Flexible Machine Research Articles

Identification of gas-liquid two-phase flow patterns based on flexible ultrasound array and machine learning

Ultrasound technology has been recognized as the mainstream approach for the identification of gas-liquid two-phase flow patterns, which holds great value in engineering domain. However, commercial rigid probes are bulky, limiting their adaptability to curved surfaces. Here, we propose a strategy for autonomous identification of flow patterns based on flexible ultrasound array and machine learning. The array features high-performance 1–3 piezoelectric composite material, stretchable serpentine wires, soft Eco-flex layers and a polydimethylsiloxane (PDMS) adhesive layer. The resulting ultrasound array exhibits excellent electromechanical characteristics and offers a large stretchability for an intimate interfacial contact to curved surface without the need of ultrasound coupling agents. We demonstrated that the flexible ultrasound array combined with machine learning can accurately identify gas-liquid two-phase flow patterns, in a circular pipeline. This work presents an effective tool for recognizing gas-liquid two-phase flow patterns, offering engineering opportunities in petroleum extraction and natural gas transportation.

A causal inference framework for leveraging external controls in hybrid trials.

We consider the challenges associated with causal inference in settings where data from a randomized trial are augmented with control data from an external source to improve efficiency in estimating the average treatment effect (ATE). This question is motivated by the SUNFISH trial, which investigated the effect of risdiplam on motor function in patients with spinal muscular atrophy. While the original analysis used only data generated by the trial, we explore an alternative analysis incorporating external controls from the placebo arm of a historical trial. We cast the setting into a formal causal inference framework and show how these designs are characterized by a lack of full randomization to treatment and heightened dependency on modeling. To address this, we outline sufficient causal assumptions about the exchangeability between the internal and external controls to identify the ATE and establish a connection with novel graphical criteria. Furthermore, we propose estimators, review efficiency bounds, develop an approach for efficient doubly robust estimation even when unknown nuisance models are estimated with flexible machine learning methods, suggest model diagnostics, and demonstrate finite-sample performance of the methods through a simulation study. The ideas and methods are illustrated through their application to the SUNFISH trial, where we find that external controls can increase the efficiency of treatment effect estimation.

Engineering flexible machine learning systems by traversing functionally invariant paths

Contemporary machine learning algorithms train artificial neural networks by setting network weights to a single optimized configuration through gradient descent on task-specific training data. The resulting networks can achieve human-level performance on natural language processing, image analysis and agent-based tasks, but lack the flexibility and robustness characteristic of human intelligence. Here we introduce a differential geometry framework—functionally invariant paths—that provides flexible and continuous adaptation of trained neural networks so that secondary tasks can be achieved beyond the main machine learning goal, including increased network sparsification and adversarial robustness. We formulate the weight space of a neural network as a curved Riemannian manifold equipped with a metric tensor whose spectrum defines low-rank subspaces in weight space that accommodate network adaptation without loss of prior knowledge. We formalize adaptation as movement along a geodesic path in weight space while searching for networks that accommodate secondary objectives. With modest computational resources, the functionally invariant path algorithm achieves performance comparable with or exceeding state-of-the-art methods including low-rank adaptation on continual learning, sparsification and adversarial robustness tasks for large language models (bidirectional encoder representations from transformers), vision transformers (ViT and DeIT) and convolutional neural networks.

Air-Writing Recognition Enabled by a Flexible Dual-Network Hydrogel-Based Sensor and Machine Learning.

Accurate air-writing recognition is pivotal for advancing state-of-the-art text recognizers, encryption tools, and biometric technologies. However, most existing air-writing recognition systems rely on image-based sensors to track hand and finger motion trajectories. Additionally, users' writing is often guided by delimiters and imaginary axes which restrict natural writing movements. Consequently, recognition accuracy falls short of optimal levels, hindering performance and usability for practical applications. Herein, we have developed an approach utilizing a one-dimensional convolutional neural network (1D-CNN) algorithm coupled with an ionic conductive flexible strain sensor based on a sodium chloride/sodium alginate/polyacrylamide (NaCl/SA/PAM) dual-network hydrogel for intelligent and accurate air-writing recognition. Taking advantage of the excellent characteristics of the hydrogel sensor, such as high stretchability, good tensile strength, high conductivity, strong adhesion, and high strain sensitivity, alongside the enhanced analytical ability of the 1D-CNN machine learning (ML) algorithm, we achieved a recognition accuracy of ∼96.3% for in-air handwritten characters of the English alphabets. Furthermore, comparative analysis against state-of-the-art methods, such as the widely used residual neural network (ResNet) algorithm, demonstrates the competitive performance of our integrated air-writing recognition system. The developed air-writing recognition system shows significant potential in advancing innovative systems for air-writing recognition and paving the way for exciting developments in human-machine interface (HMI) applications.

