An RC topology filter circuit with fault-tolerant design and its optimization method

Abstract

The present invention discloses an RC topology filtering circuit with fault-tolerant design and its optimization method; the RC topology filtering circuit includes a topology circuit and a load resistor. The topology circuit includes a plurality of topology units arranged in an n×n array. Each of the topology units includes a resistor R1, a resistor R2, a resistor R3, a resistor R4, a resistor R5, a resistor R6, a capacitor C1, a capacitor C2, a capacitor C3, and a capacitor C4. By providing the capacitors C3 and C4 in the topology unit, when the remaining resistors and capacitors fail, the capacitors C3 and C4 can provide backup paths, thereby greatly improving the fault-tolerant ability of the RC topology filtering circuit and extending the service life. In addition, the topology unit designed by the present invention can be quickly spliced into topology networks with different numbers of rows and columns, so as to be used in filtering scenarios with different fault-tolerant requirements, improving the flexibility of the topology filtering circuit.

Description

Technical Field

[0001] The present invention belongs to the technical field of power equipment detection signal filtering, and particularly relates to an RC topology filtering circuit with fault-tolerant design and its optimization method. Background Art

[0002] Due to the unique vulnerability of its electronic components, power equipment may experience the failure of some components under the influence of factors such as strong magnetic fields, strong mechanical stresses, rapid temperature changes, power surges, and general aging. Therefore, for power monitoring equipment exposed to strong magnetic fields, strong electric fields, and humid environments, such as transformer monitoring equipment, cable monitoring equipment, etc., the filtering circuit for stabilizing monitoring signals needs to have high fault tolerance; therefore, for the filtering circuit applied to power monitoring equipment, fault-tolerant design is a crucial link. Fault-tolerant design uses redundancy technology at the physical or logical level. The greater the redundancy, the higher the reliability of the device, but the power consumption will also be greater. Therefore, it is necessary to make a balance between reliability and power consumption and avoid the problem of single-point failure in circuit design. Summary of the Invention

[0003] The purpose of the present invention is to provide an RC topology filtering circuit with fault-tolerant design for power equipment and its optimization method

[0004] In a first aspect, the present invention provides an RC topology filtering circuit with fault-tolerant design, which includes a topology circuit and a load resistor R L . The topology circuit includes a plurality of topology units arranged in an n×n array, where n≥2. Each of the topology units includes a resistor R1, a resistor R2, a resistor R3, a resistor R4, a resistor R5, a resistor R6, a capacitor C1, a capacitor C2, a capacitor C3, and a capacitor C4. One end of the resistor R1, the resistor R3, and the capacitor C3 are connected together as the first horizontal connection port of the topology unit; the other end of the resistor R1, one end of the resistor R2, and one end of the resistor R5 are connected together as the first vertical connection port of the topology unit; the other end of the resistor R5, one end of the capacitor C4, and one end of the resistor R6 are connected together as the second horizontal connection port of the topology unit; the other ends of the resistor R3, the resistor R6, the resistor R4, and one end of the capacitor C2 are connected together; the other end of the capacitor C2 is used as the second vertical connection port of the topology unit; the other ends of the capacitor C3, the resistor R2, the capacitor C4, and the resistor R4 are connected together.

[0005] In the same row, the second horizontal connection port of the previous topological unit is connected to the first horizontal connection port of the next topological unit, and the second horizontal connection port of the last topological unit is connected to the first horizontal connection port of the first topological unit. In the same column, the second vertical connection port of the previous topological unit is connected to the first vertical connection port of the next topological unit. All the first vertical connection ports of the topological units in the first row are connected together as the input interface of the topological circuit. All the second vertical connection ports of the topological units in the last row are grounded. A load resistor R is connected between the input interface of the topological circuit and the ground wire. L connected.

[0006] Preferably, the topological circuit is assembled into a planar shape or a cylindrical surface shape and installed on the surface of the device.

[0007] Preferably, the resistance values of the resistor R1, resistor R2, resistor R3, resistor R4, resistor R5, and resistor R6 are the same.

