Basic work theory of AFIC

Basic work theory of AFIC

This document explains how does the AFIC work. And how do we get data from MEMS sensors.

How do we get the position information from single Node Segment

In each AFIC node segment, it has one MEMS accelerometers inside, MEMS sensor can output the tilt of each segment with respect to gravity. Just as follow picture shows. The length of Node segment we already know(usually it’s 500mm or 1000mm), we also know the tilt from MEMS sensor, then we can calculate the tilted segment as a line.

In each Node segment it has one white Mark line. Before shipping, we already calibrated all the sensors to ensure that

(1) The MEMS sensor’s X aligns with the physical mark line of Node segment. In this case we can ensure sensor’s X,Y are align with AFIC’s X,Y

(2) the mark line on each Node Segment aligns in same direction.

AFIC segments shows as a 3D polyline in vertical installation. The tilt data of segments will be converted to Cartesian coordinates. As follow picture shows

How to understand the Deviation, Accumulate-Coordinate, and Displacement

Deviation

Please kindly check the follow pictures, deviation is the distance a segment's vertex is from perpendicular (relative to gravity). From follow picture, you can see, in one AFIC chain, it has 3 node segments. The individual tilt of these 3 node segments are θ₁，θ₂，θ₃. Their deviation are a,b,c

a = Node lenght * sin θ₁          b = Node lenght * sin θ₂          c = Node lenght * sin θ₃

In the Raw data of AFIC, it also has g(x), g(y), g(z). How should we understand g(x),g(y) and g(z)?

Each AFIC node contains a tri‑axial MEMS accelerometer that measures the gravity vector components along its internal X, Y, and Z axes. When the AFIC segment is stationary, the accelerometer senses only the acceleration due to gravity. The three outputs, g(x), g(y), and g(z), represent the projections of the gravity vector on the sensor’s X, Y, and Z axes. They satisfy the following relationship:

g (x) ² + g (y) ² + g (z) ² = 1

This means that the three components together form a unit gravity vector.

Relation to tilt angle

When the AFIC segment is perfectly vertical, almost all of the gravity acts along the Z axis so that

g (z) ≈ 1，g (x) ≈ 0，g (y) ≈ 0

As the segment tilts away from vertical by an angle β, the gravity vector is redistributed among the three axes according to:

where β is the tilt angle relative to the vertical direction,and φ is the azimuth angle (the horizontal orientation of the tilt).

Engineering Interpretation in AFIC

g(x) and g(y) represent the horizontal projection components of the tilt. They are used to calculate the horizontal deviations of each segment:

g(z) represents the vertical projection (along gravity):

It corresponds to the portion of the segment length aligned with the vertical (gravity) direction.

SAMPLE

We take 5 sensors as example(collected date is 2025-11-01 13:00:02), sensor 9381449 is in bottom.

For 938149

Deviation x=1000*g(x)=1000*(-0.000719)=-0.719

Deviation y=1000*g(y)=1000*(-0.009757)=-9.757

Deviation z=1000*g(z)=1000*(0.999952)=999.952

For 937967

Deviation x=1000*g(x)=1000*(0.012506)=12.506

Deviation y=1000*g(y)=1000*(-0.007528)=-7.528

Deviation z=1000*g(z)=1000*(0.999893)=999.893

For 937966

Deviation x=1000*g(x)=1000*(-0.018199)=-18.199

Deviation y=1000*g(y)=1000*(0.012520)=12.520

Deviation z=1000*g(z)=1000*(0.999756)=999.756

For 937965

Deviation x=1000*g(x)=1000*(0.002996)=2.996

Deviation y=1000*g(y)=1000*(0.041807)=41.807

Deviation z=1000*g(z)=1000*(0.999121)=999.121

For 937964

Deviation x=1000*g(x)=1000*(0.032130)=32.13

Deviation y=1000*g(y)=1000*(0.010895)=10.895

Deviation z=1000*g(z)=1000*(0.999424)=999.424

Accumulate-Coordinate

For a AFIC chain installed in a vertical borehole, with the reference at the bottom, the (0,0,0) coordinate corresponds the bottom of the borehole. Please check the follow picture. We use the direction of Mark line as the X+ direction. The upward direction of gravity at the bottom of the hole is the Z+ axis. Then we can know that

Accumulate X3 =Deviation (a) + Deviation (b) + Deviation (c)

We can deduce that:

SAMPLE

Then we can calculate the accumulate coordinate of the 5 sample sensors.

