Test Correlation Skill

Purpose

The Test Correlation skill provides capabilities for correlating test results with analytical predictions, enabling model validation, calibration, and uncertainty quantification for mechanical systems.

Capabilities

• Test data processing and analysis
• Prediction-to-test comparison
• Model calibration techniques
• Uncertainty quantification
• Statistical analysis and regression
• Correlation report generation
• Model updating recommendations
• Validation criteria assessment

Usage Guidelines

Correlation Methodology

Data Processing

1. Test Data Preparation

   Data quality checks:
   - Missing data handling
   - Outlier detection
   - Noise filtering
   - Time synchronization
   - Unit verification
   

2. Signal Processing

   Operation	Purpose	Method
   Low-pass filter	Remove noise	Butterworth
   Resampling	Match analysis	Interpolation
   Baseline correction	Remove offset	Linear/polynomial
   Windowing	FFT preparation	Hanning, Hamming

3. Derived Quantities

   • Integrate acceleration to velocity/displacement
   • Differentiate displacement to velocity
   • Calculate strain from displacement
   • Compute stress from strain

Prediction Extraction

1. Analysis Results

   • Match output locations to sensor positions
   • Match load cases to test conditions
   • Account for coordinate systems
   • Include analysis uncertainty

2. Interpolation

   For locations between nodes:
   - Shape function interpolation
   - Nearest node approximation
   - Surface interpolation (for contours)
   

Comparison Methods

Point Comparison

Percent difference:
%diff = (Test - Analysis) / Test * 100

For near-zero values:
%diff = (Test - Analysis) / max(|Test|, |Analysis|) * 100

Absolute difference:
delta = Test - Analysis

Statistical Comparison

Metric	Formula	Purpose
Mean error	mean(Test - Analysis)	Bias detection
RMS error	sqrt(mean((Test-Analysis)^2))	Overall accuracy
Correlation coefficient	r	Linear relationship
R-squared	r^2	Variance explained

Modal Correlation

1. Frequency Comparison

   Frequency error:
   %error = (f_test - f_analysis) / f_test * 100
   
   Typical acceptance: +/- 5-10%
   

2. Mode Shape Correlation

   MAC (Modal Assurance Criterion):
   MAC = |{phi_test}^T {phi_analysis}|^2 /
         ({phi_test}^T{phi_test})({phi_analysis}^T{phi_analysis})
   
   MAC = 1: Perfect correlation
   MAC > 0.9: Good correlation
   MAC > 0.7: Acceptable correlation
   

3. Cross-Orthogonality

   XOR = {phi_test}^T [M] {phi_analysis}
   
   XOR_ii > 0.9: Good correlation
   XOR_ij < 0.1: Mode independence
   

Model Calibration

Parameter Identification

1. Sensitivity Analysis

   • Identify influential parameters
   • Rank by sensitivity
   • Define adjustment ranges

2. Optimization Methods

   Method	Application	Pros/Cons
   Manual iteration	Simple cases	Intuitive, slow
   Gradient-based	Smooth response	Fast, local minimum
   Genetic algorithm	Complex response	Global, slow
   Response surface	Multiple cases	Efficient, approximation

Common Calibration Parameters

Parameter	Structural	Thermal	CFD
Stiffness	Young's modulus	Conductivity	-
Boundary	Joint stiffness	HTC	Inlet profile
Damping	Modal damping	-	Turbulence
Mass	Density	Cp	Density
Geometry	Thickness	Contact area	Mesh

Validation Criteria

Acceptance Criteria

Typical validation targets:
- Displacement: +/- 10%
- Stress: +/- 15%
- Natural frequency: +/- 5%
- MAC: > 0.9
- Temperature: +/- 5 degrees
- Pressure: +/- 10%

Validation Levels

Level	Evidence	Application
1	Qualitative trends match	Preliminary design
2	Quantitative agreement	Detailed design
3	Statistical validation	Certification
4	Prediction capability	Production release

Uncertainty Quantification

Sources of Uncertainty

1. Test Uncertainty

   • Instrumentation accuracy
   • Environmental variation
   • Setup variability
   • Measurement resolution

2. Model Uncertainty

   • Material property variability
   • Geometry simplifications
   • Boundary condition approximations
   • Discretization error

Combined Uncertainty

u_combined = sqrt(u_test^2 + u_model^2)

Overlap criteria:
If |Test - Analysis| < 2 * u_combined:
  Results are statistically consistent

Process Integration

• ME-022: Prototype Testing and Correlation

Input Schema

{
  "test_data": {
    "file_path": "string",
    "format": "csv|mat|hdf5",
    "channels": "array of channel IDs"
  },
  "analysis_results": {
    "file_path": "string",
    "software": "ANSYS|NASTRAN|Abaqus|other",
    "output_locations": "array"
  },
  "comparison_type": "static|modal|transient|steady_state",
  "correlation_requirements": {
    "metrics": "array",
    "acceptance_criteria": "object"
  }
}

Output Schema

{
  "correlation_results": {
    "comparison_table": "array of point comparisons",
    "statistical_metrics": {
      "mean_error": "number",
      "rms_error": "number",
      "max_error": "number",
      "correlation_coefficient": "number"
    },
    "modal_metrics": {
      "frequency_errors": "array",
      "mac_matrix": "2D array"
    }
  },
  "validation_status": {
    "overall": "pass|fail|conditional",
    "by_criterion": "array"
  },
  "calibration_recommendations": [
    {
      "parameter": "string",
      "current_value": "number",
      "recommended_value": "number",
      "sensitivity": "number"
    }
  ],
  "uncertainty_analysis": {
    "test_uncertainty": "number",
    "model_uncertainty": "number",
    "combined": "number"
  }
}

Best Practices

1. Process test data before comparison
2. Match locations and coordinates carefully
3. Account for all sources of uncertainty
4. Document calibration changes
5. Validate across multiple load cases
6. Report both agreements and discrepancies

Integration Points

• Connects with FEA Structural for model results
• Feeds into Design Review for validation evidence
• Supports Test Planning for requirements
• Integrates with Requirements Flowdown for verification