and then the "equivalent configuration" and specific examples thereof will be explained.

[0069] <Condition 1>~<Condition 7> Conditions 1, 2, 3, 4, 5, and 6 in the second embodiment are the same as conditions 1, 2, 3, 4, 5, and 6 in the first embodiment, respectively. Condition 7 in the second embodiment is the same as condition 8 in the first embodiment. Therefore, the descriptions of conditions 1, 2, 3, 4, 5, 6, and 8 in the first embodiment apply mutatis mutandis to the descriptions of conditions 1, 2, 3, 4, 5, 6, and 7 in the second embodiment. Conditions 7 and 9 in the first embodiment are unnecessary in the second embodiment. Condition 8 in the second embodiment is as follows:

[0070] <Condition 8> Equation (23) holds. Equation (23) corresponds to the above-mentioned condition b). Set S is the union of sets Z(k) and is defined by equation (24). Sets S and Z(k) are written in German letters in the formula. The symbol a|b indicates that integer a is a divisor of integer b. The combination symbol | and symbol / indicates that the integer to the left of the combination symbol is not a divisor of the integer to the right of the combination symbol. The left side of the inequality in equation (23) is the jth (j∈[J]=[Σ k∈[K] Regarding the number t(j) of electrode pairs 5 connected to the conductor 7 of the kth (k∈[K]) sensor block (excluding the conductors connected to the e(k) electrode pairs or electrical conductors included in the kth (k∈[K]) sensor block), the maximum value max on the set [J] of the number t(j) j∈[J] t(j) and minimum value min j∈[J] The difference between t(j) is specifically expressed using a set. The right-hand side of the inequality in equation (23) is the same as equation (7). If M cannot be expressed as a product of K factors excluding 1, then the inequality in equation (23) holds (vacuous truth).

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[0071] Several examples of the interface sensor 2 according to the second embodiment will be described with reference to the drawings. In each drawing, in consideration of ease of viewing the drawing, when two or more identical components are present, one or more, but not all, of the two or more identical components are given reference numerals.

[0072] A first example of the second embodiment is the configuration shown in FIG. 7, a second example thereof is the configuration shown in FIG. 8, a third example thereof is the configuration shown in FIG. 9, a fourth example thereof is the configuration shown in FIG. 10, and a fifth example thereof is the configuration shown in FIG. 11. In the configuration shown in FIG. 7, M cannot be expressed as a product of K factors excluding 1, so Equation (23) holds (vacuous truth). In the configuration shown in FIG. 8, M cannot be expressed as a product of K factors excluding 1, so Equation (23) holds (vacuous truth). In the configuration shown in FIG. 9, the only factorization of M using K factors excluding 1 is M=2×2×2×2×2, so F(M,K)={{2}}. Furthermore, S={3,4}. Therefore, Equation (23) holds. In the configuration shown in FIG. 10, the only factorization of M using K factors excluding 1 is M=2×2×2×2, so F(M,K)={{2}}. Furthermore, S={2}. Therefore, equation (23) holds. In the configuration shown in FIG. 11, the only factorization of M using K factors excluding 1 is M=2×2×2×2, so F(M, K)={{2}}. Furthermore, S={2}. Therefore, equation (23) holds. These examples of the interface sensor 2 of the second embodiment include examples of the interface sensor 1 of the first embodiment, but this does not necessarily mean that the second embodiment includes the first embodiment.

[0073] FIG. 14 shows a sixth example of the second embodiment. In the sixth example, K=4 M=15 e(1)=8, e(2)=7, e(3)=8, e(4)=7, Σ k∈[K] e(k)=30 c(1)=2, c(2)=2, c(3)=2, c(4)=2 p 1,1 =1, p 1,2 =2, p 1,3 =4, p 1,4 =8, p 1,5 =9, p1,6 =10、p 1,7 =12、p 1,8 =14 p 2,1 =3、p 2,2 =5、p 2,3 =6、p 2,4 =9、p 2,5 =12、p 2,6 =13、p 2,7 =14 p 3,1 =1、p 3,2 =4、p 3,3 =7、p 3,4 =8、p 3,5 =10、p 3,6 =11、p 3,7 =12、p 3,8 =15 p 4,1 =1、p 4,2 =2、p 4,3 =6、p 4,4 =7、p 4,4 =9、p 4,4 =13、p 4,4 =14 s 1,1 =1、s 1,2 =2、s 1,3 =1、s 1,4 =2、s 1,5 =1、s 1,6 =2、s 1,7 =1、s 1,8 =2 s 2,1 =1、s 2,2 =2、s 2,3 =1、s 2,4 =2、s 2,5 =1、s 2,6 =2、s 2,7 =1 s 3,1 =1、s 3,2 =2、s 3,3 =1、s 3,4 =2、s 3,5 =1、s 3,6 =2、s 3,7 =1、s 3,8 =2 s 4,1 =1、s 4,2 =2、s 4,3 =1、s 4,4 =2、s 4,5 =1、s4,6 =2, s 4,7 =1 r(1)=2, r(2)=2, r(3)=2, r(4)=2 h(16)=0101 h(15)=0111 h(14)=1010 h(13)=1111 h(12)=0001 h(11)=0011 h(10)=1001 h(9) =0100 h(8) = 1110 h(7) = 1101 h(6) = 1000 h(5) = 1100 h(4) =0110 h(3) =0010 h(2) = 1011 h(1) =0000 max({d H (h(m),h(m+1)):∀m∈[M]})=3 It is easy to verify that equations (13), (16), and (19) hold. Since M cannot be expressed as a product of K factors excluding 1, equation (23) holds. The sequence h(m) in the sixth example is a four-digit binary counting sequence.

[0074] The explanations of [Example of coding system], [Design], [Method and algorithm for identifying the position of an interface], [Variation 1], and [Variation 2] in the first embodiment shall apply mutatis mutandis to the explanations of [Example of coding system], [Design], [Method and algorithm for identifying the position of an interface], [Variation 1], and [Variation 2] in the second embodiment.

