Hybrid Estimation Techniques for Engineering

Neural Networks can make predictions that violate basic physics or laws of thermodynamics if aimed only at minimizing a loss function. To fix this issue, ML scientists introduced PINNs - Physics Informed Neural Networks - where you penalize a neural network when it makes physically nonsense predictions. But what if you don’t know the full physics of a system? How do you penalize the neural network in that case? Universal Differential Equations (UDE) is the answer. I am writing this article in praise of this marvelous technique that is truly changing the way we are looking at how to bring science and ML together. Even a popular domain is emerging as a result: Scientific Machine Learning (SciML). Let us look at a spring-mass-damper system - a classic example in physics and engineering. Usually, it goes like this: mx''+bx'+kx=0 In a perfect world, these parameters m, c, k would be constants we measure in a lab. But in real life, your damper might behave non-linearly. So you may not know what the damping force is. That is where we can bring Universal Differential Equations into the picture. Instead of blindly trusting a neural network or strictly forcing your physical laws down the model’s throat, you merge them. In short, a UDE says: “I know some of the physics. Let me put that in. The rest that I don’t know? That’s the chunk I will replace with a neural network.” So how do we do it with the spring–mass–damper? A hybrid model: Part physics, part neural network. We know there is a second-order ODE term to account for acceleration and a ‘kx’ term for spring force. However, suppose, we suspect the damping force is not the usual linear form. Maybe it is more complicated, or partially unknown. mx''+kx+[unknown]=0 Now the “something unknown” becomes a learned function modeled by a neural network NN(θ). [unknown] = NN(θ) If you suspect a hidden/unknown effect, you can funnel that knowledge gap straight into the neural network term. Note that here the neural network is predicting the damping term. We want to predict displacement x(t). What does the UDE predict? The “neural network” alone is not the UDE. Because the UDE has to predict x(t) so that you can compare the predicted x(t) with experimental x(t) and define the loss. So how exactly does UDE predict x(t)? 1) Initial condition and experimental data fed to NN(θ) 2) Neural Network NN(θ) for the unknown term predicts damping 3) Combine with the known ODE: mx''+kx+NN(θ)=0 4) Numerical integration to predict x and x' 5) Compare predictions to experimental data 6) Back-propagation and optimization till you minimize the loss You have the final UDE model. I have made a lecture video on UDEs (for absolute beginners) on Vizuara’s YouTube channel. Do check this out. I hope you enjoy watching this lecture as much as I enjoyed making it: https://lnkd.in/gPWQuXHR

I'm very pleased to share with you my recent research in the battery state of battery (SOC and SOH) methodology for multidimensional input/ output data using hybrid Neural Network inside NNStart Toolbox™ for regression to generate Simulink® model to predict the state of battery. Accurate state estimation holds significant importance for several reasons: (i) it directly influences range estimation, (ii) it is essential for optimizing energy management, ensuring efficient power distribution and utilization, and (iii) it is crucial for the health of the battery, preventing conditions such as overcharging or deep discharging. In summary, precise estimation is paramount for range prediction, energy optimization, battery health, and overall safety, making it a central focus within the multifaceted functions of the BMS in EVs. In general, there are two ways to achieve state estimation, one is purely data-driven, and the other is model-driven. The pure data-driven approach takes the machine learning algorithm as the core, and uses the characteristic data of the battery as the basis, using the data to train the algorithm to find the potential nonlinear relationship between the internal and external characteristic parameters. The complexity of the state estimation algorithm is critical for real vehicle applications, which directly affects the real-time performance of estimation. Conversely, models based on physical principles, typically described by partial/ordinary differential equations (PDEs/ODEs), have been employed for centuries; these models have the advantages of a solid mathematical foundation and a wide array of numerical methods facilitating their solution. However, constructing PDE models, and pursuant solution techniques, is an arduous task. PDE models are often rigid, relying on explicit assumptions, or are so large as to be computationally infeasible. The primary limitation of PDE models is a lack of ability to learn new principles from observational input. NN has good nonlinear relationship processing ability, and can effectively deal with the errors caused by the linearization of the battery model by the Kalman filter method. NN method usually uses the black box principle to find out the potential nonlinear mapping relationship between voltage, current and SOC, so as to realize the estimation. However, this method is very data-dependent and often results in unstable estimates and it generally requires large -scale testing and high experimental data. The objective of hybrid models is to benefit from the advantages of each method and to obtain globally optimal estimation performance. Since the information contained in each individual estimation method is limited, the hybrid method can maximize the available information, integrate the information from individual models, and make the most of the advantages of multiple estimation methods, thereby improving the precision of the estimate.

