Carl Sandrock

Locating and characterizing the stationary points of the extended rosenbrock function

Two variants of the extended Rosenbrock function are analyzed in order to find the stationary points. The first variant is shown to possess a single stationary point, the global minimum. The second variant has numerous stationary points for high dimensionality. A previously proposed method is shown to be numerically intractable, requiring arbitrary precision computation in many cases to enumerate candidate solutions. Instead, a standard Newtonian method with multi-start is applied to locate stationary points. The relative magnitude of the negative and positive eigenvalues of the Hessian is also computed, in order to characterize the saddle points. For dimensions up to 100, only two local minimizers are found, but many saddle points exist. Two saddle points with a single negative eigenvalue exist for high dimensionality, which may appear as near local minima. The remaining saddle points we found have a predictable form, and a method is proposed to estimate their number. Monte Carlo simulation indicates that it is unlikely to escape these saddle points using uniform random search. A standard particle swarm algorithm also struggles to improve upon a saddle point contained within the initial population.

Dynamic simulation of Chemical Engineering systems using OpenModelica and CAPE-OPEN

Abstract Modelica has emerged as a strong contender in the arena of dynamic simulation languages. It was developed to be a standard, with an open specification and a large and usable standard library. OpenModelica is an Open Source implementation of a Modelica compiler and environment which is being developed actively. Modelicas object-oriented design makes it easy to develop chemical engineering unit operations and connect them to one another. Unfortunately, most proprietary databases of thermodynamic and physical properties and reaction data are not supplied in equation form, but rather as part of closed software. This means that such data must be exchanged with the programs that contain them if they are to be used in custom simulation codes. The CAPE-OPEN specification provides a standard architecture for these exchanges, in addition to support for incorporating new unit operations or algorithms into existing proprietary simulations. In this study, a Modelica library allowing interface between Modelica and CAPE-OPEN is developed. Its functionality is demonstrated using a model of a ten plate distillation column simulated in OpenModelica on a Linux machine, with thermodynamic and property data from Honeywell Unisim on aWindows machine. The data interfacing was done over a TCP/IP network using CORBA. It is found that real-time operation is possible, but that network overhead makes up a significant fraction of the running time, posing problems for faster-than-realtime off-line simulation and optimization.

Industry Expectations and Academic Practice in Control Engineering Education – A South African Survey

Abstract This paper presents an overview of the South African control systems landscape. It focuses on control engineering taught at universities and practiced in industry in South Africa and was compiled in the wake of the IFAC world congress 2014 in Cape Town. A background of engineering education in South Africa and control engineering in particular is presented. Two surveys were conducted among control engineering professionals: The first survey covers control engineering courses offered at South African universities at electrical, chemical and mechanical engineering departments. The second survey investigates control engineering in the workplace. A gap analysis maps industry expectations and university offerings.

A simplicial homology algorithm for Lipschitz optimisation

The simplicial homology global optimisation (SHGO) algorithm is a general purpose global optimisation algorithm based on applications of simplicial integral homology and combinatorial topology. SHGO approximates the homology groups of a complex built on a hypersurface homeomorphic to a complex on the objective function. This provides both approximations of locally convex subdomains in the search space through Sperner’s lemma and a useful visual tool for characterising and efficiently solving higher dimensional black and grey box optimisation problems. This complex is built up using sampling points within the feasible search space as vertices. The algorithm is specialised in finding all the local minima of an objective function with expensive function evaluations efficiently which is especially suitable to applications such as energy landscape exploration. SHGO was initially developed as an improvement on the topographical global optimisation (TGO) method. It is proven that the SHGO algorithm will always outperform TGO on function evaluations if the objective function is Lipschitz smooth. In this paper SHGO is applied to non-convex problems with linear and box constraints with bounds placed on the variables. Numerical experiments on linearly constrained test problems show that SHGO gives competitive results compared to TGO and the recently developed Lc-DISIMPL algorithm as well as the PSwarm, LGO and DIRECT-L1 algorithms. Furthermore SHGO is compared with the TGO, basinhopping (BH) and differential evolution (DE) global optimisation algorithms over a large selection of black-box problems with bounds placed on the variables from the SciPy benchmarking test suite. A Python implementation of the SHGO and TGO algorithms published under a MIT license can be found from https://bitbucket.org/upiamcompthermo/shgo/.

Modelling the Thermal Degradation and Stabilisation of PVC in a Torque Rheometer

Abstract A novel method for simulating the torque and temperature curves from a torque rheometer thermal stability test on poly(vinyl chloride) (PVC) was developed. A mathematical model was proposed which combines the chemical kinetics involved in the thermal degradation and stabilisation process of PVC with heat transfer and viscosity relationships within the torque rheometer. The model coefficients were fitted to data obtained from previous experiments with a program written in the Python programming language using the Levenberg-Marquardt Algorithm (LMA) with multiple starts. The mathematical model fits the torque rheometer data successfully depending on the characteristics of the torque curve. The model fit is successful when the torque curve follows the expected behaviour. An unsuccessful model fit occurs when the torque curve deviates from the expected shape in a very specific way. In the degradation phase the torque curve increases to a local maximum, decreases to a local minimum and then increases again. The exact reason for the dip in torque is unknown.

