FAILURE MAP
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FA-93596 / Solar tracker geometry / Open access

Torque-tube inclinometer rotation: calibration offset sign · case 01

Calibration doubles the mounting error instead of removing it.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The calibration offset is added.

VERIFIED REPAIR

Subtract the offset.

Unsuccessful approach: Subtracting the magnitude breaks negative offsets.

Case contract

ax (across-axis) and az (normal) are gravity components in g. The magnitude must be within [0.8, 1.2] g, else [None, 'fault']. Rotation = atan2(ax, az) in degrees, negated for a sensor mounted on the west side, then minus the calibration offset, normalised to (-180, 180]. Return [angle rounded 2, 'ok'].

Why this case matters

Single-axis and dual-axis solar trackers turn a sun direction into actuator commands; a sign, frame or limit mistake points a whole plant away from the sun or into a mechanical stop.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(ax, az, mount, offset):
    mag = math.hypot(ax, az)
    if not 0.8 <= mag <= 1.2:
        return [None, 'fault']
    ang = math.degrees(math.atan2(ax, az))
    if mount == 'west':
        ang = -ang
    ang += offset
    ang = (ang + 180) % 360 - 180
    if ang == -180:
        ang = 180.0
    return [round(ang, 2), 'ok']
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: calibration offset sign', [0.7778, -0.7778, 'west', 5], [-140.0, 'ok']],
  ['regression: calibration offset sign (partial repair)', [0.866, 0.5, 'east', -3], [63.0, 'ok']],
  ['control 1', [-1.1, 0.0, 'west', 0], [90.0, 'ok']],
  ['control 2', [-0.4, 0.6928, 'east', 0], [None, 'fault']]],
 [['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: calibration offset sign', [0.0, -1.0, 'east', 2], [178.0, 'ok']],
  ['regression: calibration offset sign (partial repair)', [-0.8485, 0.8485, 'east', -3],
   [-42.0, 'ok']],
  ['control 1', [-0.7778, 0.7778, 'east', 0], [-45.0, 'ok']],
  ['control 2', [0.5657, -0.5657, 'west', 2], [-137.0, 'ok']]],
 [['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: calibration offset sign', [-1.0392, -0.6, 'east', 5], [-125.0, 'ok']],
  ['regression: calibration offset sign (partial repair)', [0.0, -1.1, 'west', -3], [-177.0, 'ok']],
  ['control 1', [0.25, 0.433, 'west', 2], [None, 'fault']],
  ['control 2', [0.8485, -0.8485, 'west', -3], [-132.0, 'ok']]],
 [['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: calibration offset sign', [0.0, -1.0, 'east', 5], [175.0, 'ok']],
  ['regression: calibration offset sign (partial repair)', [-0.7071, 0.7071, 'west', -3],
   [48.0, 'ok']],
  ['control 1', [0.5657, -0.5657, 'east', -3], [138.0, 'ok']],
  ['control 2', [-0.6, 1.0392, 'east', 0], [-30.0, 'ok']]],
 [['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: calibration offset sign', [-0.866, -0.5, 'west', 2], [118.0, 'ok']],
  ['regression: calibration offset sign (partial repair)', [-0.5657, 0.5657, 'east', -3],
   [-42.0, 'ok']],
  ['control 1', [0.6928, 0.4, 'east', 5], [None, 'fault']],
  ['control 2', [-0.55, 0.9526, 'east', 2], [-32.0, 'ok']]]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
boundary: magnitude at lower bound[0.0, 'ok'][0.0, 'ok']Passed
boundary: magnitude at upper bound[90.0, 'ok'][90.0, 'ok']Passed
boundary: upside-down reading[180.0, 'ok'][180.0, 'ok']Passed
regression: calibration offset sign[-130.0, 'ok'][-140.0, 'ok']Failed
regression: calibration offset sign (partial repair)[57.0, 'ok'][63.0, 'ok']Failed
control 1[90.0, 'ok'][90.0, 'ok']Passed
control 2[None, 'fault'][None, 'fault']Passed

