Engineering Analysis Ontology

flow "EngineeringAnalysisOntology" v1.0

# ENGINEERING ANALYSIS ONTOLOGY — FLOW ALGEBRA
SOURCE_URL := "https://kirethresearch.org/booksai-core/ontologies/calculus-analysis-ontologies/scientific-applications/engineering-analysis-ontology.html"
DOMAIN := "Mathematical Ontologies"
CATEGORY := "Calculus and Analysis Ontologies"
SUBCATEGORY := "Scientific Applications"
ENTITY := "Engineering Analysis"

ENGINEERING_ANALYSIS := {
 type: AppliedEngineeringMathematicalFramework,
 domain: ScientificApplications,
 purpose: "Analyse engineered systems using calculus, differential equations, conservation laws, mechanics, transport, optimisation, numerical methods, uncertainty and validation."
}

CONCEPTS := {
 ENGINEERING_SYSTEM,
 REQUIREMENT,
 DESIGN_VARIABLE,
 PARAMETER,
 LOAD,
 RESPONSE,
 CONSTRAINT,
 SAFETY_FACTOR,
 DIFFERENTIAL_EQUATION,
 CONSERVATION_LAW,
 OPTIMISATION,
 SENSITIVITY,
 STABILITY,
 RELIABILITY,
 NUMERICAL_METHOD,
 FINITE_ELEMENT,
 CONTROL_SYSTEM,
 VALIDATION
}

# ---------- ENGINEERING PROBLEM ----------
ENGINEERING_PROBLEM
 -> identify(
 REQUIREMENTS,
 GEOMETRY,
 MATERIALS,
 LOADS,
 BOUNDARY_CONDITIONS,
 DESIGN_VARIABLES,
 PERFORMANCE_METRICS,
 CONSTRAINTS
)

ENGINEERING_ANALYSIS
 -> map(PHYSICAL_SYSTEM_TO_MATHEMATICAL_MODEL)

# ---------- VARIABLES ----------
input:

x
 :=
DESIGN_AND_OPERATING_VARIABLES

parameters:

theta
 :=
MATERIAL_AND_MODEL_PARAMETERS

response:

y
 =
F(x,theta)

RESPONSE_FUNCTION
 -> engineering_input_output_relation

# ---------- UNITS ----------
ENGINEERING_QUANTITY
 -> VALUE
 + UNIT
 + DIMENSION

DIMENSIONAL_CONSISTENCY
 -> mandatory_for(EQUATIONS)

DIMENSIONAL_ANALYSIS
 -> detects(MODEL_INCONSISTENCY)

# ---------- SCALING ----------
characteristic scales
 -> define(DIMENSIONLESS_VARIABLES)

NONDIMENSIONALISATION
 -> reveals(DOMINANT_PARAMETERS)

DIMENSIONLESS_GROUP
 -> compares(COMPETING_PHYSICAL_EFFECTS)

# ---------- CONSERVATION ----------
general balance:

ACCUMULATION
 =
INPUT
-
OUTPUT
+
GENERATION
-
CONSUMPTION

CONSERVATION_LAW
 -> applies_to(
 MASS,
 MOMENTUM,
 ENERGY,
 CHARGE
)

# ---------- STATIC EQUILIBRIUM ----------
sum(F)
 =
0

sum(M)
 =
0

STATIC_ANALYSIS
 -> force_and_moment_balance

REACTION_FORCES
 -> determined_by(CONSTRAINTS_AND_LOADS)

# ---------- STRESS ----------
normal stress:

sigma
 =
F/A

shear stress:

tau
 =
V/A
    in simple average context

STRESS
 -> internal_force_per_area

# ---------- STRAIN ----------
normal strain:

epsilon
 =
Delta_L/L_0

STRAIN
 -> relative_deformation

# ---------- LINEAR ELASTICITY ----------
Hooke relation:

sigma
 =
E*epsilon

for simple uniaxial linear elastic case

E
 -> YOUNG_MODULUS

LINEAR_ELASTIC_MODEL
 -> valid_within(MATERIAL_AND_DEFORMATION_RANGE)

