Numerical and Experimental Study of a Device for Electrical Power Lines Probing for a Tunnel-Boring Complex Control System †

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Article Numerical and Experimental Study of a Device for Electrical Power Lines Probing for a Tunnel-Boring Complex Control System †

Andrew V. Zhivodernikov, Alexander V. Pavlenko * and Vladimir S. Puzin

Research Institute of Electromechanics, Platov South-Russian State Polytechnic University (NPI), 346428 Novocherkassk, Russia; [email protected] (A.V.Z.); [email protected] (V.S.P.) * Correspondence: [email protected]; Tel.: 8-8635-25-51-13 † This paper is an extended version of our conference paper.: Zhivodernikov, A.; Pavlenko, A.; Puzin, V. Ele tric communications sounding device for the tunneling machine control system. Development and research. 2020 International Russian Automation Conference, Sochi, Russia, 6–12 September 2020.

Abstract: The article considers the problems of the magnetic field distribution, generated by a power electric cable at the micro-tunnel-boring shield arrangement site by numerical modeling with a further full-scale device model experiment. The impact of foreign magnetic field sources on readings of three-component sensors was established in the process of the study. The considerable existence of parasitic noises, conditioned by external magnetic fields and high sensitivity of the probes, which will require the use of additional filters, was established. When using three-component ferroprobes, the most informative is the probe component coinciding with the tunnel shield longitudinal axis Z. The study showed that with current values greater than 200 A and changes in cable location during the experiment, it is possible to record signals from other sensor components and subsequently determine Citation: Zhivodernikov, A.V.; the location and orientation of the current-carrying cable. The experimental results obtained confirm Pavlenko, A.V.; Puzin, V.S. Numerical the feasibility of a multi-sensor probing device for the micro-tunneling machine shield movement and Experimental Study of a Device control system. for Electrical Power Lines Probing for a Tunnel-Boring Complex Control System. Machines 2021, 9, 35. Keywords: micro-tunneling; tunneling shield; probing device; electromagnetic location; ferroprobe; https://doi.org/10.3390/ modeling; experimental studies machines9020035

Academic Editor: Hamid Reza Karimi 1. Introduction Received: 5 January 2021 During the construction of municipal gravity and pressure sewerage systems, heat- Accepted: 3 February 2021 ing mains, gas pipelines and other underground utilities, micro-tunnel-boring machines Published: 7 February 2021 (shields) are used [1]. At the same time, during subsurface tunneling operations, it is important to detect power electric cables in the ground to protect workers, tunneling Publisher’s Note: MDPI stays neutral equipment and power system equipment from electric shock. It should be noted that with regard to jurisdictional claims in in big cities most power cable routes are located in the ground, and the total number of published maps and institutional afﬁl- performed excavation works in municipal areas in developed countries may exceed several iations. million [2]. This work was carried out as part of a project to develop a micro-tunnel-boring shield for tunneling 1.4 m in diameter for supply utilities of various purposes. In this case, the customer’s requirement for the probing system was to be able to be installed on the micro-tunnel-boring shield and to be able to detect power cable lines along the boring path. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. 2. Applicability This article is an open access article Because the operation of the complex is assumed in the territory of industrial zones distributed under the terms and and urban development, the probing of power cable lines from the daylight surface in some conditions of the Creative Commons cases is not possible. Back in the early 1980s, subsurface probing systems (for example, Attribution (CC BY) license (https:// BoRaTec [3,4]) were presented, but they did not allow probing along the trajectory of the creativecommons.org/licenses/by/ boring without restrictions. In 1997–1998, the BEAM [5], TRT [6], SSP [6] and TR-GEO-01 [7] 4.0/).

Machines 2021, 9, 35. https://doi.org/10.3390/machines9020035 https://www.mdpi.com/journal/machines Machines 2021, 9, 35 2 of 18

systems were presented, which allow detecting communications on the tunneling trajectory. These systems use georadiolocation or seismic-acoustic methods to detect underground supply utility constructions. As a rule, such systems have a low resolution (0.5–1.5 m), which does not allow detecting power cable lines in a number of cases. For example, in the case of a cable line laid outside the cable tray or in a small cross-section (0.3 × 0.3 m) concrete cable tray. In addition, the negative impact on the quality of probing can significantly worsen when working on waterlogged soil, the impossibility of ensuring a close contact of the probe emitter with the soil, structurally inhomogeneous soil, etc. For this reason, as well as to meet customer requirements, a magnetometric probing method [8] for power cable line detecting was chosen. Modern works, addressing the detection of underground power cable lines, focus not only on the spatial arrangement of the power cable but also on possible parameters of the power cable line [9–12]. However, it is not necessary to determine the power cable parameters during tunneling operations; it is sufficient to record its arrangement in the ground and its orientation relative to the tunneling shield to ensure safe tunneling operations [13,14]. At the same time, it may be difficult to detect the arrangement of power cable lines due to present major construction objects above the worksite or by a considerable depth of tunneling operations, preventing cable line detection from the daylight surface [15,16]. In such cases, due to the small size of the tunnels, magnetometric sensors can be arranged right only on the micro-tunnel-boring shield and can complement or be integrated into the existing advanced multi-sensor daylight surface probing system [17–19] to detect power cable lines. Thus, until now, such probing systems have not been used as a part of the micro- tunnel-boring shields. The aim of this project considered the creation of a new probing system designed to be installed on tunnel-boring shields (diameter 0.9–1.5 m). Such a system is compact in size, but due to the chosen probing method, it is designed only for use in urban areas and industrial zones. This is due to its ability to detect power cable lines, steel pipelines, steel and reinforced concrete structures and its inability to detect natural obstacles (cavities, rocks that are too strong, etc.). Unlike earlier studies, in the project of this paper, we considered a wider range of currents in the cable and put full-scale experiments on full-size dummy micro-tunnel-boring shield housing.

