## Functional principal component analysis

Functional Principal Component Analysis (FPCA) is a generalization of PCA. The FPCA can be used to find the dominant modes of a set of functions.

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December 20, 2017

Functional Principal Component Analysis (FPCA) is a generalization of PCA. The FPCA can be used to find the dominant modes of a set of functions.

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December 4, 2017

Scheduling constrained resources over time is a tough problem. In fact, the problem is NP-hard. One part of the problem is to find a feasible solution where all constraints are satisfied simultaneously. Another part is to also find a solution which also satisfies some measure of optimality. In practice, it is often sufficient to solve the problem partially such that the solution is better than the first feasible solution which has been found.

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November 20, 2017

Since the introduction of separable software components and virtual testing, the development of software for mechatronic systems is taking place parallel to the procedure of producing the hardware. The progress has made it possible to shrink the time for development and also gain knowledge, through testing, at an earlier stage of the process.

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November 9, 2017

Ordinary linear differential equations can be solved as trajectories given some initial conditions. But what if your initial conditions are given as distributions of probability? It turns out that the problem is relatively simple to solve.

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October 16, 2017

Bayesian Regression has traditionally been very difficult to work with since analytical solutions are only possible for simple problems. Hence, the frequentist method called “least-squares regression” has been dominant for a long time. Bayesian approaches, however, has the advantage of working with probability distributions such that the estimated parameters of a model are represented by a probability distribution (formally we talk about “likelihood” for parameters and “probability” for random variables).

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4 October 2017

Combine Control Systems visited this year’s UAS Forum conference in Linköping. UAS is the abbreviation for Unmanned Aerial System which has been an interest at the company since the first master’s thesis regarding the subject started in 2012. For two days the UAS Forum with lectures, presentations and fair was held in connection with the international workshop on research, education and development on unmanned aerial systems (RED-UAS) which has been held every second year since 2011. This substantiates the fact that Linköping is Sweden’s capital regarding aviation.

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25 September 2017

This first blog post will be a brief survey about the use of virtual verification within the development of mechatronic systems. There will also be some considerations about future concepts within the field, which will give you some clues about possible topics for the upcoming posts.

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11 September 2017

In a classical design of experiments (DoE) you usually choose a set of points according to some rule and perform experiments to be able to, for example, create a response surface. But when the properties of the process you are trying to describe is difficult to understand and can be destroyed if wrong parameters are applied we have to try something different.

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9 August 2017

When trying to describe data using a function you often know something about the process generating the data a priori. When you do not completely understand why the data looks like it does but want to try to describe it any way you can start trying different things ad hoc.

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5 May 2017

Remember this little fellow? Combine’s favourite pet has been adopted by a new pair of owners! The hexapod, as you may know, is a six-legged robot that has served as the platform for master thesis projects at the Combine Lund office. The hexapod projects started out as a vision of an autonomous robot that could navigate areas where humans cannot go.

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19 April 2017

The maximum spacing estimation (MSE or MSP) is one of those not-so-known statistic tools that are good to have in your toolbox if you ever bump into a misbehaving ML estimation. Find something about it is a bit tricky, because if you look for something on MSE, you will find “Mean Squared Error” as one of the top hits.

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7 January 2017

Hi all! you may have been following the blog for some time, or this may be your first visit. But just the fact that you are here, taking some time to read and learn new things is awesome. Well, guess what: we want to hire awesome people who enjoy learning new things. More specifically about data science.

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26 December 2016

The Kolmogorov-Smirnov test (KS test) is a test which allows you to compare two univariate, continuous distributions by looking at their CDFs. Such CDFs can both be empirical (two-sample KS) or one of them can be empirical, and the other one built parametrically (one-sample).

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8 December 2016

As most of you probably know, Combine has hosted several master thesis works during the last few years, e.g. the hexacopter and hexapod in Lund, the balancing cube in Gothenburg and the ROV in Linköping. For the students, this is a great opportunity to use what they have learned during their studies to complete a highly challenging project.

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8 December 2016

What is MPC? Model predictive control (MPC) refers to a class of control algorithms that compute a sequence of control moves based on an explicit prediction of outputs within some future horizon.

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16 November 2016

And here we go with the copula package in (the sandbox of) statsmodels! You can look at the code first here. I am in love with this package. I was in love with statsmodels already, but this tiny little copula package has everything one can hope for!

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2 November 2016

A few weeks back, Mathworks hosted their annual EMAB (European MATLAB Advisory Board). The EMAB is a set of seminars stretching over three days, with the purpose of presenting news from the current MATLAB release, presenting planned features of future releases, and get feedback from customers on issues and/or desired functionality.