Measurement and machining error assessment method for cycloid pump rotor profile based on STEP

Abstract The contour shape and machining precision of the rotor of an cycloid pump directly determine the sealing performance of the pump cavity. Precise measurement of contour machining errors is a crucial step in the manufacturing process. However, rotor contour curves are often designed by enterprises based on actual engineering needs, leading to inconsistency between the measured baseline contour and the designed contour, thus failing to accurately reflect the actual machining condition of the rotor. Therefore, this paper proposes a method for measuring the contour of the cycloid pump rotor and evaluating machining errors based on the standard for the exchange of product (STEP) files necessary for product design in manufacturing. Firstly, utilizing NX/OPEN API functions, contour coordinate points and unit normal vectors are obtained from the rotor’s STEP design data. Subsequently, by planning the process of measuring the closed continuous contour of the rotor, the transformation between the workpiece coordinate system and the measurement coordinate system is achieved to position the tested rotor, followed by analyzing the influence of different starting points on error measurement and evaluation determines the optimal starting point. Finally, a measurement sampling point strategy is established to collect data points of the actual machining contour of the rotor. By achieving the best matching between the actual machining contour and the measured baseline contour, a contour deviation calculation model is established. Utilizing gauge blocks enables accurate assessment of pitch deviation, radial runout, and tooth-to-tooth distance deviation, resulting in assessment results that better fit the actual meshing situation of the rotor. Experimental results verifies consistency between the measurements of the one-dimensional probe and Gleason measurements. This theory and method not only expand the measurement range of the one-dimensional probe but also provide more accurate and efficient guidance for the flexible machining of the rotor.

Filling Process Optimization of a Fully Flexible Machine through Computer Simulation and Advanced Mathematical Modeling

Filling Process Optimization of a Fully Flexible Machine through Computer Simulation and Advanced Mathematical Modeling

The performance of prognostic models depended on the choice of missing value imputation algorithm: a simulation study

ObjectiveThe development of clinical prediction models is often impeded by the occurrence of missing values in the predictors. Various methods for imputing missing values before modelling have been proposed. Some of them are based on variants of multiple imputation by chained equations, while others are based on single imputation. These methods may include elements of flexible modelling or machine learning algorithms, and for some of them user-friendly software packages are available. The aim of this study was to investigate by simulation if some of these methods consistently outperform others in performance measures of clinical prediction models. Study Design and SettingWe simulated development and validation cohorts by mimicking observed distributions of predictors and outcome variable of a real data set. In the development cohorts, missing predictor values were created in 36 scenarios defined by the missingness mechanism and proportion of non-complete cases. We applied three imputation algorithms that were available in R software: mice, aregImpute and missForest. These algorithms differed in their use of linear or flexible models, or random forests, the way of sampling from the predictive posterior distribution, and the generation of a single or multiple imputed data sets. For multiple imputation we also investigated the impact of the number of imputations. Logistic regression models were fitted with the simulated development cohorts before (full data analysis) and after missing value generation (complete case analysis), and with the imputed data. Prognostic model performance was measured by the scaled Brier score, c-statistic, calibration intercept and slope, and by the mean absolute prediction error evaluated in validation cohorts without missing values. Performance of full data analysis was considered as ideal. ResultsNone of the imputation methods achieved the model’s predictive accuracy that would be obtained in case of no missingness. In general, complete case analysis yielded the worst performance, and deviation from ideal performance increased with increasing percentage of missingness and decreasing sample size. Across all scenarios and performance measures, aregImpute and mice, both with 100 imputations, resulted in highest predictive accuracy. Surprisingly aregImpute outperformed full data analysis in achieving calibration slopes very close to 1 across all scenarios and outcome models. The increase of mice’s performance with 100 compared to 5 imputations was only marginal. The differences between the imputation methods decreased with increasing sample sizes and decreasing proportion of non-complete cases. ConclusionIn our simulation study, model calibration was more affected by the choice of the imputation method than model discrimination. While differences in model performance after using imputation methods were generally small, multiple imputation methods as mice and aregImpute that can handle linear or nonlinear associations between predictors and outcome are an attractive and reliable choice in most situations.

