CN117875131A - A hybrid simplified modeling method based on the time-domain bouncing ray method and transmission line equation - Google Patents

Abstract

The invention discloses a mixed simplified modeling method based on a time domain bouncing ray method and a transmission line equation, which comprises the following steps: firstly, reading triangular surface metadata in a target body grid file, and creating a virtual incident surface according to the target triangular surface metadata; secondly, generating a ray tube by a virtual incidence plane, detecting the intersection with a target triangular surface element and tracking the ray field intensity; then calculating the field intensity of the time domain near field of the target according to the time domain bouncing ray algorithm to obtain the field distribution at the position of the transmission line; and finally substituting the field intensity at the position of the transmission line into a transmission line equation, and calculating to obtain the voltage value and the current value of the position of the port of the transmission line. The invention solves the limitation of slow operation speed of the existing electric large-size structure for calculating the field-line coupling, and finally realizes the rapid analysis of the electric large-size structure for the field-line coupling.

Description

A hybrid simplified modeling method based on the time-domain bouncing ray method and transmission line equation

Technical Field

The invention belongs to the technical field of electromagnetic pulse effect analysis, and in particular is a hybrid simplified modeling method based on a time domain bouncing ray method and a transmission line equation.

Background technique

With the development of wireless communication technology and electromagnetic pulse technology, the surrounding electromagnetic environment has become more and more complex. The electromagnetic environment includes natural interference sources such as lightning and static electricity, as well as strong artificial interference sources such as high-power radar, electronic interference equipment, and strong electromagnetic radiation jammers. For electronic devices in RF microwave systems in complex electromagnetic environments, especially sensitive circuits and exposed transmission line structures, they are easily interfered by external electromagnetic pulses. Under the influence of electromagnetic pulses, these cable transmission lines can act as containers for collecting a large amount of electromagnetic energy, and these electromagnetic energies can be transmitted through metal wires, affecting various electronic and electrical equipment. This impact may only cause electromagnetic interference to the equipment, but in extreme cases it may cause damage to or even burn out electronic devices. In the past, numerical calculation methods such as Finite-Difference Time-Domain (Finite-Difference Time-Domain) often showed problems of low efficiency and long calculation time when analyzing field-line-circuit coupling structures, especially large-scale structures. Therefore, in view of the shortcomings of existing methods for analyzing field-line-circuit coupling structures, it is necessary to provide a general and fast analysis method.

Summary of the invention

The purpose of the present invention is to provide a hybrid simplified modeling method based on the time domain bouncing ray method and the transmission line equation, so as to solve the limitation of the slow operation rate of the existing calculation of the field-line-circuit coupled electrically large-sized structure and realize the rapid analysis of the field-line-circuit coupled electrically large-sized structure.

The technical solution to achieve the purpose of the present invention is: a hybrid simplified modeling method based on the time domain bouncing ray method and the transmission line equation to perform rapid electromagnetic analysis on the field-line-circuit coupling structure target, including the following steps:

Step 1, read the triangle metadata in the target body mesh file, and create a virtual incident surface according to the target triangle metadata;

Step 2: Generate a ray tube from the virtual incident surface and perform intersection detection with the target triangular surface element. If the ray tube intersects with the target triangular surface element, the ray tube is valid.

Step 3, track the field intensity of the effective ray tube, and calculate the time domain near field intensity of the target according to the time domain bouncing ray method to obtain the field distribution at the transmission line position;

Step 4: Substitute the field strength at the transmission line position into the transmission line equation to calculate the voltage and current values at the transmission line port position.

Furthermore, the step 1 specifically includes: let the number of triangle face vertices read be N, and the three-dimensional coordinates of the triangle face vertices be Q (x, y, z), according to Calculate the two-dimensional vertex coordinates on the virtual incident surface/> Where F is the coordinate transformation matrix, which traverses the N triangle surface vertices and projects these vertices onto the virtual incident surface to obtain all the two-dimensional vertices that constitute the virtual incident surface.

11. According to a hybrid simplified modeling method based on the time domain bouncing ray method and the transmission line equation according to claim 2, it is characterized in that the coordinate transformation matrix F is:

Among them, θ and Indicates the incident angle of the electromagnetic wave, θ is the angle between the incident direction and the positive direction of the Z axis, and its value range is 0～π;/> It is the angle between the projection of the incident direction in the XOY plane and the positive direction of the X-axis, and its value range is 0 to 2π.