[0008] Preferably, the capacitance values of the capacitor C1, capacitor C2, capacitor C3, and capacitor C4 are the same.

[0009] Preferably, the value of n is 5.

[0010] Preferably, the load resistor R L adopts a variable resistor. By adjusting the resistance value of the load resistor R L the passband range of the RC topological filter circuit is adjusted.

[0011] Preferably, the load resistor R L has a resistance value of 50 kΩ to 200 kΩ.

[0012] In a second aspect, the present invention provides an optimization method for the foregoing RC topological filter circuit, which includes the following steps:

[0013] Step 1: Set the design requirements of the RC topological filter circuit: a. When the frequency is less than f1, the attenuation is less than L1. b. When the frequency is greater than f2, the attenuation is greater than L2. f1 and f2 are two preset frequency thresholds respectively, and f1 < f2; L1 and L2 are two preset attenuation thresholds respectively, and L1 < L2.

[0014] Step 2: Construct an expression for the Laplace transform value Y(s) of the admittance as follows:

[0015]

[0016] where s is the Laplace operator; R is the resistance value of a single resistor in the topological unit; C is the capacitance value of a single capacitor in the topological unit.

[0017] Step 3. Construct the loss function \(J(R, C)\) as follows:

[0018] \(J(R, C)=\max\{-L1 + L dB (f1), L2 - L dB (f2)\}

[0019] where \(L dB (f)\) is the attenuation at frequency \(f\).

[0020] The attenuation \(L dB (f)\) is expressed as follows:

[0021]

[0022] where \(A P (fRC)\) and represent the amplitude and phase of the circuit admittance at frequency \(f\) respectively; \(j\) is the imaginary unit.

[0023] Step 4. By adjusting the values of the resistance \(R\) and the capacitance \(C\), make the loss function \(J(R, C)\) negative and reach the minimum; obtain the resistance values \(R\) of all the resistors and the capacitance values \(C\) of all the capacitors in the topological circuit.

[0024] Preferably, the transfer function of the RC topological filter circuit is as follows:

[0025]

[0026] where \(I L (s)\) is the Laplace transform value of the load current; \(I S (s)\) is the Laplace transform value of the output current; \(R L is the resistance value of the load resistor.

[0027] Thirdly, the present invention provides a splicing construction method for an RC topological filter circuit, which is used to construct the aforementioned RC topological filter circuit; the splicing construction method is specifically as follows: install each topological unit on an independent PCB board; four wiring terminals are arranged on the PCB board, which are respectively connected to the first horizontal connection port, the second horizontal connection port, the first vertical connection port, and the second vertical connection port of the topological unit. According to the working scenario of the RC topological filter circuit, determine the number of rows and columns \(n\); take \(n\times n\) PCB boards installed with topological units, and use the wiring terminals on each PCB board for splicing to form an \(n\times n\) topological circuit; connect the topological circuit in parallel with the load resistor \(R L to form an RC topological filter circuit.

[0028] Fourth aspect, a cable detection device, includes a device main body, two mechanical grippers and the aforementioned RC topology filtering circuit; the device main body is cylindrical and can be bent and deformed; the two mechanical grippers are respectively installed at both ends of the device main body; the RC topology filtering circuit is arranged on a flexible PCB board in the shape of a parallelogram; the topological units in the same row are arranged along the length direction of one group of parallel opposite sides of the flexible PCB board; the topological units in the same column are arranged along the length direction of the other group of parallel opposite sides of the flexible PCB board; the flexible PCB board is wound around the device main body, one group of opposite sides of the flexible PCB board is arranged along the axis direction of the device main body, and the other group of opposite sides is wound into a helix on the device main body; the RC topology filtering circuit is connected to the output interface of the sensor on the device main body.

[0029] For the diagonal θ less than 90° of the parallelogram-shaped flexible PCB board, the circumference c of the circular cross-section of the device main body, and the side length b of the flexible PCB board arranged along the axis of the device main body, the following relational expression is satisfied:

[0030] b·tanθ ≤ c.