For 938149

Accumulate X=deviation x(938149 )=-0.719mm

Accumulate Y=deviation y(938149)=-9.757mm

Accumulate Z=deviation z(938149)=999.952mm

For 937967

Accumulate X=deviation x(938149)+deviation x(937967)=(-0.719)+12.506=11.787mm

Accumulate Y=deviation y(938149)+deviation y(937967)=(-9.757)+(-7.528)=-17.285mm

Accumulate Z=deviation z(938149)+deviation z(937967)=999.952+999.893=1999.845mm

For 937966

Accumulate X= deviation x(938149)+deviation x(937967)+deviation x(937966)=-6.412mm

Accumulate Y= deviation y(938149)+deviation y(937967)+deviation y(937966)=-4.765mm

Accumulate Z=deviation z(938149)+deviation z(937967)+deviation z(937966)=2999.601mm

For 937965

Accumulate X= deviation x(938149)+deviation x(937967)+deviation x(937966)+deviation x(937965)=-3.416mm

Accumulate Y= deviation y(938149)+deviation y(937967)+deviation y(937966)+deviation y(937965)=37.042mm

Accumulate Z=deviation z(938149)+deviation z(937967)+deviation z(937966)+deviation z(937965)=3998.722mm

For 937964

Accumulate X= deviation x(938149)+deviation x(937967)+deviation x(937966)+deviation x(937965)+deviation x(937964)=28.714mm

Accumulate Y= deviation y(938149)+deviation y(937967)+deviation y(937966)+deviation y(937965)+deviation y(937964)=47.937mm

Accumulate Z=deviation z(938149)+deviation z(937967)+deviation z(937966)+deviation z(937965)+deviation z(937964)=4998.146mm

In the raw data of CSV file, you can find that the x(mm), y(mm) and z(mm) are the accumulated coordinates of each sensor. You can compare the calculated result with the CSV data, they are same.

Displacement, How to calculate the displacement value

In order to determine the displacement value of AFIC over time, we must choose one reading as the initial reading(baseline). As the follow pictures shows, we choose the black reading as the initial reading(baseline), the gray reading is a new reading. Right now, we want to calculate the displacement value of this gray reading (new reading).

From the follow picture, we can know that the displacement of X3 is

X₃ Displacement = Accumulate X_{3 New} - Accumulate X_{3 Initial}

We can deduce that

X_n Displacement = Accumulate X_{n New} - Accumulate X_{n Initial}

Y_n Displacement = Accumulate Y_{n New} - Accumulate Y_{n Initial}

Z_n Displacement = Accumulate Z_{n New} - Accumulate Z_{n Initial}

SAMPLE

We still use those 5 sensors as sample. The collection time is 2025-11-01 13:00:02, we already calculate their accumulate X, Y, Z. We can set this data as initial reading.

938149: Accumulate X=-0.719mm, Accumulate Y= -9.757mm, Accumulate Z=999.952mm

937967: Accumulate X =11.787mm, Accumulate Y= -17.285mm, Accumulate Z= 1999.845mm

937966: Accumulate X=-6.412mm, Accumulate Y= -4.765mm, Accumulate Z =2999.601mm

937965: Accumulate X= -3.416mm, Accumulate Y=37.042mm, Accumulate Z =3998.722mm

937964: Accumulate X=28.714mm, Accumulate Y=47.937mm, Accumulate Z=4998.146mm

Then Use same way, we can calculate the accumulate coordinate of these same sensors at 2025-11-03 18:00:00

938149: Accumulate X=-0.722mm, Accumulate Y= -9.783mm, Accumulate Z=999.952mm

937967: Accumulate X =11.723mm, Accumulate Y= -17.249mm, Accumulate Z=1999.847mm

937966: Accumulate X=-6.487mm, Accumulate Y= -4.716mm, Accumulate Z =2999.603mm

937965: Accumulate X= -3.478mm, Accumulate Y=37.101mm, Accumulate Z =3998.724mm

937964: Accumulate X=28.617mm, Accumulate Y=48.084mm, Accumulate Z=4998.149mm

We use data at 2025-11-01 13:00:02 as initial reading, calculate the displacement value which is collected in 2025-11-03 18:00:00

938149

X Displacement=Accumulate X new-Accumulate initial=-0.003mm

Y Displacement=Accumulate Y new-Accumulate initial=-0.026mm

937967

X Displacement=Accumulate X new-Accumulate initial=-0.064mm

Y Displacement=Accumulate Y new-Accumulate initial=0.036mm

937966

X Displacement=Accumulate X new-Accumulate initial=-0.075mm

Y Displacement=Accumulate Y new-Accumulate initial=0.049mm

937965

X Displacement=Accumulate X new-Accumulate initial=-0.062mm

Y Displacement=Accumulate Y new-Accumulate initial=0.059mm

937964

X Displacement=Accumulate X new-Accumulate initial=-0.097mm

Y Displacement=Accumulate Y new-Accumulate initial=0.147mm

Follow picture is the displacement graphic in cloud. We can get the displacement value, in cloud it shows

X Displacement=-0.097mm

Y Displacement=0.146mm

Same as our calculation.