3. Problem Formulation The present work studied magnetic ﬁeld distribution, generated by a power electric cable at the front of the micro-tunnel-boring shield, and determined the possibility of its detection using magneto-sensitive shield sensors. The problem was solved by numerical simulation with a further experiment. The problem under consideration is a common application of the Biot–Savart–Laplace law. In the general case, the source of the electromagnetic ﬁeld is an extended conductor with the current. The value of the magnetic induction at any point in space can be calculated in accordance with the equation of the law:

→ → → µ id s × r dB = 0 (1) 4πr3

where µ0–vacuum permeability, i–current value in the conductor, ds–conductor element, and r–full displacement vector from the wire element (ds) to the point at which the ﬁeld is being computed. The analytical method for calculating the value of magnetic induction was used to ver- ify the mathematical and numerical FEM models of the three-dimensional computational domain in the work [9]. To simulate a magnetic ﬁeld topology, the three-dimensional computational domain was used. It was bounded by the rectangular parallelepiped, 17 × 10.5 × 8.5 m in size (Figure1). The computational domain contains a power cable with a diameter of 8 mm Machines 2021, 9, 35 3 of 18

(straight cylinder) and massive ferromagnetic parts (supporting structural elements, rotor and its drive) of the micro-tunnel-boring shield. The shield body is made in the form of a pipe with an outer diameter of 1.42 m, a length of 4 m and a wall thickness of 20 mm. Machines 2021, 9, x FOR PEER REVIEW 3 of 17

and its drive) of the micro-tunnel-boring shield. The shield body is made in the form of a pipe with an outer diameter of 1.42 m, a length of 4 m and a wall thickness of 20 mm. The a-formulation of the electromagnetic field is obtained from the weak form of the Ampere Equation:

(ν curl a, curl a')Ω - (js, a)Ωs = 0 (2) where a–magnetic vector potential, Ω–bounded computational domain, ν–magnetic reluctivity, and js–current density in the source domain Ωs. At the boundary Γ of the computational domain Ω, the Dirichlet boundary conditions are applied (the values of the vector magnetic potential are reduced to zero). To reduce the computational complexity of the process of solving a system of linear equations, the tree-cotree gauge [20] was applied, which ensures the regularization of the matrix of unknowns. To solve the numerical simulation problem, the software complex GMSH+GetDP was used [21,22]. The finite element mesh was created by using the GMSH mesh generator utilizing the algorithm Frontal [23] for 2D objects and HXT for 3D objects [24]. The finite Machines 2021, 9, 35 4 of 18 element mesh contained nodes and 8.5–10.2 mln. tetrahedrons with linear sizes of edges from 1.75 to 400 mm.

Figure 1. Geometrical modelFigure of 1.theGeometrical computational model of domain. the computational domain.

a For ferromagnetic elementsThe -formulation of the ofmicro-tu the electromagneticnnel-boring field shield is obtained structure, from the the weak nonlin- form of the Ampere Equation: ear magnetic characteristics were set as for steel 1020. (ν curl a, curl a’)Ω − (js, a)Ωs = 0 (2) The system of linear equations consisted of 5.02 − 5.3 × 106 equations. The density of where a—magnetic vector potential, Ω—bounded computational domain, ν—magnetic the matrix of unknowns is about 0.00014%–0.00015%. The solution of the numerical prob- reluctivity, and js—current density in the source domain Ωs. lem was performed in theAt theGetDP boundary environmentΓ of the computational using the domain MUMPSΩ, the solver Dirichlet [25] boundary (as part conditions of the PETSc toolkit [26]).are appliedNonlinear (the values problem of the was vector solved magnetic by potentialthe Newton–Raphson are reduced to zero). iteration To reduce the with the intermediatecomputational solving the complexity simultan of theeous process linear of solving algebraic a system equations of linear equations,using the the tree- cotree gauge [20] was applied, which ensures the regularization of the matrix of unknowns. Cholesky method (OpenBLASTo solve [27] the numerical routines simulation for SLAE problem, solving the was software used) complex with ordering GMSH+GetDP by was the METIS algorithmused [28]. [21 Time,22]. The for finite calculating element meshthe magnetic was created field by using was the 0.5–1.5 GMSH hours mesh generatorfor each shield position utilizing(PC with the FX-8320 algorithmЕ Frontalprocessor, [23] for 32GB 2D objects RAM andand HXT 240GB for 3D SSD objects storage [24]. Thefor finite out-of-core factorization).element In mesh all containedcases, the nodes solving and 8.5–10.2of a nonlinear mln. tetrahedrons numerical with problem linear sizes re- of edges quired 2–4 iterationsfrom to achieve 1.75 to 400 an mm. error of 0.1%. For ferromagnetic elements of the micro-tunnel-boring shield structure, the nonlinear The arrangementmagnetic of magneto-se characteristicsnsitive were elements set as for steel(the 1020. models are made as ferroprobe cores) is shown on theThe shield system conventional of linear equations geometric consisted model of 5.02 −(Figure5.3 × 106 2) equations. as positions The density "D1"..."D4". "D1" andof "D3" the matrixelements of unknowns are arranged is about along 0.00014–0.00015%. the power cable The axis solution direction of the and numerical align with the tunnelingproblem shield. was "D2" performed and "D4" in the elements GetDP environment are arranged using in the the MUMPS plane perpen- solver [25] (as part of the PETSc toolkit [26]). Nonlinear problem was solved by the Newton–Raphson dicular to the shielditeration axis. It withshould the intermediatebe noted that solving there the is simultaneous no need to linear record algebraic the magnetic equations using the Cholesky method (OpenBLAS [27] routines for SLAE solving was used) with ordering by the METIS algorithm [28]. Time for calculating the magnetic field was 0.5–1.5 h for each shield position (PC with FX-8320E processor, 32GB RAM and 240GB SSD storage for out-of-core factorization). In all cases, the solving of a nonlinear numerical problem required 2–4 iterations to achieve an error of 0.1%. The arrangement of magneto-sensitive elements (the models are made as ferroprobe cores) is shown on the shield conventional geometric model (Figure2) as positions “D1” ... ”D4”. “D1” and “D3” elements are arranged along the power cable axis direction and align with the tunneling shield. “D2” and “D4” elements are arranged in the plane perpendicular to the shield axis. It should be noted that there is no need to record the magnetic induction vector component normal to the shield housing surface as its value is close to zero. Machines 2021, 9, x FOR PEER REVIEW 4 of 17