Jet mixing optimization using a flexible nozzle, distributed actuators, and machine learning

In this paper, we introduce the first jet nozzle allowing simultaneous shape variation and distributed active control, termed “Smart Nozzle” in the sequel. Our Smart Nozzle manipulates the jet with an adjustable flexible shape via 12 equidistant stepper motors and 12 equidistantly placed inward-pointing minijets. The mixing performance is evaluated with a 7 × 7 array of Pitot tubes at the end of the potential core. The experimental investigation is carried out in three steps. First, we perform an aerodynamic characterization of the unforced round jet flow. Second, we investigate the mixing performance under five representative nozzle geometries, including round, elliptical, triangular, squared, and hexagonal shapes. The greatest mixing area is achieved with the square shape. Third, the symmetric forcing parameters are optimized for each specified nozzle shape with a machine learning algorithm. The best mixing enhancement for a symmetric active control is obtained by the squared shape, which results in a 1.93-fold mixing area increase as compared to the unforced case. Symmetrically unconstrained forcing achieves a nearly 4.5-fold mixing area increase. The Smart Nozzle demonstrates the feasibility of novel flow control techniques that combine shape variation and active control, leveraging the capabilities of machine learning optimization algorithms.

Dynamic scheduling of hybrid flow shop problem with uncertain process time and flexible maintenance using NeuroEvolution of Augmenting Topologies

AbstractA hybrid flow shop is pivotal in modern manufacturing systems, where various emergencies and disturbances occur within the smart manufacturing context. Efficiently solving the dynamic hybrid flow shop scheduling problem (HFSP), characterised by dynamic release times, uncertain job processing times, and flexible machine maintenance has become a significant research focus. A NeuroEvolution of Augmenting Topologies (NEAT) algorithm is proposed to minimise the maximum completion time. To improve the NEAT algorithm's efficiency and effectiveness, several features were integrated: a multi‐agent system with autonomous interaction and centralised training to develop the parallel machine scheduling policy, a maintenance‐related scheduling action for optimal maintenance decision learning, and a proactive scheduling action to avoid waiting for jobs at decision moments, thereby exploring a broader solution space. The performance of the trained NEAT model was experimentally compared with the Deep Q‐Network (DQN) and five classical priority dispatching rules (PDRs) across various problem scales. The results show that the NEAT algorithm achieves better solutions and responds more quickly to dynamic changes than DQN and PDRs. Furthermore, generalisation test results demonstrate NEAT's rapid problem‐solving ability on test instances different from the training set.

Optimising production efficiency: Managing flexibility in Industry 4.0 systems via simulation

The digital transformation, propelled by Industry 4.0, is essential for businesses to adapt to evolving market demands and sustainability pressures. This study addresses the need for improved plant optimisation by enhancing machinery and workstations through advanced digital modelling. Using the Tecnomatix Plant Simulation environment, we developed a simulation platform to assess the feasibility of a flexible production system. The model, based on a validated case study, demonstrated a 15% improvement in system performance by incorporating varying levels of machine flexibility. This improvement highlights the importance of designing production systems that can adapt to changing requirements efficiently. The study shows how increased flexibility in manufacturing environments can enhance operational efficiency and machine utilisation across different scenarios.

Generalized Propensity Score Methods to Assess CKD-Associated Physiologic Factors and Risk of Kidney Failure in the Chronic Renal Insufficiency Cohort (CRIC) Study.

Epidemiologic studies have identified many biochemical risk factors for chronic kidney disease (CKD) progression that are correlates of kidney function, termed here 'CKD-associated physiologic factors'. Uncertainty remains if these factors are risk factors or risk markers accounting for aspects of kidney function not otherwise captured. We aimed to use flexible machine learning, a dynamic covariate history including kidney function informative markers, and generalized propensity score (GPS) weighting, to better control confounding for such exposures. We studied 3,052 adults with CKD in the Chronic Renal Insufficiency Cohort Study. We established a 2-year run-in period and assembled 90 variables that characterize variability and trends of selected CKD-associated physiologic factors and confounders. Using SuperLearner, we created a GPS for each CKD-associated physiologic factor and performed GPS-weighted Cox regressions. For context, we also evaluated results from traditional multivariable Cox proportional hazards models as in prior studies. Similar to traditional approaches, bicarbonate, calcium, potassium, hemoglobin, and PTH were each associated with risk of kidney failure using GPS weighting. The GPS approach detected non-linear associations in many factors, some of which were not detected with traditional models. We conclude that many associations between CKD-associated physiologic factors and kidney outcomes remain strong after GPS weighting.

