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In fast nonlinear model predictive control the sensitivitycomputation is one of the key aspects to reducecomputational burden, in fact specific automated andefficient procedures for that have been developed. Howeverthe number of sensitivity computations required toadequately approximate the nonlinear dynamics is typicallyhigh and fixed a priori. In this paper, we developa sensitivity updating scheme capable of reducing thenumber of sensitivity computations exploiting an onlinecurvature-based measure of nonlinearity of the system.The proposed strategy is applied to the sequentialquadratic programming framework with specific attentionto the Real-Time Iteration implementation. Simulationson the inverted pendulum benchmark show asignificant reduction of the number of the sensitivity updates,hence a reduction of the overall computationaltime.

Deep Learning approaches have revolutionized in the past decade the field of Computer Vision and, as a consequence, they are having a major impact in Industry 4.0 applications like automatic defect classification. Nevertheless, additional data, beside the image/video itself, is typically never exploited in a defect classification module: this aspect, given the abundance of data in data-intensive manufacturing environments (like semiconductor manufacturing) represents a missed opportunity. In this work we present a use case related to Scanning Electron Microscope (SEM) images where we exploit a  Bayesian approach to improve defect classification. We validate our approach on a real-world case study and by employing modern Deep Learning architectures for classification.

The advent of the Industrial Internet of Things (IIoT) has led to the availability of huge amounts of data, that can be used to train advanced Machine Learning algorithms to perform tasks such as Anomaly Detection, Fault Classification and Predictive Maintenance. Even though not all pieces of equipment are equipped with sensors yet, usually most of them are already capable of logging warnings and alarms occurring during operation. Turning this data, which is easy to collect, into meaningful information about the health state of machinery can have a disruptive impact on the improvement of efficiency and up-time. The provided dataset consists of a sequence of alarms logged by packaging equipment in an industrial environment. The collection includes data logged by 20 machines, deployed in different plants around the world, from 2019-02-21 to 2020-06-17. There are 154 distinct alarm codes, whose distribution is highly unbalanced. This data can be used to address the following tasks: 

1. Next alarm forecasting: this problem can be framed as a supervised multi-class classification task, or a binary classification task when a specific alarm code is considered.
2. Predicting alarms occurring in a future time frame: here the goal is to forecast the occurrence of certain alarm types in a future time window. Since many alarms can occur, this is a supervised multi-label classification.
3. Future alarm sequence prediction: here the goal is predicting an ordered sequence of future alarms, in a sequence-to-sequence forecasting scenario.
4. Anomaly Detection: the task is to detect abnormal equipment conditions, based on the pattern of alarms sequence. This task can be either unsupervised, if only the input sequence is considered, or supervised if future alarms are taken into account to assess whether or not there is an anomaly.

 All of the above tasks can also be studied from a continual learning perspective. Indeed, information about the serial code of the specific piece of equipment can be used to train the model; however, a scalable model should also be easy to apply to new machines, without the need of a new training from scratch. The collection and release of this dataset has been supported by the Regione Veneto project PreMANI (MANIFATTURA PREDITTIVA: progettazione, sviluppo e implementazione di soluzioni di Digital Manufacturing per la previsione della Qualita e la Manutenzione Intelligente - PREDICTIVE MAINTENANCE: design, development and implementation of Digital Manufacturing solutions for the intelligent quality and maintenance systems).

Machine Learning-based Anomaly Detection (AD) approaches are efficient tools to monitor complexprocesses. One of the advantages of such approaches is that they provide a unique anomaly indicator,a quantitative index that captures the degree of ’outlierness’ of the process at hand considering possiblyhundreds or more variables at the same time, the typical scenario in semiconductor manufacturing. Oneof the drawback of such approaches is that Root Cause Analysis is not guided by the system itself. Inthis work, we show the effectiveness of a method, called DIFFI, to equip Isolation Forest, one of themost popular AD algorithms, with interpretability traits that can help corrective actions and knowledgeunderstanding. Such approach is validated on real world semiconductor manufacturing data related to aChemical Vapor Deposition process.

We propose a Deep Learning (DL)-based approach for production performance forecasting in fresh products packaging. On the one hand, this is a very demanding scenario where high throughput is mandatory; on the other, due to strict hygiene requirements, unexpected downtime caused by packaging machines can lead to huge product waste. Thus, our aim is predicting future values of key performance indexes such as Machine Mechanical Efficiency (MME) and Overall Equipment Effectiveness (OEE). We address this problem by leveraging DL-based approaches and historical production performance data related to measurements, warnings and alarms. Different architectures and prediction horizons are analyzed and compared to identify the most robust and effective solutions. We provide experimental results on a real industrial case, showing advantages with respect to current policies implemented by the industrial partner both in terms of forecasting accuracy and maintenance costs. The proposed architecture is shown to be effective on a real case study and it enables the development of predictive services in the area of Predictive Maintenance and Quality Monitoring for packaging equipment providers.