[0075] [Equivalent structure to the second embodiment] Next, a "configuration equivalent to a configuration satisfying all of conditions 1, 2, 3, 4, 5, 6, 7, and 8" and specific examples thereof will be described. A "configuration equivalent to a configuration satisfying all of conditions 1, 2, 3, 4, 5, 6, 7, and 8" is a configuration that has a different configuration from a "configuration satisfying all of conditions 1, 2, 3, 4, 5, 6, 7, and 8" but has the same function from the perspective of an electrical circuit. Because it is impossible to list all "equivalent configurations," and because a person skilled in the art can easily implement various equivalent configurations, only an example of an "equivalent configuration" in the sixth example of the second embodiment will be described.

[0076] max({d H If (h(m),h(m+1)):∀m∈[M]}) is less than K, the electrode pairs 5 can be arranged in Y columns. Y is the sum of max({d H (h(m),h(m+1)):∀m∈[M]})≦Y≦K−1. In the sixth example of the second embodiment, max({d H Since (h(m),h(m+1)):∀m∈[M]})=3, 3≦Y≦K-1=3. Therefore, the electrode pairs 5 can be arranged in three columns. Furthermore, K conductors 7--kth (k∈[K]) sensor block B k The c(k)+1th group of conducting wires 7 in the above can be replaced with one conducting wire. Therefore, an example of the "equivalent configuration" of the sixth example (FIG. 14) of the second embodiment has the configuration shown in FIG.

[0077] [Third embodiment] The interface sensor 3 of the third embodiment differs from the first embodiment in that all of the other electrodes 5b are replaced with first electrical conductors. Therefore, here, the substantial differences between the first and third embodiments will be described, and for other technical matters, the description of the first embodiment will be applied mutatis mutandis to the description of the third embodiment. Therefore, the description of the first embodiment, excluding the substantial differences, is expressly incorporated herein mutatis mutandis. By applying the description of the first embodiment to the description of the third embodiment, for example, "interface sensor 1" can be rephrased as "interface sensor 3."

[0078] As will be described later, the interface sensor 3 of the third embodiment includes a first electrical conductor 50a and a Σ k∈[K] The first electrical conductor 50a and the second electrical conductor 50b are connected to the conductor 70. k∈[K] Between the e(k) second electrical conductors 50b, Σ k∈[K] The position of the interface between the first material and the second material is determined by the two electrodes (i.e., the first electrical conductor 50a and Σ k∈[K] This is achieved by utilizing a physical quantity that occurs in the electrode pair depending on the properties of the first or second substance that exists between any one of the e(k) second electrical conductors 50b. For the reasons already mentioned, capacitance is used as the physical quantity that occurs in the electrode pair, and an explanation of an example in which electrical resistance is used as the physical quantity will be omitted.

[0079] The interface sensor 3 is a sensor having a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9, or a configuration equivalent to said configuration. First, we will explain the "configuration that satisfies all of conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9" and specific examples thereof, and then we will explain the "equivalent configuration" and specific examples thereof.

[0080] <Condition 1> The interface sensor 3 includes a first electrical conductor 50a and K sensor blocks {B k: k ∈ [K]}, where K is a predetermined integer satisfying 2 ≤ K < M. K preferably satisfies the above formula (8). M is a predetermined integer satisfying 8 ≤ M except when K = 2, and is a predetermined odd integer satisfying 9 ≤ M when K = 2. M determines the resolution of the interface sensor 3. That is, M corresponds to the total number of the above-mentioned "observation points".

[0081] The first electric conductor 50a is, for example, a metal. The first electric conductor 50a may be one electric conductor or may include two or more electric conductors.

[0082] When the first electric conductor 50a is one electric conductor, the shape of the first electric conductor 50a may be a flat plate or a cylinder without being limited to the following examples. When the first electric conductor 50a has a cylindrical shape, the cross-sectional shape of the cylinder in a cross-section perpendicular to the longitudinal direction of the cylinder is, for example, a circle or a rectangle. When the first electric conductor 50a has a cylindrical shape, the K sensor blocks {B k : k ∈ [K]} are usually arranged inside the first electric conductor 50a, but this is not the case.

[0083] When the first electric conductor 50a includes two or more electric conductors, the shape of each of the electric conductors included in the first electric conductor 50a may be a flat plate without being limited to the following examples, or the shape of each of the components for constituting the above-mentioned cylinder (for example, the shape of an object obtained by cutting the above-mentioned cylinder in a direction perpendicular to its longitudinal direction (that is, a cylinder shorter than the above-mentioned cylinder), the shape of an object obtained by cutting the above-mentioned cylinder in its longitudinal direction (for example, in the case of a circular cylinder, a 1 / 4 circular cylinder shape)). When the first electric conductor 50a includes two or more electric conductors, the two or more electric conductors may be independent of each other. However, it is desirable that the two or more electric conductors included in the first electric conductor 50a have the same potential as each other, for example, by contacting each other.

[0084] Hereinafter, from the perspective of ease of understanding of the interface sensor 3, in the example shown in FIG. 16 and the example shown in FIG. 17, the first electric conductor 50a is one electric conductor. In FIGS. 16 and 17, for ease of viewing the figure, the edge of the first electric conductor 50a is explicitly illustrated, and the first electric conductor 50a is drawn as if it were transparent.

[0085] <Condition 2> For any k ∈ [K], among the K sensor blocks {B k : k ∈ [K]}, the k-th sensor block B k includes e(k) second electric conductors 50b and c(k) conducting wires 70. e(k) is a predetermined integer satisfying 1 ≤ e(k) < M. c(k) is a predetermined integer satisfying 2 ≤ c(k) ≤ e(k) except when e(k) = 1, and is 1 when e(k) = 1.