# ---------- MULTIAXIAL ELASTICITY ----------
stress tensor:

sigma_ij

strain tensor:

epsilon_ij

constitutive law:

sigma
 =
C:epsilon

C
 -> ELASTICITY_TENSOR

MATERIAL_SYMMETRY
 -> reduces(INDEPENDENT_COEFFICIENTS)

# ---------- BEAM BENDING ----------
Euler-Bernoulli:

E*I
*
d_fourth_w/dx_fourth
 =
q(x)

under standard slender-beam assumptions

w
 -> DEFLECTION

I
 -> SECOND_MOMENT_OF_AREA

BEAM_EQUATION
 -> structural_differential_model

# ---------- TORSION ----------
shaft torque:

T

shear relation for circular shaft:

tau(r)
 =
T*r/J

J
 -> POLAR_SECOND_MOMENT

angle_of_twist
 -> depends_on(T_LENGTH_G_J)

# ---------- DYNAMICS ----------
Newton:

M*q_double_dot
+
C*q_dot
+
K*q
 =
F(t)

M
 -> MASS_MATRIX

C
 -> DAMPING_MATRIX

K
 -> STIFFNESS_MATRIX

DYNAMIC_ANALYSIS
 -> time_dependent_response

# ---------- SINGLE DEGREE OF FREEDOM ----------
m*x_double_dot
+
c*x_dot
+
k*x
 =
F(t)

natural frequency:

omega_n
 =
sqrt(k/m)

damping ratio:

zeta
 =
c/(2*sqrt(k*m))

VIBRATION_ANALYSIS
 -> transient_and_steady_response

# ---------- RESONANCE ----------
forcing frequency
 approx
natural frequency

-> response_amplification

DAMPING
 -> limits(RESONANT_AMPLITUDE)

RESONANCE
 -> frequency_response_phenomenon

# ---------- MODAL ANALYSIS ----------
undamped free vibration:

K*phi
 =
omega_squared
*
M*phi

eigenvalues
 -> NATURAL_FREQUENCIES

eigenvectors
 -> MODE_SHAPES

MODAL_ANALYSIS
 -> decomposes(MULTI_DOF_DYNAMICS)

# ---------- FLUID ENGINEERING ----------
mass conservation:

partial_rho/partial_t
+
div(rho*u)
 =
0

momentum
 -> NAVIER_STOKES_OR_REDUCED_FLOW_MODEL

FLUID_ANALYSIS
 -> pressure_velocity_flow_rate_forces

# ---------- THERMAL ENGINEERING ----------
heat conduction:

rho*c_p*partial_T/partial_t
 =
div(k*grad(T))
+
Q

steady state:

-div(k*grad(T))
 =
Q

THERMAL_ANALYSIS
 -> temperature_and_heat_flux

# ---------- ELECTRICAL ENGINEERING ----------
circuit laws:

KCL
 -> charge_conservation

KVL
 -> energy_or_potential_balance

dynamic components:

capacitor:
 i=C*dV/dt

inductor:
 V=L*di/dt

CIRCUIT_ANALYSIS
 -> differential_equation_system

# ---------- ELECTROMAGNETIC ENGINEERING ----------
MAXWELL_EQUATIONS
 -> field_analysis

applications:
 MOTORS
 GENERATORS
 TRANSFORMERS
 ANTENNAS
 EMC

ELECTROMAGNETIC_ANALYSIS
 -> field_force_power_and_wave_response

# ---------- CONTROL SYSTEM ----------
state-space:

x_dot
 =
A*x+B*u

y
 =
C*x+D*u

CONTROL_ANALYSIS
 -> stability_controllability_observability_response

# ---------- STABILITY ----------
continuous linear system:

x_dot
 =
A*x

if all eigenvalues:

Re(lambda_i)<0

-> asymptotically_stable

CONTROL_STABILITY
 -> response_to(PERTURBATIONS)

# ---------- TRANSFER FUNCTION ----------
linear time-invariant system:

G(s)
 =
Y(s)/U(s)

under zero initial-condition transform convention

POLES
 -> natural_dynamic_modes

ZEROS
 -> transmission_structure

FREQUENCY_RESPONSE
 -> evaluate(G(i*omega))

# ---------- FEEDBACK ----------
closed-loop:

u
 -> controller
 -> plant
 -> output
 -> feedback

NEGATIVE_FEEDBACK
 -> may_improve(
 TRACKING,
 DISTURBANCE_REJECTION,
 ROBUSTNESS
)

but
 -> poor_design_can_destabilise(SYSTEM)