In modern manufacturing scenarios, detecting anomalies in production systems is pivotal to keep high-quality standards and reduce costs. Even in the Industry 4.0 context, realworld monitoring systems are often simple and based on the use of multiple univariate control charts. Data-driven technologies offer a whole range of tools to perform multivariate data analysis that allow to implement more effective monitoring procedures. However, when dealing with complex data, common data-driven methods cannot be directly used, and a feature extraction phase must be employed. Feature extraction is a particularly critical operation, especially in anomaly detection tasks, and it is generally associated with information loss and low scalability. In this paper we consider the task of Anomaly Detection with twodimensional, image-like input data, by adopting a Deep Learningbased monitoring procedure, that makes use of convolutional autoencoders. The procedure is tested on real Optical Emission Spectroscopy data, typical of semiconductor manufacturing. The results show that the proposed approach outperforms classical feature extraction procedures.

Two methods based on Regression are presented to determine the moisture content of items, e.g. clothes and the like, which are introduced in a household laundry dryer appliance. The aim of this work is to develop Soft Sensors (SS) for a household Heat Pump Washer-Dryer (WD-HP) to provide an estimation of the desired signal (the laundry moisture during drying) avoiding the use of additional physical sensors with the goal of improving the current performance in terms of precision and energy consumption of the automatic drying cycle end and using the machine equipment already available. On an algorithmic point of view, the SS developed in this work exploits regularization methods and Genetic Programming for Symbolic Regression in order to find suitable models for the purpose at hand. Proposed approaches have been tested on real data provided by an industrial partner.

Industry 4.0 encapsulates methods, technologies, and procedures that transform data into informed decisions and added value inan industrial context. In this regard, technologies such as Virtual Metrology or Soft Sensing have gained much interest in thelast two decades due to their ability to provide valuable knowledge for production purposes at limited added expense. However,these technologies have struggled to achieve wide-scale industrial adoption, largely due to the challenges associated with handlingcomplex data structures and the feature extraction phase of model building. This phase is generally hand-engineered and basedon specific domain knowledge, making it time consuming, difficult to automate, and prone to loss of information, thus ultimatelylimiting portability. Moreover, in the presence of complex data structures, such as 2-dimensional input data, there are no establishedprocedures for feature extraction. In this paper, we present a Deep Learning approach for Virtual Metrology, called DeepVM,that exploits semi-supervised feature extraction based on Convolutional Autoencoders. The proposed approach is demonstratedusing a real world semiconductor manufacturing dataset where the Virtual Metrology input data is 2-dimensional Optical EmissionSpectrometry data. The feature extraction method is tested with different types of state-of-the-art autoencoder.

In the past recent years, Machine Learning methodologies have been applied in countless application areas. In particular, they play a key role in enabling Industry4.0. However, one of the main obstacles to the diffusion of Machine Learning-based applications is related to the lack of interpretability of most of these methods. In this work, we propose an approach for defining a ‘feature importance’ in Anomaly Detection problems. Anomaly Detection is an important Machine Learning task that has an enormous applicability in industrial scenarios. Indeed, it is extremely relevant for the purpose of quality monitoring. Moreover, it is often the first step towards the design of a Machine Learning based smart monitoring solutions because Anomaly Detection can be implemented without the need of labelled data. The proposed feature importance evaluation approach is designed for Isolation Forest, one of the most commonly used algorithm for Anomaly Detection. The efficacy of the proposed method is tested on synthetic and real industrial datasets.

Embedding household appliances with smart capabilities is becoming common practice among major fabric-care producers that seek competitiveness on the market by providing more efficient and easy-to-use products. In Vertical Axis Washing Machines (VA-WM), knowing the laundry composition is fundamental to setting the washing cycle properly with positive impact both on energy/water consumption and on washing performance. An indication of the load typology composition (cotton, silk, etc.) is typically provided by the user through a physical selector that, unfortunately, is often placed by the user on the most general setting due to the discomfort of manually changing configurations. An automated mechanism to determine such key information would thus provide increased user experience, better washing performance, and reduced consumption; for this reason, we present here a data-driven soft sensor that exploits physical measurements already available on board a commercial VA-WM to provide an estimate of the load typology through a machine-learning-based statistical model of the process. The proposed method is able to work in a resource-constrained environment such as the firmware of a VA-WM.

The aim is to develop soft sensors (SSs) to provide an estimation of the laundry moisture of clothes introduced in a household Heat Pump Washer–Dryer (WD-HP) appliance. The developed SS represents a cost-effective alternative to physical sensors, and it aims at improving the WD-HP performance in terms of drying process efficiency of the automatic drying cycle. To this end, we make use of appropriate Machine Learning models, which are derived by means of Regularization and Symbolic Regression methods. These methods connect easy-to-measure variables with the laundry moisture content, which is a difficult and costly to measure variable. Thanks to the use of SSs, the laundry moisture estimation during the drying process is effectively available. The proposed models have been tested by exploiting real data through an experimental test campaign on household drying machines.