SHA-256 / 02d18f1dd4250b0ac398c2b40273ae056f86f8ab8665abac79196e5c7d966ae8

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(ax, az, mount, offset):
    mag = math.hypot(ax, az)
    if not 0.8 <= mag <= 1.2:
        return [None, 'fault']
    ang = math.degrees(math.atan2(ax, az))
    if mount == 'west':
        ang = -ang
    ang -= abs(offset)
    ang = (ang + 180) % 360 - 180
    if ang == -180:
        ang = 180.0
    return [round(ang, 2), 'ok']
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: calibration offset sign', [0.7778, -0.7778, 'west', 5], [-140.0, 'ok']],
  ['regression: calibration offset sign (partial repair)', [0.866, 0.5, 'east', -3], [63.0, 'ok']],
  ['control 1', [-1.1, 0.0, 'west', 0], [90.0, 'ok']],
  ['control 2', [-0.4, 0.6928, 'east', 0], [None, 'fault']]],
 [['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: calibration offset sign', [0.0, -1.0, 'east', 2], [178.0, 'ok']],
  ['regression: calibration offset sign (partial repair)', [-0.8485, 0.8485, 'east', -3],
   [-42.0, 'ok']],
  ['control 1', [-0.7778, 0.7778, 'east', 0], [-45.0, 'ok']],
  ['control 2', [0.5657, -0.5657, 'west', 2], [-137.0, 'ok']]],
 [['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: calibration offset sign', [-1.0392, -0.6, 'east', 5], [-125.0, 'ok']],
  ['regression: calibration offset sign (partial repair)', [0.0, -1.1, 'west', -3], [-177.0, 'ok']],
  ['control 1', [0.25, 0.433, 'west', 2], [None, 'fault']],
  ['control 2', [0.8485, -0.8485, 'west', -3], [-132.0, 'ok']]],
 [['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: calibration offset sign', [0.0, -1.0, 'east', 5], [175.0, 'ok']],
  ['regression: calibration offset sign (partial repair)', [-0.7071, 0.7071, 'west', -3],
   [48.0, 'ok']],
  ['control 1', [0.5657, -0.5657, 'east', -3], [138.0, 'ok']],
  ['control 2', [-0.6, 1.0392, 'east', 0], [-30.0, 'ok']]],
 [['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: calibration offset sign', [-0.866, -0.5, 'west', 2], [118.0, 'ok']],
  ['regression: calibration offset sign (partial repair)', [-0.5657, 0.5657, 'east', -3],
   [-42.0, 'ok']],
  ['control 1', [0.6928, 0.4, 'east', 5], [None, 'fault']],
  ['control 2', [-0.55, 0.9526, 'east', 2], [-32.0, 'ok']]]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
boundary: magnitude at lower bound[0.0, 'ok'][0.0, 'ok']Passed
boundary: magnitude at upper bound[90.0, 'ok'][90.0, 'ok']Passed
boundary: upside-down reading[180.0, 'ok'][180.0, 'ok']Passed
regression: calibration offset sign[-140.0, 'ok'][-140.0, 'ok']Passed
regression: calibration offset sign (partial repair)[57.0, 'ok'][63.0, 'ok']Failed
control 1[90.0, 'ok'][90.0, 'ok']Passed
control 2[None, 'fault'][None, 'fault']Passed

SHA-256 / b59a49839d753ebe7e80b07334735b784ecf64fd2c7419d727e29f42f38eeb16

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(ax, az, mount, offset):
    mag = math.hypot(ax, az)
    if not 0.8 <= mag <= 1.2:
        return [None, 'fault']
    ang = math.degrees(math.atan2(ax, az))
    if mount == 'west':
        ang = -ang
    ang -= offset
    ang = (ang + 180) % 360 - 180
    if ang == -180:
        ang = 180.0
    return [round(ang, 2), 'ok']
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: calibration offset sign', [0.7778, -0.7778, 'west', 5], [-140.0, 'ok']],
  ['regression: calibration offset sign (partial repair)', [0.866, 0.5, 'east', -3], [63.0, 'ok']],
  ['control 1', [-1.1, 0.0, 'west', 0], [90.0, 'ok']],
  ['control 2', [-0.4, 0.6928, 'east', 0], [None, 'fault']]],
 [['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: calibration offset sign', [0.0, -1.0, 'east', 2], [178.0, 'ok']],
  ['regression: calibration offset sign (partial repair)', [-0.8485, 0.8485, 'east', -3],
   [-42.0, 'ok']],
  ['control 1', [-0.7778, 0.7778, 'east', 0], [-45.0, 'ok']],
  ['control 2', [0.5657, -0.5657, 'west', 2], [-137.0, 'ok']]],
 [['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: calibration offset sign', [-1.0392, -0.6, 'east', 5], [-125.0, 'ok']],
  ['regression: calibration offset sign (partial repair)', [0.0, -1.1, 'west', -3], [-177.0, 'ok']],
  ['control 1', [0.25, 0.433, 'west', 2], [None, 'fault']],
  ['control 2', [0.8485, -0.8485, 'west', -3], [-132.0, 'ok']]],
 [['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: calibration offset sign', [0.0, -1.0, 'east', 5], [175.0, 'ok']],
  ['regression: calibration offset sign (partial repair)', [-0.7071, 0.7071, 'west', -3],
   [48.0, 'ok']],
  ['control 1', [0.5657, -0.5657, 'east', -3], [138.0, 'ok']],
  ['control 2', [-0.6, 1.0392, 'east', 0], [-30.0, 'ok']]],
 [['boundary: magnitude at lower bound', [0.0, 0.8, 'east', 0], [0.0, 'ok']],
  ['boundary: magnitude at upper bound', [1.2, 0.0, 'east', 0], [90.0, 'ok']],
  ['boundary: upside-down reading', [0.0, -1.0, 'east', 0], [180.0, 'ok']],
  ['regression: calibration offset sign', [-0.866, -0.5, 'west', 2], [118.0, 'ok']],
  ['regression: calibration offset sign (partial repair)', [-0.5657, 0.5657, 'east', -3],
   [-42.0, 'ok']],
  ['control 1', [0.6928, 0.4, 'east', 5], [None, 'fault']],
  ['control 2', [-0.55, 0.9526, 'east', 2], [-32.0, 'ok']]]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
boundary: magnitude at lower bound[0.0, 'ok'][0.0, 'ok']Passed
boundary: magnitude at upper bound[90.0, 'ok'][90.0, 'ok']Passed
boundary: upside-down reading[180.0, 'ok'][180.0, 'ok']Passed
regression: calibration offset sign[-140.0, 'ok'][-140.0, 'ok']Passed
regression: calibration offset sign (partial repair)[63.0, 'ok'][63.0, 'ok']Passed
control 1[90.0, 'ok'][90.0, 'ok']Passed
control 2[None, 'fault'][None, 'fault']Passed

SHA-256 / 095033d5bd70f6f4b6e32b825b5e83d39fdef30cf92807a3c09a0e2cf0df57bd

Verification & scope

Deterministic stipulated toy contract for teaching; no claim of conformance with any standard, vendor protocol or production controller. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:51:56.570889+00:00.

Case digest / 05d130ffc28249a4c2798fa88632d6a0fc6043bf762a2998bf993d556f2bf0a6