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System dynamics

Improving vehicle models with neuro network modelling methodBy Shawn You, MTS Hemanth Kolera, MSC Software

As automotive manufactures face pressures to cut costs and accelerate product development timelines, the availability of a vehicle prototype for testing has become less. Predictive simulation models are required at the beginning of the engineering development process to identify and resolve issues in the absence of a prototype. Prototypes can then be used only to validate the design determined by the simulation-based analysis. Vehicle models such as the ones that Adams can create help designers understand systems-level effects

However, building predictive system-level vehicle models is not easy. A bottleneck to attain the right amount of fidelity is in the behavior of non-linear, frequency-dependent components such as dampers, bushings. A predictive non-linear

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model would capture the frequency dependencies and the effect of the loading histories. Traditionally dampers and bushings are modelled using spline fits, and the modelled response is only dependent on the current state. Spline-based models do not factor in the loading history and the hysteresis effects.

The emergence of Artificial Intelligence and Machine learning techniques such as Neural Networks provides the option to use purely data-based representations of component behavior. These techniques offer more fidelity than simplistic physics-based approaches to component modelling, such as through spline fits. MTS has invested in developing these methods through a proprietary solution called Empirical Dynamic Modelling (EDM).

The output/response from the EDM method is based on a series of inputs and not just based on the current state. The initial column in the Neural Network is the input of loading histories. Each layer after that is a set of simple mathematical functions that connect the loading histories to the predicted output, that is, the force response. The coefficients for each of these layers are then optimised to ensure that the model responses are accurately predicted.

The EDM approach has several advantages. The EDM model is a Blackbox, and the underlying complexity in the Neural Network model is abstracted out. Therefore, no specialised user training is required. EMD models capture any non-linearity in the system, the type of input does not matter, and an arbitrary number of inputs and outputs are supported. The EDM method can capture the behavior of active components and predicts the behavior in real-time.

Original Lab Measurement

Spline Model Predictions

EDM model Predictions

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The differences in the spline model and the EDM model are shown . Spline models can capture non-linearity but not the hysteresis, while the EDM model can capture both.

The EDM model was deployed to capture several different applications, including regular and active dampers, mounts, and low-frequency vehicle events.

Results for the Regular damper simulations are shown. The damper has a pretty strong hysteresis effect, so the velocity/load effect is very thick in the measured response. While the spline model only predicted a curve, the EDM model matched actual measurements well. While the spline prediction only indicates the curve’s behavior, the EDM model factors in the hysteresis and the response’s thickness.

Furthermore, the EDM models are much better than the spline models in capturing the peak loads. The peaks impact prediction of fatigue damage and fatigue life.

The value of EDM models is also evident in the simulation of active and semi-active components used in high-end car designs. When used in a suspension system, these active and semi-active dampers vary the suspension characteristics to match changing road or dynamics conditions. Examples are continuous-damping control (CDC dampers) and Magnetorheological dampers. These are very difficult to model as they show non-linear hysteresis effects. Since the damper properties change with current, it was included as an additional input to the neural network.

Damper Test - Hysterisis Comparison: Real Measurment vs EDM Model (left) and Real Measurement vs Spline Model Prediction (right)

Damper Test - EDM Model (left) and Spline Model Prediction (right) Comparison , Red: lab response; Blue: model prediction; Orange: model error

Comparison between EDM models and Spline models for prediction of Peak loads

The image shows the test setup for a CDC damper. A current source is used to vary the damping characteristics, and the system is excited with random vertical displacements. A EDM model was built using the measured data and was compared against a spline based model.

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Hysterisis Comparison: Real Measurment vs EDM Model (left) and Real Measurement vs Spline Model Prediction (right)

EDM Model (left) and Spline Model Prediction (right) Comparison , Red: lab response; Blue: model prediction; Orange: model error

Hysterisis Comparison- Low Frequency Test: Real Measurment vs EDM Model (left) and Real Measurement vs Spline Model Prediction (right)

The EDM model’s accuracy was much better than the spline-based model’s accuracy for both constant current inputs and randomly varying current inputs.

Also, for CDC dampers the hysteresis effect is very significant and that is not captured by the spline based model as shown.

EDM models can predict responses at all kinds of frequencies from 150-200 Hz and very low frequencies (0.1 Hz) where friction is dominant. Hysteresis is significant as an impact of low friction during these event.

Besides dampers, MTS also tested other components such as liquid-filled mounts. The behavior of liquid-filled engine mounts and solid rubber mounts is highly frequency-dependent. Displacements in all three directions were input to the model, and the Forces were the output from the model.

EDM Model (left) and Spline Model Prediction (right) Comparison , Red: lab response; Blue: model prediction; Orange: model error

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Autonomous vehicles

As the impact of hysteresis increased, the EDM model showed a better ability to capture the mount behavior as compared to the spline model

The construction of a EDM model is simple. Similar to the spline model, measured data needs to be created on forces, displacements, etc.

For an one input – one output model,

Real Measurement vs Spline Model Prediction

Real Measurement vs EDM Model Prediction

a random noise data file 60 sends long will have enough information to create a neural network model. It takes a couple of minutes to go through the optimisation process and isolate the neural network’s coefficients. Even though the EDM models have more parameters than a spline model, the computation of these parameters are based on simple mathematical functions.

Therefore, these models can be run in real-time and can be implemented into an Adams model without any computational overhead. This ability to be executed in real-time makes the EDM model ideal for applications such as emulating driving simulators. With accurate EDM models to represent nonlinear components in the driving simulators, the driving simulation will be more realistic.

Conclusion

The Neural Network-based EDM model is more accurate than the spline model. It captures hysteresis effects, load spikes, and a wide range of frequency effects more accurately. EDM models can be constructed quickly and run in real-time and provide an attractive option to simplistic physical modelling approaches.