Intelligent Solutions for Machine Tools Using System Sinumerik

The management of computerized numerical control (CNC) machines in production processes often involves complexities associated with programming efficiency and precision. This study investigates whether the Sinumerik system can enhance the productivity and flexibility of CNC machine programming. The integration of the Sinumerik system into CNC machines will lead to increased programming efficiency and reduced errors, thereby improving overall productivity in manufacturing operations. The study utilized a comparative analysis approach, examining the programming capabilities of CNC machines with and without the Sinumerik system. This involved the use of the Sinutrain Operate training program and the ShopTurn software environment to simulate and analyse different programming methods and their impacts on machine tool performance. Results indicate that the Sinumerik system significantly enhances the programming flexibility and efficiency of CNC machines. Machines equipped with Sinumerik demonstrated a higher precision in component production with considerably reduced programming times. The use of advanced managerial systems and interfaces provided by Sinumerik allowed for a streamlined programming process and minimized human error, confirming the system's effectiveness in improving manufacturing productivity.

Springback characteristics and influencing laws of four-axis flexible roll bending forming for aluminum alloy.

This study aims to solve the problem of springback control of aluminum alloy components in the rolling process, and the method of combining experiment and simulation is adopted. Firstly, a series of aluminum alloy samples are designed, and the four-axis flexible bending machine is used for precision roll bending. Secondly, the three-dimensional (3D) shape change data of the workpiece before and after roll bending is monitored and recorded in real-time by a high-precision 3D scanner. Meanwhile, aiming at different rolling process parameters of each group (including roll bend speed, feed rate, pre-deformation amount, mold curvature radius, and other factors), advanced finite element software is used to carry out detailed simulation and calculations. In addition, the coincidence is compared and analyzed between the actual experiment results and the simulation prediction. The stress-strain distribution and springback evolution of aluminum alloy during roll bending are described accurately. The experimental and simulation results show that the springback rate of aluminum alloy fluctuates in the range of 5% to 15% after four-axis flexible roll bending, and the specific springback value is influenced by various process parameters. For example, under the premise of keeping other conditions unchanged, when the roll bending speed is increased from 30mm/s to 60mm/s, the springback rate shows an upward trend of about 3%. By increasing the feed rate by 20%, an average decrease of about 7% in springback quantity is observed. It can be seen that the increase in roll bending speed can aggravate the springback phenomenon, and the appropriate increase in feed rate can play a certain role in restraining the springback. Further analysis shows that the choice of the mold curvature radius and pre-deformation amount also has a decisive influence on the springback characteristics. There is a nonlinear relationship between the two parameters and the amount of springback. Changing these two parameters in a specific range can effectively regulate the springback effect.

Mathematical Approach towards Adaptive Machine Learning Models for Dynamic Security Threats in Industrial IoT

The always changing nature of security dangers within the Industrialization Internet of Things (IIoT) makes it exceptionally difficult for standard security strategies to work. Since of this, versatile machine learning (ML) models got to be made that can respond to unused dangers in genuine time. This study proposes the utilize of versatile machine learning procedures as a better approach to form IIoT situations more secure. To begin with, the paper addresses the most security issues that IIoT frameworks have, cantering on how the frameworks must be able to alter to address unused dangers. Cutting edge online dangers are exceedingly cleverly and alter quickly, frequently resisting conventional security measures. This appears how vital it is to discover arrangements that can alter rapidly. The proposed customizable machine learning show employments real-time information streams sent by IIoT gadgets to keep risk recognizable proof and defence strategies up to date. These models utilize strategies such as design acknowledgment, peculiarity discovery, and prescient analytics to distinguish bizarre behavior which will indicate a security breach. By learning from past information and adjusting to modern designs and patterns, the models can distinguish known and obscure dangers more precisely and rapidly. A key angle that creates this customizable machine learning models work so well is the truth that they can operate autonomously in IIoT situations. They complement standard rule-based strategies with energetic data-driven bits of knowledge and work consistently with current security frameworks. This combination permits you to halt dangers some time recently they happen and react rapidly, decreasing the probability of a security occurrence and the harm it may cause. The study also covers the technical pieces and strategies required to convey adaptable machine learning in an IIoT environment. She talks approximately the challenges that emerge in collecting and planning information, preparing models, and drawing conclusions in genuine time. She emphasizes the significance of having a high-performance, versatile framework that can handle huge sums of information of different sorts. The study talks about important issues like privacy, data security, and following the rules when using flexible machine learning models in IIoT ecosystems that are sensitive. It supports open and responsible methods to make sure that release is done in an ethical way and that operations are safe from threats from enemies.