Furthermore, generating a ray tube from the virtual incident surface in step 2 specifically includes: determining a division step of the ray tube according to a wavelength λ of the incident electromagnetic field, subdividing the virtual incident surface into a plurality of triangular meshes based on the division step, and for each triangular mesh, three vertices of the mesh form a group of ray tubes, which are respectively used as starting points of three incident rays in the corresponding ray tube.

Furthermore, the intersection detection with the target triangular surface element in step 2 specifically includes: calculating the intersection point of the ray tube and the target triangular surface element by combining the equation of the straight line propagated by the ray tube and the equation of the plane where the target triangular surface element is located. If the intersection point is located in the target triangular surface element, the ray tube is valid.

Furthermore, the straight line equation of the ray tube propagation is:

In the formula, is the starting point of ray propagation, /> is the propagation direction of the ray, and the parameter t represents the distance between the ray origin and the intersection point;

Assume that the position vectors of the three vertices of the target triangle are and Then the plane equation of the triangle element is:

in, Represents the normal vector of the plane where the triangle is located,/> Represents the position vector of any point on the plane.

Furthermore, the intersection point of the ray tube and the target triangle element is:

Furthermore, the step 3 specifically includes:

Through the i-th intersection of the ray and the target The field strength of the ray is used to obtain the i+1th intersection point between the ray and the target/> The field strength at is:

in, is the distance the ray moves from the reflection point of the i-th reflection to the reflection point of the i+1-th reflection, e ^-jkd is the phase change caused by the propagation process, /> is the i-th reflection point/> The reflection coefficient at is the i-th reflection point/> The reflected electric field at the i-th reflection point is DF (d0 _i is the reflected electric field at the i-th reflection point of the ray/> The divergence factor at .

When a ray tube is incident on the target surface or reflected from the target surface, if the ray tube passes through the observation point Q during the bounce process, then is the incident electric field when the ray tube intersects the target, /> is the reflected electric field when the ray tube intersects with the target, and The phase in is separated and expressed as:

Where ω represents the angular frequency, represents the incident electric field, /> Indicates the starting position where the ray tube intersects the target surface, /> represents the position of the ray tube beam when it passes through the observation point, l _GO is the projection of the observation point Q on the propagation path of the central ray target surface of the optical ray tube; the time domain reflection electric field of the observation point Q is obtained by Fourier transform:

Where t represents time, Γ(t) represents the time domain reflection coefficient, _td represents the total time delay, represents the incident electric field in the time domain, and s(t) represents the incident source.

Furthermore, the transmission line equation affected by the electromagnetic field in step 4 is:

Among them, r represents the resistance per unit length, g represents the conductance per unit length, c represents the capacitance per unit length, V(z,t) represents the voltage vector on the transmission line, I(z,t) represents the current vector on the transmission line, V _F (z,t) represents the equivalent voltage source, I _F (z,t) represents the equivalent current source, E ⁱ represents the incident field, and l represents the length of the transmission line.

Furthermore, the voltage value and current value at the transmission line port position in step 4 are:

in, represents the length of the line unit added to the two ports of the transmission line, Δt represents the time interval, _Rs represents the resistance value connected at the beginning of the transmission line, R _L , C ₁ and L ₁ represent the load resistance value, capacitance value and inductance value of the terminal connection respectively, /> represents the line integral of the electric field component of the vertically incident transmission line, /> It represents the difference between the tangential electric field component of the transmission line and the tangential electric field component of the shielding cavity surface, /> represents the current value, V ⁿ⁺¹ represents the voltage value, V ₁ ⁿ⁺¹ ,/> and/> Represents the boundary conditions of voltage and current at the beginning and end of the transmission line, respectively. R, C and L represent the resistance, capacitance and inductance of the transmission line connection, respectively.