[0086] The K sensor blocks {B k : k ∈ [K]} are formed on Q substrates 9 having a flat plate shape without being limited to the following examples. That is, the second electric conductors 50b and the conducting wires 70 are formed on the substrates 9. The substrates 9 are waterproof-coated except for the second electric conductors 50b. Q is a predetermined integer satisfying 1 ≤ Q ≤ K. When Q < K, there are substrates 9 having two or more sensor blocks. In the example shown in FIG. 16 and the example shown in FIG. 17, Q = 1. When Q ≥ 2, the Q substrates 9 may be arranged on one plane without being limited to the following examples, may be arranged like angle steel or channel steel, or may be arranged like triangular pipes or square pipes.

[0087] The second electric conductor 50b is, for example, metal. The shape of the second electric conductor 50b may be a rectangular flat plate or a circular flat plate without being limited to the following examples. The k-th (k ∈ [K]) sensor block B kIn the equation, e(k) electrode pairs are formed between the first electrical conductor 50a and the e(k) second electrical conductors 50b. When e(k)≠1, the gaps between the e(k) electrode pairs—in other words, the e(k) gaps formed by the first electrical conductor 50a and the e(k) second electrical conductors 50b—are filled with, for example, a first substance, and the e(k) electrode pairs have the same capacitance C k From another perspective, when e(k)≠1, "when the gap between each of the e(k) electrode pairs is filled with, for example, the first substance, the e(k) electrode pairs have the same capacitance C k In order to satisfy the condition that "has k-th (k∈[K]) sensor block B k The area of ​​the ith (i∈[e(k)]) second electrical conductor 50b among the e(k) second electrical conductors 50b included in the sensor block B and the distance between the ith (i∈[e(k)]) second electrical conductor 50b and the first electrical conductor 50a are appropriately set. For example, the area of ​​the kth (k∈[K]) sensor block B k 16 and 17, the shape of the first electrical conductor 50a is a rectangular plate having an area larger than the area of ​​the substrate 9. In the examples shown in FIGS. 16 and 17, the kth (k∈[K]) sensor block B k is located on one surface of the substrate 9, and the first electrical conductor 50a is located parallel to and faces the one surface of the substrate 9. When the interface sensor 3 is viewed from the front (i.e., when the paper surface of FIGS. 16 and 17 is viewed from the front), the first electrical conductor 50a is located on one surface of the substrate 9. k∈[K] The k-th sensor block B covers e(k) second electrical conductors 50b, and the distance between the edge of the first electrical conductor 50a and each second electrical conductor 50b is sufficiently large. k The capacitance C of each of the e(k) electrode pairs included in kis the jth (j≠k) sensor block B j The capacitance C of each of the e(j) electrode pairs included in j Each of the c(k) conducting wires 70 is connected to one of the K sensor blocks {B k :k∈[K]}, and as will be described later in relation to condition 5, the interface sensor 3 has Σ k∈[K] At least one of the e(k) second electrical conductors 50b is connected to the second electrical conductor 50b. The c(k) conducting wires 70 are connected to the measurement circuit described above. In the drawing, for ease of viewing, only some of the second electrical conductors and some conducting wires are labeled.

[0088] <Condition 3>~<Condition 4> Conditions 3 and 4 in the third embodiment are the same as conditions 3 and 4 in the first embodiment. Therefore, the explanation of conditions 3 and 4 in the first embodiment applies mutatis mutandis to the explanation of conditions 3 and 4 in the third embodiment. By applying the explanation of the first embodiment mutatis mutandis to the explanation of the third embodiment, for example, "interface sensor 1" can be rephrased as "interface sensor 3" and "electrode pair 5" as "second electrical conductor 50b."

[0089] <Condition 5> For any (k,i)∈[K]×[e(k)], there are K sensor blocks {B k :k∈[K]}, the kth sensor block B k In the equation, the i-th second electrical conductor 50b among the e(k) second electrical conductors 50b is the s k,i It is connected to the 70th conductor. k,i is expressed by the above formula (10). In this example, the second electrical conductor 50b and the second electrical conductor s k,i The second conductors 70 are connected to each other via branch lines 70x.

[0090] <Condition 6>~<Condition 7> Conditions 6 and 7 in the third embodiment are the same as conditions 6 and 7 in the first embodiment. Therefore, the explanation of conditions 6 and 7 in the first embodiment applies mutatis mutandis to the explanation of conditions 6 and 7 in the third embodiment. By applying the explanation of the first embodiment mutatis mutandis to the explanation of the third embodiment, for example, "interface sensor 1" can be rephrased as "interface sensor 3" and "electrode pair 5" as "second electrical conductor 50b."

[0091] <Condition 8> From condition 2, the kth (k∈[K]) sensor block B k includes c(k) conducting wires 70. Therefore, in order for the total number of conducting wires 70 drawn out from the interface sensor 3 to be less than the total number of observation points, i.e., the number M of planes, it is sufficient that equation (25) is established.

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[0092] <Condition 9> Condition 9 in the third embodiment is the same as condition 9 in the first embodiment. Therefore, the explanation of condition 9 in the first embodiment applies mutatis mutandis to the explanation of condition 9 in the third embodiment. By applying the explanation of the first embodiment mutatis mutandis to the explanation of the third embodiment, for example, "interface sensor 1" can be rephrased as "interface sensor 3" and "electrode pair 5" as "second electrical conductor 50b."

[0093] An example of an interface sensor 3 according to the third embodiment will be described with reference to the drawings. As mentioned above, the third embodiment differs from the first embodiment in that all of the other electrodes 5b are replaced with first electrical conductors, and therefore only an example of an interface sensor 3 based on the first example of the first embodiment (see FIG. 7) is shown in FIG. 16. In FIG. 16, in consideration of ease of viewing the drawing, when two or more identical components are present, reference numerals are assigned to one or more, but not all, of the two or more identical components.

