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Publisher Copyright: © 2021 The first step for any graph signal processing (GSP) procedure is to learn the graph signal representation, i.e., to capture the dependence structure of the data into an adjacency matrix. Indeed, the adjacency matrix is typically not known a priori and has to be learned. However, it is learned with errors. A little attention has been paid to modelling such errors in the adjacency matrix, and studying their effects on GSP methods. However, modelling errors in the adjacency matrix will enable both to study the graph error effects in GSP and to develop robust GSP algorithms. In this paper, we therefore introduce practically justifiable graph error models. We also study, both analytically when possible and numerically, the graph error effect on the performance of GSP methods in different types of problems such as filtering of graph signals and independent component analysis of graph signals (graph decorrelation). (c) 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

Dispersion and aggregation of wind power plants lower the uncertainty of wind power by reducing wind power forecasting errors. Using quantitative methods, this paper studies the dispersion's impact on the uncertainty of the aggregated wind power production. A method to simulate day‐ahead forecast error distributions at different dispersion and forecasting skill scenarios is presented. The proposed method models the uncertainty of wind power forecasting on an annual basis and at different levels of production. As a result, the uncertainty in the forecasting of spatially dispersed wind power plants is modelled using two continuous distributions: Laplace and beta distribution. The analysis shows that even the production level uncertainty can be modelled in various dispersion and forecasting skill scenarios. The model for aggregated forecast error distributions requires only four variables: capacity‐weighted distance of the total wind power plant fleet, mean of the site‐specific mean absolute errors (MAEs), number of aggregated wind power plants, and the mean variability of the elevations from the proximities of the aggregated wind power plants. The results are especially promising when the number of aggregated wind power plants exceeds five, the terrain complexity is low or moderate, and the aggregation region is large. This is demonstrated through a case study for Texas, United States.

As the share of wind power increases in the power system, also the share of uncertain generation increases. This, in turn, increases the total balancing energy, real-time balancing power requirements and ramping of the balancing generation. In this study, the impact of wind power forecast errors on the real-time balancing need was investigated for different shares of wind energy (4–30%) in Finland and the Nordic region (comprising Denmark, Finland, Norway and Sweden). The size of the aggregation area of the net imbalances has an impact on the net imbalance volumes. The larger the size of the area is, the smaller the normalised net imbalance volumes are. In Finland, the impact of wind forecast errors on the net imbalance volumes and the largest net imbalances is almost two times as large as the impact of wind power forecast errors in the Nordic region. A shorter forecast horizon has an impact of similar magnitude both on reducing the net imbalance volumes and the largest net imbalances and on aggregating imbalances from large spatial areas. When day-ahead forecasts are not corrected intraday (ID) the impact on the net imbalance volumes and the largest net imbalances is twice as large as when ID forecasts are used.

With a change of signal notion to graph signal, new means of performing blind source separation (BSS) appear. Particularly, existing independent component analysis (ICA) methods exploit the non-Gaussianity of the signals or other types of prior information. For graph signals, such prior information is present in a graph of dependencies in the signals. We propose BSS of graph signals which uses the prior information presented by the signal graph together with nonGaussianity. We derive the identifiability conditions for the proposed method and compare them to the conditions when only graph or non-Gaussianity approach is used. In simulation studies, we verify that the new method can separate a broader range of graph signals and show that it is also more efficient when both approaches are useful.

Blind source separation (BSS) is a well-known signal processing tool which is used to solve practical data analysis problems in various fields of science. In BSS, we assume that the observed data consists of linear mixtures of latent variables. The mixing system and the distributions of the latent variables are unknown. The aim is to find an estimate of an unmixing matrix which then transforms the observed data back to latent sources. In this paper we present the R packages JADE and BSSasymp. The package JADE offers several BSS methods which are based on joint diagonalization. Package BSSasymp contains functions for computing the asymptotic covariance matrices as well as their data-based estimates for most of the BSS estimators included in package JADE. Several simulated and real datasets are used to illustrate the functions in these two packages. peerReviewed