Compared with the prior art, the present invention has the following advantages: (1) the present invention adopts a method of generating a ray tube by using a virtual incident surface, which only requires a small amount of triangulated surface element data to fit the target surface shape, thereby reducing the need to store triangulated surface element information and reducing memory usage; (2) the present invention adopts a hybrid of the time domain bouncing ray method and the transmission line equation method to solve the time domain near-field strength of electrically large targets. Compared with the precise full-wave analysis method, the present invention does not need to discretize the fine structure of the transmission line and the free space, which greatly reduces the calculation time and improves the operation efficiency.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of a hybrid simplified modeling method based on the time-domain bouncing ray method and the transmission line equation in the present invention.

FIG. 2( a ) is a schematic diagram of a target body model in the present invention, and FIG. 2( b ) is a schematic diagram of a triangular facet subdivision of a target body in the present invention.

FIG. 3 is a schematic diagram of the intersection of rays and triangular face elements in the present invention.

FIG. 4 is a schematic diagram of the first incident ray and the corresponding pentahedron in the present invention.

FIG. 5 is a schematic diagram of continuous reflection of rays and corresponding pentahedrons in the present invention.

FIG. 6 is a schematic diagram of ray emission and the corresponding pentahedron in the present invention.

FIG. 7 is a schematic diagram of a simulation of a field-line coupling process in the present invention.

FIG8( a ) and FIG8( b ) are schematic diagrams showing comparisons of the voltage values of the left and right ports of the transmission line generated by the method of the present invention and the voltage values of the left and right ports generated by simulation using the CST software.

FIG9(a) and FIG9(b) are schematic diagrams for comparing the current values of the left and right ports of the transmission line generated by the method of the present invention and the current values of the left and right ports generated by simulation using the CST software.

Detailed ways

The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. The methods and means used in the description of the specific embodiments of the present invention are only used to fully and clearly explain the present invention and are not intended to limit the present invention.

In conjunction with FIG1 , the present invention provides a hybrid simplified modeling method based on a time domain bouncing ray method and a transmission line equation, comprising the following steps:

Step 1: Read the triangle metadata in the target entity mesh file, and create a virtual incident surface based on the target triangle metadata, as follows:

Combined with Figure 2, firstly, model the model in commercial software and perform triangular face segmentation. Secondly, read the triangular face metadata in the triangular mesh file, including the number of triangular face elements M, the number of triangular face element vertices N, and the coordinates of the triangular face element vertices. Finally, combined with Figure 3, create a virtual incident surface based on the read target triangular face metadata, as follows:

For example, the vertex coordinates of a triangle are Q(-0.1, 0.5, 0.0). According to the coordinate conversion formula:

The two-dimensional vertex coordinates Q'(-0.27884,-0.42426) on the virtual incident surface can be calculated. Similarly, the three-dimensional vertex coordinates Q(x, y, z) of all triangular face elements on the virtual incident surface can be calculated in turn according to the above method. Then find all the two-dimensional coordinate points in y _θ and /> The maximum and minimum values in the direction can be obtained by using y _θmax , y _θmin , /> Defines the boundaries of the virtual incident surface to form a rectangular area.

Step 2: Generate a ray tube from the virtual incident surface and perform intersection detection with the target triangle surface element, as follows:

The division step of the ray tube is determined according to the wavelength λ of the incident electromagnetic field. To achieve the ideal accuracy, the spacing between the ray tubes is usually required to be no more than one tenth of a wavelength. Therefore, when λ/10 is used as the spacing between the dividing rays, the virtual incident surface can be subdivided into several triangular meshes. For each triangular mesh, the three vertices of the mesh form a group of ray tubes, which serve as the starting points of the three incident rays in the corresponding ray tubes, respectively, for the subsequent ray-surface intersection detection, and the center of the grid is used to record the field strength information and phase information of the ray tube.

In conjunction with FIG3 , when performing intersection detection between a ray and a target triangle face, the straight line path of the ray propagation can be expressed by the following straight line equation:

In the formula, is the starting point of ray propagation, /> is the propagation direction of the ray, and the parameter t represents the distance between the ray origin and the intersection point. Assume that the position vectors of the three vertices of the plane triangle element are/> and Then the plane where the triangle face element lies can be expressed as:

By combining equations (9) and (10), we can get:

Therefore, the intersection point of the ray and the triangle is:

Step 3: Track the field intensity of the effective ray, and calculate the time-domain near-field field intensity of the target according to the time-domain bouncing ray algorithm to obtain the field distribution at the transmission line position:

When a ray intersects a target, the field strength of the reflected ray is determined by the field strength of the incident ray and the reflection coefficient of the target surface. The field strength is used to deduce the i+1th intersection point with the target/> The field strength at.