[0094] The explanations of [Example of coding system], [Design], [Method and algorithm for identifying the position of an interface], [Variation 1], and [Variation 2] in the first embodiment shall apply mutatis mutandis to the explanations of [Example of coding system], [Design], [Method and algorithm for identifying the position of an interface], [Variation 1], and [Variation 2] in the third embodiment.

[0095] [Equivalent structure to the third embodiment] Next, a "configuration equivalent to a configuration that satisfies all of conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9" and specific examples thereof will be described. A "configuration equivalent to a configuration that satisfies all of conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9" is a configuration that has a different configuration from a "configuration that satisfies all of conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9," but has the same function from the perspective of an electrical circuit. Because it is impossible to list all "equivalent configurations," and because a person skilled in the art can easily implement various equivalent configurations, only the example of the interface sensor 3 shown in FIG. 16 and examples of "equivalent configurations" will be described.

[0096] max({d H If {(h(m),h(m+1)):∀m∈[M]}) is less than K, the second electrically conductive bodies 50b can be arranged in Y columns. Y is the sum of max({d H (h(m),h(m+1)):∀m∈[M]})≦Y≦K−1. H (h(m),h(m+1)):∀m∈[M]})=1. Therefore, 1≦Y≦K−1=3. Therefore, the second electrical conductors 50b can be arranged in one row (see FIG. 17).

[0097] [Fourth embodiment] The interface sensor 4 of the fourth embodiment is an interface sensor whose configuration is determined by the adopted coding system and its specific code words, and whose configuration satisfies the above-mentioned condition b). In this respect, the fourth embodiment differs from the third embodiment. From another perspective, the fourth embodiment differs from the second embodiment in that all of the other electrodes 5b are replaced with first electrical conductors.

[0098] Here, the substantial differences between the third and fourth embodiments will be described, and for other technical matters, the description of the third embodiment will be applied mutatis mutandis to the description of the fourth embodiment. Therefore, the description of the third embodiment, excluding the substantial differences, is expressly incorporated mutatis mutandis herein. Furthermore, through the incorporation of the description of the third embodiment, the description of the first embodiment is also expressly incorporated mutatis mutandis herein. By applying the descriptions of the first and third embodiments mutatis mutandis to the description of the fourth embodiment, for example, "interface sensor 1" and "interface sensor 3" can be rephrased as "interface sensor 4."

[0099] The interface sensor 4 of the fourth embodiment is a sensor having a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, and 8, or a configuration equivalent to said configuration. First, the "configuration that satisfies all of conditions 1, 2, 3, 4, 5, 6, 7, and 8" and specific examples thereof will be described, and then the "equivalent configuration" and specific examples thereof will be described.

[0100] <Condition 1>~<Condition 7> Conditions 1, 2, 3, 4, 5, and 6 in the fourth embodiment are the same as conditions 1, 2, 3, 4, 5, and 6 in the third embodiment, respectively. Condition 7 in the fourth embodiment is the same as condition 8 in the third embodiment. Therefore, the descriptions of conditions 1, 2, 3, 4, 5, 6, and 8 in the third embodiment apply mutatis mutandis to the descriptions of conditions 1, 2, 3, 4, 5, 6, and 7 in the fourth embodiment. Conditions 7 and 9 in the third embodiment are unnecessary in the fourth embodiment. Condition 8 in the fourth embodiment is as follows.

[0101] <Condition 8> Condition 8 in the fourth embodiment is the same as condition 8 in the second embodiment. Therefore, the explanation of condition 8 in the second embodiment applies mutatis mutandis to the explanation of condition 8 in the fourth embodiment.

[0102] An example of an interface sensor 4 according to a fourth embodiment will be described with reference to the drawings. As mentioned above, the fourth embodiment differs from the second embodiment in that all of the other electrodes 5b are replaced with first electrical conductors, and therefore only an example of an interface sensor 4 based on the sixth example of the second embodiment (see FIG. 14) is shown in FIG. 18. In FIG. 18, in consideration of ease of viewing the drawing, when two or more identical components are present, reference numerals are assigned to one or more, but not all, of the two or more identical components.

[0103] The explanations of [Example of coding system], [Design], [Method and algorithm for identifying the position of an interface], [Variation 1], and [Variation 2] in the first embodiment shall apply mutatis mutandis to the explanations of [Example of coding system], [Design], [Method and algorithm for identifying the position of an interface], [Variation 1], and [Variation 2] in the fourth embodiment.

[0104] [Equivalent structure to the fourth embodiment] Next, we will explain a "configuration equivalent to a configuration that satisfies all of conditions 1, 2, 3, 4, 5, 6, 7, and 8," and specific examples thereof. A "configuration equivalent to a configuration that satisfies all of conditions 1, 2, 3, 4, 5, 6, 7, and 8" is a configuration that has a different configuration from a "configuration that satisfies all of conditions 1, 2, 3, 4, 5, 6, 7, and 8," but has the same function from the perspective of an electrical circuit. Because it is impossible to list all "equivalent configurations," and because a person skilled in the art can easily implement various equivalent configurations, we will only explain an example of an "equivalent configuration" for the example interface sensor 4 shown in FIG. 18.

[0105] max({d H If {(h(m),h(m+1)):∀m∈[M]}) is less than K, the second electrically conductive bodies 50b can be arranged in Y columns. Y is the sum of max({d H (h(m),h(m+1)):∀m∈[M]})≦Y≦K−1. H (h(m),h(m+1)):∀m∈[M]})=3. Therefore, 3≦Y≦K−1=3. Therefore, the second electrical conductors 50b can be arranged in three rows (see FIG. 19).

[0106] <Addendum 1> The technical features disclosed in the various embodiments and their modifications described above are not necessarily mutually exclusive, and technical features of one embodiment or its modifications may be applied to technical features of another embodiment or its modifications, provided that there is no contradiction from a technical viewpoint.