The growing proportion of wind power in the Nordic power system increases day-ahead forecasting errors, which have a link to the rising need for balancing power. However, having a large interconnected synchronous power system has its benefits, because it enables to aggregate imbalances from large geographical areas. In this paper, day-ahead forecast errors from four Nordic countries and the impacts of wind power plant dispersion on forecast errors in areas of different sizes are studied. The forecast accuracy in different regions depends on the amount of the total wind power capacity in the region, how dispersed the capacity is and the forecast model applied. Further, there is a saturation effect involved, after which the reduction in the relative forecast error is not very large anymore. The correlations of day-ahead forecast errors between areas decline rapidly when the distance increases. All error statistics show a strong decreasing trend up to the area sizes of 50,000 km2. The average mean absolute error (MAE) in different regions is 5.7% of installed capacity. However, MAE of a smaller area can be over 8% of the capacity, but when all the Nordic regions are aggregated together, the capacity-normalized MAE decreases to 2.5%. The average of the largest errors for different regions is 39.8% and when looking at the largest forecast errors for smaller areas, the largest errors can exceed 80% of the installed capacity, whereas at the Nordic level, the maximum forecast error is only 13.5% of the installed capacity. Copyright © 2016 John Wiley & Sons, Ltd.

The classical second order source separation methods use approximate joint diagonalization of autocovariance matrices with several lags to estimate the unmixing matrix. Based on recent asymptotic results, we propose a novel unmixing matrix estimator which selects the best lag set from a finite set of candidate sets specified by the user. The theory is illustrated by a simulation study.

One of the most promising ways of de-carbonising the energy sector is through increasing the amounts of variable renewable energy (VRE) generation in power systems. While the inherent uncertainty of VRE generation is a challenge, it can be mitigated through improved forecasting and energy system modelling. Typically, stochastic energy system studies have focused on the day-ahead horizon of 36 h ahead of time, while studies about hydro-thermal scheduling and expansion planning often neglect uncertainty of VRE generation entirely. In this work, the potential benefits of extending the horizon of VRE forecasts on the operation of power systems with significant amounts of hydropower was examined using a future Nordic system case study. 15-day ensemble weather forecasts were processed into realistic VRE and demand forecasts up to 348 h ahead of time, and their impact on power system operations was simulated using stochastic unit commitment and economic dispatch optimisation. Increasing the length of the modelled forecast horizon reduced the total yearly operational costs of the system by 0.18–0.41%, as well as the spillage of run-of-river hydropower and the curtailment of wind power by 0.42–0.47 and 0.05–0.07% points respectively.

Blind source separation (BSS) is a signal processing tool, which is widely used in various fields. Examples include biomedical signal separation, brain imaging and economic time series applications. In BSS, one assumes that the observed $p$ time series are linear combinations of $p$ latent uncorrelated weakly stationary time series. The aim is then to find an estimate for an unmixing matrix, which transforms the observed time series back to uncorrelated latent time series. In SOBI (Second Order Blind Identification) joint diagonalization of the covariance matrix and autocovariance matrices with several lags is used to estimate the unmixing matrix. The rows of an unmixing matrix can be derived either one by one (deflation-based approach) or simultaneously (symmetric approach). The latter of these approaches is well-known especially in signal processing literature, however, the rigorous analysis of its statistical properties has been missing so far. In this paper, we fill this gap and investigate the statistical properties of the symmetric SOBI estimate in detail and find its limiting distribution under general conditions. The asymptotical efficiencies of symmetric SOBI estimate are compared to those of recently introduced deflation-based SOBI estimate under general multivariate MA$(\infty)$ processes. The theory is illustrated by some finite-sample simulation studies as well as a real EEG data example.

Signals, recorded over time, are often observed as mixtures of multiple source signals. To extract relevant information from such measurements one needs to determine the mixing coefficients. In case of weakly stationary time series with uncorrelated source signals, this separation can be achieved by jointly diagonalizing sample autocovariances at different lags, and several algorithms address this task. Often the mixing estimates contain close-to-zero entries and one wants to decide whether the corresponding source signals have a relevant impact on the observations or not. To address this question of model selection we consider the recently published second-order blind identification procedures SOBIdef and SOBIsym which provide limiting distributions of the mixing estimates. For the first time, such distributions enable informed decisions about the presence of second-order stationary source signals in the data. We consider a family of linear hypothesis tests and information criteria to perform model selection as second step after parameter estimation. In simulations we consider different time series models. We validate the model selection performance and demonstrate a good recovery of the true zero pattern of the mixing matrix.

