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Damper Modelling Using Neural Networks by Mark Burnett, Andy Dixon & Jon Webb, MIRA. As a result of an internal research initiative called Integrated Corner Technology (ICT), MIRA has increased its analytical and experimental capability for the development of vehicle suspension systems. MIRA has not only explored the possibilities that off-the-shelf modelling tools offer, but has also developed its own experimental, analytical and hybrid modelling techniques.

Integrated Corner Technology load time histories for ride and pave surfaces were used to predict component loads in a vehicle assembly

Background The use of linear modelling techniques to represent vehicle suspensions is well understood. Such techniques are only useful when considering the most rudimentary description of a vehicle suspension system. This is because many ride attributes depend on the non-linear behaviour of elastomeric and fluid-filled components such as bushes, dampers and tyres, which may also be highly frequency-dependent. MIRA has been studying and developing suspension systems for many years using traditional

experimental methods with support from off-the-shelf analytical modelling tools such as ADAMS and NASTRAN. Indeed, the group’s analytical and experimental capabilities have increased as a result of an internal research initiative called Integrated Corner Technology (ICT). The challenge presented by the ICT project was to find a means of representing all the necessary component characteristics of suspension corner systems, and indeed whole vehicles, within a model or set of models that can be run concurrently. This has involved the generation and cor-

relation of virtual equivalents of the tools that MIRA traditionally uses for vehicle development. These tools include individual component test rigs, Kinematics & Compliance (K&C) facility, MIRA’s extensive proving ground and also some public road surfaces. The use of ADAMS has been pivotal in the creation of these virtual tools and is complemented by MIRA’s own ride model, bespoke to ICT, constructed in the Matlab/Simulink environment. Non-linear models are also relevant to both handling and durability. In a parallel MIRA research programme, Integrated Durability Engineering (IDE), load time histories for ride and pave surfaces were used to predict component loads in a vehicle assembly during a durability cycle. Although the principles are generic and can be extended to other non-linear components, this discussion extends only to the modelling of dampers, as they are single input single output components.

Modelling requirements for dampers

Figure 1: MIRA ride model’s neural network.

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A linear component will generate an output that is a constant multiple of some input. For example, a road spring can be considered linear up to its elastic limit, as the generated force is equal to a conAutoTechnology 4/ 2003

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stant spring stiffness multiplied by the differential displacement. A basic non-linear damper model must take into account non-linearity with respect to frequency and amplitude. Frequency dependency can be modelled using transfer functions although they cannot easily encapsulate the velocity dependence of the level of damping. This point can be illustrated by measuring a damper’s frequency response in both the free and locked condition. In the free condition the breakaway load of the damper is overcome and the damper appears to be less stiff. A consequence of this is that during modal analysis the damper can be represented as either a locked or free stiffness. The amplitude dependency may be characterised by a simple non-linear function, for example tanh(x), or through an empirically derived look-up table. Combining these approaches to create a complete representation of a component such as a damper or a bush can be problematic. An

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Figure 2: Measured & predicted loads from the ride model neural network.

understanding of the physical mechanisms responsible for the component performance is required in order to construct an appropriate model. This can be difficult for elastomeric or fluidfilled components. An alternative approach is to characterise the component as a “black box", i.e. as some unknown function relating the output to the input. An effective method of achieving this involves the use of simple neural networks whereby a component’s

response to a representative test sequence is used to train a series of neural networks. The neural network is then used to calculate the component’s response from a given state.

A basic nonlinear damper model

Neural Network Vs. Look-Up Tables MIRA’s ride model is exercised in the time domain allowing nonstationary or transient signals, such as impacts, to be considered.

