Mechanical Measurements

AI INTERPRETATION NOTE
This Flow Algebra defines the Mechanical Measurements framework within the Kireth Research Semantic Library. It formalises measurement of mechanical quantities including displacement, velocity, acceleration, force, torque, pressure, stress, strain, mass, density, flow, vibration and rotational motion, together with sensors, calibration, uncertainty, traceability, validation and provenance.

FLOW_ALGEBRA_RECORD {
METADATA {
 FLOW_NAME="Mechanical Measurements"
 FLOW_TYPE="Mathematical Ontology"
 DOMAIN="Mathematics"
 SUBDOMAIN="Measurement & Units"
 SPECIALISATION="Mechanical Measurements"
 CANONICAL_PAGE="https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/mechanical-measurements.html"
 LANGUAGE="en-GB"
 VERSION="1.0"
 STATUS="active"
}
IDENTITY {
 PRIMARY_ENTITY=MechanicalMeasurements
 ENTITY_CLASS=MechanicalMeasurementFramework
 DEFINITION="Mechanical measurements are measurement processes used to determine mechanical quantities describing position, motion, force, deformation, pressure, mass, flow and dynamic behaviour of physical systems."
 SEMANTIC_ROLE="Machine-readable semantics for mechanical measurands, sensors, transducers, measurement models, calibration, uncertainty, traceability and validation."
}
SCOPE {
 INCLUDE=[MechanicalMeasurement,MechanicalQuantity,Measurand,Measurement,MeasurementSystem,MeasurementMethod,MeasurementProcedure,MeasurementModel,MeasurementEquation,MeasurementResult,MeasurementUncertainty,Length,Displacement,Position,Distance,Velocity,Speed,Acceleration,JerkRelationship,AngularPositionRelationship,AngularVelocityRelationship,AngularAccelerationRelationship,RotationRelationship,Frequency,VibrationRelationship,OscillationRelationship,AmplitudeRelationship,PhaseRelationship,Force,Torque,MomentRelationship,Pressure,Stress,Strain,Mass,Weight,Density,Volume,FlowRelationship,MassFlowRelationship,VolumeFlowRelationship,Momentum,ImpulseRelationship,Energy,Work,Power,StiffnessRelationship,ComplianceRelationship,DampingRelationship,FrictionRelationship,MechanicalImpedanceRelationship,LoadRelationship,StaticMeasurementRelationship,DynamicMeasurementRelationship,QuasiStaticMeasurementRelationship,DirectMeasurementRelationship,IndirectMeasurementRelationship,ContactMeasurementRelationship,NonContactMeasurementRelationship,SensorRelationship,TransducerRelationship,LoadCellRelationship,StrainGaugeRelationship,AccelerometerRelationship,VelocitySensorRelationship,DisplacementSensorRelationship,LVDTRelationship,PotentiometricSensorRelationship,CapacitiveSensorRelationship,InductiveSensorRelationship,EddyCurrentSensorRelationship,LaserDisplacementSensorRelationship,OpticalEncoderRelationship,RotaryEncoderRelationship,TachometerRelationship,GyroscopeRelationship,InertialMeasurementUnitRelationship,IMURelationship,ForceTransducerRelationship,TorqueTransducerRelationship,PressureTransducerRelationship,PressureGaugeRelationship,ManometerRelationship,BarometerRelationship,VacuumGaugeRelationship,FlowMeterRelationship,OrificePlateRelationship,VenturiRelationship,TurbineFlowMeterRelationship,CoriolisFlowMeterRelationship,UltrasonicFlowMeterRelationship,MassBalanceRelationship,WeighingRelationship,BalanceRelationship,CoordinateMeasuringMachineRelationship,CalliperRelationship,MicrometerRelationship,DialIndicatorRelationship,ExtensometerRelationship