# Daniel Nicolas WilkeUniversity of Pretoria | UP · Department of Mechanical & Aeronautical Engineering

Daniel Nicolas Wilke

PhD

Breaking rocks, virtually that is.

## About

127

Publications

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1,025

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Introduction

The Gradient-Only Optimization Guy - Optimization for Information is my Passion - Generative Modeling my Application - Nvidia GPUs my Calculator

Additional affiliations

January 2010 - December 2018

## Publications

Publications (127)

This paper proposes a generic approach to obtain semi-analytical mesh sensitivities and shows how to compute mesh updates for any tetrahedral mesher. The proposed strategy allows sensitivities to be computed for a given mesh or first improve an initial mesh and then compute sensitivities. The strategy is based on a modification of Persson and Stran...

Industrial-scale discrete element simulations typically generate Gigabytes of data per time step, which implies that even opening a single file may require 5 - 15 minutes on conventional magnetic storage devices. Data science’s inherent multi-disciplinary nature makes the extraction of useful information challenging, often leading to undiscovered d...

Discrete element modelling (DEM) is widely used to simulate granular systems, nowadays routinely on graphical processing units. Graphics processing units (GPUs) are inherently designed for parallel computation, and recent advances in the architecture, compiler design and language development are allowing general-purpose computation to be computed o...

Force chain networks are generally applied in granular materials to gain insight into inter-particle granular contact. For conservative spherical particle systems, i.e. frictionless and undamped, force chains are information complete due to symmetries resulting from isotropy and constant curvature of a sphere. In fact, for conservative spherical pa...

This paper introduces a boundary condition scheme for weakly compressible (WC) renormalised first-order accurate meshless Lagrangian methods (MLM) by considering both solid and free surface conditions.
A hybrid meshless Lagrangian method-finite difference (MLM-FD) scheme on prescribed boundary nodes is proposed to enforce Neumann boundary condition...

Causal models are an essential part of engineering. Physics-based causal models such as Finite Element Models, are prevalent in engineering. However, with the availability of large quantities of sensor data, data-driven causal models are much needed. A major challenge with causal models is capturing complex functional forms and maintaining the inte...

Latent variable models are important for condition monitoring as they learn, without any supervision, the healthy state of a physical asset as part of its latent manifold. This negates the need for labelled fault data and the application of supervised learning techniques. Latent variable models offer information from which health indicators can be...

Force chain networks are generally applied in granular materials to gain insight into inter-particle granular contact. For conservative spherical particle systems, i.e. frictionless and undamped, force chains are information complete due to symmetries resulting from isotropy and constant curvature of a sphere. In fact, for conservative spherical pa...

The development of ultrasonic guided wave monitoring systems has become increasingly important as they have demonstrated the ability to detect damage in structures. An example of such a system is the Ultrasonic Broken Rail Detection system which uses pitch-catch piezoelectric transducers permanently attached to the rail to excite and receive ultras...

It is important to develop reliable fault diagnosis and prognosis methods for critical mechanical assets such as wind turbines. Reliable fault diagnosis and prognosis methods ensure that the damage is detected early, the damage modes are accurately characterised, and the correct remaining life is inferred. This enables the appropriate maintenance d...

Condition monitoring for rotating machines under time-varying environmental and operating conditions remains an important research problem for several industries, including wind turbines within the renewable energy sector; ship, train and freight transport within the supply-chain sector; crushing and grinding comminution within the mining sector. P...

Advances in signal processing are complemented by advances in machine and deep learning and vice versa. In general, machine and deep learning are employed as discriminative models within a supervised setting. Progress in unsupervised generative modelling allows for generative models to be employed in discriminative (discrete classes) and deviation...

In this chapter, the fundamentals of learning-based techniques are introduced in a condition monitoring context. The objective is to provide a general overview of learning-based techniques and detail how these techniques are used in vibration-based condition monitoring. This chapter introduces learning-based techniques and introduces the notable di...

