Simulation Result Verification and Experimental Data Comparison Method

In the rapidly evolving landscape of applied electromagnetics and high-precision engineering, numerical simulation has become an indispensable pillar of the design process. Whether engineers are optimizing electromagnetic shielding structures, designing induction heating coils, or developing complex magnetic levitation and plasma confinement systems, computational tools provide the predictive power necessary to visualize physical fields before a single component is manufactured.

However, the utility of a simulation is strictly limited by its fidelity. A model that fails to reflect physical reality can lead to catastrophic design failures or costly iterative delays. Therefore, establishing a rigorous, systematic methodology for Simulation Result Verification and Experimental Data Comparison is essential. This process serves as the critical bridge between theoretical mathematical models and physical implementation, ensuring that digital twins accurately represent the real world.

I. Foundational Principles: Verification vs. Validation

To implement a scientific comparison, one must first distinguish between two fundamental concepts that are often conflated: Verification and Validation.

• Verification asks, "Are we solving the equations correctly?" It focuses on the mathematical integrity of the numerical method, ensuring that the software implementation and the discretization (meshing) accurately represent the underlying mathematical model.
• Validation asks, "Are we solving the right equations?" It focuses on the physical accuracy of the model, ensuring that the assumptions, boundary conditions, and material properties used in the simulation truly reflect the physical phenomena being studied.

To ensure a scientifically sound comparison between simulation and experiment, three core principles must be observed:

1. Parameter Consistency and Control: The experimental environment must mirror the simulation setup as closely as possible. This includes strict alignment of boundary conditions, material properties (such as magnetic permeability $\mu$, electrical conductivity $\sigma$, and permittivity $\epsilon$), and excitation sources (frequency, amplitude, and waveform).
2. Grid Convergence Study: Before comparing results with experimental data, one must prove that the numerical solution is independent of the mesh density. A Grid Convergence Study must be performed to ensure that further refinement of the mesh does not significantly alter the results, thereby confirming that the error is not a byproduct of discretization.
3. Spatiotemporal Alignment: For transient electromagnetic phenomena, synchronization is critical. The simulation output must be precisely aligned with the experimental data in both the time domain (sampling frequency and timestamps) and the spatial domain (the exact coordinates of the measurement probes).

II. Multidimensional Comparison Strategies

Depending on the application, the comparison between simulation and experiment can be categorized into three distinct dimensions, ranging from macro-level system responses to micro-level field distributions.

1. Global Response Metrics

This is the most fundamental level of comparison, focusing on the macroscopic performance of the system. In induction heating, this involves comparing input impedance, operating current, and resonant frequency. In magnetic levitation, it refers to the total levitation force and guidance force. These metrics provide a high-level assessment of energy conversion efficiency and system stability.

2. Time and Frequency Domain Waveforms

By utilizing oscilloscopes and spectrum analyzers, engineers can capture real-time electrical signals—such as induced voltages or transient current responses—to compare against simulated waveforms. This dimension is vital in Electromagnetic Compatibility (EMC) testing, where the goal is to verify peak interference levels and harmonic distributions.

3. Spatial Field Distribution

This represents the most rigorous form of validation. It involves mapping the physical fields—such as magnetic flux density or temperature gradients—and comparing them to simulation "cloud maps." Techniques such as magnetic field scanning or infrared thermography (which converts electromagnetic loss into a thermal field) allow for point-to-point or regional statistical comparisons.

The following table summarizes the focus areas and challenges across different electromagnetic sub-domains:

III. Error Attribution and Model Refinement

When a discrepancy arises between simulation and experiment, the objective should not be to "force" the simulation to match the data through arbitrary parameter tuning. Instead, a systematic Error Attribution process must be conducted:

• Geometric and Boundary Abstractions: CAD models are often simplified for computational efficiency (e.g., omitting fillets, bolt holes, or small gaps). In electromagnetics, these "minor" omissions can significantly alter local magnetic reluctance or electric field distortions.
• Material Nonlinearity and Frequency Dependence: Standard material datasheets often provide static or low-frequency values. However, in high-frequency applications, properties such as magnetic core loss and skin depth change dynamically. Models must incorporate frequency-dependent constitutive relations to be accurate.
• Measurement Artifacts (The Observer Effect): The act of measurement can itself perturb the field. For instance, placing a metallic probe within a high-frequency magnetic field can induce eddy currents, thereby altering the very field being measured.

IV. Industrial Workflow: A Closed-Loop Approach

In professional engineering environments, the relationship between simulation and experiment is managed through a closed-loop iterative workflow:

1. Preliminary Exploration: Engineers begin with simplified lumped-parameter models or 2D Finite Element Method (FEM) models to perform rapid trend analysis and define the design envelope.
2. High-Fidelity Detailed Design: Once the design space is narrowed, full 3D multi-physics models are constructed. Advanced Design Exploration algorithms are used to optimize the structure under various constraints.
3. Prototyping and Iterative Correction: A physical prototype is manufactured and subjected to standardized testing. If the deviation between the experimental data and the simulation exceeds a predefined engineering threshold (commonly $\pm 10%$), the experimental data is used to back-calculate or "invert" the correct material parameters or boundary conditions. This refined data is then used to solidify the simulation template for future iterations.

By adhering to this standardized and systematic approach, engineers can significantly enhance the reliability of complex electromagnetic systems, reduce development cycles, and ensure that theoretical designs are successfully translated into high-performance physical products.