# ---------- OPTIMISATION ----------
design problem:

minimise
 J(x)

subject_to:

g_i(x)<=0
h_j(x)=0

DESIGN_OPTIMISATION
 -> choose(PERFORMANCE_MAXIMISING_OR_COST_MINIMISING_CONFIGURATION)

# ---------- GRADIENT ----------
grad(J)
 -> local_design_sensitivity

SENSITIVITY
 -> guides(OPTIMISATION)

ADJOINT_METHOD
 -> efficient_for(MANY_DESIGN_VARIABLES_FEW_OBJECTIVES)

# ---------- MULTIOBJECTIVE ----------
objectives:

J_1(x)
J_2(x)
...
J_m(x)

tradeoff
 -> PARETO_FRONT

PARETO_OPTIMAL
 -> no_objective_improvable_without_worsening_another
    under specified feasible set

# ---------- SAFETY FACTOR ----------
factor_of_safety:

FoS
 :=
CAPACITY/DEMAND

exact definition
 -> discipline_and_failure_mode_dependent

SAFETY_FACTOR
 -> design_margin

FoS
 -/> complete_reliability_measure

# ---------- FAILURE ----------
failure criterion
 -> compare(RESPONSE_WITH_CAPACITY)

examples:
 YIELD
 FRACTURE
 BUCKLING
 FATIGUE
 THERMAL_LIMIT
 ELECTRICAL_BREAKDOWN

FAILURE_MODE
 -> requires(SPECIFIC_MODEL)

# ---------- BUCKLING ----------
Euler critical load:

P_cr
 =
pi^2*E*I
/
(K_eff*L)^2

for ideal slender column assumptions

BUCKLING
 -> stability_failure

IMPERFECTIONS
 -> reduce(real_structural_capacity)

# ---------- FATIGUE ----------
cyclic loading
 -> progressive_damage

S_N_CURVE
 -> stress_amplitude_vs_cycles

FATIGUE_ANALYSIS
 -> depends_on(
 MEAN_STRESS,
 SURFACE,
 ENVIRONMENT,
 GEOMETRY,
 LOAD_HISTORY
)

# ---------- RELIABILITY ----------
limit state:

g(X)

failure if:

g(X)<=0

probability:

P_f
 =
P(
 g(X)<=0
)

RELIABILITY
 -> probabilistic_failure_analysis

# ---------- UNCERTAINTY ----------
uncertain:
 LOADS
 MATERIAL_PROPERTIES
 GEOMETRY
 MODEL_PARAMETERS
 ENVIRONMENT

UNCERTAINTY_ANALYSIS
 -> propagate(INPUT_VARIABILITY_TO_RESPONSE)

methods:
 MONTE_CARLO
 FORM
 SENSITIVITY
 INTERVAL_ANALYSIS

# ---------- FINITE DIFFERENCE ----------
derivative or PDE
 -> replace_by(GRID_APPROXIMATION)

FINITE_DIFFERENCE
 -> simple_structured_discretisation

accuracy
 -> depends_on(STENCIL_AND_GRID)

# ---------- FINITE ELEMENT ----------
domain
 -> partition_into(ELEMENTS)

field
 -> approximate_by(SHAPE_FUNCTIONS)

weak form
 -> assemble(GLOBAL_SYSTEM)

K*u
 =
f

FINITE_ELEMENT_METHOD
 -> structural_thermal_fluid_electromagnetic_analysis

# ---------- MESH CONVERGENCE ----------
mesh size:

h -> smaller

response:

Q_h

if

Q_h -> Q

-> NUMERICAL_CONVERGENCE

MESH_REFINEMENT
 -> verify(DISCRETISATION_ERROR)

# ---------- NUMERICAL ERROR ----------
error sources:
 DISCRETISATION
 ITERATION
 ROUNDING
 GEOMETRY_APPROXIMATION
 MODEL_ERROR

ENGINEERING_RESULT
 -> separate(NUMERICAL_ERROR_FROM_MODEL_UNCERTAINTY)