Consider a multivariate time series where each component series is assumed to be a linear mixture of latent mutually independent stationary time series. Classical independent component analysis (ICA) tools, such as fastICA, are often used to extract latent series, but they don't utilize any information on temporal dependence. Also financial time series often have periods of low and high volatility. In such settings second order source separation methods, such as SOBI, fail. We review here some classical methods used for time series with stochastic volatility, and suggest modifications of them by proposing a family of vSOBI estimators. These estimators use different nonlinearity functions to capture nonlinear autocorrelation of the time series and extract the independent components. Simulation study shows that the proposed method outperforms the existing methods when latent components follow GARCH and SV models. This paper is an invited extended version of the paper presented at the CDAM 2016 conference.

In this paper we assume that the observed pp time series are linear combinations of pp latent uncorrelated weakly stationary time series. The problem is then to find an estimate for an unmixing matrix that transforms the observed time series back to uncorrelated time series. The so called SOBI (Second Order Blind Identification) estimate aims at a joint diagonalization of the covariance matrix and several autocovariance matrices with varying lags. In this paper, we propose a novel procedure that extracts the latent time series one by one. The limiting distribution of this deflation-based SOBI is found under general conditions, and we show how the results can be used for the comparison of estimates. The exact formula for the limiting covariance matrix of the deflation-based SOBI estimate is given for general multivariate View the MathML sourceMA(∞) processes. Finally, a whole family of estimates is proposed with the deflation-based SOBI as a special case, and the limiting properties of these estimates are found as well. The theory is widely illustrated by simulation studies. peerReviewed

Deflation-based FastICA is a popular method for independent component analysis. In the standard deflation-base d approach the row vectors of the unmixing matrix are extracted one after another always using the same nonlinearities. In prac- tice the user has to choose the nonlinearities and the efficiency and robustness of the estimation procedure then strongly depends on this choice as well as on the order in which the components are extracted. In this paper we propose a novel adaptive two- stage deflation-based FastICA algorithm that (i) allows one to use different nonlinearities for different components and (ii) optimizes the order in which the components are extracted. Based on a consistent preliminary unmixing matrix estimate and our theoretical results, the algorithm selects in an optimal way the order and the nonlinearities for each component from a finite set of candidates specified by the user. It is also shown that, for each component, the best possible nonlinearity is obtained by using the log-density function. The resulting ICA estimate is affine equivariant with a known asymptotic distribution. The excellent performance of the new procedure is shown with asymptotic efficiency and finite-sample simulation studies.

Wind power is increasingly integrated into power systems through electricity markets. To make the market operation economically possible for wind power producers, the period between bids and delivery (gate closure time) is crucial. Wind power will experience larger forecast errors the longer the gate closure time. This paper presents a case study for wind power producers in Portugal (MIBEL) and Finland and Denmark (Nordpool). Historical wind power forecasts and realized generation together with market prices are used as an example. First the day-ahead and balancing prices are analyzed to see impacts of existing wind power in the markets. Then analyses of imbalance costs are made to illustrate the benefits of shorter gate closure times for wind power producers. The option for wind power producers to become active agents also in imbalance markets is explored, by bidding part of the forecast error one hour before.

This paper focuses on the computational aspects of symmetrized Mestimators of scatter, i.e. the multivariate M-estimators of scatter computed on the pairwise differences of the data. Such estimators do not require a location estimate, and more importantly, they possess the important block and joint independence properties. These properties are needed, for example, when solving the independent component analysis problem. Classical and recently developed algorithms for computing the M-estimators and the symmetrized M-estimators are discussed. The effect of parallelization is considered as well as new computational approach based on using only a subset of pairwise differences. Efficiencies and computation time comparisons are made using simulation studies under multivariate elliptically symmetric models and under independent component models. peerReviewed

In this paper, we assume that the observed p time series are linear combinations of p latent uncorrelated weakly stationary time series. The problem is then, using the observed p -variate time series, to find an estimate for a mixing or unmixing matrix for the combinations. The estimated uncorrelated time series may then have nice interpretations and can be used in a further analysis. The popular AMUSE algorithm finds an estimate of an unmixing matrix using covariances and autocovariances of the observed time series. In this paper, we derive the limiting distribution of the AMUSE estimator under general conditions, and show how the results can be used for the comparison of estimates. The exact formula for the limiting covariance matrix of the AMUSE estimate is given for general MA ( ∞ ) processes.