A machine learning algorithm for the automatic classification of Phytophthora infestans genotypes into clonal lineages

AbstractPremiseThe prompt categorization of Phytophthora infestans isolates into described clonal lineages is a key tool for the management of its associated disease, potato late blight. New isolates of this pathogen are currently classified by comparing their microsatellite genotypes with characterized clonal lineages, but an automated classification tool would greatly improve this process. Here, we developed a flexible machine learning–based classifier for P. infestans genotypes.MethodsThe performance of different machine learning algorithms in classifying P. infestans genotypes into its clonal lineages was preliminarily evaluated with decreasing amounts of training data. The four best algorithms were then evaluated using all collected genotypes.ResultsmlpML, cforest, nnet, and AdaBag performed best in the preliminary test, correctly classifying almost 100% of the genotypes. AdaBag performed significantly better than the others when tested using the complete data set (Tukey HSD P < 0.001). This algorithm was then implemented in a web application for the automated classification of P. infestans genotypes, which is freely available at https://github.com/cpatarroyo/genotypeclas.DiscussionWe developed a gradient boosting–based tool to automatically classify P. infestans genotypes into its clonal lineages. This could become a valuable resource for the prompt identification of clonal lineages spreading into new regions.

Similarity coefficient and TOPSIS methods for designing flexible machine cell layout: a case study of electrical and electronic industries

Similarity coefficient and TOPSIS methods for designing flexible machine cell layout: a case study of electrical and electronic industries

A causal machine-learning framework for studying policy impact on air pollution: A case-study in COVID-19 lockdowns.

When studying the impact of policy interventions or natural experiments on air pollution, such as new environmental policies and opening or closing an industrial facility, careful statistical analysis is needed to separate causal changes from other confounding factors. Using COVID-19 lockdowns as a case-study, we present a comprehensive framework for estimating and validating causal changes from such perturbations. We propose using flexible machine learning-based comparative interrupted time series (CITS) models for estimating such a causal effect. We outline the assumptions required to identify causal effects, showing that many common methods rely on strong assumptions that are relaxed by machine learning models. For empirical validation, we also propose a simple diagnostic criterion, guarding against false effects in baseline years when there was no intervention. The framework is applied to study the impact of COVID-19 lockdowns on NO2 in the eastern US. The machine learning approaches guard against false effects better than common methods and suggest decreases in NO2 in Boston, New York City, Baltimore, and Washington D.C. The study showcases the importance of our validation framework in selecting a suitable method and the utility of a machine learning based CITS model for studying causal changes in air pollution time series.

Research Progress and Prospect on Profile Roll Forming Methods and Equipment

Abstract: In recent years, with the development of aerospace, automotive, rolling stock, shipbuilding, military weapons and other industries, the demand for bent and rolled parts is increasing, and the requirements for roll forming accuracy are growing. With the rapid development of coal power, hydropower, nuclear power, wind power, and petrochemical industries, the design and research on roll bending machine and the profile roll forming methods have come into focus. The purpose of this study is to summarize the classification and characteristics of roll bending equipment, analyze the reasons that affect the accuracy of profile bending, and propose specific solutions. This paper summarizes the research status and patents on the existing roll bending equipment, introduces its structural characteristics, differences, and molding effects, and focuses on the difficulties, optimization, and improvement methods of roll bending molding. In this paper, the mechanical structures of the existing roll forming equipment have been analyzed and compared, the effects of different roll forming equipment on the profile bending results have been determined, and the reasons affecting the bending accuracy have been pointed out. By summarizing the patents and research on profile roll forming methods and equipment, the current situation and future research prospects of roll forming equipment are discussed. The roll forming equipment is divided into a roll bending machine, a CNC roll bending machine, and a flexible roll bending machine. Each design can meet different profile processing needs. From the design point of view, the optimization under the given processing profile can achieve relatively high processing accuracy. However, the processing of different profiles will still produce geometric defects, and there is some space for improvement in the structure of roll forming equipment, the materials of processing rollers, and the NC interactive system. Thus, further research on profile roll forming is needed in the future.