,ProfilometerRelationship,VibrometerRelationship,LaserDopplerVibrometerRelationship,DataAcquisitionRelationship,SignalConditioningRelationship,AmplifierRelationship,BridgeCircuitRelationship,WheatstoneBridgeRelationship,FilteringRelationship,SamplingRelationship,SamplingRateRelationship,AliasingRelationship,QuantisationRelationship,Resolution,Accuracy,Precision,Repeatability,Reproducibility,Sensitivity,Linearity,HysteresisRelationship,DeadBandRelationship,ThresholdRelationship,RangeRelationship,SpanRelationship,ZeroOffsetRelationship,DriftRelationship,StabilityRelationship,ResponseTimeRelationship,BandwidthRelationship,FrequencyResponseRelationship,ResonanceRelationship,CrossSensitivityRelationship,LoadingEffectRelationship,EnvironmentalInfluenceRelationship,TemperatureInfluence,VibrationInfluenceRelationship,AlignmentRelationship,CosineErrorRelationship,AbbeErrorRelationship,ParallaxRelationship,Calibration,MechanicalCalibrationRelationship,ForceCalibrationRelationship,TorqueCalibrationRelationship,PressureCalibrationRelationship,AccelerationCalibrationRelationship,DimensionalCalibrationRelationship,FlowCalibrationRelationship,ReferenceStandard,PrimaryStandard,SecondaryStandard,WorkingStandard,ReferenceMaterialRelationship,MeasurementTraceability,MetrologicalTraceability,TraceabilityChain,Metrology,MechanicalMetrologyRelationship,DimensionalMetrologyRelationship,MassMetrologyRelationship,PressureMetrologyRelationship,ForceMetrologyRelationship,UncertaintyBudgetRelationship,StandardUncertainty,CombinedStandardUncertainty,ExpandedUncertainty,CoverageFactor,UncertaintyPropagation,CorrelationRelationship,CovarianceRelationship,SystematicEffectRelationship,RandomEffectRelationship,MeasurementError,BiasRelationship,CorrectionRelationship,Verification,Validation,MeasurementValidationRelationship,SensorValidationRelationship,ModelValidationRelationship,ErrorAnalysis,Provenance,MeasurementProvenance,CalibrationProvenance,SensorProvenanceRelationship,ReferenceStandardProvenance,BIPMrelationship,SIbrochureRelationship,VIMRelationship,GUMRelationship]
 EXCLUDE_AS_PRIMARY=[ElectricalMeasurementWhenElectricalQuantityIsPrimary,ThermalMeasurementWhenTemperatureOrHeatIsPrimary,OpticalMeasurementWhenOpticalQuantityIsPrimary,ChemicalMeasurementWhenChemicalCompositionIsPrimary]
 DISAMBIGUATION_RULE="Interpret mechanical measurements as measurements whose primary measurand is mechanical or geometrical. Preserve distinctions among quantity, sensor output, indication, calibrated result, unit, uncertainty and inferred mechanical property."
}
CORE_CONCEPTS {
 MechanicalMeasurement="Measurement process whose primary measurand is a mechanical quantity."
 MechanicalQuantity="Quantity describing geometry, motion, force, deformation, pressure, mass, flow or mechanical energy behaviour."
 SensorRelationship="Device relationship converting a mechanical input into an observable signal."
 TransducerRelationship="Transformation relationship between input and output quantities used in measurement."
 Calibration="Operation establishing relationships between standards and instrument indications or values."
 MeasurementUncertainty="Non-negative parameter characterising dispersion of quantity values attributed to a measurand."
 MeasurementTraceability="Property linking a result to a reference through a documented unbroken calibration chain."