Exploiting the huge amount of data collected by industries is definitely one of the main challenges of the so-called Big Data era. In this sense, Machine Learning has gained growing attention in the scientific community, as it allows to extract valuable information by means of statistical predictive models trained on historical process data. In Semiconductor Manufacturing, one of the most extensively employed data-driven applications is Virtual Metrology, where a costly or unmeasurable variable is estimated by means of cheap and easy to obtain measures that are already available in the system. Often, these measures are multi-dimensional, so traditional Machine Learning algorithms cannot handle them directly. Instead, they require feature extraction, that is a preliminary step where relevant information is extracted from raw data and converted into a design matrix. Features are often hand-engineered and based on specific domain knowledge. Moreover, they may be difficult to scale and prone to information loss, affecting the effectiveness and maintainability of machine learning procedures. In this paper, we present a Deep Learning method for semi-supervised feature extraction based on Convolutional Autoencoders that is able to overcome the aforementioned problems. The proposed method is tested on a real dataset for Etch rate estimation. Optical Emission Spectrometry data, that exhibit a complex bi-dimensional time and wavelength evolution, are used as input.

In the context of Smart Monitoring and Fault Detection and Isolation in industrial systems, the aim of Predictive Maintenance technologies is to predict the happening of process or equipment faults. In order for a Predictive Maintenance technology to be effective, its predictions have to be both accurate and timely for taking strategic decisions on maintenance scheduling, in a cost-minimization perspective. A number of Predictive Maintenance technologies are based on the use of “health factors” quantitative indicators associated with the equipment wear that exhibit a monotone evolution. In real industrial environment, such indicators are usually affected by measurement noise and non-uniform sampling time. In this work we present a methodology, formulated as a stochastic filtering problem, to optimally predict the evolution of the aforementioned health factors based on noisy and irregularly sampled observations. In particular, a hidden Gamma process model is proposed to capture the nonnegativity and nonnegativity of the derivative of the health factor. As such filtering problem is not amenable to a closed form solution, a numerical Monte Carlo approach based on particle filtering is here employed. An adaptive parameter identification procedure is proposed to achieve the best trade-off between promptness and low noise sensitivity. Furthermore, a methodology to identify the risk function associated to the observed equipment based on previous maintenance data is proposed. The present study is motivated and tested on a real industrial Predictive Maintenance problem in semiconductor manufacturing, with reference to a dry etching equipment.

Fabric care home appliances are pervasive inhouses worldwide and manufactures are constantly working for improving product performance, efficiency, and usability. From a manufacturing perspective, increase of performancehas to be attained while minimizing the increase of production costs. In this context, a Soft Sensor for estimating the clothes load weight in a horizontal axis household washing machines ishere presented. The proposed Soft Sensor is based on Machine Learning approaches. Several methodologies, both time-seriesand feature-based, are employed and compared. The approach has been tested on real world data on commercial household washing machines.

In laundry treatment appliances, the weight ofthe laundry loaded by the user inside the drum dramaticallyaffects the operating behavior. Therefore, it is important toobtain a good estimate of the said quantity in order tocorrectly configure the machine before the washing/dryingstarts. In Vertical Axis Washing Machinesthe laundry weightis computed by exploiting the quantity of water absorbed bythe clothes. However, such approach does not grant accurateresults because the water absorption depends on the clothesfabric. For this reason, we propose a Soft Sensing approachfor weight estimation that exploits the information obtainedfrom physical sensors available on board without added costs.Data-driven Soft Sensors are developed, where, using MachineLearning techniques, a statistical model of the phenomenon ofinterest is created from a set of sample data.

The laundry weight of the loaded in the drum of a laundry treatment machine is an important piece of information; laundry weight can be used to set various washing/drying cycle parameters and to optimize performances and efficiency. Unfortunately, dedicated weight sensors cannot be included in consumer laundry equipment given the related costs. For this reason, we present in this work a soft sensor approach for estimating laundry weight based on sensors already in place in a laundry treatment equipment; in particular, we consider here a heat pump tumble dryer as case study. The proposed soft sensor is based on regularization, a popular approach in Machine Learning to provide models without overfitting the training data. Different studies are provided in this work, by considering different constrains on timing and complexity of the Soft Sensor solution. The developed Soft Sensors have been tested on laboratory data provided by an industrial partner.