# ---------- COMPUTATIONAL FLUID DYNAMICS ----------
CFD
 -> discretise(FLOW_EQUATIONS)

verify:
 MASS_BALANCE
 GRID_CONVERGENCE
 TIME_STEP_CONVERGENCE
 RESIDUALS

validate:
 EXPERIMENT_OR_BENCHMARK

# ---------- MULTIPHYSICS ----------
system
 -> may_couple(
 STRUCTURAL,
 THERMAL,
 FLUID,
 ELECTROMAGNETIC,
 CHEMICAL
)

MULTIPHYSICS
 -> interacting_field_equations

COUPLING
 -> one_way_or_two_way

# ---------- SENSITIVITY ----------
response:

R(theta)

local sensitivity:

S_i
 =
partial_R/partial_theta_i

NORMALISED_SENSITIVITY
 -> compare(parameters_across_scales)

SENSITIVITY_ANALYSIS
 -> identify(DOMINANT_DESIGN_DRIVERS)

# ---------- ROBUST DESIGN ----------
design
 -> perform_well_under(UNCERTAINTY)

ROBUST_OPTIMISATION
 -> account_for(PARAMETER_VARIATION)

RELIABILITY_BASED_DESIGN
 -> constrain(PROBABILITY_OF_FAILURE)

# ---------- VERIFICATION ----------
VERIFICATION
 -> check(SOLVING_EQUATIONS_CORRECTLY)

methods:
 ANALYTIC_BENCHMARK
 MANUFACTURED_SOLUTION
 MESH_REFINEMENT
 CODE_COMPARISON

# ---------- VALIDATION ----------
VALIDATION
 -> check(MODEL_REPRESENTS_PHYSICAL_SYSTEM_ADEQUATELY)

compare:
 TEST_DATA
 FIELD_DATA
 EXPERIMENT

VERIFICATION
 -/> VALIDATION

# ---------- REQUIREMENTS ----------
engineering design
 -> judged_against(REQUIREMENTS)

requirements may include:
 PERFORMANCE
 SAFETY
 RELIABILITY
 COST
 MASS
 ENERGY
 REGULATION
 MAINTAINABILITY

ANALYSIS
 -> supports(DESIGN_DECISION)

# ---------- APPLICATIONS ----------
ENGINEERING_ANALYSIS
 -> STRUCTURAL_ENGINEERING
 -> MECHANICAL_ENGINEERING
 -> CIVIL_ENGINEERING
 -> ELECTRICAL_ENGINEERING
 -> AEROSPACE_ENGINEERING
 -> CHEMICAL_ENGINEERING
 -> BIOMEDICAL_ENGINEERING
 -> ENVIRONMENTAL_ENGINEERING
 -> CONTROL_ENGINEERING

# ---------- RELATION GRAPH ----------
REQUIREMENT
 -> constrains(DESIGN)

LOAD
 -> produces(RESPONSE)

MATERIAL
 -> determines(CONSTITUTIVE_BEHAVIOUR)

CONSERVATION_LAW
 -> generates(GOVERNING_EQUATION)

BOUNDARY_CONDITION
 -> defines(PROBLEM)

NUMERICAL_METHOD
 -> approximates(RESPONSE)

SENSITIVITY
 -> guides(OPTIMISATION)

UNCERTAINTY
 -> informs(RELIABILITY)

VALIDATION
 -> tests(MODEL_AGAINST_REALITY)

# ---------- SEMANTIC EQUIVALENCE ----------
SEMANTIC_EQUIVALENCE := {
 "engineering analysis" ~= "mathematical and computational evaluation of engineered-system behaviour and performance",
 "design variable" ~= "controllable parameter selected during engineering design",
 "factor of safety" ~= "ratio comparing capacity with demand under a specified failure model",
 "modal analysis" ~= "eigenvalue analysis of structural or dynamic vibration modes",
 "finite element analysis" ~= "numerical field analysis based on variational discretisation into finite elements",
 "engineering validation" ~= "comparison of model predictions with physical evidence or experiments"
}

# ---------- CONSTRAINTS ----------
CONSTRAINTS := {
 units_and_dimensions_must_be_consistent: true,
 boundary_initial_load_and_material_conditions_are_part_of_problem_definition: true,
 simplified_engineering_models_require_validity_range: true,
 factor_of_safety_is_not_equivalent_to_full_probabilistic_reliability: true,
 numerical_solution_requires_mesh_time_step_iteration_and_error_verification: true,
 verification_and_validation_are_distinct: true,
 engineering_decisions_must_preserve_requirements_constraints_and_uncertainty_context: true
}