Development of a Generic Model of a Ruthenium Reactor

Conference paper : 12th International Symposium on Process Systems Engineering and 25th European Symposium on Computer Aided Process Engineering, 31-4 June 2015, Copenhagen, Denmark.

Best of breed control of platinum precipitation reactors

Abstract An existing batch precipitation reactor in the mining industry was modelled from first principles using MATLAB S-function language and wrapped into Simulink custom blocks. The model was validated with open loop simulations to evaluate the response to step changes in the model inputs. Two PID controllers with different parameters were implemented on the model at different operating points and their temperature control performance was evaluated based on their ability track a temperature of the industrial reactor as a set-point. The performance of the controllers was measured and compared using an integral time-domain performance measure. A commercial advanced process controller (APC) was implemented on the model, a communication interface between the model in Simulink and the commercial controller was developed with Industrial Data Xchange (IDX); an OPC client and server.

Eigenvector Analysis for the Ranking of Control Loop Importance

Abstract A method for optimizing the prioritization of base layer control loop maintenance by identifying control loops that have the greatest impact on overall plant-wide profitability is presented. The method is based on a modified form of the LoopRank algorithm originally proposed by Farenzena and Trierweiler (2009) and takes into account connectivity metric, performance measures and economical attributes. Various methods of obtaining a connectivity metric are discussed. The well-known Tennessee Eastman Plant problem is used to demonstrate the effectiveness of the method.

A generic framework for stochastic dynamic simulation of chemical engineering systems using free/open source software

Chemical engineering process modelling and simulation pose significant challenges to the computer program developer. Chemical processes are invariably described by non-linear equations such as chemical reaction kinetics, flow-pressure relationships and physical properties. Dynamic simulation of such systems involves the solution of sets of non-linear differential and algebraic equations. There is also uncertainty associated with the model equations themselves (model uncertainty), their parameters (parametric uncertainty) and the inputs into the model (input uncertainty). Tools that aid chemical engineers in the solution of these problems have been successfully commercialised and enjoy a measure of success, although the adoption of dynamic and stochastic simulation packages is lagging behind the steady-state flowsheeting tools. Commercial software solutions can be prohibitively expensive in addition to confining users to adhere to proprietary standards. The Free Software and Open Source movements have made inroads into providing non-proprietary alternatives to many commercial software packages, which has encouraged the adoption of open standards. This work presents a framework for the development of stochastic dynamic simulations of chemical processes using only free and open source software. The large problem of stochastic dynamic simulation has been broken down into stages: 1. Input modelling using Markov chain models trained on process data or seeded by hand in addition to stationary distribution models. This enables dynamic scenarios to be handled with the minimum of special case code generation. 2. Process modelling using an object-oriented approach in the Modelica language. Modelica has an actively developed open source implementation called OpenModelica and is an open standard modelling language. 3. Monte Carlo simulation using extensions to the OpenModelica compiler that ease parallel simulations 4. Postprocessing, including visualisation and statistical analysis. Statistics that are generated can be used for control evaluation purposes. The Tennessee-Eastman challenge process is used to illustrate its capabilities.

Control of a batch pulp digester using a simplified mechanistic model to predict degree of polymerisation

Effective control of the sulphite pulp digestion process in the production of dissolved pulp in a batch digester is limited by three important restrictions, namely: • the inability to measure the degree of polymerisation (DP) of the cellulose in the wood pulp, which is the controlled variable, • the fact that flowrate of steam to an external heat exchanger, through which the cooking liquor circulates, is the only manipulated variable available and that, • due to scheduling requirements, cook time per digester is fixed. The availability of substantial computational capability in industrial environments has rendered the traditional S-factor prediction of cook time to control DP inadequate, compared to what can be achieved with more sophisticated predictive models. A fundamental model, in simplified form, with adjustable parameters, was developed and its accuracy to predict DP based on given operating conditions was tested using available plant data. This model was built into a control structure for implementation on an operational batch digester. Because the parameters form part of fundamental relationships in the model, realistic bounds can be placed on them during the optimisation process, enabling a better understanding of the behaviour of the model. Overall control of the batch digestion process takes place in three interdependent, but distinct time frames, namely continuous control of digester temperature based on a calculated setpoint, using a model-based approach to predict DP on a cook-to-cook basis and lastly while the final DP must be kept on target through a number of cooks (N cooks), taking into account long-term changes in the process. This long-term optimisation takes place in the third time frame.