The focus of UQ&M is on capturing all of the uncertainties, whether they are easy to express numerically in terms of error bounds on input variables or other more difficult quantities such as expert opinion.
Typically such uncertainties fall into 3 broad categories: (i) parameter uncertainty (where deterministic model values do not capture the inherent variability in real systems), (ii) model uncertainties (wherein the physical world is approximated by mathematical models), and (iii) numerical uncertainties (where the complexity of solving a model introduces errors). A particular form of knowledge that is difficult to represent within mathematical models is expert opinion. The specific area of “expert elicitation” tackles this challenge.
Whatever the form of the uncertainty, once identified, characterised and quantified it must them be propagated through the simulation model in order to understand the impact on the outputs (including uncertainty in the performance of any products that the system is used to design). This is where the fun (and the statistics) starts! With potentially numerous inputs, a simple combination of uncertainties at each iterative step of a simulation will likely result in a very large (and incorrect) output uncertainty. Input uncertainties are often highly correlated, so the rules for propagation need to take account of this.
So that’s how uncertainty quantification is defined. Quantification means describing the uncertainty, if possible numerically, and the management of it means how you address consequences in the way those uncertainties propagate in your processes.
Companies are interested in UQ&M for two main reasons: Firstly, if existing methods of understanding uncertainty (risk) are overly conservative (for example if they do not account for correlated input uncertainty) then the engineering margins (safety factors) applied may limit product performance. Better UQ&M leads to better product optimisation. Secondly, if UQ&M is less mature in an organisation then the bounds of applicability of a given simulation toolset may be based purely on experience with the organisation's existing (even legacy) products. This can make it very hard to move to new design variants. If the tools are to be applied beyond the current product portfolio (for example to design a radically different aircraft, jet turbine, car or building type) the greater reliance on the tools is needed. If formally UQ&M is not available, then movement to a new product line will be based on the organisation’s tolerance for risk based on judgement only. Regardless of the engineering skill of the organisation, this reliance will introduce cost and delay.
So that’s why UQ&M can enable you to extend the reach of your existing processes and tools, or at least to understand the uncertainties in them and how you might go about addressing them, usually by reducing the uncertainty of the input variables.
Interest in the adoption of UQ&M is growing in industry. Innovate UK and The KTN have set up a Special Interest Group (SIG) and website portal which provides a forum for discussion and lists a number of use cases. These are providing an avenue for further discovery and progression, where practitioners in UQ&M can demonstrate exactly what impact it is having on their organisation. The sectors where UQ&M is initially most predominant are automotive, aerospace, renewable and nuclear, though the group is growing. The UK is generally regarded as lagging behind the US when it comes to UQ&M and so an intervention from Innovate UK is timely and welcome. The UK is very well positioned - with high value manufacturing and world-leading researchers in modelling and mathematics - to take advantage of UQ&M.
Engineering companies often rely on a series of design reviews to stage gate their product development, at which there is an assessment of the risk or uncertainty. If that risk and uncertainty assessment is based purely upon the experience or the insight of given experts who are present, then design reviews can introduce delay - as further information is requested to support governance and engineering oversight. Formal UQ&M provides a principled risk assessment where all of the managed uncertainties are accounted for, and is a more powerful input to the design review process. Rather than introducing a costly overhead, UQ&M properly implemented will likely accelerate the design process via design reviews.
The current initiative - led by the UQ&M SIG - is really about a revolution in thinking. Particularly for sectors in engineering that are inherently quite deterministic, the introduction of probabilistic (stochastic) methods requires investment and time. The use of real industrial examples from across sectors is a cornerstone of the UQ&M SIG activity to promote and share best practise.
It has been said that the beauty of expert opinions is that there are so many to choose from! Indeed it is sometimes surprising how much experts can disagree if they are such … experts! To make sense of this, and to establish the best way to collect and reconcile expert views the area of “expert elicitation” is becoming an area of expertise on its own right. Needless to say, it is not without its own controversy ...
Early methods in the application of UQ&M to large-scale simulation were very computationally expensive - and a real barrier to adoption. Most organisations aspire just to secure enough resource to complete a single, forward evaluation of a design variant using a simulation tool on time and to budget - let alone a whole set of simulations covering variation in a number of inputs. However, more advanced statistical methods are being developed now, which are far more efficient. They are still more expensive than the baseline tools, but the difference is shrinking and the trend is for further improvement. The global mega-trends of exponential increase in the amount of processing power, data storage and data transfer rates should make UQ&M for large-scale simulation more mainstream.
In terms of adoption of UQ&M, I predict many small companies will follow the leads of industry primes. If you look at the UQ&M SIG, it is largely the primes that are recognising the need to take an interest. But as soon as the primes start assigning value to do UQ&M as part of their supply chain, the small companies will rapidly see the value - and they will want support to be able to do that. What will be important in growing the required skill sets are intermediary organisations who can facilitate and identify best practice and the best ways to incorporate UQ&M into their tools.
If you’re interested in finding out more about UQ&M, further information about the UQ&M Special Interest Group (SIG) can be found here.