Software developed by Dr. Mohammed Hussein and Dr. Hugh Hunt

The PiP model is a fully-three-dimensionsional predictive model whose computational accuracy has been validated to within 1dB against other predictive models. For reference to the published validations see publications, an extract from which is shown as the last slide in the powerpoint presentation below.

In this presentation the PiP model has been used to vary certain parameters by a small amount, consistent with uncertainies in measured data. The predicted vibration levels vary significantly, often by more than 10dB. This error cannot be forecast.

In the presentation, changes are made to as set of arbitrary initial parameters (Case 1) as follows:

> Case 2. - soil parameters (Compressive and Shear Wave velocities and density changed by 15%) changes vibration prediction by up to 6dB

> Case 3. - bending stiffness of track slab increased substantially - increases vibration by up to 5dB

> Case 4. - mass of slab increased and natural frequency of slab decreased shows performance of Floating Slab Track

> Case 5. - measurement position changed by 5m horizontally, changes vibration by more than 5dB

So we have shown by example that if more than 5dB prediction error results from even small uncertainties in soil parameters and measurement position it cannot be sensible in general to rely on prediction models for accumulated accuracy better than 10dB. Of course there will be circumstances where data is known accurately and as a result prediction accuracy can be improved, but it will always be prudent to run the simulation a number of times with variation of the parameters (within estimated bounds of uncertainty) to assess the actual prediction error. Bear in mind also that features such as soil layering, ground water, piled foundations, voids adjacent to the tunnel etc etc can only be included in very sophisticated models. Such models are very difficult to validate, and their accuracy depends critically on the accuracy of the input data - and sophisticated models require a great deal more input data than simpler models.

While we are questioning the use of numerical models to *predict* vibration with great accuracy,
we believe that modelling is very useful for assessing changes in vibration levels in response to small changes in
model parameters. Models such as the PiP model are therefore useful for determining the performance of vibration countermeasures
and to estimate *insertion gain*.
The insertion gain is not nearly so sensitive to uncertainty, such as the exact determination of soil parameters.

Numerical models are also subject to error in the same way as spelling mistales can creep into any document. A stray minus sign, or a mistyped variable may not cause a computer programme to fail and it will produce seeimgly correct results.

It is necessary to benchmark numerical models against eachother in as many circumstances as possible so as to test their limits of applicability. If these limits are not known then it will not be possible to know when to expect the results to be in error.

This all requires engineering judgement and different users of the software will make different assumptions, producing different predictions.

Models of whatever type are only of use if their quality (fitness for purpose) has been quantified, documented and communicated to potential users.
It may not be appropriate to talk of a valid model, but only of a model that has agreed upon regions of applicability and
quantified levels of performance (accuracy) when tested upon certain specific and appropriate data sets. Scientific and statistical
evaluations can enhance our confidence in models developed for environmental problems. Quality determination requires at least:
A sensitivity analysis, an uncertainty analysis and a model intercomparison may also provide useful information on model quality.
Additionally effective guidance for the wise interaction between the user and the model is essential, and can be provided by best practice
guidelines. |

Our feeling is that we all fall very far short of the standards set here by the microscale meteorologists. As a community working in the area of vibration from railways, we do not have any agreed best-practice guidelines and we have no agreed strategy by which predictive models can be assessed for quality assurance.

The PiP model has been developed alongside collaboration with, and support from, the research team at K.U.Leuven led by Prof Geert Degrande. They have allowed us generous access to their FEM-BEM models in order to produce independent and robust model intercomparison for PiP.

Acknowledgement is also owed to our partners in CONVURT