We introduce a numerically efficient simulation algorithm for Hawkes process with exponentially decaying intensity, a special case of general Hawkes process that is most widely implemented in practice. This computational method is able to exactly generate the point process and intensity process, by sampling interarrival-times directly via the underlying analytic distribution functions without numerical inverse, and hence avoids simulating intensity paths and introducing discretisation bias. Moreover, it is flexible to generate points with either stationary or non-stationary intensity, starting from any arbitrary time with any arbitrary initial intensity. It is also straightforward to implement, and can easily extend to multi-dimensional versions, for further applications in modelling contagion risk or clustering arrival of events in finance, insurance, economics and many other fields. Simulation algorithms for one dimension and multi-dimension are represented, with numerical examples of univariate and bivariate processes provided as illustrations.

Exact simulation of Hawkes process with exponentially decaying intensity

Under the influence of extrinsic curing conditions and intrinsic properties of carbon fiber reinforced resin composites, the formation of curing deformation is inevitable, which makes the shape of the manufactured components differ from the designed structure, and even exceeds the assembly tolerance, resulting in the scrap of parts. Therefore, it is very urgent and important to optimize the curing deformation of carbon fiber reinforced resin composites. In this paper, the mechanism of stress and curing deformation is reviewed firstly, and then the factors affecting the curing deformation are summarized. In particular, from the point of view of materials in curing process, three curing deformation control strategies, including (i) reinforcement structure optimization, (ii) resin modification and process optimization, (iii) die surface compensation and tool-part contact optimization, were proposed. And with the development of curing deformation simulation technology, the (iv) inverse design strategy before curing and (v) hot sizing method from the view of after cured were further put forward, respectively. By analyzing the link between processing details and curing deformation, it is found that the dominant factor affecting deformation may change under different conditions, so the interaction between factors needs to be further discussed. Subsequently, the effect of these distortion control methods on curing deformation was analyzed and evaluated, and the shortcomings were pointed out. Finally, the challenges existed in curing deformation research were identified, in order to contribute to the development of curing deformation research. 

Review of curing deformation control methods for carbon fiber reinforced resin composites

Residual stresses are detrimental to composite structures as they induce processing defects like debonding, delamination, and matrix cracking which significantly decrease their load-bearing capability. In this research, a new in-situ approach using digital image correlation is utilized to analyze the effect of the cure cycle modification on residual stress evolution during processing. It was found that the modified cure cycle comprising abrupt cooling after gelation reduces the residual stresses. Five different layup configurations are investigated to examine the effect of fiber direction. A maximum average residual stress reduction of 31.8% is observed for the balanced unsymmetric [30/-30/60/-60] laminate. The residual stress reduction results in an increase in failure strength between 4 and 12% in the different layups and can lead up to a 22% increase in first-ply failure strength.

Residual stress reduction during composite manufacturing through cure modification: In situ analysis

Despite a vast application of temporal point processes in infectious disease
 diffusion forecasting, ecommerce, traffic prediction, preventive
 maintenance, etc, there is no significant development in improving the
 simulation and prediction of temporal point processes in real-world
 environments. With this problem at hand, we propose a novel methodology for
 learning temporal point processes based on one-dimensional numerical
 integration techniques. These techniques are used for linearising the
 negative maximum likelihood (neML) function and enabling backpropagation of
 the neML derivatives. Our approach is tested on two real-life datasets.
 Firstly, on high frequency point process data, (prediction of highway
 traffic) and secondly, on a very low frequency point processes dataset,
 (prediction of ski injuries in ski resorts). Four different point process
 baseline models were compared: second-order Polynomial inhomogeneous
 process, Hawkes process with exponential kernel, Gaussian process, and
 Poisson process. The results show the ability of the proposed methodology to
 generalize on different datasets and illustrate how different numerical
 integration techniques and mathematical models influence the quality of the
 obtained models. The presented methodology is not limited to these datasets
 and can be further used to optimize and predict other processes that are
 based on temporal point processes

/pdf/a-machine-learning-approach-for-learning-temporal-point-2y8jv1bi.pdf

A machine learning approach for learning temporal point process

Secondary crashes or crashes that occur in the wake of a preceding or primary crash are among the most critical incidents occurring on highways, due to the exceptional danger they present to the first responders and victims of the primary crash. In this work, we developed a self-exciting temporal point process to analyze crash events data and classify it into primary and secondary crashes. Our model uses a self-exciting function to describe secondary crashes while primary crashes are modeled using a background rate function. We fit the model to crash incidents data from the Florida Department of Transportation, on Interstate-4 (I-4) highway for the years 20152017, to determine the model parameters. These are used to estimate the probability that a given crash is secondary crash and to find queue times. To represent the periodically varying traffic levels and crash incidents, we model the background rate, as a stationary function, a sinusoidal non-stationary function, and a piecewise non-stationary function. We show that the sinusoidal nonstationary background rate fits the traffic data better and replicates the daily and weekly peaks in crash events due to traffic rush hours. Secondary crashes are found to account for up to 15.09% of traffic incidents, depending on the city on the I4 Highway.

/pdf/point-process-modeling-of-secondary-crashes-2ddi2qb8qd.pdf

Point-Process modeling of Secondary Crashes

Cure shrinkage of the polymer matrix during the composite manufacturing process leads to residual stresses, which can adversely affect the structural integrity and dimensional stability of composite structures. In this paper, a novel approach is developed for measuring the resin shrinkage and strain evolution of an epoxy resin (EPON-862) in the composite manufacturing environment. The resin is cured in a custom designed autoclave with borosilicate viewports, while digital image correlation (DIC) is used to analyze the strain evolution throughout the cure cycle. These processing induced strains are correlated to the cure-state using differential scanning calorimetery (DSC). The different mechanisms involved in the polymer strain evolution during composite processing are discussed.

Samarth Motagi

Papers

Point-Process modeling of Secondary Crashes

In-Situ Investigation of Resin Shrinkage in the Composite Manufacturing Environment