## 6 Experimental Evaluation and Results  
### Experimental Setup  
To validate the effectiveness of the proposed privacy-preserving polymorphic heterogeneous security architecture, we conducted comprehensive simulation experiments targeting a cloud-edge collaboration industrial control scenario focused on natural gas pipeline pressure control systems. In this critical infrastructure scenario, the pipeline pressure must be maintained within \(\pm 3\%\) of the setpoint value (e.g., \(8.6\) MPa \(\pm\) 3%), with compressor stations automatically regulating pipeline pressure through pressure control valves, compressor units, and blowdown valves. The edge node collaborates with the cloud platform to process monitoring data and distribute control commands throughout the system.  
The experimental scenario considers sophisticated adversaries capable of launching false data injection attacks that manipulate pressure regulation data from executors, thereby erroneously controlling pressure valves and compressor units. Such attacks can lead to dangerously high pressure conditions (creating pipeline rupture risks) or excessively low pressure states (causing transmission interruptions). We model emergency shutdown conditions when pipeline pressure exceeds the safe operating range of (6.2, 11.0) MPa, triggering maintenance protocols that require emergency depressurization, system inspection, gradual pressure restoration, and system stabilization phases. The system pressure regulation capability is uniformly configured at 0.15 MPa/min, while emergency depressurization during high-pressure shutdowns operates at an accelerated rate of 0.25 MPa/min with fully opened blowdown valves. The communication bandwidth is 10 MB between the edge node and the cloud platform.  
The simulation environment was implemented using Python 3.12.8 with a total simulation duration of 14,400 s (4 h) and a sampling frequency of 5 s. To evaluate system resilience under attack conditions, we configured three distinct attack scenarios occurring at 20, 100, and 170 min (corresponding to 1200 s, 6000 s, and 10,200 s, respectively), with each attack persisting for 30 min.  
The experimental testbed consisted of an Intel(R) Core(TM) i7-4790 processor operating at 3.60 GHz, equipped with 20 GB DDR3 memory, running on the Windows 10 operating system. To accurately reflect the computational constraints of edge environments, executors and arbiter (i.e., the arbitration and scheduling module) were configured withCPU frequencies limited to 1.2 GHz, while the cloud platform maintained full computational capacity at 3.6 GHz. For cryptographic operations, we implemented the Paillier cryptosystem to realize homomorphic computations, utilizing the GNU Multiple Precision Arithmetic Library (GMP) for efficient handling of large integer operations required by the cryptographic protocols, with a key size of 2048 bits to ensure adequate security strength.  
The experimental evaluation encompasses three primary comparative analyses to thoroughly assess the proposed architecture's effectiveness. First, we compare the defense capabilities of our proposed scheme against conventional static redundancy and moving target defense approaches, measuring their respective abilities to maintain system availability and output correctness under attacks. Second, we evaluate the arbitration latency introduced by the privacy-preserving arbitration mechanisms, quantifying the computational and communication overhead associated with homomorphic encryption operations while ensuring data confidentiality. Finally, we analyze the impact of our proposed scheduling algorithm by comparing it against event-triggered and periodic scheduling strategies, assessing how different scheduling approaches influence the overall availability and security posture of the polymorphic heterogeneous architecture.