Smart production monitoring is a crucial activity in advanced manufacturing for quality, control and maintenance purposes. Advanced Monitoring Systems aim to detect anomalies and trends; anomalies are data patterns that have different data characteristics from normal instances, while trends are tendencies of production to move in a particular direction over time. In this work, we compare state-of-the-art ML approaches (ABOD, LOF, onlinePCA and osPCA) to detect outliers and events in high-dimensional monitoring problems. The compared anomaly detection strategies have been tested on a real industrial dataset related to a Semiconductor Manufacturing Etching process

Advanced Monitoring Systems are fundamental in advanced manufacturing for control, quality and maintenance purposes. Nowadays, with the increasing availability of data in production and equipment, the need for high-dimensional Anomaly Detection techniques is thriving; anomalies are data patterns that have different data characteristics from normal production instances and that may be associated with faults or drifts in production. Tools for dealing with high-dimensional monitoring problems are provided by Machine Learning: in this paper, we test the performance of a state-of-the-art anomaly detection technique, called Isolation Forest, on a real industrial dataset related to Etching, one of the most important semiconductor manufacturing process. The monitoring has been performed exploiting Optical Spectroscopy Data.

Virtual Metrology is one of the most prominentAdvanced Process Control applications in SemiconductorManufacturing. The goal of Virtual Metrology is to provideestimations of quantities that are important for production andto assess process quality, but are costly or impossible to bemeasured. Virtual Metrology solutions are based on MachineLearning approaches. The bottleneck of developing VirtualMetrology solutions is generally the feature extraction phase thatcan be time-consuming, and can deeply affect the estimationperformance. In particular, in presence of data with additionaldimensions, such as time, feature extraction is typicallyperformed by means of heuristic approaches that may pickfeatures with poor predictive capabilities. In this work, wepropose the usage of modern Deep Learning approaches tobypass manual feature extraction and to provide highperformanceautomatic Virtual Metrology modules. Theproposed methodology is tested on a real industrial datasetrelated to Etching. The dataset at hand contains OpticalEmission Spectroscopy data and it is paradigmatic of the featureextraction problem under examination.

The invention relates to a method for the determination of a laundry weight in a laundry treatment appliance comprising: Selecting a laundry program in the laundry treatment appliance; Starting the selected laundry program; Sensing a plurality of parameters indicating operating conditions of the laundry treatment appliance during the laundry program; and Predicting a weight of the laundry present within the laundry treatment appliance based on said plurality of parameters by means of a data-driven soft sensor.

In this paper an approach to deal with Predictive Maintenance (PdM) problems with time-series data is discussed. PdM is a important approach to tackle maintenance and it is gaining an increasing attention in advanced manufacturing to minimize scrap materials, downtime, and associated costs. PdM approaches are generally based on Machine Learning tools that require the availability of historical process and maintenance data. Given the exponential growth in data logging in modern equipment, time series dataset are increasingly available in PdM applications. To exploit time series data for PdM, a functional learning methodology, namely Supervised Aggregative Feature Extraction (SAFE), is here employed on a semiconductor manufacturing maintenance problem.

In this paper a multiple classifier machine learning methodology for Predictive Maintenance (PdM) is presented. PdM is a prominent strategy for dealing with maintenance issues given the increasing need to minimize downtime and associated costs. One of the challenges with PdM is generating so called ’health factors’ or quantitative indicators of the status of a system associated with a given maintenance issue, and determining their relationship to operating costs and failure risk. The proposed PdM methodology allows dynamical decision rules to be adopted for maintenance management and can be used with high-dimensionaland censored data problems. This is achieved by training multiple classification modules with different prediction horizons to provide different performance trade-offs in terms of frequency of unexpected breaks and unexploited lifetime and then employing this information in an operating cost based maintenance decision system to minimise expected costs. The effectiveness of the methodology is demonstrated using a simulated example and a benchmark semiconductor manufacturing maintenance problem.

In semiconductor manufacturing, wafer quality control strongly relies on product monitoring and physical metrology. However, the involved metrology operations, generally performed by means of scanning electron microscopes, are particularly cost-intensive and time-consuming. For this reason, in common practice a small subset of only a productive lot is measured at the metrology stations and it is devoted to represent the entire lot. Virtual Metrology (VM) methodologies are able to obtain reliable predictions of metrology results at process time, without actually performing physical measurements; this goal is usually achieved by means of statistical models and by linking process data and context information to target measurements. Since semiconductor manufacturing processes involve a high number of sequential operations, it is reasonable to assume that the quality features of a given wafer (such as layer thickness and critical dimensions) depend on the whole processing and not on the last step before measurement only. In this paper, we investigate the possibilities to enhance VM prediction accuracy by exploiting the knowledge collected from previous process steps. We present two different schemes of multi-step VM, along with dataset preparation indications; special consideration will be reserved to regression techniques capable of handling high-dimensional input spaces. The proposed multi-step approaches are tested on production data provided by a partner semiconductor manufacturing industry. 

