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  Sensitivity Analysis Lab Kit: Sobol Indices Calculator + Case Dataset
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DEFINITION
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The Sensitivity Analysis Lab Kit: Sobol Indices Calculator + Case Dataset is a
modular, open-architecture resource designed to compute global sensitivity
measures—specifically first-order and total-order Sobol indices—for process
simulation models integrated into digital twin frameworks. It provides standardized
computational workflows, pre-validated case datasets, and interoperable interfaces
for model coupling (e.g., via FMU or REST APIs). The kit enables quantitative
attribution of output variance to individual input parameters and their interactions,
supporting robustness assessment and parameter prioritization in dynamic engineering
systems.

OVERVIEW
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Sobol sensitivity analysis is a variance-based global method that decomposes the
output variance of a computationally expensive model into contributions from
individual inputs and their higher-order interactions. Unlike local methods (e.g.,
derivatives), it operates over the full joint input distribution—typically uniform
or Gaussian—and yields dimensionless, normalized indices ranging from 0 to 1. The
lab kit implements efficient quasi-Monte Carlo sampling (e.g., Sobol sequences) and
leverages estimator algorithms (e.g., Saltelli’s extension) to compute both
first-order (Si) and total-order (STi) indices with reduced sample requirements and
improved convergence. The included case dataset comprises a curated set of benchmark
process simulation scenarios—such as a continuous stirred-tank reactor (CSTR) with
kinetic uncertainty, a distillation column with thermodynamic property variability,
and a battery thermal management digital twin—each accompanied by ground-truth
parameter distributions, reference outputs, and metadata describing model fidelity,
runtime constraints, and validation metrics. Integration is facilitated through
containerized Python modules (with NumPy/SciPy backend), JupyterLab notebooks for
pedagogical walkthroughs, and API wrappers compatible with Modelica-based simulators
and industrial digital twin platforms (e.g., Siemens XHQ, AspenTech DMC3). This
enables engineers and data scientists to rapidly assess parameter influence without
reimplementing core sensitivity logic, thereby accelerating model calibration,
uncertainty quantification, and digital twin trustworthiness evaluation.

KEY COMPONENTS
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1. Sobol Indices Computation Engine
2. Benchmark Process Simulation Case Dataset
3. Digital Twin Integration Interface (FMU/REST)

APPLICATIONS
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  - Prioritizing calibration efforts in chemical process digital twins
  - Identifying non-influential parameters for model reduction
  - Quantifying uncertainty propagation in real-time predictive maintenance systems

KEY FORMULAS
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First-Order Sobol Index (Si): S_i = \frac{\mathbb{V}_{X_i}[\mathbb{E}_{\mathbf{X}_{\sim i}}[Y \mid X_i]]}{\mathbb{V}[Y]}
  -> Measures the main (unconditional) effect of input Xi on output variance Y, accounting for all interactions involving Xi only through its marginal contribution.
Total-Order Sobol Index (STi): ST_i = \frac{\mathbb{E}_{\mathbf{X}_{\sim i}}[\mathbb{V}_{X_i}[Y \mid \mathbf{X}_{\sim i}]]}{\mathbb{V}[Y]}
  -> Captures the total contribution of input Xi—including all interaction effects with other inputs—to the output variance.
Variance Decomposition Identity: \mathbb{V}[Y] = \sum_i V_i + \sum_{i<j} V_{ij} + \cdots + V_{12\dots k}
  -> Expresses total output variance as sum of partial variances attributable to individual inputs and all possible interaction terms up to k-way.

RELATED CONCEPTS
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  - Global Sensitivity Analysis
  - Uncertainty Quantification
  - Digital Twin Validation

REFERENCES
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Global Sensitivity Indices for Nonlinear Mathematical Models and Their Monte Carlo Estimates (https://doi.org/10.1016/S0378-4754(00)00270-6)
SALib: An Open-Source Python Library for Sensitivity Analysis (https://salib.readthedocs.io)
Digital Twin in Process Systems Engineering: A Review and Perspectives (https://doi.org/10.1016/j.compchemeng.2022.107942)

TAGS
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sensitivity-analysis, digital-twin, process-simulation