}
MEASURAND_FAMILIES {
 GEOMETRIC=[Length,Distance,Position,Displacement,Angle,SurfaceProfile,Thickness,Diameter]
 KINEMATIC=[Velocity,Speed,Acceleration,AngularVelocity,AngularAcceleration,Frequency]
 DYNAMIC=[Force,Torque,Momentum,Impulse,Power,Vibration]
 DEFORMATION=[Stress,Strain,Stiffness,Compliance,Deflection]
 FLUID_MECHANICAL=[Pressure,VolumeFlow,MassFlow,Density]
 MASS_PROPERTIES=[Mass,Weight,CentreOfMassRelationship,MomentOfInertiaRelationship]
}
RELATIONS {
 MechanicalMeasurement--targets-->MechanicalQuantity
 Measurement--targets-->Measurand
 MeasurementSystem--contains-->SensorRelationship
 SensorRelationship--produces-->MeasurementSignal
 Calibration--establishes-->IndicationReferenceRelationship
 MeasurementResult--has_associated-->MeasurementUncertainty
 MeasurementTraceability--links-->MeasurementResultToReferenceStandard
 Force--relates_to-->MassAndAcceleration
 Torque--relates_to-->ForceAndLeverArm
 Stress--relates_to-->ForceAndArea
 Strain--relates_to-->ChangeInLengthAndReferenceLength
 Pressure--relates_to-->NormalForceAndArea
 Velocity--relates_to-->DisplacementAndTime
 Acceleration--relates_to-->VelocityChangeAndTime
}
OPERATORS {
 VELOCITY(displacement,time):=displacement/time
 ACCELERATION(delta_velocity,time):=delta_velocity/time
 FORCE(mass,acceleration):=mass*acceleration
 TORQUE(force,lever_arm,angle):=force*lever_arm*sin(angle)
 PRESSURE(force,area):=force/area
 STRESS(force,area):=force/area
 ENGINEERING_STRAIN(delta_length,reference_length):=delta_length/reference_length
 POWER(work,time):=work/time
 MASS_FLOW(mass,time):=mass/time
 VOLUME_FLOW(volume,time):=volume/time
 CALIBRATED_VALUE(indication,calibration_model):=apply_calibration(indication,calibration_model)
 PROPAGATE_UNCERTAINTY(model,inputs):=uncertainty_propagation(model,inputs)
 TRACE(result):=metrological_traceability_chain(result)
}
AXIOMS {
 A1="A mechanical measurand must be identified before a measurement result is interpreted."
 A2="A sensor indication is not automatically equal to the measurand value."
 A3="Measurement results require units and uncertainty where quantitatively meaningful."
 A4="Static and dynamic measurements can require different sensor and calibration models."
 A5="Force, torque, pressure, stress and strain are distinct quantity kinds."
 A6="Mass and weight are distinct; weight is a force."
 A7="Sensor loading can alter the system being measured."
 A8="Bandwidth and frequency response are material for dynamic mechanical measurements."
 A9="Calibration does not eliminate measurement uncertainty."
 A10="Metrological traceability requires a documented chain to stated references."
}
REASONING {
 R1=identify(measurand,quantity_kind,expected_range,dynamics,environment,required_uncertainty)
 R2=select_direct_or_indirect_measurement_model)
 R3=select_sensor_transducer_instrument_and_data_acquisition_chain)
 R4=verify_units_dimensions_and_quantity_equation)
 R5=evaluate_range_sensitivity_resolution_linearity_hysteresis_loading_and_bandwidth)
 R6=identify_reference_standard_and_calibration_model)
 R7=apply_zero_scale_alignment_temperature_dynamic_and_other_corrections)
 R8=evaluate_random_systematic_environmental_sampling_and_model_uncertainties)
 R9=validate_result_against_physical_constraints_references_and_repeat_measurements)
 R10=record_method_instrument_calibration_uncertainty_traceability_and_provenance)
}
CONSTRAINTS {
 C1="Mechanical quantity kinds must remain semantically distinct even when dimensions coincide."
 C2="Static calibration must not automatically be assumed valid for dynamic response."
 C3="Instrument range must encompass the expected measurand without unacceptable overload or saturation."
 C4="Sampling rate and bandwidth must be sufficient for the mechanical dynamics being measured."
 C5="Sensor mass, stiffness, contact force or mounting can introduce loading effects."