Machines 2021, 9, 35 5 of 18 induction vector component normal to the shield housing surface as its value is close to zero.

Figure 2. Arrangement of magneto-sensitive elements in shield housing grooves. Figure 2. Arrangement of magneto-sensitive elements in shield housing grooves. 4. Numerical Study of Magnetic Field Distribution 4. NumericalNumerical Study modeling of Magnetic of the magnetic Field Distribution field distribution pattern was performed for the followingNumerical cases: modeling of the magnetic field distribution pattern was performed for the following1. The cases: power cable axis and tunneling shield longitudinal axis are in the same plane. The angle between axes varies within the range from 0 to 90 degrees. 1. The power cable axis and tunneling shield longitudinal axis are in the same plane. 2. The tunneling shield longitudinal axis is offset parallel to the power cable axis. TheThe angle angle between between axes axes varies (with an within offset the between range projections from 0 to of90 the degrees. axes) varies within the range2. The from tunneling 0 to 90 degrees. shield longitudinal As the angle betweenaxis is offset the tunneling parallel to shield the power power cablecable andaxis. The anglelongitudinal between axisaxes changes (with an (with offset their between arrangement projections in the sameof the plane), axes) magneticvaries within flows the get range fromredistributed 0 to 90 degrees. between As opposite the angle (relative between to the the tunneling tunneling shield shield longitudinal power cable axis) zones and longitu- of dinalD1–D3 axis and changes D2–D4 (with sensors. their At arrangement the same time, in the the magnetic same plane), induction magnetic vectorcomponent, flows get redis- tributedparallel between to the tunneling opposite shield (relative longitudinal to the tunneling axis, recorded shield by longitudinal “D2” and “D4” axis) magneto- zones of D1– D3sensitive and D2–D4 elements sensors. (hereinafter At the same referred time, to th ase “X” magnetic component) induction changes vector when component, the angle par- between the power cable and the tunneling shield longitudinal axis changes within the allel to the tunneling shield longitudinal axis, recorded by "D2" and "D4" magneto-sensi- range from 0 to 90 degrees proportionally with a change in sign, i.e., the magnetic flow tivechanges elements direction (hereinafter at 45 degrees referred and to reaches as "X" the component) maximum andchanges minimum when values the angle at 0 and between the90 power degrees cable (Figure and3). the The tunneling same components shield longitudinal in zones of D1 axis and changes D3 sensors within have the the range same from 0 tosign 90 anddegrees values, proportionally lower by order with than ina change D2 and D4in zones.sign, i.e., the magnetic flow changes di- rectionComponents at 45 degrees of and the magnetic reaches inductionthe maximum vector and along minimum the Z and Yvalues axes vary at 0 dependingand 90 degrees (Figureon the 3). angle Thebetween same components the tunneling in shieldzones longitudinalof D1 and D3 axis sensors and power have cable the same axis. Thesign and values,values lower of magnetic by order field than induction in D2 and components D4 zones. along the Y and Z axes, recorded by D3 andComponents D4 elements, of slightly the magnetic increase induction with angle vector increase along (Figures the 4Z and and5 ,Y “Y3”, axes “Y4”,vary “Z3”depending and “Z4” dependences). The values of vector components recorded by the D1 and D2 on the angle between the tunneling shield longitudinal axis and power cable axis. The elements remain nearly unchanged. In this case, values of the components along the D1 valuessensor of Z-axis magnetic and D2field sensor induction Y-axis decrease,componen whilets along the D2 the element Y and Z Z component axes, recorded and D1 by D3 andelement D4 elements, Y component slightly increase. increase with angle increase (Figures 4 and 5, "Y3", "Y4", "Z3" and "Z4” dependences). The values of vector components recorded by the D1 and D2 elements remain nearly unchanged. In this case, values of the components along the D1 sensor Z-axis and D2 sensor Y-axis decrease, while the D2 element Z component and D1 element Y component increase.

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Figure 3. Dependence of the magnetic induction vector component along the X-axis in the cores of ferromagnetic probes ("X1"–"X4" curves correspond to "D1"−"D4" elements).

FigureFigure 3. 3.Dependence Dependence of of the the magnetic magnetic induction induction vector vector component component along along the X-axisthe X-ax inis the in cores the cores of of Figure 3. Dependence of the magnetic induction vector component along the X-axis in the cores of ferromagnetic probes ("X1"–"X4" curves correspond to "D1"− −"D4" elements). ferromagneticferromagnetic probes probes (“X1”–”X4” ("X1"–"X4" curves curves correspond correspond to to “D1” "D1"”D4”−"D4" elements). elements).

Figure 4. Dependence of the magnetic induction vector component along the Y-axis in the cores of ferromagnetic probes ("Y1"–"Y4" curves correspond to "D1"–"D4" elements).