[0031] The beneficial effects of the present invention are as follows:

[0032] 1. By setting capacitors C3 and C4 in the topological unit, when the other resistors and capacitors fail, capacitors C3 and C4 can provide a backup path, thereby greatly improving the fault tolerance of the RC topology filtering circuit and extending the service life.

[0033] 2. The designed topological unit of the present invention can be quickly spliced into topological networks with different numbers of rows and columns, so as to be used in filtering scenarios with different fault tolerance requirements, improving the flexibility of the topology filtering circuit.

[0034] 3. The topological circuit in the present invention is formed by splicing topological units; a single topological unit can be arranged on an independent rigid PCB or flexible PCB, so that the provided RC topology filtering circuit can form a complex geometric shape, not only can form a planar structure, but also can form a spatial structure, so as to facilitate arranging the RC topology filtering circuit into the internal voids of the original equipment without increasing the volume of the equipment. Description of the Drawings

[0035] Figure 1 is the circuit schematic diagram of the present invention.

[0036] Figure 2 is the equivalent circuit diagram of the present invention.

[0037] Figure 3 is the circuit schematic diagram of a single topological unit in the present invention.

[0038] Figure 4Comparison diagram of the amplitude-frequency characteristics of the traditional RC circuit and the topology circuit provided in the present invention (Part A is the amplitude-frequency characteristic curve of the traditional RC circuit, and Part B is the amplitude-frequency characteristic curve of the traditional RC circuit.

[0039] Figure 5 Comparison diagram of the amplitude-frequency characteristics of the topology circuit provided in the present invention before and after parameter optimization (Part A is the amplitude-frequency characteristic curve before parameter optimization, and Part B is the amplitude-frequency characteristic curve after parameter optimization.

[0040] Figure 6 Schematic diagram of the fast splicing method of the RC topology filter circuit in the present invention.

[0041] Figure 7 Reuse flowchart of two RC topology filter circuits with different numbers of rows and columns in the present invention.

[0042] Figure 8 Schematic diagram of arranging the RC topology filter circuit on the cable detection device in Embodiment 3 of the present invention.

[0043] Figure 9 Schematic diagram of the RC topology filter circuit arranged on a parallelogram PCB in Embodiment 3 of the present invention. Detailed implementation mode

[0044] The present invention will be further described below with reference to the accompanying drawings.

[0045] Embodiment 1

[0046] As Figure 1 and 2 shown, an RC topology filter circuit with a fault-tolerant design includes a topology circuit and a load resistor R L . The topology circuit includes a plurality of topology units arranged in an n×n array. The value of n is 5.

[0047] As Figure 1 and 3As shown, the structures of all topological units are the same; the first topological unit in the first row includes resistors R1, R2, R3, R4, R5, R6, capacitors C1, C2, C3, and C4. One end of resistors R1, R3, and capacitor C3 are connected together as the first lateral connection port of the topological unit; the other end of resistor R1, resistor R2, and one end of resistor R5 are connected together as the first longitudinal connection port of the topological unit; the other end of resistor R5, capacitor C4, and one end of resistor R6 are connected together as the second lateral connection port of the topological unit; the other ends of resistors R3, R6, resistor R4, and one end of capacitor C2 are connected together; the other end of capacitor C2 is used as the second longitudinal connection port of the topological unit; the other ends of capacitor C3, resistor R2, capacitor C4, and resistor R4 are connected together. Resistors R1, R2, R3, R4, R5, and R6 have the same resistance value; capacitors C1, C2, C3, and C4 have the same capacitance value.

[0048] In the same row, the second lateral connection port of the previous topological unit is connected to the first lateral connection port of the next topological unit. The second lateral connection port of the last topological unit is connected to the first lateral connection port of the first topological unit.

[0049] In the same column, the second longitudinal connection port of the previous topological unit is connected to the first longitudinal connection port of the next topological unit.