Reliable condition monitoring methods are required for rotating machines operating under time-varying operating conditions. The measured vibration signals typically contain information related to the different interacting components (e.g. gear mesh components, bearing fault components), the transmission paths between the excitation sources and the...

The Prototype Bootstrapping Method (PBM) is a sampling technique for nonlinear system identification specifically when applied to Accelerated Fatigue Testing (AFT). This application requires the number of samples taken to be limited as much as possible to preserve the integrity of the test. The work presents a generalization of this technique by re...

Oscillation-based testing of analogue electronic filters removes the need for test signal synthesis. Parametric faults in the presence of normal component tolerance variation are challenging to detect and diagnose. This study demonstrates the suitability of statistical learning and deep learning techniques for parametric fault diagnosis and detecti...

An under-resolved coupling strategy for the discrete element method (DEM) and the weakly compressible (WC) generalised finite difference method (GFD) is proposed. A novel filtering technique is proposed that allows for the recovery of a continuum porosity field in an arbitrary domain from DEM information. This allows fine spherical DEM particles to...

This paper presents a general and reliable shape optimization scheme for snap-through structures to match a target load-deflection curve. The simulation of the snap-through structures typically requires the Arc Length Control (ALC) method. The adaptive stepping in ALC creates unavoidable discontinuities in the objective function. A discontinuous ob...

Response reconstruction is used to obtain accurate replication of vehicle structural responses of field recorded measurements in a laboratory environment, a crucial step in the process of Accelerated Destructive Testing (ADA). Response Reconstruction is cast as an inverse problem whereby an input signal is inferred to generate the desired outputs o...

Selected chapters to be published and announced under
https://www.springer.com/series/13418

Mini-batch sub-sampling (MBSS) is favored in deep neural network training to reduce the computational cost. Still, it introduces an inherent sampling error, making the selection of appropriate learning rates challenging. The sampling errors can manifest either as a bias or variances in a line search. Dynamic MBSS re-samples a mini-batch at every fu...

Screw conveyors are widely used in several industries to transport various granular materials needed to manufacture products or components in a product chain. Degradation of the material and variable packing in the screw pitches are some of the significant operational concerns. This paper explores the effect that particle shape has on the material’...

This paper introduces a new method for model calibration. The model calibration procedure is applied on water networks for leak detection and can be used for other inverse and model calibration problems. The calibration process uses Artificial Neural Networks to transform the measurements to a fixed network. This technique is compared to the conven...

The Discrete Element Method (DEM) is increasingly used to study the failure behavior of rock. Despite DEM's intrinsic capability to capture the mechanical behavior of discontinua, there remains several open questions that include the numerical modelling of the meso-fracture evolution and behavior of brittle rock bodies. A Cohesive Fracture Model (C...

Learning rates in stochastic neural network training are currently determined a priori to training, using expensive manual or automated iterative tuning. Attempts to resolve learning rates adaptively, using line searches, have proven computationally demanding. Reducing the computational cost by considering mini-batch sub-sampling (MBSS) introduces...

The use of the Discrete Element Method to model engineering structures implementing granular materials has proven to be an efficient method to response under various behaviour conditions. However, the computational cost of the simulations increases rapidly, as the number of particles and particle shape complexity increases. An affordable solution t...

The possibility of accurately inferring the external forces applied to a vehicle can directly contribute to better safety systems and thus lowers the chance of injury or loss of life. These external forces are applied to a vehicle through the tyres and are challenging to measure directly. Still, it is possible to measure acceleration, deformation,...

A permanently installed Ultrasonic Broken Rail Detection system monitors the Sishen-Saldanha railway line in South Africa [1]. The system detects complete rail breaks at long-range using guided wave ultrasound. For the system to be reliable, its damage detection performance must be evaluated under actual environmental and operational conditions (EO...

The Discrete Element Method (DEM) was introduced 40 years ago by Cundall and Strack [1]. At the time, modelling large industrial scale applications was not possible, but as computation capabilities increased over the years, DEM has become the numerical method of choice for analysing granular materials in all kinds of industries. Examples include bu...