In order to calculate the field strength at a certain point Q on the transmission line, it is necessary to determine whether the ray tube passes through this point during propagation. This problem will have three different scenarios, each of which involves determining the relative position relationship between the observation point and the pentahedron in space, as follows:

(1) First, in conjunction with Figure 4, the process of the first intersection of the ray and the target, that is, the path of the initial ray tube on the virtual incident surface and the target triangular surface element. The coordinates of the three corner point rays defined by a ray tube on the virtual incident surface are marked as v ₁ , v ₂ , and v _3. When this ray tube intersects with the target triangular surface element, the corresponding initial intersection coordinates are marked as u ₁ , u ₂ , and u ₃ , respectively. The geometric structure composed of these six points forms a pentahedron. Therefore, the question of whether the ray tube passes through point Q during this propagation can be regarded as the positional relationship between point Q and this pentahedron in space.

(2) Next, in conjunction with Figure 5, the process of the ray from the n-1th reflection surface to the nth reflection surface. Assume that at the n-1th reflection, the positions where the three corner point rays of a certain ray tube intersect with the split surface element are marked as v ₁ , v ₂ and v ₃ , respectively, and at the nth reflection, the positions where the three corner point rays of the ray tube intersect with the surface element are marked as u ₁ , u ₂ and u ₃ , respectively. These six points form a pentahedron. Therefore, the question of whether the ray tube of this beam passes through the observation point Q during this propagation can be regarded as the positional relationship between the observation point Q and this pentahedron in space.

(3) Finally, combined with Figure 6, which shows the process of the last reflection of the ray, the positions where the three corner point rays of a certain beam of ray tube intersect with the triangular surface element on the last reflection surface are marked as v ₁ , v ₂ and v ₃ respectively. (/> Represents the ray emission direction, m is a sufficiently large number to ensure the accuracy of the calculation) can be obtained as the three vertices u ₁ , u ₂ and u ₃ of the virtual emission surface, and the geometric structure composed of these six points forms a pentahedron. Therefore, the question of whether the beam of rays passes through the observation point Q during this transmission can be regarded as the position relationship between the observation point Q and the pentahedron in space.

Considering the above three situations, in each process of field intensity tracking, it is necessary to determine the positional relationship between the pentahedron generated by each beam tube in the propagation stage and the observation point one by one. If point Q is inside the pentahedron, the phase information can be obtained by projecting point Q on the central ray path, and the overall electric field of point Q can be obtained by accumulating the field intensity vector.

When a ray tube is incident on a target surface or reflected from a target surface, if the ray tube passes through point Q during the bounce process, it can be set is the incident electric field when the ray tube intersects the target, /> is the reflected electric field when the ray tube intersects with the target, and The phase in can be separated and expressed as:

Through Fourier transform, the time domain incident electric field and time domain reflected electric field of the observation point Q can be expressed as:

in, is the total time delay.

According to the above steps, the time domain near-field intensity of the target can be calculated to obtain the field distribution at the transmission line location.

Step 4: Substitute the field strength at the transmission line into the transmission line equation to calculate the voltage and current values at the transmission line port, as follows:

Combined with Figure 7, the transmission line equation affected by the electromagnetic field is expressed as:

Among them, r represents the resistance per unit length, g represents the conductance per unit length, c represents the capacitance per unit length, V(z,t) represents the voltage vector on the transmission line, I(z,t) represents the current vector on the transmission line, V _F (z,t) represents the equivalent voltage source, I _F (z,t) represents the equivalent current source, E ⁱ represents the incident field, and l represents the length of the transmission line.

Substituting the field strength at the transmission line position obtained in step 3 into equations (12) to (15), the voltage and current values at the transmission line port position can be obtained:

in, represents the length of the line unit added to the two ports of the transmission line, Δt represents the time interval, _Rs represents the resistance value connected at the beginning of the transmission line, R _L , C ₁ and L ₁ represent the load resistance value, capacitance value and inductance value of the terminal connection respectively, /> represents the line integral of the electric field component of the vertically incident transmission line, /> It represents the difference between the tangential electric field component of the transmission line and the tangential electric field component of the shielding cavity surface, /> represents the current value, V ⁿ⁺¹ represents the voltage value, V ₁ ⁿ⁺¹ ,/> and/> They represent the boundary conditions of voltage and current at the beginning and end of the transmission line respectively, and R, C and L represent the resistance, capacitance and inductance of the transmission line connection respectively.