Here is our latest paper published in Ocean Engineering (Elsevier): "Predicting the lateral capacity of short step-tapered and straight piles in cohesionless soils using an FE–AI hybrid technique" We developed a hybrid framework combining 3D finite element modeling (PLAXIS 3D) with an evolutionary polynomial regression AI model (EPR-MOGA) to predict the lateral capacity of short piles with high accuracy. ✅ 580 simulations ✅ Predictive equations ✅ Applicable to straight and step-tapered piles ✅ Validated against field tests, Broms’ and CLM methods Open Access – Read the full article here: https://lnkd.in/gWAurtiF This work was completed under the supervision of Prof. Hany El Naggar, and in collaboration with my colleagues Farrukh Choksi and Habib Amin at Dalhousie University. #GeotechnicalEngineering #PileDesign #FiniteElement #ArtificialIntelligence #PLAXIS3D #LateralLoads #SoilStructureInteraction

Are you working with hybrid systems models and curious about the saltation matrix and various tools we have built in recent years for it? If your system has changing contact conditions (or other hybrid events), you need to understand the saltation matrix and determine if should be accounted for in your work. We have put together a collection of example code & tutorials for calculating the saltation matrix and using it for state estimation and control. Specifically, this has code for our salted Kalman filter (SKF), hybrid iterative linear quadratic regulator (h-iLQR), and analysis of simple systems from our tutorial paper. The code is in Matlab and Python (with more python code coming soon!): https://lnkd.in/eZX5VgjW Our tutorial paper on saltation matrices is here (and you can now run all of the examples from this paper in the tutorial code): https://lnkd.in/e9xbKwA7 We had bits and pieces of code out before, but we've cleaned it up and brought it all together in this repository. Sorry we didn't post this earlier! Hope this helps, and let me know if you have any issues. Thanks to Diana Frias Franco, Joshua Ramos, Derek Fan, and Karla Soto Cuevas for getting this out, and to Nathan Kong, Joe Payne, and James Zhu for their earlier code. (My students actually finished this months ago and I forgot to post about it...)

🎗️ #Hybrid_HAZOP and Quantitative Deviation Analysis (A Dynamic Approach) 1️⃣ Technology: #AspenTechnology and #Hybrid_Modeling 2️⃣ Use Cases: PHA 3️⃣ Value: Preclude the Risk of Un-Necessary Cost resulting from Qualitative 📖 Methods The integration of Aspen Technology and Hybrid Modeling brings a transformative approach to #PHA (Process Hazard Analysis), combining the strengths of process dynamics with the AI. This enables teams to quantitatively assess risks, precluding unnecessary costs that often arise from purely qualitative methods. 💡 Background The continuous evolution of #AI technology is driving improvements in operational excellence while prioritizing #ProcessSafety. This is what we do as R&D and consultants in #AspenTech. The Dynamic Hybrid Modeling approach exemplifies these advancements by uniting the capabilities of Process Dynamics and Industrial AI into a comprehensive framework. 💰 Success Story: ORYX GTL In a Naphtha Splitter system, the HAZOP process was enhanced with Dynamic Hybrid Modeling, addressing knock-on effects on system KPIs quantitatively. The primitive method involving HYSYS models, #HMB (Heat & Mass Balance), PFDs, and P&IDs were upskilled to enable the delivery of a Hybrid HAZOP (dynamic concept). Implementation Steps 1️⃣ Ensure a validated #HYSYS model for systems undergoing HAZOP/PHA. 2️⃣ Employ #Aspen_MultiCase to generate big data within system constraints and safe operating limits. 3️⃣ Utilize #AIMB to build neural networks from Jason files derived from #Aspen_MultiCase. 4️⃣ Run the #AIMB model in #HYSYS. 5️⃣ Switch to dynamics mode to examine all #HAZOP scenarios using Event Scheduler option in HYSYS Dynamics. 🔑 Value Delivered This systematic approach ensures an informed decision-making during safety reviews. 💰 Call to Action Avoid out-of-sequence engineering by following the above steps to streamline your safety sessions and achieve optimal results adopting Hybrid HAZOP #HybridHAZOP #PHA #AIMB #AspenMultiCase #HYSYS #AI #ANN #ROM #Dynamics #Cost

🌟 Revolutionizing Process Engineering with Hybrid Modeling 🌟 The demand for more accurate, real-time predictions in complex process systems is catalyzing a significant transformation in process engineering: the rise of hybrid modeling. By integrating first-principles simulations, such as conservation laws, reaction kinetics, and thermodynamics with cutting-edge machine learning algorithms, hybrid models are overcoming the limitations of traditional mechanistic approaches. This fusion of deep scientific theory and data-driven insights provides a robust solution to dynamic process challenges. Sample 𝗨𝘀𝗲 𝗖𝗮𝘀𝗲𝘀 𝗳𝗼𝗿 𝗛𝘆𝗯𝗿𝗶𝗱 𝗠𝗼𝗱𝗲𝗹𝗶𝗻𝗴: 1. Predicting Off-Spec Events in Reactive Distillation: Traditional mechanistic models often struggle to forecast off-spec occurrences in reactive distillation units due to the complex, non-linear nature of reactions. Hybrid models enhance accuracy by combining experimental and operational data with fundamental chemical kinetics. 2. Optimizing Heat Exchanger Networks: Conventional models frequently fall short in accounting for complex, time-varying conditions in heat exchangers. Hybrid modeling facilitates real-time optimization by merging machine learning predictions with established thermodynamic principles, leading to more reliable and energy-efficient operations. At #Ingenero, we harness the power of hybrid modeling to tackle intricate, multivariable problems in real time. This approach enables more precise predictions, optimized performance, and swift responses to deviations. By blending scientific rigor with machine learning, we bridge the gap between theory and practical application, empowering our clients to achieve unprecedented operational efficiency. Hybrid models offer the best of both worlds: proven deterministic models and innovative machine learning techniques. This integration drives better decision-making, minimizes downtime, and enhances process stability. The future of process engineering lies in the seamless integration of theoretical foundations and advanced machine learning technologies. How are you leveraging hybrid models to tackle your most complex challenges? #ProcessEngineering #HybridModeling #MachineLearning