In this paper we study the theoretical properties of the deflation-based FastICA method, the original symmetric FastICA method, and a modified symmetric FastICA method, here called the squared symmetric FastICA. This modification is obtained by replacing the absolute values in the FastICA objective function by their squares. In the deflation-based case this replacement has no effect on the estimate since the maximization problem stays the same. However, in the symmetric case we obtain a different estimate which has been mentioned in the literature, but its theoretical properties have not been studied at all. In the paper we review the classic deflation-based and symmetric FastICA approaches and contrast these with the squared symmetric version of FastICA in a unified way. We find the estimating equations and derive the asymptotical properties of the squared symmetric FastICA estimator with an arbitrary choice of nonlinearity. This allows the main contribution of the paper, i.e., efficiency comparison of the estimates in a wide variety of situations using asymptotic variances of the unmixing matrix estimates. HighlightsThe formal definition of the squared symmetric FastICA estimator is given.The asymptotical properties of the squared symmetric FastICA are derived.Asymptotic variances of different FastICA estimators are compared.

In independent component analysis it is assumed that the components of the observed random vector are linear combinations of latent independent random variables, and the aim is then to find an estimate for a transformation matrix back to these independent components. In the engineering literature, there are several traditional estimation procedures based on the use of fourth moments, such as FOBI (fourth order blind identification), JADE (joint approximate diagonalization of eigenmatrices), and FastICA, but the statistical properties of these estimates are not well known. In this paper various independent component functionals based on the fourth moments are discussed in detail, starting with the corresponding optimization problems, deriving the estimating equations and estimation algorithms, and finding asymptotic statistical properties of the estimates. Comparisons of the asymptotic variances of the estimates in wide independent component models show that in most cases JADE and the symmetric version of FastICA perform better than their competitors., Published at http://dx.doi.org/10.1214/15-STS520 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)

This paper focuses on a wind power forecast monitoring system for the need of a Transmission System Operator, using a case of Finland as an example. Wind power monitoring tool development was done closely with the operators from the TSO's control room to make sure all information needed for system operation was captured. The system operators highlighted the need for simple graphical views, with warnings for events like ramps and uncertainty metrics. Uncertainty was captured with probabilistic forecasts of wind power with 95 % exceedance level. More detailed information on wind power forecasts locally and regionally are needed for congestion management. The user experience showed the importance of accuracy of input Scada data - warnings for dubious data are needed. The forecasting and monitoring tool would need to be integrated to the other tools in control room in future.

Blind source separation (BSS) is a multivariate data analysis method, whose roots are in the signal processing community. BSS is applied in diverse fields, including, for example, brain imaging and economic time series analysis. In the BSS model there are interesting latent uncorrelated variables, and the aim is to estimate the latent variables from multiple linear combinations of them. In this article we assume that these variables are weakly stationary time series, and we consider estimation methods which are based on approximate joint diagonalization of autocovariance matrices. In the popular SOBI estimator, a set of matrices is most diagonal when the sum of squares of their diagonal elements is maximal. Here we investigate other criteria to measure the diagonality of matrices. Applying both asymptotic results and simulations, we will study how the use of different diagonality measures affects the separation performance. Also, a method to choose the measure optimally based on data is proposed.

This paper describes and tests two prototype series of pressure transducer arrays based on electromechanical film (EMFi). By offering high (/spl sim/T/spl Omega/) resistance, EMFi is an excellent material for low-current long-term measurement applications. About 50 transducer arrays were designed and tested using different configurations and electrode materials to sense low-frequency pressure pulsations on the radial artery in the wrist. Essential requirements included an adequate linear response in the desired temperature range and uniform quality. Transducer sensitivity was tested as a function of temperature in the range of 25/spl deg/C-45/spl deg/C at varying dc and ac pressures. The average sensitivity of the EMFi used in the transducers proved adequate (/spl sim/2.2mV/mmHg and /spl sim/7 mV/mmHg for normal and high-sensitive films) for the intended purpose. Moreover, EMFi's spectral response covered the required range for biomedical applications, but it was unable to measure static pressure (f/sub 3 dB//spl ap/38 /spl mu/Hz). The sensitivity of the EMFi material was sufficiently constant for measuring blood pressure pulses in the desired range (0-300 mmHg), and the best achieved deviation in sensitivity was /spl plusmn/5.1%. It was also established that in addition to sensitivity and its standard deviation, crosstalk between electrode elements also depends strongly on electrode thickness.