[0107] The claims recited in the claims of the present application at the time of filing do not necessarily comprehensively claim all the inventions disclosed in this specification. In this regard, it should not be understood or interpreted that the applicant of the present application has waived the right to obtain a patent for inventions not claimed at the time of filing of the present application prior to filing. As long as the laws and regulations or treaties of the country or region that has accepted the filing of the present application permit, the applicant of the present application reserves the right to obtain a patent for inventions not claimed in the present application, the right to file a divisional application for such inventions, the right to claim such inventions by amendment, and all other rights. However, this is not the case when the applicant of the present application has made an express and definitive statement of opposition.

[0108] An example of the summary of the present disclosure based on another perspective is as follows.

[0109] The sensor based on the first perspective is a sensor for specifying the position of the interface between the first substance and the second substance, and has a configuration that satisfies all of the following conditions 1, condition 2, condition 3, condition 4, condition 5, condition 6, condition 7, condition 8, and condition 9, or has a configuration equivalent to the said configuration. Condition 1) The said sensor includes K sensor blocks {B k : k ∈ [K]}. However, K is a predetermined integer that satisfies 2 ≤ K < M, M is a predetermined integer that satisfies 8 ≤ M except when K = 2, and when K = 2, M is a predetermined odd number that satisfies 9 ≤ M. The symbol [X] represents the set {x ∈ N: 1 ≤ x ≤ X} determined by the positive integer X, and N is the set of all positive integers. Condition 2) For any k ∈ [K], the k-th sensor block B among the said K sensor blocks k includes e(k) electrode pairs and c(k) + 1 conducting wires. However, e(k) is a predetermined integer that satisfies 1 ≤ e(k) < M, c(k) is a predetermined integer that satisfies 2 ≤ c(k) ≤ e(k) except when e(k) = 1, and when e(k) = 1, it is 1. Condition 3) The Σ that the said sensor hask∈[K] Each of the e(k) electrode pairs is located on one of M planes that are mutually disjoint and parallel, where the M planes are arranged in order according to the original ordering relationship of the set [M], and the Σ k∈[K] At least one electrode pair out of the e(k) electrode pairs is located. Condition 4) For any k∈[K], the k-th sensor block B k The i-th electrode pair among the e(k) electrode pairs included in k,i When it is located in the th plane, ∀k∈[K],i,j∈[e(k)],i>j ⇒ p k,i >p k,j where ∀(k,i)∈[K]×[e(k)],p k,i ∈[M]. Condition 5) For any (k,i)∈[K]×[e(k)], the kth sensor block B k In the above, one electrode of the i-th electrode pair among the e(k) electrode pairs is s among the c(k)+1 conducting wires. k,i The other electrode is connected to the c(k)+1th conductor of the c(k)+1 conductors.

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[0110] The sensor based on the second perspective is a sensor for specifying the position of the interface between the first substance and the second substance, and has a configuration that satisfies all of the following Conditions 1, Condition 2, Condition 3, Condition 4, Condition 5, Condition 6, Condition 7, and Condition 8, or has a configuration equivalent to the said configuration. Condition 1 The said sensor includes \(K\) sensor blocks \(\{B\) k \(_{k}:k\in[K]\}\). Here, \(K\) is a predetermined integer satisfying \(2\leq K\lt M\), \(M\) is a predetermined integer satisfying \(8\leq M\) except when \(K = 2\), and \(M\) is a predetermined odd number satisfying \(9\leq M\) when \(K = 2\). The symbol \([X]\) represents the set \(\{x\in N:1\leq x\leq X\}\) determined by the positive integer \(X\), and \(N\) is the set of all positive integers. Condition 2 For any \(k\in[K]\), the \(k\) - th sensor block \(B\) k among the said \(K\) sensor blocks includes \(e(k)\) electrode pairs and \(c(k)+1\) conducting wires. Here, \(e(k)\) is a predetermined integer satisfying \(1\leq e(k)\lt M\), \(c(k)\) is a predetermined integer satisfying \(2\leq c(k)\leq e(k)\) except when \(e(k)=1\), and \(c(k)=1\) when \(e(k)=1\). Condition 3 The above sensor has Σ k∈[K] Each of the e(k) electrode pairs is located on one of M planes that are mutually disjoint and parallel, where the M planes are arranged in order according to the original ordering relationship of the set [M], and the Σ k∈[K] At least one electrode pair out of the e(k) electrode pairs is located. Condition 4) For any k∈[K], the k-th sensor block B k The i-th electrode pair among the e(k) electrode pairs included in k,i When it is located in the th plane, ∀k∈[K],i,j∈[e(k)],i>j ⇒ p k,i >p k,j where ∀(k,i)∈[K]×[e(k)],p k,i ∈[M]. Condition 5) For any (k,i)∈[K]×[e(k)], the k-th sensor block B k In the above, one electrode of the i-th electrode pair among the e(k) electrode pairs is s of the c(k)+1 conducting wires. k,i The other electrode is connected to the c(k)+1th conductor of the c(k)+1 conductors.