[0050] All the first longitudinal connection ports of the topological units in the first row are connected to the input interface of the signal to be processed. All the second longitudinal connection ports of the topological units in the last row are grounded. The input interface of the signal to be processed is connected to the ground wire through the load resistor R L connected to the ground wire. The output signal is the current flowing through the load resistor R L and is obtained by detecting the voltage across the resistor R L at both ends.

[0051] In each topological unit, capacitors C1 and C2 are external capacitors; capacitors C3 and C4 are internal capacitors; the overall topological circuit is assembled into shapes such as a plane or a cylindrical surface.

[0052] In this embodiment, setting the value of the number of rows and columns n to 5 is only a specific case; topological network circuits with different numbers of rows and columns can be applied to different occasions; for example: for scenarios with high requirements for circuit security, a circuit with a larger number of rows and columns n is adopted to improve the fault tolerance of the circuit. For scenarios with relatively low requirements for circuit security, a topological circuit with a smaller number of rows and columns n is used to build a filter circuit to save power resources.

[0053] Because the topological circuit has a circular symmetric structure, its admittance expression is not complex. As Figure 2 shown, V AB and i respectively represent the voltage and input current between the two circuit terminals A and B of the topological circuit. As Figure 3 shown, due to the symmetry of the circuit, the current flowing into each topological unit in the first row is all i / n. This current splits into three currents at the top of the topological unit, and the value of each current becomes i / 3n; then it converges again at the bottom of the topological unit, and the current becomes i / n again. Therefore, in the Laplace domain, the overall current-voltage relationship of the circuit is represented by Equation (1):

[0054]

[0055] where, V AB is the input voltage of the topological circuit; n is the number of rows and columns, which takes the value of 5 in this embodiment; R is the resistance value of a single resistor in the topological unit; I(s) is the Laplace transform value of the current flowing into the topological circuit; s is the Laplace operator; C is the capacitance value of a single capacitor in the topological unit; Y(s) is the Laplace transform value of the admittance of the topological circuit.

[0056] The comparison of the amplitude-frequency characteristic curve of the topological circuit in this embodiment with that of the traditional RC circuit is as Figure 4 shown; the following two design requirements a and b are proposed for the low-pass filter:

[0057] a. When the frequency is less than f1 = 10 Hz, the attenuation is less than 3 dB.

[0058] b. When the frequency exceeds f2 = 500 Hz, the attenuation is greater than 20 dB.

[0059] As can be seen from Figure 4 , the amplitude-frequency characteristic curve of the traditional RC circuit intersects with the restricted area and cannot meet the design requirements; moreover, once any electrical component in the traditional RC circuit fails, the entire filter circuit will break down.

[0060] The expression of the admittance Y(s) of the topological unit in this embodiment as a first-order expression is very convenient for program design. Under the nominal operating conditions (i.e., no faults), the topological units in each row of the topological circuit and the three vertical circuits inside the topological unit are all at the same potential level. Therefore, no current passes through the two internal capacitors (i.e., capacitors C3 and C4) connecting the topological units and the external capacitor (i.e., capacitor C1) located between columns; when a part of the resistors R1-R6 and the capacitor C2 fail, the capacitors C1, C3, and C4 can provide alternative current paths for the faulty components, thereby providing a higher fault tolerance for the filter circuit.

[0061] The fault tolerance of the RC topology filter circuit provided in this embodiment is specifically illustrated by the following simulation:

[0062] First, determine the possible fault forms of the circuit, including short - circuit and open - circuit faults of resistors R1 - R6 and capacitors C1 - C4. Then, initially assume that the proportion of faulty components in the topology circuit is 10%. Next, use the Monte Carlo method to randomly simulate the positions of faulty components. For this purpose, use the Multisim circuit simulation software to perform simulation tests on the topology circuit.

[0063] For illustrative purposes, a practical example is introduced here. The load resistor R L = 100 kΩ, and the following two design requirements need to be met:

[0064] a. When the frequency is less than f1 = 10 Hz, the attenuation is less than L1 = 3 dB.

[0065] b. When the frequency exceeds f2 = 500 Hz, the attenuation is greater than L2 = 20 dB.