Faulty operations of Heating, Ventilation and Air Conditioning (HVAC) chiller systems can lead to discomfort for the occupants, energy wastage, unreliability and shorter equipment life. Such faults need to be detected early to prevent further escalation and energy losses. Commonly, data regarding unforeseen phenomena and abnormalities are rare or are not available at the moment of HVAC systems installation: for this reason in this paper an unsupervised One-Class SVM classifier employed as a novelty detection system to identify unknown status and possible faults is presented. The approach, that exploits Principal Component Analysis to accent novelties w.r.t. normal operations variability, has been tested on a HVAC literature dataset.

Technological advances and the ever-growing human quest for improving the resolution of telescope observations are motivating the design of larger and larger ground telescopes: indeed, the larger is the telescope lens diameter, the better is the diffraction limited resolution of the telescope. Unfortunately, the terrestrial atmospheric turbulence, if not properly compensated, negatively affects the telescope observations, limiting its real resolution. Adaptive Optics (AO) systems are used in large ground telescopes in order to compensate the effect of the atmosphere, and hence to make the real telescope resolution be determined by the diffraction properties of the lens.

Technological advances and the ever-growing human quest for improving the resolution of telescope observations are motivating the design of larger and larger ground telescopes: indeed, the larger is the telescope lens diameter, the better is the diffraction limited resolution of the telescope. Unfortunately, the terrestrial atmospheric turbulence, if not properly compensated, negatively affects the telescope observations, limiting its real resolution. Adaptive Optics (AO) systems are used in large ground telescopes in order to compensate the effect of the atmosphere, and hence to make the real telescope resolution be determined by the diffraction properties of the lens. AO systems exploit the measurements of wavefront sensors to estimate the current values of the atmospheric turbulence, and compensate its effect by properly adapting the shape of a set of deformable mirrors. As the size of the telescope lenses is increasing, then the size of the AO system (e.g. the number of deformable mirror actuators and the size of the wavefront sensor) is increasing as well. This causes the increase of the computational burden needed to compute a proper compensation of the effect of the atmosphere. Consequently, as the potential telescope resolution increases, the task of the AO systems becomes more challenging. Motivated by the need of providing AO solutions useful for the next generations of ground telescopes, then a number of efficient algorithms have been recently considered in the literature to solve the problems related to the AO system. This paper considers the combination of a recently proposed very efficient phase reconstruction method, namely the CuRe, with a properly defined Kalman filter in order to obtain a dynamic compensation of the atmospheric turbulence. The performance of the proposed approach is investigated in some simulations.

Turbulence simulation methods are of fundamental importance for evaluating the performance of control strategies for Adaptive Optics (AO) systems. In order to obtain a reliable evaluation of the performance a statistically accurate turbulence simulation method has to be used. This work generalizes a previously proposed method for turbulence simulation based on the use of a multiscale stochastic model. The main contributions of this work are: first, a multiresolution local PCA representation is considered. In typical operating conditions, the computational load for turbulence simulation is reduced approximately by a factor of 4, with respect to the previously proposed method, by means of this PCA representation. Second, thanks to a different low resolution method, based on a moving average model, the wind velocity can be in any direction (not necessarily that of the spatial axes). Finally, this paper extends the simulation procedure to generate, if needed, turbulence samples by using a more general model than that of the frozen flow hypothesis.

In semiconductor fabrication processes, effectivemanagement of maintenance operations is fundamental todecrease costs associated with failures and downtime. PredictiveMaintenance (PdM) approaches, based on statistical methodsand historical data, are becoming popular for their predictivecapabilities and low (potentially zero) added costs. We presenthere a PdM module based on Support Vector Machines forprediction of integral type faults, that is, the kind of failuresthat happen due to machine usage and stress of equipmentparts. The proposed module may also be employed as a healthfactor indicator. The module has been applied to a frequentmaintenance problem in semiconductor manufacturing industry,namely the breaking of the filament in the ion-source ofion-implantation tools. The PdM has been tested on a realproduction dataset.

In semiconductor manufacturing plants, monitoring physical properties of all wafers is crucial to maintain good yield and high quality standards. However, such an approach is too costly, and in practice, only few wafers in a lot are actually monitored. Virtual metrology (VM) systems allow to partly overcome the lack of physical metrology. In a VM scheme, tool data are used to predict, for every wafer, metrology measurements. In this paper, we present a VM system for a chemical vapor deposition (CVD) process. On the basis of the available metrology results and of the knowledge, for every wafer, of equipment variables, it is possible to predict CVD thickness. In this work, we propose a VM module based on least angle regression to overcome the problem of high dimensionality and model interpretability. We also present a statistical distance-based clustering approach for the modeling of the whole tool production. The proposed VM models have been tested on industrial production data sets.

Models typically used to simulate the influence of atmospheric turbulence on ground telescope observations are usually based on the frozen flow hypothesis. However, the frozen flow model of the atmosphere is valid at time scales of the order of tens/hundreds of milliseconds. This paper generalizes a previous model for turbulence simulation to ensure reliable tests of AO system performance in realistic working conditions. The proposed method relies on the use of two simulation models: First, the part of turbulence that shows a coherent flow at short time scales is simulated by means of a multiscale autoregressive-moving average model, which allows to efficiently simulate (with computational complexity O(n)) the coherent evolution of the turbulence. Secondly, an approach similar to that considered for dynamic textures, is used to simulate aberrations caused by processes that evolve on much longer time scales. The proposed procedure is tested on simulations.