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[0111] The sensor based on the third aspect is a sensor for specifying the position of the interface between the first substance and the second substance, and has a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, 8, 9, or a sensor having a configuration equivalent to the said configuration. Condition 1 The said sensor includes a first electrical conductor and K sensor blocks \(\{B\) k : \(k\in[K]\}\). However, K is a predetermined integer satisfying \(2\leq K\lt M\), M is a predetermined integer satisfying \(8\leq M\) except when \(K = 2\), and M is a predetermined odd number satisfying \(9\leq M\) when \(K = 2\). The symbol \([X]\) represents the set \(\{x\in N:1\leq x\leq X\}\) determined by the positive integer X, and N is the set of all positive integers. Condition 2 For any \(k\in[K]\), the k-th sensor block \(B\) k among the said K sensor blocks includes \(e(k)\) second electrical conductors and \(c(k)\) conducting wires. However, \(e(k)\) is a predetermined integer satisfying \(1\leq e(k)\lt M\), \(c(k)\) is a predetermined integer satisfying \(2\leq c(k)\leq e(k)\) except when \(e(k)=1\), and \(c(k)=1\) when \(e(k)=1\). Condition 3 The \(\sum\) that the said sensor has k∈[K]Each of the e(k) second electrical conductors is located on one of M planes that are mutually disjoint and parallel, where the M planes are arranged in an order according to the ordering relation of the elements of the set [M], and the Σ k∈[K] At least one second electrical conductor is located among the e(k) second electrical conductors. Condition 4) For any k∈[K], the k-th sensor block B k The i-th second electrical conductor among the e(k) second electrical conductors included in k,i When it is located in the th plane, ∀k∈[K],i,j∈[e(k)],i>j ⇒ p k,i >p k,j where ∀(k,i)∈[K]×[e(k)],p k,i ∈[M]. Condition 5) For any (k,i)∈[K]×[e(k)], the k-th sensor block B k In the above, the i-th second electrical conductor among the e(k) second electrical conductors is the s k,i connected to the conductor, except that

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[0112] The sensor based on the fourth aspect is a sensor for specifying the position of the interface between the first substance and the second substance, having a configuration that satisfies all of the following Conditions 1, Condition 2, Condition 3, Condition 4, Condition 5, Condition 6, Condition 7, and Condition 8, or having a configuration equivalent to the said configuration. Condition 1 The said sensor includes a first electrical conductor and K sensor blocks \(\{B\) k : \(k\in[K]\}\). Here, K is a predetermined integer satisfying \(2\leq K\lt M\), M is a predetermined integer satisfying \(8\leq M\) except when \(K = 2\), and when \(K = 2\), M is a predetermined odd number satisfying \(9\leq M\). The symbol \([X]\) represents the set \(\{x\in N:1\leq x\leq X\}\) determined by the positive integer X, and N is the set of all positive integers. Condition 2 For any \(k\in[K]\), the k-th sensor block \(B\) among the said K sensor blocks k includes \(e(k)\) second electrical conductors and \(c(k)\) conducting wires. Here, \(e(k)\) is a predetermined integer satisfying \(1\leq e(k)\lt M\), \(c(k)\) is a predetermined integer satisfying \(2\leq c(k)\leq e(k)\) except when \(e(k)=1\), and when \(e(k)=1\), \(c(k)\) is 1. Condition 3 The above sensor has Σ k∈[K] Each of the e(k) second electrical conductors is located on one of M planes that are mutually disjoint and parallel, where the M planes are arranged in an order according to the ordering relation of the elements of the set [M], and the Σ k∈[K] At least one second electrical conductor is located among the e(k) second electrical conductors. Condition 4) For any k∈[K], the k-th sensor block B k The i-th second electrical conductor among the e(k) second electrical conductors included in k,i When it is located in the th plane, ∀k∈[K],i,j∈[e(k)],i>j ⇒ p k,i >p k,j where ∀(k,i)∈[K]×[e(k)],p k,i ∈[M]. Condition 5) For any (k,i)∈[K]×[e(k)], the kth sensor block B k In the above, the i-th second electrical conductor among the e(k) second electrical conductors is the s k,i connected to the conductor, except that

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[0113] A sensor according to the fifth aspect is a sensor according to the third or fourth aspect, For any k∈[K], the k-th sensor block B k a distance between one of any two second electrical conductors among the e(k) second electrical conductors included in the matrix and the first electrical conductor is equal to a distance between the other second electrical conductor and the first electrical conductor; The sensor is characterized by the above.

[0114] The liquid level meter of the present disclosure comprises: a sensor according to any one of the first aspect to the fifth aspect, The first substance is a liquid, The second substance is a gas, In this liquid level meter, the normal direction of the M planes in the sensor based on any one of the first to fifth aspects may be a vertical direction.

[0115] <Addendum 2> While the present invention has been described with reference to exemplary embodiments, those skilled in the art will recognize that various changes can be made and equivalents can be substituted for elements thereof without departing from the scope of the invention. Furthermore, many modifications can be made to adapt a particular system, device, or component thereof to the teachings of the present invention without departing from the essential scope of the invention. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed for carrying out this invention, but rather that the invention will include all embodiments falling within the scope of the appended claims.

[0116] Furthermore, the use of terms such as "first," "second," etc., when used in this specification and / or the appended claims, does not denote any order or importance, and terms such as "first," "second," etc., are used to distinguish between elements. The terms used herein are for the purpose of describing embodiments and are not intended to limit the invention in any way. The term "comprises" and its conjugations, when used in this specification and / or the appended claims, reveal the presence of referenced features, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and / or groups thereof. The term "and / or" includes any and all combinations of one or more of the associated listed elements, if any. In the claims and the specification, unless otherwise specified, the use of words such as "connected," "coupled," "joined," "connected," or synonyms thereof, and all word forms thereof, does not necessarily negate the presence of one or more intermediate elements between two elements, e.g., "connected" or "coupled" to each other or "connected" to each other. In the claims and the specification, the term "any," if any, should be understood as a term that has the same meaning as the universal symbol ∀, unless otherwise specified. For example, the phrase "for any X" has the same meaning as "for all X" or "for each X." A phrase such as "at least one of A, B, and C" (e.g., "at least one of A, B, and C," "at least one of A, B, or C," "at least one of A, B, and / or C"), if any, should be understood as a term that has the same meaning as the universal symbol ∀, unless otherwise specified. S This means that we arbitrarily select one element from the set P excluding the empty set φ. In this example, S={A,B,C},2 S={φ,{A},{B},{C},{A,B},{A,C},{B,C},{A,B,C}},P={{A},{B},{C},{A,B},{A,C},{B,C},{A,B,C}}, which means that one element (e.g., {A,C}) is arbitrarily selected from the set P.

