Multi-rate Approach in CRUISE™ M, Component Library Can Do More

Significant Simulation Time Reduction by the Multi-rate Approach in CRUISE™ M

The simulation of typical CRUISE™ M applications as for instance hybrid, battery and fuel cell electric vehicle models requires the coupling of electric, mechanical, fluid and thermal networks. Each network is established by combining the physical equations and connection structure of elementary components and results in a differential algebraic equation (DAE). In order to speed up the simulation, a non-iterative multi-rate time integration co-simulation method for the system of coupled DAEs has been developed and released in CRUISE™ M 2019 R2.

credits: AVL

MathConsult has been doing cooperative research in automotive simulation together with AVL since 2002.  

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Michael Liebrecht gave talk at NUMIFORM 2019

Michael Liebrecht presented our results on the modelling and simulation of leveling machines at NUMIFORM 2019 in Portsmouth, New Hampshire (see the abstract below). These were obtained jointly with voestalpine Grobblech.

Process Model for the Industrial Plate Leveling Operation with Special Emphasis on Online Control

M. Liebrecht, A.-K. Baum, R. Wahl, M. Aichinger, and E. Parteder

To produce high quality steel plates that meet the customer’s requirements, physically based models are increasingly used in the automation systems of the production process. In this work, a 2D model to describe the levelling process of the heavy plate production is presented. The model is based on Euler beam theory and features isotropic hardening of the material and the elastic response of the leveling machine. It enables the computation of the full stress-strain-history, all contact points and contact forces between the plate and the levelling rolls as well as the power consumption. The results are validated using the multi-purpose finite element software ABAQUS and compared to measured forces recorded during production. Core of the implementation is a damped Quasi-Newton method to minimize the free enthalpy of the system. Changes of the mechanical properties of the plate caused by the levelling operation can be calculated from the stress-strain history.

The computation time of the presented full 2D model is dramatically lower compared to the multi-purpose finite element solution. Nevertheless, due to time constraints during the production process, it is not feasible to apply the full 2D model in order to determine the optimal positions of each levelling roll before plates enter the leveler. To achieve this goal, a surrogate model based on vast parameter studies was developed. The parameter studies were performed using the full 2D model and cover all possible levelling roll positions and a wide range of material behaviour.

leveling maschine, credits: Voest Alpine
This picture shows the plastic-equivalent strain of a plate inside the leveler, credits: MathConsult GmbH
(y-axis is not enlarged), credits: MathConsult GmbH

UnRisk presented PRIIPs results at a seminar by Finanzverlag

On May 23, 2019, UnRisk presented their mathematical and computational PRIIPs results in a seminar organized by Finanzverlag. Other speakers included representatives of the Autrian Financial Market Authority (FMA). 

The PRIIPs regulation leads to serious problems when interest rates become negative. For the Euribor1m, this was the case for the first time in Sept. 2014.

The images show Euribor1m paths starting on Sept. 5 and on Sept. 8, 2014. Negative interest rates on Sept. 8 lead to completely different distributions when obeying the PRIIPs regulation.

MathConsult’s got Talent 2019

In summer 2019, MathConsult will employ 3 talents from Austrian high Schools to work as “Young Talents” interns. Two of them will analyse data in computational finance, one will work on Adaptive Optics for Extremely Large Telescopes.

Yet another winning talent!

Every year in spring, the Austrian research funding organization (in German “FFG – Forschungsförderungs-gesellschaft” awards the best 20 “young talents” out of 1500 high school students who did an internship in various companies and scientific research institutions for four weeks during the summer before. Young talents internships allow high school students to experience research and development live. The aim is to encourage girls and boys to follow natural sciences, engineering and technology. Each internship is funded with 1,200 Euro.

This is obviously one slice of a computer tomography scan of Andreas Binder’s nose sinuses (very left) + some artificial noise added (the other three images).
Credits: MathConsult GmbH

Well, as mentioned above, only 20 students can win, now it’s my pleasure to proudly announce that Robert Niebsch is one of the lucky winners! He did his internship at MathConsult GmbH in Linz, Austria, a hosting company. The topic of Robert’s internship was “Medical image processing by diffusion filters”. Robert did a very good job. Congratulations!

The award ceremony took place on March 7, 2019 at Vienna’s Urania, where all 2018 winners met and talked about their topics – and, finally they found their way back home, accompanied by a new iPad mini and holding a nice certificate in their hands.

Robert explaining what the skeleton is about.
Credits: Astrid Knie
The lucky talent with his – also very lucky (and proud) – supervisors
Andreas Binder and Markus Pöttinger.
Credits: Astrid Knie

The Limitations of Cornish-Fisher

In the MathBox entry from 13 December, we showed the implied distribution of DAX returns when using the Cornish Fisher expansion.

As a rule of thumb, this works nicely as long as the excess kurtosis is smaller than 8. What happens if the implied distribution of returns is really fat-tailed?

The exchange rate of EUR and Swiss Franc between the years 2013 and 2017 showed an excess kurtosis of 590. The Cornish-Fisher transformation between the implied distribution of returns and the standard normal distribution is not bijective any more and leads to weird distributions.

The plots show the implied “distribution” density (that is not a density) for the CHF EUR exchange rate return for a time horizon of 1, 16, and 256 business days, respectively. Applying the Cornish-Fisher formulae for extreme cases like CHFEUR leads to misleading results in the risk reward section of a PRIIPs KID.

MathConsult lectures PRIIPs in Wuppertal

On Dec. 13, 2018, Andreas Binder gave a guest lecture on PRIIPs at the Bergische Universität Wuppertal “The Mathematics of PRIIPs”.

Andreas Binder

With the European Regulation 1286/2014 and the Commission Delegated Regulation 2017/653, manufacturers of packaged retail and insurance-based investment products (PRIIPs) are required to equip their PRIIPs with key information documents (KIDs) describing the risk and the possible returns of these products on not more than 3 pages.

For so called category 2 instruments, the distribution of daily returns is based on their means, variance, skewness and curtosis and a Cornish-Fisher expansion. By doing so, fatter-tailed distributions are taken into account.

The plot shows the implied distribution derived form the Cornish-Fisher expansion for daily returns of the DAX between 2013 and 2017 (yellow line) compared to the normal distribution with the same variance (blue line). During this time period, Dax returns were left-skewed (skewness is negative) and fatter-tailed (excess kurtosis is positive).

Marie Curie and MathConsult

MathConsult participates in the project “ROMSOC” within the Marie-Sklodowska-Curie action funded by the European Union. Onkar Jadhav, who joined us in Nov. 2018, will work on a European Industrial Doctorate on Reduced Order Models for Financial Risk Analysis (subproject Nr. 6 of ROMSOC, joint project between TU Berlin and MathConsult).

In the risk analysis of financial instruments (or portfolios of them), one key task is to calculate future returns and the possible risk under a wide range of scenarios. In extreme cases, this may require the calculation of millions of scenarios, calibrate financial models from these scenarios, and solve a stochastic or partial differential equation for each of the calibrated models.

Developing reduced order models is a key technology in obtaining competitive solutions.

The image shows 1000 Monte Carlo paths (in the physical measure) with a
time horizon of 1 year for a stock price.