In the case of the tunneling shield parallel displacement relative to the power cable, the type of dependences of the magnetic induction vector components on the angle be-

tween the tunneling shield longitudinal axis and power cable axis changes. Thus, when FiguretheFigure tunnel 4. 4.Dependence Dependence shield is ofdisplaced of the the magnetic magnetic by induction1.5 induction m, the vector type vector componentof component"X" component along along the change Y-axisthe Y-ax in becomesis the in cores the cores ofasym- of Figure 4. Dependence of the magnetic induction vector component along the Y-axis in the cores of metricferromagnetic for all probesmagneto-sensitive ("Y1"–"Y4" curves elements correspond (Figure to "D1"–"D4"6). elements). ferromagneticferromagnetic probes probes (“Y1”–”Y4” ("Y1"–"Y4" curves curves correspond correspond to to “D1”–”D4” "D1"–"D4" elements). elements). In the case of the tunneling shield parallel displacement relative to the power cable, In the case of the tunneling shield parallel displacement relative to the power cable, the type of dependences of the magnetic induction vector components on the angle be- the type of dependences of the magnetic induction vector components on the angle between the tunneling shield longitudinal axis and power cable axis changes. Thus, when tween the tunneling shield longitudinal axis and power cable axis changes. Thus, when the tunnel shield is displaced by 1.5 m, the type of "X" component change becomes asym- the tunnel shield is displaced by 1.5 m, the type of "X" component change becomes asymmetric for all magneto-sensitive elements (Figure 6). metric for all magneto-sensitive elements (Figure 6).

FigureFigure 5. 5.Dependence Dependence of of the the magnetic magnetic induction induction vector vect “Z”or "Z" component component in the in coresthe cores of magneto- of magneto- sensitivesensitive (“Z1”–”Z4” ("Z1"–"Z4" curvescurves correspond correspond to to “D1”–”D4” "D1"–"D4" elements). elements).

In the case of the tunneling shield parallel displacement relative to the power cable, the type of dependences of the magnetic induction vector components on the angle between the tunneling shield longitudinal axis and power cable axis changes. Thus, when the tunnel

Figure 5. Dependence of the magnetic induction vector "Z" component in the cores of magneto- Figure 5. Dependence of the magnetic induction vector "Z" component in the cores of magneto- sensitive ("Z1"–"Z4" curves correspond to "D1"–"D4" elements). sensitive ("Z1"–"Z4" curves correspond to "D1"–"D4" elements).

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Machines 2021, 9, x FOR PEER REVIEW 6 of 17 Machines 2021, 9, x FOR PEER REVIEW 6 of 17 shield is displaced by 1.5 m, the type of “X” component change becomes asymmetric for all magneto-sensitive elements (Figure6).

Figure 6. Dependence of the magnetic induction vector component along the X-axis in ferroprobe FigureFigure 6. 6.Dependence Dependence of of the the magnetic magnetic induction induction vector vector component component along along theX-axis the X-axis in ferroprobe in ferroprobe cores ("X1"–"X4" curves correspond to "D1"–"D4" elements) with a parallel displacement of the tun- corescores (“X1”–”X4” ("X1"–"X4" curves correspondcorrespond toto “D1”–”D4”"D1"–"D4" el elements)ements) with a parallel displacementdisplacement ofof thethe tunnel shield relative to the power cable. tunnelnel shield shield relative relative to to the the power power cable. cable. Depending on the measure of the angle between the power cable and tunneling DependingDepending on on the the measure measure of the of angle the betweenangle between the power the cable power and cable tunneling and shieldtunneling axes,shield the axes, type the of thetype dependence of the dependence of magnetic of magnetic induction induction vector components, vector components, recorded rec- by shield axes, the type of the dependence of magnetic induction vector components, rec- magneto-sensitiveorded by magneto-sensitive elements onelements the value on ofthe tunneling value of tunneling shield parallel shield displacement parallel displace- also orded by magneto-sensitive elements on the value of tunneling shield parallel displace- fundamentallyment also fundamentally changes [29 changes]. In particular, [29]. In particular, for the “X” for componentsthe "X" components of “D2” of and "D2" “D4” and elementsment"D4" elements also (Figure fundamentally (Figure3), their 3), sharptheir changes sharp change [29]. change is In observed particular, is observed when for when the the shield the"X" shieldcomponents is displaced is displaced of by "D2" an by and amount"D4"an amount elements greater greater (Figure than than its diameterits3), diametertheir sharp with with anchange an increase increase is observed in in the the angle angle when between between the shield the the power poweris displaced cable cable by andanand amount tunneltunnel shield shieldgreater axesaxes than toto 45–90its45–90 diameter degreesdegrees with (Figure (Figure an increase7 ).7). If If angle angle in valuesthe values angle are are between close close to to zero, thezero, power values values cable ofandof thethe tunnel “X”"X" component shield axes changes to 45–90 smoothly degrees andand (Figure proportionallyprop ortionally7). If angle toto values thethe offsetoffset are valuevalueclose increase.toincrease. zero, values of the "X" component changes smoothly and proportionally to the offset value increase.