[0117] Unless otherwise specified, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Furthermore, terms such as those defined in commonly used dictionaries should be interpreted to have a meaning consistent with their meaning in the context of the relevant art and this disclosure, and should not be interpreted ideally or excessively formally unless explicitly defined.

[0118] It will be understood that in describing the present invention, many techniques and steps are disclosed. Each of these has distinct advantages, and each can be used in combination with one or more, or in some cases all, of the other disclosed techniques. Therefore, to avoid cluttering, this specification will refrain from describing every possible combination of individual techniques or steps. Nevertheless, the specification and claims should be read with the understanding that such combinations are fully within the scope of the present invention and claims.

[0119] The corresponding structure, material, acts, and equivalents of all functional elements combined with means or steps in the following claims are intended to include the structure, material, or acts, if any, that perform the function in combination with other elements.

[0120] Although the present invention has been described above with reference to exemplary embodiments, it is not limited to these embodiments. Various modifications and variations are possible without departing from the spirit of the present invention. The selected and described embodiments are intended to illustrate the principles of the present invention and its practical application. The present invention may be used in various embodiments with various modifications or variations, which are determined according to the expected use. All such modifications and variations are intended to be included within the scope of the present invention, as defined by the appended claims, and are intended to be accorded the same protection when interpreted in accordance with the breadth that is fairly, legally, and equitably to be given. [Explanation of symbols]

[0121] 1 Interface sensor 2 Interface sensor 3 Interface sensor 4 Interface sensor 5 electrode pairs 5a electrode 5b electrode 7 Conductor 9 Substrate 50a First electrical conductor 50b Second electrical conductor 70 Conductor B k Sensor Block

Claims

1. A sensor for identifying the position of the interface between a first substance and a second substance, which has a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9, or a configuration equivalent to said configuration. Condition 1) The sensor is divided into K sensor blocks {B k : k∈[K]}, where K is a predetermined integer satisfying 2≦K<M, M is a predetermined integer satisfying 8≦M except when K=2, and is a predetermined odd number satisfying 9≦M when K=2, the symbol [X] represents a set {x∈N:1≦x≦X} determined by positive integers X, and N is the set of all positive integers. Condition 2) For any k∈[K], the k-th sensor block B k includes e(k) electrode pairs and c(k)+1 conducting wires, where e(k) is a predetermined integer satisfying 1≦e(k)<M, and c(k) is a predetermined integer satisfying 2≦c(k)≦e(k) except when e(k)=1, in which case it is 1. Condition 3) The above sensor has Σ k∈[K] Each of the e(k) electrode pairs is located on one of M planes that are not coincident with each other and are parallel to each other. However, the M planes are arranged in an order according to the order relation of the elements of the set [M], and the Σ k∈[K] At least one electrode pair out of the e(k) electrode pairs is located. Condition 4) For any k∈[K], the k-th sensor block B k The i-th electrode pair among the e(k) electrode pairs included in k,i When it is located in the th plane, ∀k∈[K],i,j∈[e(k)],i>j ⇒ p k,i >p k,j where ∀(k, i)∈[K]×[e(k)], p k,i ∈[M]. Condition 5) For any (k, i)∈[K]×[e(k)], the k-th sensor block B k In the above, one electrode of the i-th electrode pair among the e(k) electrode pairs is s of the c(k)+1 conducting wires. k,i The other electrode is connected to the c(k)+1-th conductor of the c(k)+1 conductors. [Number 48] Condition 6) non-negative integer g m,k of, [Number 49] and the codeword h(m) is [Number 50] In the case where it is determined by a)m 1 ,m 2 ∈[M+1],m 1 ≠m 2 ⇒ h(m 1 )≠h(m 2 )、 or b) m 1 , m 2 ∈[M], m 1 ≠m 2 ⇒ h(m 1 )≠h(m 2 ), and h(1)=h(M+1), holds true. Condition 7) max({d H (h(m),h(m+1)) : ∀m∈[M]}) = 1 holds. However, d H (h(m), h(m+1)) is the Hamming distance between codeword h(m) and codeword h(m+1). Condition 8) [Equation 51] holds true. Condition 9) [Number 52] holds true.

2. A sensor for identifying the position of the interface between a first substance and a second substance, which has a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, and 8, or a configuration equivalent to said configuration. Condition 1) The sensor is divided into K sensor blocks {B k : k∈[K]}, where K is a predetermined integer satisfying 2≦K<M, M is a predetermined integer satisfying 8≦M except when K=2, and is a predetermined odd number satisfying 9≦M when K=2, the symbol [X] represents a set {x∈N:1≦x≦X} determined by positive integers X, and N is the set of all positive integers. Condition 2) For any k∈[K], the k-th sensor block B k includes e(k) electrode pairs and c(k)+1 conducting wires, where e(k) is a predetermined integer satisfying 1≦e(k)<M, and c(k) is a predetermined integer satisfying 2≦c(k)≦e(k) except when e(k)=1, in which case it is 1. Condition 3) The above sensor has Σ k∈[K] Each of the e(k) electrode pairs is located on one of M planes that are not coincident with each other and are parallel to each other. However, the M planes are arranged in an order according to the order relation of the elements of the set [M], and the Σ k∈[K] At least one electrode pair out of the e(k) electrode pairs is located. Condition 4) For any k∈[K], the k-th sensor block B k The i-th electrode pair among the e(k) electrode pairs included in k,i When it is located in the th plane, ∀k∈[K],i,j∈[e(k)],i>j ⇒ p k,i >p k,j where ∀(k, i)∈[K]×[e(k)], p k,i ∈[M]. Condition 5) For any (k, i)∈[K]×[e(k)], the k-th sensor block B k In the above, one electrode of the i-th electrode pair among the e(k) electrode pairs is s of the c(k)+1 conducting wires. k,i The other electrode is connected to the c(k)+1-th conductor of the c(k)+1 conductors. [Number 53] Condition 6) non-negative integer g m,k of, [Number 54] and the codeword h(m) is [Number 55] In the case where it is determined by a)m 1 ,m 2 ∈[M+1],m 1 ≠m 2 ⇒ h(m 1 )≠h(m 2 )、 or b) m 1 , m 2 ∈[M], m 1 ≠m 2 ⇒ h(m 1 )≠h(m 2 ), and h(1)=h(M+1), holds true. Condition 7) [Number 56] holds true. Condition 8) [Number 57] holds true.