According to the method of the present invention, the field-line-circuit coupling structure shown in Figures 2(a) and 2(b) is simulated and calculated, and the geometric dimensions of the model are: transmission line length d=1m, height h=2cm, radius r=2mm. The shielding box is a pure metal structure, 20cm long, 20cm wide, and 10cm high. One end of the transmission line is connected to a load resistor R ₁ =150Ω, and the other end extends into the metal shielding box and is connected to a set of parallel impedance element circuits, including a load resistor R ₂ =100Ω, a capacitor C=20pF, and an inductor L=5μH. In addition, the position of the excitation source is set, and a Gaussian pulse wave with a center frequency f ₀ =6GHz is used as the incident source. Its main parameters are E ₀ =1000V/m, τ=2ns, and t ₀ =0.8τ. The pulse incident direction is along θ=45°, Vertical polarization. Figures 8(a), 8(b), 9(a) and 9(b) compare the calculation results of the field-line-circuit coupling structure rapid analysis method based on time-domain bouncing rays and transmission line equations of the present invention with the simulation results of CST software. It can be seen that the results of the method of the present invention are basically consistent with the results of CST software, proving the accuracy of the method of the present invention. Combined with Table 1, it can be seen that the method of the present invention is superior to the CST software in terms of calculation time.

Table 1 Comparison of calculation time between the method of the present invention and CST software

Table 1 Comparison of calculation time

In summary, the hybrid simplified modeling method based on the time-domain bouncing ray method and the transmission line equation of the present invention greatly reduces the calculation time of the electrically large-sized structure of the field-line-circuit coupling, and realizes the rapid analysis of the electrically large-sized structure of the field-line-circuit coupling.

The above is only a preferred embodiment of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered as the protection scope of the present invention. All components not specified in this embodiment can be implemented by existing technologies.

Claims (10)