Motivated by the increasing importance of Adap- tive Optics (AO) systems for improving the real resolution of large ground telescopes, and by the need of testing the AO system performance in realistic working conditions, in this paper we address the problem of simulating the turbulence effect on ground telescope observations at high resolution. The multiscale approach presented here generalizes that in [3]: First, a relevant computational time reduction is obtained by exploiting a local spatial principal component analysis (PCA) representation of the turbulence. Furthermore, differently from [3], the turbulence at low resolution is modeled as a moving average (MA) process. While in [3] the wind velocity was restricted to be directed along one of the two spatial axes, the approach proposed here allows to evolve the turbulence indifferently in all the directions. In our simulations the pro- posed procedure reproduces with good accuracy the theoretical statistical characteristics of the turbulent phase.

Motivated by the increasing importance of adaptive optics (AO) systems for improving the real resolution of large ground telescopes, and by the need of testing the AO system performance in realistic working conditions, in this paper we address the problem of simulating the turbulence effect on ground telescope observations at high resolution. The procedure presented here generalizes the multiscale stochastic approach introduced in our earlier paper [Appl. Opt. 50, 4124 (2011)], with respect to the previous solution, a relevant computational time reduction is obtained by exploiting a local spatial principal component analysis (PCA) representation of the turbulence. Furthermore, the turbulence at low resolution is modeled as a moving average (MA) process, while previously [Appl. Opt. 50, 4124 (2011)] the wind velocity was restricted to be directed along one of the two spatial axes, the use of such MA model allows the turbulence to evolve indifferently in all the directions. In our simulations, the proposed procedure reproduces the theoretical statistical characteristics of the turbulent phase with good accuracy.

In large ground telescopes the Adaptive Optics (AO) system aims at compensating the atmosphere effect on telescope measurements, and, the use of optimal filtering is fundamental for such task. This work is motivated by two important characteristics of new AO systems: on one hand, because of the request of very high measurement resolutions, the size of new telescopes, and of their sensors, is quickly increasing in the last decades, thus imposing to the AO systems the analysis of larger amount of data. On the other hand, the optimal filter has to be periodically updated according to temporal changes in atmosphere characteristics. Hence, it is of fundamental importance the use of computationally efficient algorithms for the update of the optimal filter gain.
This paper proposes some changes to a recently presented method for the efficient computation, in the frequency domain, of the Kalman gain for large AO systems [15]. The proposed changes, which mainly aim at correcting some issues due to the conversion spatial–frequency domain, and viceversa, allow to compute a better approximation of the optimal Kalman gain, and, consequently, significantly improve the performance of the AO system.

In current and next generation of ground tele- scopes, Adaptive Optics (AO) are employed to overcome the detrimental effects induced by the presence of atmospheric turbulence, that strongly affects the quality of data transmission and limits the actual resolution of the overall system. The analysis as well as the prediction of the turbulent phase affecting the light wavefront is therefore of paramount importance to guarantee the effective performance of the AO solution.
In this work, a layered model of turbulence is proposed, based on the definition of a Markov-Random-Field whose pa- rameters are determined according to the turbulence statistics. The problem of turbulence estimation is formalized within the stochastic framework and conditions for the identifiability of the turbulence structure (numbers of layers, energies and velocities) are stated. Finally, an algorithm to allow the layer detection and characterization from measurements is designed. Numerical simulations are used to assess the proposed procedure and validate the results, confirming the validity of the approach and the accuracy of the detection.

Smart management of maintenances has become fundamental in manufacturing environments in order to decrease downtime and costs associated with failures. Predictive Maintenance (PdM) systems based on Machine Learning (ML) techniques have the possibility with low added costs of drastically decrease failures-related expenses; given the increase of availability of data and capabilities of ML tools, PdM systems are becoming really popular, especially in semiconductor manufacturing. A PdM module based on Classification methods is presented here for the prediction of integral type faults that are related to machine usage and stress of equipment parts. The module has been applied to an important class of semiconductor processes, ion-implantation, for the predictionof ion-source tungsten filament breaks. The PdM has been tested on a real production dataset.