The self-mixing effect in a diode laser and the Doppler technique are used for quantitative measurements of the cardiovascular pulses from radial arteries of human individuals. 738 cardiovascular pulses from 10 healthy volunteers were studied. The Doppler spectrograms reconstructed from the Doppler signal, which is measured from the radial displacement of the radial artery, are compared to the first derivative of the blood pressure signals measured from the middle finger by the Penaz technique. The mean correlation coefficient between the Doppler spectrograms and the first derivative of the blood pressure signals was 0.84, with a standard deviation of 0.05. Pulses with the correlation coefficient less than 0.7 were neglected in the study. Percentage of successfully detected pulses was 95.7%. It is shown that cardiovascular pulse shape from the radial artery can be measured noninvasively by using the self-mixing interferometry.

Direct addition of dimethyl malonate anion to a 1,4-conjugate iminium salt of 3-ethylindolo[2,3- a ]quinolizidine 4a (regenerated from the corresponding α-aminonitrile 4b ) afforded enamine 5. Catalytic hydrogenation of compound 5 led stereoselectively to compound 6 ( pseudo ), which is the highly desired intermediate for the preparation of several Corynanthe alkaloids, including (±)-hirsutine 7.

Independent component analysis (ICA) is a widely used signal processing tool having applications in various fields of science. In this paper we focus on affine equivariant ICA methods. Two such well-established estimation methods, FOBI and JADE, diagonalize certain fourth order cumulant matrices to extract the independent components. FOBI uses one cumulant matrix only, and is therefore computationally very fast. However, it is not able to separate identically distributed components which is a major drawback. JADE overcomes this restriction. Unfortunately, JADE uses a huge number of cumulant matrices and is computationally very heavy in high-dimensional cases. In this paper, we hybridize these two methods. The affine equivariant FOBI estimate is used as an initial value for JADE, and only a small subset of most informative cumulant matrices is then diagonalized. In simulation studies we show that the new affine equivariant estimate is almost as good as JADE, and it is computationally much faster.

10-Methoxydihydrocorynantheol and 10-methoxycorynantheidol were synthesized from 5-methoxytryptophol and 3-acetylpyridine. (13)C-NMR data of the prepared compounds and their synthetic intermediates are given.

The Claisen rearrangement of vinyl allyl ether 3 in refluxing toluene leads to a mixture of (±)- Z -geissoschizine 5 and (±)-15-epi- E -geissoschizine 6 [= (±)-3-epi- E -geissoschizine 6′], whereas vinyl allyl ether 4, under the same reaction conditions, affords only (±)-15-epi- Z -geissoschizine 15 [= (±)-3-epi- Z -geissoschizine 15′]. No (±)- E -geissoschizine 16 was formed. However, the formation of (±)-15-epi- E -geissoschizine 6 [ = (±)-3-epi- E -geissoschizine 6′], which has earlier been transformed to (±)- E -geissoschizine 16, represents a new, formal total synthesis of (±)- E -geissoschizine 16. A conformational study of the prepared compounds, mainly based on nmr measurements, is presented.

Syntheses are reported for isositsirikine isomers 1 – 6 and (16S*)-and (16R*)-17-deoxy- E -isositsirikines 9 and 10 (Model compounds 1,2 for the “synthetically missing” (16R)- and (16S)- E -isositsirikines 7 and 8 , respectively). Predominant conformations of the compounds, and of their C-16 configurations were determined on the basis of nmr measurements, especially NOE difference spectroscopy. The large difference in chemical shifts (δ 4.31 ppm versus δ 3.9 ppm), between the C-3-H-signals of (16R)- and (16S)- E -isositsirikines 7 and 8 is explained. The 13 C-nmr data confirm the non-identity of compounds 1 – 6 with rhazimanine and bhimberine, alkaloids isolated from Rhazya stricta .