[0066] According to Equation (1), Y(s)=3sC / (2sRC + 3) can be obtained. Therefore, the transfer function from the current source to the load current can be expressed as:

[0067]

[0068] where, I L (s) is the Laplace transform value of the load current; I S (s) is the Laplace transform value of the output current; R L is the load resistor;

[0069] According to Equation (2), initially select R = 1 kΩ and C = 30 nF to meet the above two design requirements. As Figure 5 shown by the solid black line in part A of, the attenuation values of the topology circuit current at 10 Hz and 500 Hz are 0.24 dB and 21.50 dB respectively, meeting the design requirements. However, under 10% random faults, the amplitude - frequency curve of the topology circuit varies between the two dashed lines in Figure 5 part A of. It can be seen that in the presence of random faults, the topology circuit may not meet the design requirements. Specifically, Figure 5 the upper and lower dashed lines in part A of represent the upper and lower boundaries of the amplitude - frequency curve under 1000 Monte Carlo methods respectively.

[0070] Therefore, when designing the filter, the possible impact of faults needs to be taken into account. For this purpose, represent the admittance of the proposed topology circuit as:

[0071]

[0072] Among them, A P (fRC) and respectively represent the amplitude and phase of the circuit admittance at frequency f; j is the imaginary unit.

[0073] The attenuation L of the filter dB (f) (in dB) is expressed as:

[0074]

[0075] In the process of fault-tolerant design of the topological circuit, by reasonably selecting R and C, the loss function J(R, C) is minimized. The loss function is defined as:

[0076] J(R, C) = max{-L1 + L dB (f1), L2 - L dB (f2)} (5)

[0077] If J(R, C) is positive, the current topological network corresponding to the resistance R and capacitance C must not meet the design requirements. Therefore, the optimization goal is to obtain a negative loss value and make this loss value as small as possible to obtain a good stability boundary. By adjusting the values of the resistance R and capacitance C within 100 decades around the initial design (1 kΩ, 30 nF) and calculating the loss value of the loss function.

[0078] According to the design requirements in this embodiment, by selecting R = 2.5 kΩ and C = 53 nF, a smaller loss J(R, C) = -1.8 dB is obtained, and its frequency response is as Figure 5 shown in part B of. It can be seen that the optimized topological circuit meets the design requirements in all 1000 Monte Carlo runs.

[0079] Embodiment 2

[0080] A fast splicing method for obtaining an RC topological filter circuit that meets different requirements by quickly splicing different numbers of topological units according to actual needs is as follows:

[0081] Each topological unit is respectively installed on an independent PCB board; there are four wiring terminals on the PCB board, which are respectively electrically connected to the first lateral connection port, the second lateral connection port, the first longitudinal connection port, and the second longitudinal connection port of the topological unit. According to the filtering requirements, different numbers of rows and columns n are selected;

[0082] Take n × n PCB boards installed with topological units, and use the wiring terminals on each PCB board for quick splicing to form an n × n topological circuit; connect the topological circuit to the load resistance R LThey are connected in parallel to form an RC topology filter circuit.

[0083] This fast splicing method and the RC topology filter circuit obtained by splicing are applied to the filter circuit for transformer fault monitoring. Since there is a strong and continuously changing electromagnetic field at the transformer monitoring equipment site, the operating environment is extremely harsh, and the detected signals are affected by various interferences. Therefore, a filter circuit is used to filter the collected signals. Since the transformer monitoring equipment is exposed to a high-energy magnetic field environment for a long time, the circuit is more likely to fail than general power equipment. Therefore, the present invention adopts a standby replacement method to improve the reliability of the filter circuit. A set of 2×2 topology filter circuits and a set of 5×5 topology filter circuits are set for the transformer monitoring equipment at the same time. As Figure 7 shown, under normal circumstances, the input signal passes through the 2×2 topology filter circuit. This is because considering the issue of power resource consumption, a small-scale topology filter circuit is used to work to save power resources. However, once the 2×2 topology filter circuit fails, it automatically switches to the larger-scale 5×5 topology filter circuit to ensure the reliability of the filtering function.