 C6="Alignment errors can create cross-axis or cosine errors."
 C7="Temperature and environment can affect sensor response, dimensions and material properties."
 C8="Resolution alone does not determine total measurement uncertainty."
 C9="Derived mechanical results inherit uncertainty from all significant input quantities and model parameters."
 C10="Traceability claims require documented reference standards, calibration history and uncertainty."
}
VALIDATION {
 V1="Measurand and quantity kind are explicit."
 V2="Units and dimensional equations are consistent."
 V3="Instrument range, sensitivity and resolution are appropriate."
 V4="Dynamic measurements satisfy bandwidth and sampling requirements."
 V5="Calibration status and reference standards are identified."
 V6="Loading, alignment and environmental effects are considered where material."
 V7="Corrections are documented and applied consistently."
 V8="Uncertainty propagation reflects the measurement model."
 V9="Result validation includes physical, repeatability or reference checks."
 V10="Traceability and provenance records are retained."
}
CONFIDENCE {
 BASE_CONFIDENCE=0.99
 MEASURAND_IDENTIFICATION=0.99
 DIMENSIONAL_REASONING=0.99
 SENSOR_SELECTION_REASONING=0.98
 DYNAMIC_MEASUREMENT_REASONING=0.98
 CALIBRATION_REASONING=0.99
 UNCERTAINTY_REASONING=0.98
 TRACEABILITY_REASONING=0.99
 POLICY="Reduce confidence when measurand, range, dynamic behaviour, sensor configuration, calibration, environmental conditions or uncertainty model are underspecified."
}
AI_CONSUMPTION {
 PURPOSES=[SemanticSearch,OntologyGrounding,MechanicalMeasurementReasoning,MeasurandReasoning,SensorReasoning,TransducerReasoning,DimensionalReasoning,ForceReasoning,TorqueReasoning,PressureReasoning,StressStrainReasoning,MotionReasoning,VibrationReasoning,FlowReasoning,CalibrationReasoning,UncertaintyReasoning,TraceabilityReasoning,VerificationValidation,KnowledgeGraphConstruction,RecursiveInference]
}
EXECUTION_RULES {
 E1="Activate MechanicalMeasurements when the primary measurand is mechanical or geometrical."
 E2="Identify quantity kind, range, dynamics, environment and uncertainty requirement."
 E3="Choose measurement principle and sensor according to measurand and dynamic behaviour."
 E4="Validate dimensional and unit consistency before numerical interpretation."
 E5="Evaluate range, resolution, sensitivity, linearity, hysteresis, loading and bandwidth."
 E6="Apply calibration and correction models with retained provenance."
 E7="Propagate significant uncertainty sources through the measurement model."
 E8="Validate results against physical constraints, standards or independent measurements."
 E9="Record instrument, method, calibration, uncertainty, traceability and provenance."
}
RECURSION {
 ENTRY=MechanicalMeasurements
 EXPAND(MechanicalMeasurements)->[Length,Displacement,Velocity,Acceleration,Force,Torque,Pressure,Stress,Strain,Mass,Density,FlowRelationship,VibrationRelationship,Frequency,Power,SensorRelationship,TransducerRelationship,LoadCellRelationship,StrainGaugeRelationship,AccelerometerRelationship,LVDTRelationship,OpticalEncoderRelationship,TachometerRelationship,PressureTransducerRelationship,FlowMeterRelationship,CoordinateMeasuringMachineRelationship,ExtensometerRelationship,VibrometerRelationship,DataAcquisitionRelationship,SignalConditioningRelationship,SamplingRelationship,BandwidthRelationship,Calibration,ReferenceStandard,MeasurementUncertainty,MeasurementTraceability,MechanicalMetrologyRelationship,Verification,Validation,MeasurementProvenance]
 EXPAND(MeasurementFamilies)->[DimensionalAndDisplacementMeasurement,VelocityAccelerationAndRotationalMeasurement,ForceTorqueAndLoadMeasurement,PressureStressStrainAndDeformationMeasurement,MassDensityAndFlowMeasurement,VibrationFrequencyAndDynamicMeasurement,SensorsTransducersSignalConditioningAndDataAcquisition,CalibrationUncertaintyTraceabilityValidationAndProvenance]
 STOP_CONDITION="Stop when measurand, measurement model, sensor chain, calibration, uncertainty, validation and provenance are resolved."