Measurements of large ground telescopes are af- fected by the presence of the terrestrial atmospheric turbulence: local changes of the atmospheric refraction index (e.g. due to wind and temperature variations) cause a non flat surface of the wavefront of light beams incoming on the telescope, thus degrading the quality of the observed images. Adaptive Optics (AO) systems are of fundamental importance to reduce such atmospheric influence on ground telescopes and thus to obtain high resolution observations. The goal of the AO system is that of estimating and compensating the atmospheric turbulence effect by properly commanding a set of deformable mirrors.
Because of delays in the closed loop system, the Kalman filter plays an important role in ensuring an effective control perfor- mance by providing good atmosphere predictions. However, the need of periodically updating the Kalman filter gain because of changes in the atmosphere characteristics, the increase of telescopes and sensors resolutions and the high sampling rate impose quite strict restrictions to the computational load for computing the Kalman gain.
Motivated by the above considerations, some strategies have been recently considered in the system theory and astronomical communities for the efficient computation of the Kalman gain for large AO systems. Specifically, this paper presents some changes to a recently proposed procedure: the proposed approach, which exploits some results in the control theory of distributed systems, computes an approximation of the optimal gain in the frequency domain exploiting the spatial homogeneity of the system. Then, the control strategy takes advantage of some information on the turbulent phase dynamic, that is estimated from the turbulence measurements. Performances of the proposed method are investigated in some simulations.

Ion Implantation is one of the most sensitiveprocesses in Semiconductor Manufacturing. It consists inimpacting accelerated ions with a material substrate and isperformed by an Implanter tool. The major maintenanceissue of such tool concerns the breaking of the tungstenfilament contained within the ion source of the tool. Thiskind of fault can happen on a weekly basis, and theassociated maintenance operations can last up to 3 hours.It is important to optimize the maintenance activities bysynchronizing the Filament change operations with otherminor maintenance interventions. In this paper, a PredictiveMaintenance (PdM) system is proposed to tackle such issue;the filament lifetime is estimated on a statistical basisexploiting the knowledge of physical variables acting onthe process. Given the high-dimensionality of the data,the statistical modeling has been based on RegularizationMethods: Lasso, Ridge Regression and Elastic Nets. Thepredictive performances of the aforementioned regularizationmethods and of the proposed PdM module have beentested on actual productive semiconductor data.

Silicon Epitaxial Deposition is a process strongly influenced by wafer temperature behaviour, that has to be constantly monitored to avoid the production of defective wafers. However, temperature measurements are not reliable and the sensors have to be appropriately calibrated with some dedicated procedure. A Predictive Maintenance (PdM) System is proposed here with the aim of predicting process behaviour and scheduling control actions on the sensors in advance. Two different prediction techniques have been employed and compared: the Kalman predictor and the Particle Filter with Gaussian Kernel Density Estimator. The accuracy of the PdM module has been tested on real industrial production datasets.

Soft Sensors (SSs) are on-line estimators of “hardly to be measured” quantities of a process. The difficultyin measuring can be related to economic or temporal costs that cannot be afforded in a high-intensivemanufacturing production. In semiconductor manufacturing this technology goes with the name of Virtual Metrology(VM) systems. While a lot of efforts in research have been produced in the past years to identify the bestregression algorithms for these statistical modules, small amount of work has been done to develop algorithms fordata clustering of the entire production. This paper contains a new Information Theory-based approach to dataclustering for Virtual Metrology and Soft Sensors; the proposed algorithm allows to automatically split the datasetinto groups to be equally modeled. The proposed approach has been tested on real industrial dataset.

Virtual Metrology (VM) module have become popular in the past years and they are now widely adopted in the semiconductor plants. However, nowadays, still few works have been presented to deal with the interaction between VM and Run-to-Run (R2R), the most common control approach in the fabs. We present in this paper a new strategy to integrate VM with R2R based on Information Theory measure. The proposed control method penalizes statistical measure based on their statistical distance from the physical measure. This new approach also cope with the virtual loop control, where the R2R runs for several process iterations without in-situ measures, but based only on VM predictions. The results are compared with the actual state-of-the-art. 

Semiconductor manufacturing is one of the most technologically advanced industrial sectors. Process quality and control are critical for decreasing costs and increasing yield. The contribution of automatic control and statistical modeling in this area can drastically impact production performance. For this reason in the past decade major collaborative research projects have been undertaken between fab industries and academia in the areas of Virtual Metrology, Predictive Maintenance, Fault Detection, Run-to-Run control and modeling. In this paper we review some this research, discuss its impact on production and highlight current challenges. 

In semiconductor manufacturing plants, monitoringphysical properties of all wafers is fundamental in order tomaintain good yield and high quality standards. However, suchan approach is too costly and in practice only few wafers in a lotare actually monitored. Virtual Metrology (VM) systems allowto partly overcome the lack of physical metrology. In a VMscheme, tool data are used to predict, for every wafer, metrologymeasurements. In this paper, we present a VM system for aChemical Vapor Deposition (CVD) process. On the basis ofthe available metrology results and of the knowledge, for everywafer, of equipment variables, it is possible to predict CVDthickness. In this work we propose a VM module based onLARS to overcome the problem of high dimensionality andmodel interpretability. The proposed VM models have beentested on industrial production data sets.