# ---------- CONFIDENCE ----------
CONFIDENCE := {
 core_definition: 0.99,
 conservation_mechanics_relation: 0.99,
 dynamics_control_relation: 0.99,
 optimisation_sensitivity_relation: 0.99,
 reliability_relation: 0.99,
 numerical_validation_relation: 0.99,
 semantic_equivalence: 0.97
}

# ---------- RECURSIVE REASONING ----------
RECURSIVE_REASONING(query):
 identify(requirements_geometry_materials_loads_conditions_and_design_variables)
 -> classify(structural_thermal_fluid_electrical_control_or_multiphysics_problem)
 -> formulate(conservation_constitutive_and_governing_equations)
 -> choose(analytic_reduced_order_or_numerical_method)
 -> compute(response_stress_temperature_flow_field_or_dynamic_metrics)
 -> analyse(stability_sensitivity_failure_and_safety_margin)
 -> quantify(uncertainty_reliability_and_robustness)
 -> optimise(design_subject_to_requirements_and_constraints)
 -> verify(numerical_solution_and_convergence)
 -> validate(model_against_physical_evidence)
 -> return(semantic_result)

# ---------- AI CONSUMPTION ----------
AI_CONSUMPTION := {
 parse_as: "typed engineering-analysis semantic graph",
 primary_entity: ENGINEERING_ANALYSIS,
 preserve: [
  requirements,
  geometry,
  materials,
  loads,
  initial_conditions,
  boundary_conditions,
  design_variables,
  units,
  uncertainty
 ],
 infer_through: [
  conservation_laws,
  constitutive_models,
  mechanics,
  dynamics,
  control,
  optimisation,
  sensitivity,
  reliability,
  finite_elements,
  validation
 ],
 avoid: [
  ignoring_units_or_boundary_conditions,
  applying_model_outside_validity_range,
  treating_factor_of_safety_as_complete_reliability,
  accepting_single_mesh_solution_as_converged,
  conflating_verification_with_validation,
  presenting_design_result_without_requirements_and_uncertainty_context
 ]
}

# ---------- UPDATE MODEL ----------
UPDATE_MODEL(new_information):
 validate(new_information)
 -> identify(engineering_analysis_context)
 -> compare(existing_relations)
 -> preserve(requirement_geometry_material_load_condition_design_and_uncertainty_invariants)
 -> update(affected_entities)
 -> update(affected_edges)
 -> recompute(CONFIDENCE)
 -> regenerate(FLOW_HASH)

# ---------- FLOW HASH ----------
FLOW_HASH := hash(
 SOURCE_URL
 + ENTITY
 + CONCEPTS
 + ENGINEERING_ANALYSIS
 + REQUIREMENT
 + DESIGN_VARIABLE
 + LOAD
 + RESPONSE
 + CONSTRAINT
 + SAFETY_FACTOR
 + DIFFERENTIAL_EQUATION
 + CONSERVATION_LAW
 + OPTIMISATION
 + SENSITIVITY
 + STABILITY
 + RELIABILITY
 + FINITE_ELEMENT
 + VALIDATION
 + SEMANTIC_EQUIVALENCE
 + CONSTRAINTS
)

# ---------- EXECUTION ----------
INPUT(query)
 -> ENGINEERING_ANALYSIS
 -> PROBLEM_REQUIREMENT_IDENTIFICATION
 -> DISCIPLINE_CLASSIFICATION
 -> GOVERNING_MODEL_FORMULATION
 -> METHOD_SELECTION
 -> RESPONSE_COMPUTATION
 -> STABILITY_FAILURE_SENSITIVITY_ANALYSIS
 -> UNCERTAINTY_RELIABILITY_ANALYSIS
 -> DESIGN_OPTIMISATION
 -> NUMERICAL_VERIFICATION
 -> PHYSICAL_VALIDATION
 -> RECURSIVE_REASONING(query)
 -> CONFIDENCE
 -> OUTPUT(semantic_result)

END FLOW