Parameter selection during the construction of surrogates is often conducted by minimizing the Mean Squared Cross-Validation Error (MSE-CV). Surrogates constructed using MSE are poorly optimized using gradient-based optimizers. Hence, Nelder–Mead like optimizers are often favoured, which is unfortunate as surrogates make analytical gradients freely...

A modelling framework for ultrasonic inspection of waveguides with arbitrary discontinuities, excited using piezoelectric transducers, is developed. The framework accounts for multi-modal, dispersive and damped one dimensional propagation over long distances. The proposed model is applied to simulate a realistic guided wave-based inspection of a we...

Gradient-only and probabilistic line searches have recently reintroduced the ability to adaptively determine learning rates in dynamic mini-batch sub-sampled neural network training. However, stochastic line searches are still in their infancy and thus call for an ongoing investigation. We study the application of the Gradient-Only Line Search that...

A generic framework for prognostics and health monitoring (PHM) which is rapidly deployable to heterogeneous fleets of assets would allow for the automation of predictive maintenance scheduling directly from operational data. Deep learning based PHM implementations provide part of the solution, but their main benefits are lost when predictions stil...

Gradient-only line searches (GOLS) adaptively determine step sizes along search directions for discontinuous loss functions resulting from dynamic mini-batch sub-sampling in neural network training. Step sizes in GOLS are determined by localizing Stochastic Non-Negative Associated Gradient Projection Points (SNN-GPPs) along descent directions. Thes...

Granular material (GM) is the second most manipulated substance in the world and is present in most industries either as raw materials or finished products. Often the temperature of the granular material needs to be manipulated for example in the case of heating iron ore to induce a phase change or to be kept within a certain temperature range in t...

Learning rates in stochastic neural network training are currently determined a priori to training, using expensive manual or automated iterative tuning. This study proposes gradient-only line searches to resolve the learning rate for neural network training algorithms. Stochastic sub-sampling during training decreases computational cost and allows...

In this study, transient non-Fourier heat transfer in a solid cylinder is analytically solved based on dual-phase-lag for constant axial heat flux condition. Governing equations for the model are expressed in two-dimensional cylindrical coordinates; the equations are nondimensionalized and exact solution for the equations is presented by using the...

Calibration remains an important challenge in the estimation of discrete element parameters. Importantly, the usability of the discrete element method (DEM) is directly dependent on the quality of the parameter estimation. Numerous approaches have been developed to characterize discrete element parameters directly from experimental data, often char...

Sinkholes are a common occurrence in Centurion, South Africa. The mechanisms associated with the propagation of a subsurface cavity to the soil surface during the formation of a sinkhole are poorly understood, resulting in overly conservative and potentially unrealistic methods for assessing the size of sinkholes. A series of deep-seated trapdoor e...

In this study we examine the rotational (in)variance of the differential evolution (DE) algorithm. We show that the classic DE/rand/1/bin algorithm, which uses constant mutation and standard crossover, is rotationally variant. We then study a previously proposed rotationally invariant formulation in which the crossover operation takes place in an o...

Choosing appropriate step sizes is critical for reducing the computational cost of training large-scale neural network models. Mini-batch sub-sampling (MBSS) is often employed for computational tractability. However, MBSS introduces a sampling error, that can manifest as a bias or variance in a line search. This is because MBSS can be performed sta...

Choosing appropriate step sizes is critical for reducing the computational cost of training large-scale neural network models. Mini-batch sub-sampling (MBSS) is often employed for computational tractability. However, MBSS introduces a sampling error, that can manifest as a bias or variance in a line search. This is because MBSS can be performed sta...

Fully resolved fluid–solid coupling is explored with the gradient corrected weakly compressible SPH methodology being used to simulate an incompressible Newtonian fluid as well as being used to obtain the coupling force information required to accurately represent these interactions. Gradient correction allows for the application of the Neumann bou...

