Pulse-modulation eddy current probes for imaging of external corrosion in nonmagnetic pipes

Characteristics Regarding Lift-Off Intersection of Pulse-Modulation Eddy Current Signals for Evaluation of Hidden Thickness Loss in Cladded Conductors

“…Based on ETREE modeling for transient eddy current inspection [11], the closed-form expression of z -component of the net magnetic field at an arbitrary position in Region II can be written as:Bz(r,z,t)=4μ0τI(t)⊗Λ(r,z,t)=4μ0τI(t)⊗IFT[Λ(r,z,ω)] where ⊗ denotes circular convolution; μ 0 is the vacuum permeability; I ( t ) stands for the PMEC excitation current signal whose expression can be found in Reference [10]; τ is the density of the coil winding, τ = N [ H ( r 2 − r 1 )] −1 , where N is the number of turns of the excitation coil; and Λ( r , z , t ) is the function depicting the field response to the conductor when the ferrite-cored excitation coil is driven by the impulse current in the Dirac delta function of time. This can be readily computed with its spectral form Λ( r , z , ω ) in conjunction with the Inverse Fourier Transform (IFT) [25]. Note that in Equation (1), ω denotes the angular frequency of each harmonic within the PMEC excitation current.…”

“…The current in the pulse modulation waveform for driving the excitation coil is shown in Figure 2. The frequencies of the carrier wave ( f c = 800 Hz) and modulation waves ( f m = 80 Hz) of the current waveform are chosen as per the rule of thumb elaborated in References [10] and [25]. During simulations, in an attempt to simulate the cases with flawed specimens, for the thickness loss in the clad layer, d 1 varies whilst d 2 is fixed.…”

A Capsule-Type Electromagnetic Acoustic Transducer for Fast Screening of External Corrosion in Nonmagnetic Pipes

“…Therefore, the analytical modeling is applicable for fast and accurate solutions to the related electromagnetic quantities. In light of this, a 3D hybrid model integrating the analytical modeling i.e., the Extended Truncated Region Eigenfunction Expansion (ETREE) modeling for solving electromagnetic problems [ 16 , 17 , 18 ] with 3D FEM for simulations of the ultrasonic field [ 8 ] is proposed. The schematic illustration of the 3D hybrid model is portrayed in Figure 2 .…”

Imaging of Subsurface Corrosion Using Gradient-Field Pulsed Eddy Current Probes with Uniform Field Excitation

“…It is noteworthy that in Equations (1) and (2) ζ mn ( t ) denotes the time-domain expression of the conductor reflection coefficient [ 8 , 21 ]. It can be readily computed via inverse Fourier transform of its time-harmonic form ζ mn ( ω ), where, ω denotes the angular frequency of each harmonic in the spectrum of the excitation current [ 22 ]. For a two-layer conductor comprising an upper layer with the finite thickness d and a bottom layer with infinite thickness (as shown in Figure 2 ), ζ mn ( ω ) can be written as: where, , i = 1, 2. σ i and μ i denote the conductivity and relative permeability of each layer, respectively.…”

“…Consequently, in the presence of the subsurface corrosion the plate thickness decreases with Δ d from the back surface. By referring to [ 8 , 21 , 22 ], the response of x -component of the net magnetic field B x to the initial subsurface corrosion with Δ d →0 is written as: where, ζ ′ mn ( t ) can be readily recovered via the inverse Fourier transform of ∂[ ζ mn ( ω )]/∂ d which is formulated as: …”