3. A sensor for identifying the position of the interface between a first substance and a second substance, which has a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9, or a configuration equivalent to said configuration. Condition 1) The sensor includes a first electrical conductor and K sensor blocks {B k : k∈[K]}, where K is a predetermined integer satisfying 2≦K<M, M is a predetermined integer satisfying 8≦M except when K=2, and is a predetermined odd number satisfying 9≦M when K=2, the symbol [X] represents a set {x∈N:1≦x≦X} determined by positive integers X, and N is the set of all positive integers. Condition 2) For any k∈[K], the k-th sensor block B k includes e(k) second electrical conductors and c(k) conducting wires, where e(k) is a predetermined integer satisfying 1≦e(k)<M, and c(k) is a predetermined integer satisfying 2≦c(k)≦e(k) except when e(k)=1, in which case it is 1. Condition 3) The above sensor has Σ k∈[K] Each of the e(k) second electrical conductors is located on one of M planes that are mutually disjoint and parallel, where the M planes are arranged in an order according to the ordering relation of the elements of the set [M], and the Σ k∈[K] At least one second electrical conductor is located among the e(k) second electrical conductors. Condition 4) For any k∈[K], the k-th sensor block B k The i-th second electrical conductor among the e(k) second electrical conductors included in k,i When it is located in the th plane, ∀k∈[K],i,j∈[e(k)],i>j ⇒ p k,i >p k,j where ∀(k, i)∈[K]×[e(k)], p k,i ∈[M]. Condition 5) For any (k, i)∈[K]×[e(k)], the k-th sensor block B k In the above, the i-th second electrical conductor among the e(k) second electrical conductors is the s k,i connected to the conductor, except that [Number 58] Condition 6) non-negative integer g m,k of, [Number 59] and the codeword h(m) is [Number 60] In the case where it is determined by a)m 1 ,m 2 ∈[M+1],m 1 ≠m 2 ⇒ h(m 1 )≠h(m 2 )、 or b) m 1 , m 2 ∈[M], m 1 ≠m 2 ⇒ h(m 1 )≠h(m 2 ), and h(1)=h(M+1), holds true. Condition 7) max({d H (h(m),h(m+1)) : ∀m∈[M]}) = 1 holds. However, d H (h(m), h(m+1)) is the Hamming distance between codeword h(m) and codeword h(m+1). Condition 8) [Number 61] holds true. Condition 9) [Number 62] holds true.

4. A sensor for identifying the position of the interface between a first substance and a second substance, which has a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, and 8, or a configuration equivalent to said configuration. Condition 1) The sensor includes a first electrical conductor and K sensor blocks {B k : k∈[K]}, where K is a predetermined integer satisfying 2≦K<M, M is a predetermined integer satisfying 8≦M except when K=2, and is a predetermined odd number satisfying 9≦M when K=2, the symbol [X] represents a set {x∈N:1≦x≦X} determined by positive integers X, and N is the set of all positive integers. Condition 2) For any k∈[K], the k-th sensor block B k includes e(k) second electrical conductors and c(k) conducting wires, where e(k) is a predetermined integer satisfying 1≦e(k)<M, and c(k) is a predetermined integer satisfying 2≦c(k)≦e(k) except when e(k)=1, in which case it is 1. Condition 3) The above sensor has Σ k∈[K] Each of the e(k) second electrical conductors is located on one of M planes that are mutually disjoint and parallel, where the M planes are arranged in an order according to the ordering relation of the elements of the set [M], and the Σ k∈[K] At least one second electrical conductor is located among the e(k) second electrical conductors. Condition 4) For any k∈[K], the k-th sensor block B k The i-th second electrical conductor among the e(k) second electrical conductors included in k,i When it is located in the th plane, ∀k∈[K],i,j∈[e(k)],i>j ⇒ p k,i >p k,j where ∀(k, i)∈[K]×[e(k)], p k,i ∈[M]. Condition 5) For any (k, i)∈[K]×[e(k)], the k-th sensor block B k In the above, the i-th second electrical conductor among the e(k) second electrical conductors is the s k,i connected to the conductor, except that [Number 63] Condition 6) non-negative integer g m,k of, [Number 64] and the codeword h(m) is [Number 65] In the case where it is determined by a)m 1 ,m 2 ∈[M+1],m 1 ≠m 2 ⇒ h(m 1 )≠h(m 2 )、 or b) m 1 , m 2 ∈[M], m 1 ≠m 2 ⇒ h(m 1 )≠h(m 2 ), and h(1)=h(M+1), holds true. Condition 7) [Number 66] holds true. Condition 8) [Number 67] holds true.

5. The sensor according to claim 3 or claim 4, For any k∈[K], the k-th sensor block B k a distance between one of any two second electrical conductors among the e(k) second electrical conductors included in the matrix and the first electrical conductor is equal to a distance between the other second electrical conductor and the first electrical conductor; Sensor.

6. A liquid level meter, A sensor according to any one of claims 1 to 4, the first substance is a liquid; The second substance is a gas, Liquid level gauge.

7. 7. The liquid level meter according to claim 6, The normal direction of the M planes is the vertical direction. Liquid level gauge.

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