Heavy-load Nonapod: A novel flexible redundant parallel kinematic machine for multi-DoF forming process

The high-performance multi-DoF forming process (MDFP) necessitates a 6-DoF forming machine tool with high normal and lateral stiffness to bear large normal and lateral forming force of millions of Newton (MN). However, the payload of parallel kinematic machine (PKM) is generally limited to thousands of Newton (kN), which restricts its application in MDFP. Therefore, this paper aims to develop a novel heavy load PKM with high stiffness for MDFP. To maximise the normal stiffness, a 6-PSS PKM with zero base angle and horizontal driver is proposed. Further, the inner force transfer model of 6-PSS PKM is established, indicating that the normal stiffness will be maximised when the link force approaches to be vertical. Consequently, a design criterion for maximising normal stiffness, i.e., the root mean square error (RMSE) for horizontal projection of all links should be minimised, is established. To maximise the lateral stiffness, general force balance equations of 6-PSS PKM are derived, indicating that lateral force can cause unintended negative force of links, significantly reducing the lateral stiffness. Thus, a novel auxiliary 3-SPS configuration is employed to provide additional force system to mitigate this negative force via hydraulic links. Correspondingly, a design criterion for maximising lateral stiffness, i.e., all link force should remain positive, is proposed. By combining aforementioned design criterion and kinetostatic models, a near-singular 6-PSS PKM with maximising normal stiffness is achieved, and dimension parameters of 3-SPS PKM with maximising lateral stiffness are optimised. On this basis, a novel flexible redundant 6-PSS/3-SPS PKM with both high normal and lateral stiffness is proposed, and a novel heavy load Nonapod with payload of 8 MN and payload-mass ratio of 40 is developed, showing good stiffness performance. The plastic deformation mechanisms of multi-DoF formed aviation bevel gear are revealed, and experimentally formed aviation bevel gear in the new Nonapod achieves good accuracy, microstructure and mechanical performance. This work provides a new methodology for synthesis of heavy load PKM with high normal and lateral stiffness, and has significant application prospect in PKM under heavy load working condition.

Machine learning based on functional principal component analysis to quantify the effects of the main drivers of wheat yields

Assessing the response of crop yield to year-to-year climate variability at the field scale is often done using process-based models and regression techniques. Although powerful, these tools rely on strong assumptions and can lead to substantial prediction errors. In this study, we investigate the use of a flexible machine learning algorithm combining Functional Principal Component Analysis and Random Forest, to relate field scale wheat yield to local daily climate variables. Instead of computing seasonal, monthly or any other arbitrary time-frame climate averages, climate time series are decomposed by Functional Principal Component Analysis into a few data-driven basis functions, called Principal Curves, in order to summarize the dynamic of key climate variables by a limited number of interpretable components. Scores associated to these components are then used as inputs of a Random Forest algorithm for yield prediction and for analysing important factors responsible for yield variability. To evaluate our approach, we use a French national database including wheat yield data as well as climate and management practice data for 298 farm fields from 2011 to 2016 in four main producing regions. Depending on the regions, our approach can explain from 62 % to 81 % of the yield variability when both agronomic and climate variables are included, down to 56–81 % when ignoring agronomic variables and 51–74 % when ignoring climate variables. Based on a year-by-year cross-validation, RMSE ranges from 0.5 t ha−1 to 2.1 t ha−1 in non-extreme years (2012–2015). However, prediction error can reach 3.6 t ha−1 in case of exceptional weather conditions, such as those experienced in 2016 in Northern France. We find that this new approach performs in most cases better than the same machine learning algorithm using the usual time averages of climate variables, without the need to choose an arbitrary time-frame. We then show how important patterns in weather time series can be identified and how their effects on yield can be interpreted using the proposed modelling framework.