Figure 7. Dependences of magnetic induction vector X-axis components in ferroprobe on the tunnel- ingFigure shield 7. parallelDependences displacement of magnetic for angle induction values vector between X-axis longitudinal components axes in of ferroprobe 0, 45 and 90on degreesthe tunneling shield parallel displacement for angle values between longitudinal axes of 0, 45 and 90 de- (“X2” and “X4” curves correspond to “D2” and “D4” elements). Figuregrees ("X2" 7. Dependences and "X4" curves of magneticcorrespond induction to "D2" and vector "D4" X- elements).axis components in ferroprobe on the tun- nelingConsidering shield parallel mostly displacement horizontal for arrangement angle values of between power cables longitudinal in the ground axes of and0, 45 above- and 90 de- statedgreesConsidering ("X2" type and of the"X4" mostly change curves horizontal incorresp magneticond arrangementto field "D2" topologyand "D4" of elements). forpower individual cables in magneto-sensitive the ground and elementsabove-stated with type the of change the change of mutual in magnetic position field of thetopology power for cable indi andvidual tunneling magneto-sensi- shield totive ensure elementsConsidering a significant with themostly changechange horizontal inof mutual the magnetic arrangement position field of topologythe of power power in cable thecables areaand tunnelingin of allthe magneto- ground shield and sensitiveabove-statedto ensure elements, a significant type itof isthe change recommended change in thein magnetic magnetic to change fieldfield the topologytopology arrangement forin the indi of area thevidual ferroprobesof all magneto-sensi- magneto- by theirtivesensitive elements turning elements, relative with itthe to is shield changerecommended longitudinal of mutual to changepo axissition by the 45 of degrees. arrangementthe power cable of the and ferroprobes tunneling byshield totheir ensure turning a significant relative to shieldchange longitudinal in the magnetic axis by field 45 degrees. topology in the area of all magneto- sensitiveTo continue elements, relevant it is recommended numerical studies, to change the following the arrangement changes were of madethe ferroprobes to the ge- by theirometric turning model relative of the tunneling to shield shield,longitudinal consisting axis ofby the 45 additiondegrees. of the blade part with a To continue relevant numerical studies, the following changes were made to the geometric model of the tunneling shield, consisting of the addition of the blade part with a

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cuttingTo continueedge with relevant grooves numerical for ferroprobe studies, sensors, the following oriented changes at 45 degrees were made to the to plane, the pass- geometric model of the tunneling shield, consisting of the addition of the blade part with cuttinging through edge with the grooves tunneling for shieldferroprobe and power sensors, cable oriented longitudinal at 45 degrees axes. The to the grooves plane, are pass- made a cutting edge with grooves for ferroprobe sensors, oriented at 45 degrees to the plane, ing inthrough the housing the tunneling shell to accommodateshield and power measuring cable longitudinal transducers axes. of ferroprobe The grooves sensors. are made Trans- passingducer grooves through theare tunnelingequipped shield with and a safety power stop cable to longitudinal prevent damage axes. The to grooves their contents are by in themade housing in the housingshell to accommodate shell to accommodate measuring measuring transducers transducers of ferroprobe of ferroprobe sensors. sensors. Trans- ground pressure. The modified geometric model of the blade part of the micro-tunnel- ducerTransducer grooves grooves are equipped are equipped with witha safety a safety stop stop to toprevent prevent damage damage to theirtheircontents contents by boring shield is shown in Figure 8. groundby ground pressure. pressure. The Themodified modiﬁed geometric geometric model model of of thethe bladeblade part part of of the the micro-tunnel- micro-tunnel- boringboring shield shield is isshown shown in in Figure Figure 88..

Figure 8. Arrangement of magneto-sensitive elements in cutting edge grooves of the shield housing. FigureFigure 8. Arrangement 8. Arrangement of of magneto-sensitive magneto-sensitive elements elements in in cutting cutting edge edge grooves grooves of the of shield the shield housing. housing. TheThe massive massive cutting cutting edge edge acted acted as as a magnetica magnetic ﬂux flux concentrator, concentrator, which which led to led its to its re- redistribution and increase in local magnetic ﬂux density in the area of the ferroprobe distributionThe massive and cutting increase edge in actedlocal magnetic as a magnetic flux density flux concentrator, in the area ofwhich the ferroprobeled to its re- loca- location by 10–15% (Figure9). distributiontion by 10%–15% and increase (Figure in local 9). magnetic flux density in the area of the ferroprobe location by 10%–15% (Figure 9).

Figure 9.9.Magnetic Magnetic ﬂuxes fluxes in thein the shield shield housing hous nearing near the D2 the ferroprobe D2 ferroprobe location. location. Figure 9. Magnetic fluxes in the shield housing near the D2 ferroprobe location. Based Based on on the the performed performed numerical numerical modeling modeling results, good results, symmetry good and symmetry consistency and con- ofsistency values of diametricallyvalues of diametrically opposite sensors opposite (for example,sensors (for D1 andexample, D3) for D1 X and and Z D3) compo- for X and Z nents Based (Figures on the 10 andperformed 11), as well numerical as consistency modeling of changes results, in the good components symmetry along and the con- components (Figures 10 and 11), as well as consistency of changes in the components sistencyY-axis of (Figure values 12 of) for diametrically all sensors are opposite observed. sensors (for example, D1 and D3) for X and Z componentsalong the (FiguresY-axis (Figure 10 and 12) 11), for asall wellsensors as consistencyare observed. of changes in the components along the Y-axis (Figure 12) for all sensors are observed.

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Figure 10. Dependence of the magnetic induction vector component along the X-axis in ferroprobe FigureFigure 10. 10.Dependence Dependence of of the the magnetic magnetic induction induction vector vector component componentcomponent along alongalong the X-axis thethe X-axisX-axis in ferroprobe inin ferroprobeferroprobe cores ("X1"−"X4" curves correspond to "D1"−"D4" sensors) with the shield longitudinal axis and corescores (“X1” ("X1"−−”X4”"X4" curvescurves correspond correspond to to “D1” "D1"−”D4”−"D4" sensors) sensors) with with the the shield shield longitudinal longitudinal axis andaxis and power cable axis arranged in the same plane. powerpower cable cable axis axis arranged arranged in in the the same same plane. plane.

Figure 11. Dependence of the magnetic induction vector component along the Z-axis in ferroprobe FigureFigure 11. 11.Dependence Dependence of of the the magnetic magnetic induction induction vector vector component componentcomponent along alongalong the Z-axis thethe Z-axisZ-axis in ferroprobe inin ferroprobeferroprobe cores ("Z1"−"Z4" curves correspond to "D1"−"D4" sensors) with the shield longitudinal axis and corescores (“Z1” ("Z1"−−”Z4”"Z4" curvescurves correspond correspond to to “D1” "D1"−”D4”−"D4" sensors) sensors) with with the the shield shield longitudinal longitudinal axis andaxis and power cable axis arranged in the same plane. powerpower cable cable axis axis arranged arranged in in the the same same plane. plane.