Guided wave based monitoring systems require accurate knowledge of mode propagation characteristics such as wavenumber and group velocity dispersion curves. These characteristics may be computed numerically for a rail provided that the material and geometric properties of the rail are known. Generally, the rail properties are not known with suffici...

This paper investigates an inverse analysis technique to find leaks in water networks and compares different solution strategies. Although a number of strategies have been proposed by different authors to identify leaks on a vast selection of pipe networks, limited research has been done to compare strategies and point out their weakness. Three str...

In blast furnaces, burden topography and packing density affect the stability of the burden, permeability of gas flow as well as the heat transfer efficiency. A fundamental understanding of the influence and interaction of coke and ore particles on the burden topography and packing density is therefore essential, in particular, the influence of par...

Step sizes in neural network training are largely determined using predetermined rules such as fixed learning rates and learning rate schedules, which require user input to determine their functional form and associated hyperparameters. Global optimization strategies to resolve these hyperparameters are computationally expensive. Line searches are...

Step sizes in neural network training are largely determined using predetermined rules such as fixed learning rates and learning rate schedules, which require user input to determine their functional form and associated hyperparameters. Global optimization strategies to resolve these hyperparameters are computationally expensive. Line searches are...

Mini-batch sub-sampling is likely here to stay, due to growing data demands, memory-limited computational resources such as graphical processing units (GPUs), and the dynamics of on-line learning. Sampling a new mini-batch at every loss evaluation brings a number of benefits, but also one significant drawback: The loss function becomes discontinuou...

Mini-batch sub-sampling is likely here to stay, due to growing data demands, memory-limited computational resources such as graphical processing units (GPUs), and the dynamics of on-line learning. Sampling a new mini-batch at every loss evaluation brings a number of benefits, but also one significant drawback: The loss function becomes discontinuou...

The construction of surrogate models, such as radial basis function (RBF) and Kriging-based surrogates, requires an invertible (square and full rank matrix) or pseudoinvertible (overdetermined) linear system to be solved. This study demonstrates that the method used to solve this linear system may result in up to five orders of magnitude difference...

This paper presents the development and numerical implementation of a state variable based thermomechanical material model, intended for use within a fully implicit finite element formulation. Plastic hardening, thermal recovery and multiple cycles of recrystallisation can be tracked for single peak as well as multiple peak recrystallisation respon...

The reduction in particle size of raw materials using grinding mills is an energy and cost intensive task. Optimization of grinding processes is not trivial as obtaining experimental information is extremely difficult due to the harsh environment. Thus, computational modeling is the most feasible option for obtaining information on the dynamics of...

The reduction in particle size of raw materials using grinding mills is an energy and cost intensive task. Optimization of grinding processes is not trivial as obtaining experimental information is extremely difficult due to the harsh environment. Thus, computational modeling is the most feasible option for obtaining information on the dynamics of...

The discrete element method, implemented in a modular GPU based framework that supports polyhedral shaped particles
(Blaze-DEM), was used to investigate effects of particle shape on backﬁll response behind integral bridge abutments during
temperature-induced displacement cycles. The rate and magnitude of horizontal stress build-up were found to be...

The discrete element method, implemented in a modular GPU based framework that supports polyhedral shaped particles (Blaze-DEM), was used to investigate effects of particle shape on backfill response behind integral bridge abutments during temperature-induced displacement cycles. The rate and magnitude of horizontal stress build-up were found to be...

A near real-time optimal trajectory planning framework for UAVs is presented and tested in a series of low altitude obstacle avoidance planning scenarios. The framework uses the Inverse Dynamics Trajectory Optimisation approach with a quaternion point-mass aircraft dynamic model and a hybrid Differential Evolution and Sequential Quadratic Programmi...

Room temperature experimental compression test data is available for different hardmetals. This data indicates the presence of some spatial inhomogeneity due to a compression instability, eccentric loading or time varying equivalent bending moment. To account for this, an inverse analysis is employed that determines not only the constitutive materi...