}
ROUTING {
 PARENT_ONTOLOGY="Measurement & Units Ontologies"
 RELATED_ONTOLOGIES=["Fundamental Physical Quantities","Measurement Ontology","Scientific Measurement Ontology 2","Metrology Ontology","Quantity Ontology","Physical Quantity Ontology","Dimension Ontology 2","Unit Ontology","Reference Standard Ontology","SI Base Units","SI Derived Units","Physics Ontology","Mechanics Ontology","Materials Science Ontology","Verification & Validation"]
 ROUTE_RULES=[
  "Mechanical Measurements -> Fundamental Physical Quantities for base-quantity semantics",
  "Mechanical Measurements -> SI Derived Units for force, pressure, energy and power units",
  "Mechanical Measurements -> Mechanics Ontology for physical models and equations",
  "Mechanical Measurements -> Materials Science for stress, strain and material-response semantics",
  "Mechanical Measurements -> Measurement and Metrology for calibration and traceability",
  "Mechanical Measurements -> Verification & Validation for measurement-model and result checks"
 ]
}
UPDATE_MODEL {
 MODE="append-compatible semantic versioning"
 MAJOR="ontology-breaking conceptual change"
 MINOR="new compatible mechanical quantity, sensor, measurement or calibration relationships"
 PATCH="clarification, metadata or formatting correction"
 RULES=["Preserve measurand-versus-indication distinction.","Preserve quantity-kind distinctions.","Preserve static-versus-dynamic measurement semantics.","Preserve sensor-loading semantics.","Preserve calibration-versus-correction distinction.","Preserve uncertainty-versus-error distinction.","Preserve traceability and provenance.","Preserve machine-readable mechanical-measurement semantics."]
}
OUTPUT {
 CANONICAL_DEFINITION="Mechanical measurements determine mechanical and geometrical quantities using defined measurement models, instruments, calibration and uncertainty evaluation."
 QUANTITY_SUMMARY="Core measurands include displacement, motion, force, torque, pressure, stress, strain, mass, density, flow and vibration."
 SENSOR_SUMMARY="Mechanical measurements use transducers such as load cells, strain gauges, accelerometers, displacement sensors, pressure sensors, flow meters and optical systems."
 DYNAMIC_SUMMARY="Dynamic measurements require explicit bandwidth, frequency-response, sampling and phase semantics."
 METROLOGY_SUMMARY="Reliable results require calibration, uncertainty budgets, validation, metrological traceability and provenance."
}
FLOW {
 INPUT
 -> detect_mechanical_measurement_context
 -> identify_measurand_quantity_kind_range_dynamics_environment_and_required_uncertainty
 -> choose_direct_or_indirect_measurement_model
 -> select_sensor_transducer_instrument_and_data_acquisition_chain
 -> verify_units_dimensions_and_quantity_equation
 -> evaluate_range_sensitivity_resolution_linearity_hysteresis_loading_and_bandwidth
 -> identify_reference_standard_and_calibration_model
 -> apply_required_corrections
 -> evaluate_and_propagate_measurement_uncertainty
 -> validate_result_against_physical_constraints_references_and_repeat_measurements
 -> record_method_instrument_calibration_uncertainty_traceability_and_provenance
 -> route_to_related_ontologies
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}
FLOW_HASH {
 METHOD="semantic-content-identity"
 ID="KIRETH-MATH-MEASUREMENT-UNITS-MECHANICAL-MEASUREMENTS-V1"
}
}
END_FLOW