Figure 12. Dependence of Y component of the magnetic induction vector in the cores of magneto- FigureFigure 12. 12.Dependence Dependence of of Y Y component component of theof the magnetic magnetic induction induction vector vector in the incores the cores of magneto- of magneto- sensitive elements (Y1−Y4 curves correspond to D1−D4 sensors) with the shield longitudinal axis sensitivesensitive elements elements (Y1 (Y1−Y4−Y4 curves curves correspond correspond to D1to −D1D4−D4 sensors) sensors) with with the shieldthe shield longitudinal longitudinal axis axis and power cable axis arranged in the same plane. andand power power cable cable axis axis arranged arranged in in the the same same plane. plane. As a result, it was determined that at 65 A current in a power electric cable, the values As a result, it was determined that at 65 A current in a power electric cable, the values of magnetic induction vector components in ferroprobe cores reach the following values: of magnetic induction vector components in ferroprobe cores reach the following values:

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As a result, it was determined that at 65 A current in a power electric cable, the values of magnetic2–5 µT inductionfor the "X" vector component, components 17−27 inµT ferroprobe for "Y" and cores 3-14 reach µT for the the following "Z" component. values: With2–5 theµ electricT for the current “X” component, intensity of 17 −5 27A µinT the for power “Y” and cable, 3–14 theµT forvalues the “Z”of the component. magnetic Withinduction the electric vector currentcomponents intensity in the of 5ferroprobe A in the powercores go cable, down the to values 55–620 of nT, the 1.1–3.0 magnetic µT inductionand 0.1–6.0 vector µT for components X, Y and Z in components, the ferroprobe respectively. cores go down The toresulting 55–620 nT,values 1.1–3.0 correspondµT and 0.1–6.0to the measurementµT for X, Y and range Z components, of selected respectively.ferroprobes НВ The0391.5-20/3. resulting values correspond to the measurementThus, numerical range of modeling selected ferroprobes results show HB0391.5-20/3. that the selected arrangement and orientation Thus,of ferroprobes numerical make modeling it possible results to obtain show magnetic that the selectedinduction arrangement values in the and cores, orien- cor- tationresponding of ferroprobes to the measurement make it possible range to of obtain the ferroprobes magnetic inductionwith the change values of in mutual the cores, ar- correspondingrangement and to orientation the measurement of the micro-tunne range of thel-boring ferroprobes shield with and the electromagnetic change of mutual field arrangementsource—the power and orientation electric cable. of the Cumulatively micro-tunnel-boring, it provides shield detection and electromagnetic of power cables ﬁeld of source—thethe packaged power transformer electric substations cable. Cumulatively, from 20 kVA it provides at the distance detection of at of least power 3 m cables from the of theshield packaged front. transformer substations from 20 kVA at the distance of at least 3 m from the shield front. 5. Experimental Study of Magnetic Field Distribution 5. Experimental Study of Magnetic Field Distribution The experimental facility model (Figure 13) includes the following: a steel tube with The experimental facility model (Figure 13) includes the following: a steel tube with a diameter of 1400 mm, imitating the micro-tunnel-boring shield, with four mounted a diameter of 1400 mm, imitating the micro-tunnel-boring shield, with four mounted measuring modules with ferroprobes (НВ0391.5–35 ferroprobe model) and the regulated measuring modules with ferroprobes (HB0391.5–35 ferroprobe model) and the regulated current supply (powerful laboratory power supply of ABB company). The measuring current supply (powerful laboratory power supply of ABB company). The measuring modules are connected to a laptop via an RS485-USB converter. The tested cable was lo- modules are connected to a laptop via an RS485-USB converter. The tested cable was locatedcated on on the the wooden wooden chassis chassis and and connected connected to to the adjustable currentcurrent source.source. TheThe powerpower cablecable ofof VBbShvVBbShv typetype 33× × 16(ozh)–616(ozh)–6 waswas usedused forfor thethe test.test. TheThe cablecable sectionsection waswas deﬁneddefined byby thethe maximalmaximal currentcurrent setset atat thethe tests.tests. FerroprobesFerroprobes placedplaced intointo installationinstallation notchesnotches ofof thethe tubetube imitatingimitating thethe tunneltunnel shieldshield areare equippedequipped with with biasbias windingswindings for for calibrationcalibration and and initial initial installationinstallation ofof thethe probes.probes.

FigureFigure 13.13. ExperimentalExperimental facilityfacility model.model.

TheThe cablecable chassis chassis with with the the 4-wire 4-wire armored armored cable cable ﬁxed fixed on on its its movable movable bar, bar, connected connected to theto the current current source, source, was was located located at a at distance a distance of 3 of m 3 from m from the tube.the tube. The The cable cable conductors conductors are connectedare connected in parallel in parallel two-by-two. two-by-two. At oneAt one of the of the cable cable ends, ends, the the conductors conductors are are closed closed to imitateto imitate the the real real power power cable cable connected connected to to the the load. load. The The current current in in the the cable cable was was changed changed stepwise.stepwise. The value of current current provided provided by by th thee source source was was changed changed in in the the range range from from 0 to 0 to300 300 А. A.At Atthis, this, ferroprobe ferroprobe was was adjusted adjusted to maximal to maximal sensitivity—200 sensitivity—200 mV per mV µT. per TheµT. larg- The largestest signal signal change change was was obtained obtained at atthe the Z-axis. Z-axis. For For the the setting setting of of zero zero values ofof inductioninduction components,components, the the respective respective current current values values were were set set in thein the bias bias windings. windings.Figures Figures 14 and14 and 15 represent15 represent oscillograms oscillograms of theof the output output signals signals of of the the different different channels channels of of the the ferroprobe ferroprobe measuringmeasuring module.module. TheThe datadata werewere obtainedobtained forfor differentdifferent ampliﬁcationamplification gaingain factorsfactors ofof thethe ferroprobeferroprobe measuringmeasuring modulemodule andand valuesvalues ofof thethe currentcurrent inin thethe cable.cable. GraphsGraphs onon thethe leftleft

