MOR techniques are used to reduce the complexity of mathematical models in simulations. By simplifying the model, it becomes computationally less intensive, allowing for faster simulations and real-time applications. ![[Pasted image 20240528114845.png]] ### Reduced order modelling ![[Pasted image 20240528115344.png]] ### Why Reduced Order Modelling ![[Pasted image 20240528115449.png]] ![[Pasted image 20240528115500.png]] ![[Pasted image 20240528115523.png]] ### Applications of ROM ![[Pasted image 20240528115602.png]] ![[Pasted image 20240528115633.png]] ![[Pasted image 20240528115645.png]] ![[Pasted image 20240528115716.png]] ![[Pasted image 20240528115750.png]] ### Different Approaches for Creating ROMs ![[Pasted image 20240528120153.png]] ![[Pasted image 20240528115909.png]] ![[Pasted image 20240528115930.png]] ![[Pasted image 20240528120002.png]] ![[Pasted image 20240528115930.png]] ![[Screenshot 2024-05-28 at 12.00.21.png]] ![[Pasted image 20240528120113.png]] ### Types of Model Order Reduction |**Type**|**Pros**|**Cons**|**Software Complexity**|**Time**| |---|---|---|---|---| |**Balanced Truncation**|Retains stability and controllability; suitable for linear time-invariant systems|Computationally intensive for large systems; requires Gramian calculation|Moderate to high|Time-consuming| |**Proper Orthogonal Decomposition (POD)**|Effective for systems with dominant modes; handles non-linear systems|Requires significant preprocessing; accuracy depends on mode selection|Moderate|Fast once modes are identified| |**Krylov Subspace Methods**|Efficient for large sparse systems; reduces computational cost by focusing on key frequencies|May not retain stability; primarily for linear systems|Low to moderate|Fast, especially for large systems| |**Dynamic Mode Decomposition (DMD)**|Captures dynamics of nonlinear systems; useful for data-driven modeling|Requires large data sets; sensitive to noise|Moderate|Moderate, depends on data size| |**Hankel Norm Approximation**|Preserves input-output behavior; useful for frequency response critical systems|Complex to implement; computationally expensive|High|Time-consuming| ---- In the automotive industry, particularly for thermal management, several model order reduction (MOR) techniques are commonly used to simplify complex models while retaining essential dynamics. Key techniques include: 1. **Balanced Truncation**: This method assumes access to the high-fidelity model structure and reduces the model by balancing the states based on their controllability and observability, then truncating the less significant states [[3](https://www.sae.org/publications/technical-papers/content/2019-01-0503/)]. 2. **Singular Perturbation Approximation**: This approach simplifies the model by separating the fast and slow dynamics, reducing the system by eliminating the fast dynamics [[2](https://www.researchgate.net/figure/Overview-of-model-reduction-techniques-for-automotive-control_fig2_263043773)]. 3. **Proper Orthogonal Decomposition (POD)**: POD is used to create a reduced-order model by projecting the high-dimensional system onto a lower-dimensional subspace using the most energetic modes [[1](https://www.sciencedirect.com/science/article/pii/S2405896319307207)]. 4. **Parametric Model Order Reduction**: This method focuses on creating reduced models that can handle variations in parameters efficiently, making them suitable for different operating conditions [[5](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7847468/)]. 5. **Efficient Reduced Order Models (ROM) for Transient CFD Solutions**: These models approximate transient Computational Fluid Dynamics (CFD) solutions accurately and are particularly useful in managing heat transfer in automotive applications [[4](https://www.sciencedirect.com/science/article/abs/pii/S135943112101067X)]. These techniques help in achieving real-time simulations and control in automotive thermal management systems by significantly reducing computational demands without compromising accuracy. ![[Pasted image 20240528114812.png]]