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24 October 2016

In a control system, your control algorithm utilizes some states of the system to generate the control input which satisfies your desired output. If you can not measure all the states in the system , you need an ”Observer” (or more precisely a state observer) to estimate the unmeasured states from the outputs. Kalman filter is one class of observer.

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19 October 2016

You may ask, why copulas? We do not mean this copulas. We mean the mathematical concept. Simply put, copulas are joint distribution functions with uniform marginals. The kicker, is that they allow you to study dependencies separately from marginals.

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8 October 2016

The 8th of October, Combine could be found at Kviberg Park in Gothenburg to participate in the obstacle course Toughest. The spirit was high, with the runners fueling up on bananas and chocolate bars in the cold autumn weather.

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30 September 2016

The Tesla Model S can go from 0 to 60 mph (96 km/h) in 2.5 seconds, in what the company calls ”Ludicrous mode,”, the company said in a statement. The only commercial cars on the planet that can beat the Tesla Model S, the LaFerrari and the Porsche 918 Spyder, each cost about $1 million and are ”tiny” two-seater roadsters. Is there a limit how fast it is possible to accelerate?

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29 September 2016

Recently, CCS held its annual autumn kick-off. This year, the kick-off was held in the penthouse at Avalon Hotel in Gothenburg. This years inspirational speech was given by Annelie Pompe, a professional adventurer, who among other things talked about freediving. Therefore, this seems like an excellent opportunity for a deep dive (pun very much intended) into the very exciting topic of diving!

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29 September 2016

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16 September 2016

The 16th of September the employees at Combine Control Systems met at the Avalon Hotel in Gothenburg for an autumn kick-off. The focus of the kick-off was mobility, with seminars held by leading companies in the field.

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7 September 2016

*Clears throat* what I actually mean is that every now and then, a data science practitioner will be tasked with making sense out of rare, extreme situations. The good news is, there exist mathematical tools that can help you make sense of extreme events. And some of those tools are structured under a branch of probability which has (conveniently) been named Extreme Value Theory (EVT).

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14 July 2016

If you are interested in space and control of space crafts you may have noticed that NASA has a space probe called Juno orbiting Jupiter. Juno has many sensors and is described in this (quite long) documentary. Also, here is an example of an odd spacecraft control using the yo-yo trick, as well as an adorable cat-video with potential space application!

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14 July 2016

The frequency response method is a powerful tool for the analysis and design of linear control systems. It is based on describing a linear system by a complex-valued function, the frequency-response, instead of a differential equation.

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14 July 2016

The most interesting football championship of the year has just come to an end. With a tied result after the regular time, and with both teams scoring one goal each in the extended time, the outcome of the final was determined by penalties. The winner was the runner-up of last year – TechUnited Einhoven!

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15 June 2016

The book is divided in three parts, titled (respectively) “The Old Way”, “The New Way” and “The Way Ahead”. Part 1 and Part 2, the writer pulls you into the biographical and social context of the people behind most significant pillars of modern finance. The historical recaps felt very vivid."

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8-9 June 2016

Combine som är specialister på reglerteknik ställer självklart ut!

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7 June 2016

In the last post we had a look at co-simulation using MATLAB/Simulink with MotionSolve from Altair. With a co-simulation interface between the models, it is possible to take advantage of the strengths in each software, synchronizing the models and providing them with the means to communicate. However, at the conference in Sälen I gave a short presentation of a different approach – TCP/IP communication. This approach was investigated in a master thesis project carried out at the Combine office in Lund.

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5 May 2016

Or “can daedalean words actually help make more accurate descriptions of your random variable? Part 1: Kurtosis. Is a common belief that gaussians and uniform distributions will take you a long way. Which is understandable if one considers the law of large numbers: with a large enough number of trials, the mean converges to the expectation.

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4 May 2016

When simulating controller designs, the plant model used is often developed using the K.I.S.S. approach – Keep It Simple Stupid. A model should capture relevant phenomenon with as low level of detail as possible. The general idea is to verify controller behaviour against the plant model and to do the final tuning against an actual prototype.

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6 March 2016

Remember your friend from our very first post? . Well, I am sorry to say that he never really reached French Guyana. He ended up in Carcass, one of the Malvinas/Falkland islands. And his boat was (peacefully) captured by overly friendly pirate penguins. Now he spends his days counting penguins and sheep. He did keep a coin and this calculator as a memento from his past life. You know, just in case.

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