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show the output signals of the ferroprobe measurement module, taken from microcon- showtroller the ADC output channels, signals ofcorresponding the ferroprobe to measurement magnetic field module, induction taken components from microcontroller (three axes). ADCThe distinct channels, signal corresponding change at the to magnetic Z-axis is fieldseen inductionfrom the graphs, components which (three gives axes). the possibility The distinctto assess signal the magnetic change at field the Z-axis created is seenby the from current the graphs, in the whichcable. givesSignal the change possibility at the to Y-axis assessis less the notable, magnetic which field is created connected by the with current the in cable the cable. positioning Signal change in relation at the to Y-axis the isprobe. lessGraphs notable, on the which right is connectedrepresent withdependences the cable positioningof signal differences in relation by to axes the probe. between Graphs the max- onimal the and right the represent minimal dependences values in the of signalAD converter differences units. by axes Based between on the the graphs, maximal we andcan con- theclude minimal that when values the in thecable AD is converterarranged units.perpen Baseddicular on theto the graphs, sensor we axis, can concludethe most thatinforma- when the cable is arranged perpendicular to the sensor axis, the most informative indicator tive indicator of the live conductor presence is a signal from the channel corresponding to of the live conductor presence is a signal from the channel corresponding to the Z-axis, the Z-axis, where a weak external source of the magnetic field, recorded by the ferroprobe, where a weak external source of the magnetic field, recorded by the ferroprobe, is most obviouslyis most obviously represented, represented, confirming confirming numerical modeling numerical results. modeling From graphsresults.in From Figure graphs 15, in itFigure is seen 15, that it is at seen high that gain, at the high signal gain, value the si alonggnal value the Z-axis along exceeds the Z-axis the setexceeds level atthe high set level currents,at high currents, associated associated with the microcontroller’swith the microcontroller's ADC resolution. ADC resolution. The measured The measured values of val- theues Z-component of the Z-component of the magnetic of the field magnetic induction field were induction 72 nT at were a current 72 nT of 65at Aa current and 330 nTof 65 A atand a current 330 nT of at 295 a A.current The X-and of 295 Y-components A. The X-and had Y-components a near-zero value had at a anear-zero current of value 65 A. at a Atcurrent a current of 65 of A. 295 At A, a these current components of 295 A, hadthese a valuecomponents of 45 and had 100 a nT.value of 45 and 100 nT.

FigureFigure 14. 14.Current Current sensing sensing in in cable cable with with the the gain gain ratio ratio of board of board ampliﬁers amplifiers 64. 64.

In the considered case, the currents in the biasing windings of the ferroprobe were 9.4, 54 and 13 mA (X, Y and Z channels). This is equal to 374, 2200 and 505 ADC units (for gain ratio 128). Figures 16–18 show oscillograms of sensor signals without current and for current in cables 65 A and 295 A in ADC units versus time in milliseconds. Similar to the previous experiment, the cable was located horizontally at the shield axis height and at the distance of 3 m to its frontal section. Graphs on the left show the probe signals in the microcontroller AD converter codes at three axes for the period. The period is represented by the distance between two perpendicular lines on the graph. The oscillograph recordings on the right demonstrate the signal differences at three axes in the AD converter units vs. time in ms. Figure 16 shows that the probe records the weak sinewave component signal at the absent

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current in the cable. It is connected with the presence of power lines located at a certain distance of one hundred m from the experiment site. Graphs in Figures 17 and 18 show the situation when the cable is connected to a voltage source with a distinct sinusoidal signal at the sensor output along the Z-axis, different in amplitude depending on the current Machines 2021, 9, x FOR PEER REVIEW value. On other axes, the signal is not so clear due to cable orientation. With the purpose to11 of 17

detect the cable position in relation to the tunnel shield, the following two experiments were conducted.

FigureFigure 15. 15. CurrentCurrent sensing sensing inin cablecable with with a gaina gain ratio ratio of 128.of 128. The ﬁrst experiment was to move the cable vertically. In the course of the second experiment,In the considered the cable was case, rotated the currents in relation in to th thee shieldbiasing axis. windings Measurements of the wereferroprobe carried were 9.4,out 54 atand the 13 cable mA current (X, Y and of 65 Z Achannels). and 295 AThis at 3 is m equal distance to 374, to the 2200 shield and frontal505 ADC section. units (for gainOscillograph ratio 128). recordings of magnetic induction signals in the AD converter codes for the ﬁrstFigures experiment 16–18 are show given oscillograms in Figures 19 ofand sensor 20. signals without current and for current in cables 65A and 295A in ADC units versus time in milliseconds. Similar to the previous experiment, the cable was located horizontally at the shield axis height and at the distance of 3 m to its frontal section. Graphs on the left show the probe signals in the microcontroller AD converter codes at three axes for the period. The period is represented by the distance between two perpendicular lines on the graph. The oscillograph recordings on the right demonstrate the signal differences at three axes in the AD converter units vs. time in ms. Figure 16 shows that the probe records the weak sinewave component signal at the absent current in the cable. It is connected with the presence of power lines located at a certain distance of one hundred m from the experiment site. Graphs in Figures 17 and 18 show the situation when the cable is connected to a voltage source with a distinct sinusoidal signal at the sensor output along the Z-axis, different in amplitude depending on the current value. On other axes, the signal is not so clear due to cable orientation. With the purpose to detect the cable position in relation to the tunnel shield, the following two experiments were conducted.

