| 1. |
- Blomberg, Niclas, et al.
(författare)
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Approximate regularization path for nuclear norm based H2 model reduction
- 2014
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Ingår i: Proceedings of the IEEE Conference on Decision and Control. - : IEEE conference proceedings. ; , s. 3637-3641
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Konferensbidrag (refereegranskat)abstract
- This paper concerns model reduction of dynamical systems using the nuclear norm of the Hankel matrix to make a trade-off between model fit and model complexity. This results in a convex optimization problem where this tradeoff is determined by one crucial design parameter. The main contribution is a methodology to approximately calculate all solutions up to a certain tolerance to the model reduction problem as a function of the design parameter. This is called the regularization path in sparse estimation and is a very important tool in order to find the appropriate balance between fit and complexity. We extend this to the more complicated nuclear norm case. The key idea is to determine when to exactly calculate the optimal solution using an upper bound based on the so-called duality gap. Hence, by solving a fixed number of optimization problems the whole regularization path up to a given tolerance can be efficiently computed. We illustrate this approach on some numerical examples.
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| 2. |
- Blomberg, Niclas, 1986-, et al.
(författare)
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Approximate Regularization Paths for Nuclear Norm Minimization using Singular Value Bounds : with Implementation and Extended Appendix
- 2015
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Konferensbidrag (refereegranskat)abstract
- The widely used nuclear norm heuristic for rank minimizationproblems introduces a regularization parameter which isdifficult to tune. We have recently proposed a method to approximatethe regularization path, i.e., the optimal solution asa function of the parameter, which requires solving the problemonly for a sparse set of points. In this paper, we extendthe algorithm to provide error bounds for the singular valuesof the approximation. We exemplify the algorithms on largescale benchmark examples in model order reduction. Here,the order of a dynamical system is reduced by means of constrainedminimization of the nuclear norm of a Hankel matrix.
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| 3. |
- Blomberg, Niclas, 1986-
(författare)
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On Nuclear Norm Minimization in System Identification
- 2016
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In system identification we model dynamical systems from measured data. This data-driven approach to modelling is useful since many real-world systems are difficult to model with physical principles. Hence, a need for system identification arises in many applications involving simulation, prediction, and model-based control.Some of the classical approaches to system identification can lead to numerically intractable or ill-posed optimization problems. As an alternative, it has recently been shown beneficial to use so called regularization techniques, which make the ill-posed problems ‘regular’. One type of regularization is to introduce a certain rank constraint. However, this in general still leads to a numerically intractable problem, since the rank function is non-convex. One possibility is then use a convex approximation of rank, which we will do here.The nuclear norm, i.e., the sum of the singular values, is a popular, convex surrogate of the rank function. This results in a heuristic that has been widely used in e.g. signal processing, machine learning, control, and system identification, since its introduction in 2001. The nuclear norm heuristic introduces a regularization parameter which governs the trade-off between model fit and model complexity. The parameter is difficult to tune, and thecurrent thesis revolves around this issue.In this thesis, we first propose a choice of the regularization parameter based on the statistical properties of fictitious validation data. This can be used to avoid computationally costly techniques such as cross-validation, where the problem is solved multiple times to find a suitable parameter value. The proposed choice can also be used as initialization to search methods for minimizing some criterion, e.g. a validation cost, over the parameter domain.Secondly, we study how the estimated system changes as a function of the parameter over its entire domain, which can be interpreted as a sensitivity analysis. For this we suggest an algorithm to compute a so called approximate regularization path with error guarantees, where the regularization path is the optimal solution as a function of the parameter. We are then able to guarantee the model fit, or, alternatively, the nuclear norm of the approximation, to deviate from the optimum by less than a pre-specified tolerance. Furthermore, we bound the l2-norm of the Hankel singular value approximation error, which means that in a certain subset of the parameter domain, we can guarantee the optimal Hankel singular values returned by the nuclear norm heuristic to not change more (in l2-norm) than a bounded, known quantity.Our contributions are demonstrated and evaluated by numerical examples using simulated and benchmark data.
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| 4. |
- Blomberg, Niclas, et al.
(författare)
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Regularization Paths for Re-Weighted Nuclear Norm Minimization
- 2015
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Ingår i: IEEE Signal Processing Letters. - 1070-9908 .- 1558-2361. ; 22:11, s. 1980-1984
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Tidskriftsartikel (refereegranskat)abstract
- We consider a class of weighted nuclear norm optimization problems with important applications in signal processing, system identification, and model order reduction. The nuclear norm is commonly used as a convex heuristic for matrix rank constraints. Our objective is to minimize a quadratic cost subject to a nuclear norm constraint on a linear function of the decision variables, where the trade-off between the fit and the constraint is governed by a regularization parameter. The main contribution is an algorithm to determine the so-called approximate regularization path, which is the optimal solution up to a given error tolerance as a function of the regularization parameter. The advantage is that we only have to solve the optimization problem for a fixed number of values of the regularization parameter, with guaranteed error tolerance. The algorithm is exemplified on a weighted Hankel matrix model order reduction problem.