[0084] In this embodiment, a non-essential further optimization limitation is provided: the PCB board uses a flexible PCB board, which can be flexibly deformed into any planar or spatial shape according to the requirements of different application scenarios, so that it can be arranged in the gaps inside the equipment, avoiding expanding the volume of the original equipment.

[0085] Embodiment 3

[0086] As Figure 8 and 9 shown, a cable detection device includes a device main body, two mechanical grippers, and the RC topology filter circuit described in Embodiment 1. The device main body is cylindrical and can perform bending motion under the drive of internal artificial muscles. The two mechanical grippers are respectively installed at both ends of the device main body. By the bending motion of the device main body in cooperation with the opening and closing of the two mechanical grippers, the cable detection device can move forward on the cable in a way similar to the forward movement of a caterpillar. A sensor for detecting cable faults is mounted on the device main body.

[0087] The RC topological filtering circuit is arranged on a flexible PCB board in the shape of a parallelogram and is waterproofed; the topological units in the same row are arranged along the length direction of one set of parallel opposite sides of the flexible PCB board; the topological units in the same column are arranged along the length direction of the other set of parallel opposite sides of the flexible PCB board. The flexible PCB board is wound around the device body, and the shorter set of opposite sides of the flexible PCB board is arranged along the axis direction of the device body (i.e., in contact with the generatrix of the hose-shaped device body). The longer set of opposite sides of the flexible PCB board is wound into a helix on the device body. The flexible PCB board does not overlap on the device body. The input interface of the RC topological filtering circuit is connected to the output interface of the sensor carried on the device body.

[0088] The diagonal θ less than 90° of the parallelogram-shaped flexible PCB board, the circumference c of the circular cross-section of the device body, and the side length b of the flexible PCB board arranged along the axis of the device body satisfy the following relationship:

[0089] b·tanθ ≤ c

[0090] In this embodiment, since the cross-sectional circumference of the device body is small, the side length of the square topological circuit will be greater than the circumference of the circular cross-section of the device body, which will cause repeated winding and affect the circuit performance. Therefore, the topological circuit is arranged on the parallelogram-shaped flexible PCB board to avoid the problem of one layer of the flexible PCB board covering another layer. Moreover, the flexible PCB board covers the surface of the device body, hardly increasing the volume of the cable detection device.

[0091] The function of setting the RC topological filtering circuit on the cable detection device is as follows: Since the signals collected on the cable are very weak, if they are interfered, noise signals will be superimposed on the detection results such as waveforms, graphics, and images, which will lead to false fault judgments; therefore, it is necessary to filter the collected signals.

Claims

1. An RC topology filter circuit with fault-tolerant design, including a load resistor R L ; characterized in that: It further includes a topological circuit; the topological circuit includes a plurality of topological units arranged in an n×n array, where n≥2; each of the topological units includes resistors R1, R2, R3, R4, R5, R6, capacitors C1, C2, C3, and C4; one ends of resistor R1, resistor R3, and capacitor C3 are connected together as the first lateral connection port of the topological unit; the other end of resistor R1, resistor R2, and one end of resistor R5 are connected together as the first longitudinal connection port of the topological unit; the other end of resistor R5, capacitor C4, and one end of resistor R6 are connected together as the second lateral connection port of the topological unit; the other ends of resistor R3, resistor R6, resistor R4, and one end of capacitor C2 are connected together; the other end of capacitor C2 is used as the second longitudinal connection port of the topological unit; the other ends of capacitor C3, resistor R2, capacitor C4, and resistor R4 are connected together; In the same row, the second horizontal connection port of the previous topological unit is connected to the first horizontal connection port of the next topological unit, and the second horizontal connection port of the last topological unit is connected to the first horizontal connection port of the first topological unit; in the same column, the second vertical connection port of the previous topological unit is connected to the first vertical connection port of the next topological unit; all the first vertical connection ports of the topological units in the first row are connected together as the input interface of the topological circuit; all the second vertical connection ports of the topological units in the last row are grounded; a load resistor R is connected between the input interface of the topological circuit and the ground wire L is connected.