In semiconductor manufacturing, state of the art for wafer quality control relies on product monitoring and feedback control loops; the involved metrology operations, performed by means of scanning electron microscopes, are particularly cost-intensive and time-consuming. For this reason, it is not possible to evaluate every wafer: in common practice, a small subset of a productive lot is measured at the metrology station and devoted to represent the whole lot. Virtual Metrology (VM) methodologies are able to obtain reliable predictions of metrology results at process time, without actually performing physical measurements; this goal is usually achieved by means of statistical models, linking process data and context information to target measurements. Since semiconductor manufacturing processes involve a high number of sequential operations, it is reasonable to assume that the quality features of a certain wafer (such as layer thickness, critical dimensions, electrical test results) depend on the whole processing and not only on the last step before measurement. In this paper, we investigate the possibilities to improve the Virtual Metrology quality relying on knowledge collected from previous process steps. We will present two different scheme of multistep VM, along with dataset preparation indications; special consideration will be reserved to regression techniques capable of handling high dimensional input spaces. The proposed multistep approaches will be tested against actual data from semiconductor manufacturing industry. 

This paper considers the problem of simulating the turbulence effect on ground telescope observations. The approach presented here is an evolution of a recently proposed approach [3]. The main contributions with respect to [3] are: First, the Haar transform at the basis of the multiscale model in [3] is shown to be equivalent to a local PCA representation. This equivalence allows to reduce the computational complexity of the simulation algorithm by neglecting the components in the signal with lower energy. Furthermore, the simulation of nonstationary turbulence is obtained by properly changing the values of the multiscale model: Such change is eased by the invariance of the PCA spatial basis with respect to the change of turbulence statistical characteristics. The proposed approach is validated by means of some simulations.

Epitaxy is a process strongly dependent onwafer temperature. Unfortunately, the performance ofthe pyrometers in charge of sensing wafer temperaturedeteriorate with the usage. This represents the majormaintenance issue for epitaxy process engineers who haveto frequently calibrate pyrometers emissivity coefficient. Atthe present state the change of the emissivity coefficient isheuristically based on fab tradition and process engineersexperience. We present a statistical tool to map therelationship between change in the temperature readingsand emissivity adjustments. The module has been testedon real industrial dataset.

Nowadays, the adaptive optics (AO) system is of fundamental importance to reduce the effect of atmospheric turbulence on the images formed on large ground telescopes. In this paper the AO system takes advantage of the knowledge of the current turbulence characteristics, that are estimated by data, to properly control the deformable mirrors. The turbulence model considered in this paper is based on two assumptions: considering the turbulence as formed by a discrete set of layers moving over the telescope lens, and each layer is modeled as a Markov-Random-Field. The proposed Markov-Random-Field approach is exploited for estimating the layers’ characteristics. Then, a linear predictor of the turbulent phase, based on the computed information on the turbulence layers, is constructed. Since scalability and low computational complexity of the control algorithms are important requirements for real AO systems, the computational complexity properties of the proposed model are investigated. Interestingly, the proposed model shows a good scalability and an almost linear computational complexity thanks to its block diagonal structure. Performances of the proposed method are investigated by means of some simulations.

Simulating the turbulence effect on ground telescope observations is of fundamental importance for the design and test of suitable control algorithms for adaptive optics systems. In this paper we propose a multiscale approach for efficiently synthesizing turbulent phases at very high resolution. First, the turbulence is simulated at low resolution, taking advantage of a previously developed method for generating phase screens. Then, high-resolution phase screens are obtained as the output of a multiscale linear stochastic system. The multiscale approach significantly improves the computational efficiency of turbulence simulation with respect to recently developed methods. Furthermore, the proposed procedure ensures good accuracy in reproducing the statistical characteristics of the turbulent phase.

Silicon Epitaxial Deposition is a process strongly influenced by wafer temperature behavior, that has to be constantly monitored to avoid the production of defective wafers. A Predictive Maintenance (PdM) System is here proposed with the aim of predicting process behavior and scheduling control actions in advance. Two different prediction techniques have been employed and compared: the Kalman predictor and the Particle Filter with Gaussian Kernel Density Estimator. The accuracy of the PdM module has been tested on real fab data. The proposed approach is flexible and can handle the presence of different recipes on the same equipment.

In semiconductor manufacturing plants, monitoring of all wafers is fundamental in order to maintain good yield and high quality standards. However, this is a costly approach and in practice only few wafers in a lot are actually monitored. With a Virtual Metrology (VM) system it is possible to partly overcome the lack of physical metrology. In a VM scheme, tool data are used to predict, for every wafer, metrology measurements. In this paper, we present a VM system for a Chemical Vapor Deposition (CVD) process. Various data mining techniques are proposed. Due to the huge fragmentation of data derived from CVD's mixed production, several kind of data clustering have been adopted. The proposed models have been tested on real productive industrial data sets.