Mixing of particulate systems is an important process to achieve uniformity, in particular pharmaceutical processes that requires the same amount of active ingredient per tablet. Several mixing processes exist, this study is concerned with mechanical mixing of crystalline particles using a four-blade mixer. Although numerical investigations of mixi...

Parameter tuning aims to find suitable parameter values for heuristic optimisation algorithms that allows for the practical application of such algorithms. Conventional tuning approaches view the tuning problem as two distinct problems, namely, a stochastic problem to quantify the performance of a parameter vector and a deterministic problem for fi...

Numerous practical applications of the Discrete Element Method (DEM) require a flexible description of particles that can account for irregular and non-convex particle shape features. Capturing the particle non-convexity is important since it allows to model the physical interlocking when the particles are in contact. To that end, the most flexible...

This book guides researchers away from the smooth and continuous comfort of classical optimization to the harsh realities of dealing with difficult and discontinuous functions, by using gradient-only optimization and gradient-only surrogates with ease. This work has found application from finding optimal shapes of structures to automating the train...

Permanently installed monitoring systems, which make use of guided wave ultrasound, can monitor long distances of rail track from a single transducer location. The design of these systems is complicated by the presence of numerous modes of propagation and dispersion. The dispersion characteristics are used during signal processing and need to be kn...

This chapter supplies the proofs for a number of theorems on which Chapters 1 to 4 have extensively relied on. In total nineteen proofs are presented of theorems that cover the characterization of unconstrained and constrained minima, saddle point conditions, conjugate gradient and Quasi-Newton methods.

A Taylor series expansion of a function allows us to approximate a function \(f(\mathbf {x})\) at any point \(\mathbf {x}\), based solely on information about the function at a single point \(\mathbf {x}^{i}\). Here, information about the function implies zero order, first order, second order and higher order information of the function at \(\mathb...

Care is usually taken during the mathematical modelling and numerical computation of the scalar function \(f(\mathbf{x})\) to ensure that it is smooth and twice continuously differentiable. As highlighted in Section 6.5, the presence of numerical noise in the objective function is sometimes an unintended consequence of the complicated numerical nat...

Consider the general constrained optimization problem: $$\begin{aligned} {\mathop {{{\mathrm{minimize\,}}}}_\mathbf{x}}&f(\mathbf{x})\nonumber \\ \text {such that }&g_j(\mathbf{x})\le 0\ \ j=1,2,\dots , m\\&h_j(\mathbf{x})=0\ \ j=1,2,\dots , r.\nonumber \end{aligned}$$The most simple and straightforward approach to handling constrained problems of...

Over the last 40 years many powerful direct search algorithms have been developed for the unconstrained minimization of general functions. These algorithms require an initial estimate to the optimum point, denoted by \(\mathbf{x}^0\). With this estimate as starting point, the algorithm generates a sequence of estimates \(\mathbf{x}^0\), \(\mathbf{x...

Python is a general purpose computer programming language. An experienced programmer in any procedural computer language can learn Python very quickly. Python is remarkable in that it is designed to allow new programmers to efficiently master programming. The choice of including Anaconda Python for application of our mathematical programming concep...

An extensive set of worked-out example optimization problems are presented in this chapter. They demonstrate the application of the basic concepts and methods introduced and developed in the previous three chapters. The reader is encouraged to attempt each problem separately before consulting the given detailed solution. This set of example problem...

In spite of the mathematical sophistication of classical gradient-based algorithms, certain inhibiting difficulties remain when these algorithms are applied to real-world problems. This is particularly true in the field of engineering, where unique difficulties occur that have prevented the general application of gradient-based mathematical optimiz...

The reduction of raw materials into particulate form using grinding mills is an energy and cost intensive task. Obtaining information on the dynamics of media is extremely difficult due to the harsh environment inside the mill. Computational modelling of the dynamics of the material inside the mill is the most feasible option to obtain information...