1. A hybrid simplified modeling method based on the time domain bouncing ray method and the transmission line equation, characterized by comprising the following steps: Step 1, read the triangle metadata in the target body mesh file, and create a virtual incident surface according to the target triangle metadata; Step 2: Generate a ray tube from the virtual incident surface and perform intersection detection with the target triangular surface element. If the ray tube intersects with the target triangular surface element, the ray tube is valid and step 3 is executed; Step 3, track the field intensity of the effective ray tube, and calculate the time domain near field intensity of the target according to the time domain bouncing ray algorithm to obtain the field distribution at the transmission line position; Step 4: Substitute the field strength at the transmission line position into the transmission line equation to calculate the voltage and current values at the transmission line port position. 2. The hybrid simplified modeling method based on the time-domain bouncing ray method and the transmission line equation according to claim 1 is characterized in that the step 1 specifically comprises: let the number of the read triangle surface element vertices be N, the three-dimensional coordinates of the triangle surface element vertices be Q (x, y, z), according to Calculate the two-dimensional vertex coordinates on the virtual incident surface/> Where F is the coordinate transformation matrix, which traverses the N triangle surface vertices and projects these vertices onto the virtual incident surface to obtain all the two-dimensional vertices that constitute the virtual incident surface. 3. According to a hybrid simplified modeling method based on the time domain bouncing ray method and the transmission line equation according to claim 2, it is characterized in that the coordinate transformation matrix F is: Among them, θ and Represents the incident angle of the electromagnetic wave, θ is the angle between the incident direction and the positive direction of the Z axis, and its value range is 0～π; It is the angle between the projection of the incident direction in the XOY plane and the positive direction of the X-axis, and its value range is 0 to 2π. 4. According to the hybrid simplified modeling method based on the time-domain bouncing ray method and the transmission line equation of claim 2, it is characterized in that generating a ray tube from the virtual incident surface in step 2 specifically includes: determining the division step of the ray tube according to the wavelength λ of the incident electromagnetic field, subdividing the virtual incident surface into a plurality of triangular meshes based on the division step, and for each triangular mesh, three vertices of the mesh form a group of ray tubes, which are respectively used as the starting points of the three incident rays in the corresponding ray tube. 5. According to the hybrid simplified modeling method based on the time-domain bouncing ray method and the transmission line equation of claim 4, it is characterized in that the intersection detection with the target triangular surface element in the step 2 specifically includes: calculating the intersection point of the ray tube and the target triangular surface element by combining the equation of the straight line propagated by the ray tube and the equation of the plane where the target triangular surface element is located. If the intersection point is located within the target triangular surface element, the ray tube is valid. 6. The hybrid simplified modeling method based on the time-domain bouncing ray method and the transmission line equation according to claim 5, characterized in that the straight line equation of the ray tube propagation is: in, Indicates the starting point of ray propagation, /> Indicates the propagation direction of the ray, and the parameter t indicates the distance between the ray origin and the intersection point; Assume that the position vectors of the three vertices of the target triangle are and Then the plane equation of the triangle element is: in, Represents the normal vector of the plane where the triangle is located,/> Represents the position vector of any point on the plane. 7. The hybrid simplified modeling method based on the time-domain bouncing ray method and the transmission line equation according to claim 6, characterized in that the intersection point of the ray tube and the target triangle surface element is: 8. According to the hybrid simplified modeling method based on the time-domain bouncing ray method and the transmission line equation according to claim 5, it is characterized in that the step 3 specifically comprises: Through the i-th intersection of the ray and the target The field strength of the ray is used to obtain the i+1th intersection point between the ray and the target/> The field strength at is: in, is the distance the ray moves from the reflection point of the i-th reflection to the reflection point of the i+1-th reflection, e ^-jkd is the phase change caused by the propagation process, /> is the i-th reflection point/> The reflection coefficient at is the i-th reflection point/> The reflected electric field at the i-th reflection point of the ray. DF(d) _i is the reflected electric field at the i-th reflection point of the ray. The divergence factor at ; When a ray tube is incident on the target surface or reflected from the target surface, if the ray tube passes through the observation point Q during the bounce process, then is the incident electric field when the ray tube intersects the target, /> is the reflected electric field when the ray tube intersects with the target, and The phase in is separated and expressed as: Where ω represents the angular frequency, represents the incident electric field, /> represents the starting position where the ray tube intersects the target surface, represents the position of the ray tube beam when it passes through the observation point, l _GO is the projection of the observation point Q on the propagation path of the central ray target surface of the optical ray tube; the time domain reflection electric field of the observation point Q is obtained by Fourier transform: Where t represents time, Γ(t) represents the time domain reflection coefficient, _td represents the total time delay, represents the incident electric field in the time domain, and s(t) represents the incident source. 9. The hybrid simplified modeling method based on the time domain bouncing ray method and the transmission line equation according to claim 8, characterized in that the transmission line equation affected by the electromagnetic field in step 4 is: Among them, r represents the resistance per unit length, g represents the conductance per unit length, c represents the capacitance per unit length, V(z,t) represents the voltage vector on the transmission line, I(z,t) represents the current vector on the transmission line, V _F (z,t) represents the equivalent voltage source, I _F (z,t) represents the equivalent current source, E ⁱ represents the incident field, and l represents the length of the transmission line. 10. A hybrid simplified modeling method based on the time domain bouncing ray method and the transmission line equation according to claim 9, characterized in that the voltage value and the current value at the transmission line port position in step 4 are: in, represents the length of the line unit added to the two ports of the transmission line, Δt represents the time interval, _Rs represents the resistance value connected at the beginning of the transmission line, R _L , C ₁ and L ₁ represent the load resistance value, capacitance value and inductance value of the terminal connection respectively, /> represents the line integral of the electric field component of the vertically incident transmission line, /> It represents the difference between the tangential electric field component of the transmission line and the tangential electric field component of the shielding cavity surface, /> represents the current value, V ⁿ⁺¹ represents the voltage value, V ₁ ⁿ⁺¹ ,/> and/> They represent the boundary conditions of voltage and current at the beginning and end of the transmission line respectively, and R, C and L represent the resistance, capacitance and inductance of the transmission line connection respectively.