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FigureFigure 16. 16. SignalsSignals with with no current inin thethe cable. cable.

Figure 17. Magnetic induction signals at 65 A current in a cable. Figure 17. Magnetic induction signals at 65A current in a cable.

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Figure 18. Magnetic induction signals at 295A current in a cable.

The first experiment was to move the cable vertically. In the course of the second experiment, the cable was rotated in relation to the shield axis. Measurements were carried out at the cable current of 65А and 295А at 3m distance to the shield frontal section. Oscillograph recordings of magnetic induction signals in the AD converter codes for the FigurefirstFigure experiment 18. 18. MagneticMagnetic are induction induction given in signalssignals Figures atat 295 295A19 Aand currentcurrent 20. in in a a cable. cable.

Figure 19. Changes in signals during live cable movement from bottom to top at 65 A current.

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Machines 2021, 9, 35 15 of 18 Figure 19. Changes in signals during live cable movement from bottom to top at 65A current.

Figure 20. Changes in signals during live cable movement from bottom to top at 295 A current. Figure 20. Changes in signals during live cable movement from bottom to top at 295A current. Graphs in Figures 19 and 20 show that when the cable is moved vertically, the signal alongGraphs all axes in most Figures clearly 19 changesand 20 show along that the Z-axis.when the It confirms cable is the moved possibility vertically, of recording the signal alongthe test all cableaxes most magnetic clearly field changes at its position along the change. Z-axis. The It confirms maximum the value possibility change of of record- the ingoutput the test signal cable magnitude magnetic for field this fieldat its component position change. was 415 The nT (“span”maximum graph, value the change difference of the outputbetween signal the maximummagnitude and for minimumthis field component value) for 295 was A 415 current nT (“span” value. graph, The results the differ- of encechanging between signals the formaximum the second and experiment minimum connected value) for with 295 the A current cable rotation value. in The the results plane of changingperpendicular signals to for the the tube second axis demonstrate experiment theconnected slight change with the in thecable magnetic rotation induction in the plane perpendicularsignal value, butto the its detectiontube axis isdemonstrate possible (Figures the slight 21 and change 22). in In the this magnetic case, the induction value signalchange value, of the but output its detection signal magnitude is possible for ( Fi thegures Z-component 21 and 22). was In 214this nT case, and the 14 value nT for change the ofY-component the output (295signal A currentmagnitude value). for the Z-component was 214 nT and 14 nT for the Y- component (295 A current value).

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Figure 21. Change in signals at 65 A current in a cable during its rotation. FigureFigure 21. Change inin signals signals at at 65A 65A current current in in a cablea cable during during its itsrotation. rotation.

Figure 22. Change in signals at 295 A current in a cable during its rotation. Figure 22. Change in signals at 295A current in a cable during its rotation. Figure 22. Change in signals at 295A current in a cable during its rotation. 6. Conclusions 6. ConclusionsThe results of numerical simulation of a three-dimensional magnetic field of a current-carrying conductor and a micro-tunnel-boring shield indicate the possibility of using the magnetometricThe results of methodnumerical for simulationdetecting power of a three-dimensionalcable lines. Ferroprobes magnetic can be field placed of ain current-carrying conductor and a micro-tunnel-boring shield indicate the possibility of using the magnetometric method for detecting power cable lines. Ferroprobes can be placed in

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6. Conclusions The results of numerical simulation of a three-dimensional magnetic field of a current- carrying conductor and a micro-tunnel-boring shield indicate the possibility of using the magnetometric method for detecting power cable lines. Ferroprobes can be placed in the housing of the micro-tunnel-boring shield. Based on the results of the study of changes in the topology of the magnetic field with a change in the relative position of the power cable and the orientation of the tunnel shield, the locations of the sensors were selected. It was found that the measurement of the components of the magnetic induction vector through three measuring channels of the sensor with a change in the relative position and orientation of the micro-tunnel-boring shield and cable with a current of 60–70 A and more theoretically provides the possibility of detecting power cable lines from standard complete transformer substations with a capacity of more than 20 kVA at a distance of 3 m from the cutting edge of the micro-tunnel-boring shield. The results of numerical simulation were confirmed by experimental studies on a full-size dummy of a micro-tunnel-boring shield. It was found that the most informative is the output signal of the sensor channel, which registers the magnetic field vector component that coincides with the longitudinal axis of the micro-tunnel-boring shield (Z). The significant influence of parasitic noise caused by external magnetic fields (natural magnetic background and background magnetic field of industrial zones and urban ter- ritories) and high sensitivity of the ferroprobes requires the use of additional filters, and therefore with the help of biasing windings, it is possible to compensate only the constant component of external magnetic fields. At currents of more than 200 A, it becomes possible to determine the position of the cable by the output signal from the X and Y channels of the ferroprobes. Thus, the results of the experiments confirm the possibility of practical implementation of the magnetometric sensing system for installation in the housing of the micro-tunnel-boring shield.

Author Contributions: Conceptualization, A.V.P. and A.V.Z.; methodology, A.V.P.; software, A.V.Z.; validation, A.V.Z., A.V.P. and V.S.P.; formal analysis, A.V.Z.; investigation, A.V.Z.; resources, V.S.P.; data curation, A.V.P.; writing—original draft preparation, A.V.Z.; writing—review and editing, A.V.P.; project administration, A.V.P. and V.S.P. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by Ministry of Science and Higher Education of the Russian Federation, grant subsidy № 074-11-2018-010 dated 5 June 2018 on the subject “Creating the high- quality production of import-substituting shaft-sinking and tunnelling facilities, equipped with smart control systems, with the purpose of municipal underground space development”. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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