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| 5. |
- Blomberg, Sara, et al.
(författare)
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Bimetallic nanoparticles as a model system for an industrial NiMo catalyst
- 2019
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Ingår i: Materials. - : MDPI AG. - 1996-1944. ; 12:22
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Tidskriftsartikel (refereegranskat)abstract
- An in-depth understanding of the reactionmechanismis required for the further development of Mo-based catalysts for biobased feedstocks. However, fundamental studies of industrial catalysts are challenging, and simplified systems are often used without direct comparison to their industrial counterparts. Here, we report on size-selected bimetallic NiMo nanoparticles as a candidate for a model catalyst that is directly compared to the industrial system to evaluate their industrial relevance. Both the nanoparticles and industrial supported NiMo catalysts were characterized using surface- and bulk-sensitive techniques. We found that the active Ni and Mo metals in the industrial catalyst are well dispersed and well mixed on the support, and that the interaction between Ni and Mo promotes the reduction of the Mo oxide. We successfully produced 25 nm NiMo alloyed nanoparticles with a narrow size distribution. Characterization of the nanoparticles showed that they have a metallic core with a native oxide shell with a high potential for use as a model system for fundamental studies of hydrotreating catalysts for biobased feedstocks. © 2019 by the authors.
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| 6. |
- Ha, H., et al.
(författare)
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Reweighted nuclear norm regularization : A SPARSEVA approach
- 2015
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Ingår i: IFAC-PapersOnLine. - : Elsevier. - 2405-8963. ; 48:28, s. 1172-1177
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Tidskriftsartikel (refereegranskat)abstract
- The aim of this paper is to develop a method to estimate high order FIR and ARX models using least squares with re-weighted nuclear norm regularization. Typically, the choice of the tuning parameter in the reweighting scheme is computationally expensive, hence we propose the use of the SPARSEVA (SPARSe Estimation based on a VAlidation criterion) framework to overcome this problem. Furthermore, we suggest the use of the prediction error criterion (PEC) to select the tuning parameter in the SPARSEVA algorithm. Numerical examples demonstrate the veracity of this method which has close ties with the traditional technique of cross validation, but using much less computations.
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| 7. |
- Martin, Natalia, et al.
(författare)
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Intrinsic Ligand Effect Governing the Catalytic Activity of Pd Oxide Thin Films
- 2014
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Ingår i: ACS Catalysis. - : American Chemical Society (ACS). - 2155-5435. ; 4:10, s. 3330-3334
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Tidskriftsartikel (refereegranskat)abstract
- High-pressure X-ray photoelectron spectroscopy, mass spectrometry, and density functional theory calculations have been combined to study methane oxidation over Pd(100). The measurements reveal a high activity when a two-layer PdO(101) oriented film is formed. Although a one-layer PdO(101) film exhibits a similar surface structure, no or very little activity is observed. The calculations show that the presence of an oxygen atom directly below the coordinatively unsaturated Pd atom in the two-layer PdO(101) film is crucial for efficient methane dissociation, demonstrating a ligand effect that may be broadly important in determining the catalytic properties of oxide thin films.
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| 8. |
- Nilsson, Fay Lundh, et al.
(författare)
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Transforming and Financing Intermediate-Level Technical Education During Industrialisation : Sweden 1850-1920
- 2021
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Ingår i: Nordic Journal of Educational History. - Umeå : Umeå University Library. - 2001-7766 .- 2001-9076. ; 8:2, s. 95-124
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Tidskriftsartikel (refereegranskat)abstract
- Around 1900, Sweden had transformed into a modern industrial nation. A three-level technical school system, introduced in the 1850s, ensured that Sweden maintained a strong position among other industrialised countries. In this article, we study changes in the structure and financing of the technical secondary schools, the middle level of the system, between 1850 and 1919. Both local and national actors were important in the structural changes and educational reforms, but government grants remained the same for extended periods, which led to frequent discussions and pleas for increased funding. Low salaries compared to other forms of schooling and competition from the industry gradually became a problem recruiting qualified teachers. However, stakeholders who considered the education of middle-level technicians an important matter pushed for increased funding, improvements in teachers' salaries and employment conditions, and restructuring of the teaching to keep pace with technological development.
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