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The accuracy of the prediction largely depends on the length of the training sequence

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The vehicle model has been built up as a multi-body system using three basic methods of component representation: simple lumped parameter models, rigidbody modal models and flexible modal models. Each of these component types contains individual parameter models of varying degrees of complexity, for example, non-linear damping including hysteresis. The neural network used in the ride model is a two layer feed forward network with three inputs, five elements in the hidden layer and a single element in the output, see figure 1. A hyperbolic tangent is used as the activation function for the hidden layer, and the output function is linear. The damper’s current state, i.e. its displacement, velocity and acceleration, is used as the input to the neural network rather than a time history incorporating previous states. The traditional method of modelling dampers is through the use of a look-up table whereby, during simulation, the damper model would read the relative velocity between two parts and return a force for the next step. An alternative is to use a trained neural network that can be simply substituted for the damper look-up table. The neural network was trained on a hydraulic damper rig where damper position and load were measured during the test and the neural network trained on the displacement output.

Figure 3: The effect of inadequate training of the neural network.

Figure 4: Predicted loads from impact staircase on a Virtual Proving Ground. Neural network damper vs. spline look-up table damper.

To assess the performance of the model, the damper was driven by a signal containing a similar range of frequencies and amplitudes and the force recorded. Figure 2 shows the predicted and

Figure 5: Predicted loads from a pothole strike on the Virtual Proving Ground. Neural network vs. look-up table damper.

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measured data overlaid on the same plot. The two are in close agreement accept for departures close to zero velocity where a breakaway force is required and at high velocities were the number of points become sparse in both the training and test data. There are limitations with neural network approach. The principle behind neural networks is that they learn how the system behaves from a training signal. As a result, their knowledge of the system exists only within the space defined by the training signal. An erroneous result is returned if an input signal beyond the boundaries of the trained space is encountered. Figure 3 shows the effect of inadequate training on the predicted data. Figure 4 shows the predicted damper load when a vehicle passes over a discrete impact strip on the Virtual Proving Ground. In this example, the neural network AutoTechnology 4/ 2003

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prediction is from MTS’s Empirical Data Modeller (EDM) operating in ADAMS. The prediction from a neural network damper is shown against that from a look-up table. The neural network damper returns a higher load than the look-up table and indicates that the look-up table underestimates the loads generated during simulation. This is to be expected as the look-up table used in this case is a simple spline and thus does not embody hysteresis. Figure 5 shows the predicted damper loads, again from ADAMS and EDM, produced during a pothole strike where the neural network damper ‘breaks down’ compared to the continuous solution given by the look-up table. Unfortunately, as the damper loads cannot be accurately predicted before the simulation commences, it is difficult to guard against such eventualities. One potential way round this is to give the neural network the largest training space possible. However, in practice it is difficult to subject a damper to all levels of amplitude and velocity during training. The accuracy of the prediction largely depends on the length of the training sequence but also on its quality. The training sequence needs to embody all aspects of the component’s behaviour including non-linearities, frequency dependence and hysteresis over the amplitudes and frequencies of interest. If this is achieved, only one model of the component is required for many applications. The model is verified against a separate set of test data with a known response to identify any shortcomings or under-training in the model.

Conclusions and further applications Both the neural network and the look-up table models give accurate predictions with the former giving smaller errors, in this example, if interrogated over its trained space. Highly erroneous predictions were produced from the neural network operating outside this region. Both models are sensitive to the data AutoTechnology 4/ 2003

used to either train the model or generate a look-up table. Neural networks have obvious alternative applications such as bushes with multi-axial loadings, hydro-mounts and tyres. A component’s response can be encapsulated prior to the definition of its physical parameters, early in vehicle programmes, and the trained model passed down the design chain as a target response or functionality. The use of neural networks provides an accurate

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and convenient means of characterising non-linear components. It is one of the tools that MIRA uses to predict road load data and vehicle responses from running a vehicle model over its Virtual Proving Ground. The ability to investigate ride, handling a durability aspects from CAE data alone allows component and vehicle development to be carried out early in a vehicle’s programme prior to committing to hardware.

Virtual Proving Ground

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