2. The RC topology filter circuit with fault tolerance design according to claim 1, wherein: The topological circuit is assembled into a planar or cylindrical shape and installed on the surface of the device.

3. A fault-tolerant RC topology filter circuit according to claim 1, characterized in that: The resistor values of resistors R1, R2, R3, R4, R5, and R6 are the same.

4. A fault-tolerant RC topology filter circuit according to claim 1, characterized in that: The capacitance values of capacitors C1, C2, C3, and C4 are the same.

5. A fault-tolerant RC topology filter circuit according to claim 1, characterized in that: The value of n is 5.

6. The RC topology filter circuit with fault tolerance design according to claim 1, characterized in that: Load resistor R L A variable resistor is used; by adjusting the resistance value of the load resistor R L the passband range of the RC topology filter circuit is adjusted.

7. The optimization method of an RC topology filter circuit with fault tolerance design according to claim 1, characterized in that: It includes the following steps: Step 1: Set the design requirements of the RC topological filter circuit: a. When the frequency is less than f1, the attenuation is less than L1; b. When the frequency is greater than f2, the attenuation is greater than L2; f1 and f2 are two preset frequency thresholds respectively, with f1<f2; L1 and L2 are two preset attenuation thresholds respectively, with L1<L2; Step 2: Construct the Laplace transform value of admittance The expression is as follows: ； where s is the Laplace operator; R is the resistance value of a single resistor in the topological unit; C is the capacitance value of a single capacitor in the topological unit; Step 3: Construct the loss function As follows: ； Among them, is the attenuation at frequency f; Attenuation The expression is as follows: ； wherein, and respectively represent the amplitude and phase of the circuit admittance at frequency f; j is the imaginary unit; Step 4: By adjusting the values of the resistance R and the capacitance C, make the loss function negative and minimized; obtain the resistance values R of all the resistors and the capacitance values C of all the capacitors in the topological circuit; R L is the resistance value of the load resistor.

8. The optimization method according to claim 7, characterized in that: Transfer function of the RC topology filter circuit As follows: ； Among them, is the Laplace transform value of the load current; is the Laplace transform value of the output current; R L is the resistance value of the load resistor.

9. A method for splicing and constructing an RC topology filtering circuit, characterized in that: For constructing an RC topology filter circuit with fault tolerance design as described in claim 1; the specific splicing construction method is as follows: each topology unit is respectively installed on an independent PCB board; there are four wiring terminals on the PCB board, which are respectively connected to the first lateral connection port, the second lateral connection port, the first longitudinal connection port, and the second longitudinal connection port of the topology unit; according to the working scenario of the RC topology filter circuit, determine the number of rows and columns n; take n×n PCB boards installed with topology units, and use the wiring terminals on each PCB board for splicing to form an n×n topology circuit; connect the topology circuit in parallel with the load resistor R L to form an RC topology filter circuit.

10. A cable detection device includes a device main body and two mechanical grippers; further characterized in that: It further includes the RC topological filter circuit according to any one of claims 1-6; the device body is cylindrical and can be bent and deformed; two mechanical grippers are respectively installed at both ends of the device body; the RC topological filter circuit is arranged on a flexible PCB board in the shape of a parallelogram; the topological units in the same row are arranged along the length direction of one group of parallel opposite sides of the flexible PCB board; the topological units in the same column are arranged along the length direction of the other group of parallel opposite sides of the flexible PCB board; the flexible PCB board is wound around the device body, one group of opposite sides of the flexible PCB board is arranged along the axis direction of the device body, and the other group of opposite sides is wound into a helix on the device body; the RC topological filter circuit is connected to the output interface of the sensor on the device body; The diagonal θ less than 90° of the parallelogram-shaped flexible PCB board, the circumference c of the circular cross-section of the device body, and the side length b of the flexible PCB board arranged along the axis of the device body satisfy the following relationship: 。

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