The Claisen rearrangement of vinyl allyl ether 3 in refluxing toluene leads to a mixture of (±)- Z -geissoschizine 5 and (±)-15-epi- E -geissoschizine 6 [= (±)-3-epi- E -geissoschizine 6′], whereas vinyl allyl ether 4, under the same reaction conditions, affords only (±)-15-epi- Z -geissoschizine 15 [= (±)-3-epi- Z -geissoschizine 15′]. No (±)- E -geissoschizine 16 was formed. However, the formation of (±)-15-epi- E -geissoschizine 6 [ = (±)-3-epi- E -geissoschizine 6′], which has earlier been transformed to (±)- E -geissoschizine 16, represents a new, formal total synthesis of (±)- E -geissoschizine 16. A conformational study of the prepared compounds, mainly based on nmr measurements, is presented.

Cleavage of the C-20 ethylidene side-chain of deformyl-Z-geissoschizine (1) and deformyl-E-geissoschizine (2), and their N a -Boc derivatives (11) and (12), utilizing the modified Polonovski reaction, is described. Mechanistic considerations are presented

Direct addition of dimethyl malonate anion to a 1,4-conjugate iminium salt of 3-ethylindolo[2,3- a ]quinolizidine 4a (regenerated from the corresponding α-aminonitrile 4b ) afforded enamine 5. Catalytic hydrogenation of compound 5 led stereoselectively to compound 6 ( pseudo ), which is the highly desired intermediate for the preparation of several Corynanthe alkaloids, including (±)-hirsutine 7.

Dimension measurements in metal production are getting increasingly important to improve quality and yield. One important measurement is thickness profile, in this case of copper strip. Knowing the strip profile in entrance and exit side of milling line helps optimizing the milling depth and give information about tool wearing. In this study a comparative measurement method was traversing point measurement system. It gives profile as a series of points which take a relatively long time to measure. Now presented method is based on two-side optical triangulation formed by line illuminators and CMOS-cameras and enables instantaneous thickness profile measurement. Results from both sides are fixed together using reference plates on both ends of the measurement area. From 1.3 m stand-off distance, 1.4 m wide measurement area is achieved. This paper presents the measurement method and results of laboratory and on-line tests. Using laser line illumination the accuracy of thickness was 150 μm when measuring 9 mm thick test plate. Accuracy was limited by laser speckle during static calibration. Other illumination method based on white light was therefore tested and the accuracy was 12 μm correspondingly. Measurement time for one profile was 1 second and resolution in cross machine direction 50 mm after averaging. Now presented method enables thickness profile measurement of copper and other metal sheets. Using white light the accuracy is at same level as the present traversing point measurement. Method has also continuous reference measurement to compensate errors caused by vibration; therefore the system can be realized at reasonable cost.

This paper investigates the correlation between the shape of the first derivative of a blood pressure pulse and the corresponding Doppler spectrogram, reconstructed from a Doppler signal produced by the movement of the skin above the radial artery in the human wrist. The aim is to study to what extent the arterial pulse shape can be measured using self-mixing interferometry. To obtain a point of reference, a commercial non-invasive blood pressure monitor was first used to measure both blood pressure and pulse shape. Then, a self-mixing interferometer was applied to measure the arterial pulse above the radial artery. Measurements on 10 volunteers yielded a total of 738 pulses for analysis. A cross correlation of 0.84 ± 0.05 was established between the shape of the first derivative of the pressure pulse and the Doppler spectrogram. Using an empirical constant of 0.7 as a limit for successfully detected pulses produced a detection accuracy of 95.7%. The results show that self-mixing interferometry lends itself to the measurement of the arterial pulse shape, and that the thus obtained shape is in good agreement with that produced by a commercial blood pressure monitor.

Typical surface inspection tasks using RGB vision require the analysis of tens of megabytes of image data per second, with low false alarm and error escape rates. Although automatic inspection systems have become more common on production lines, for example in sawmills, there are substantial needs to improve their performance and accuracy. Detection is one very important part of image flow before defect recognition. Detection is used in order to find suspicious regions of the image, containing possibly defective areas, since defect detection has to cope with very high data rates. It has to be based on relative simple methods. In this paper we describe the effect of different thresholding methods in RGB defect detection. Threshold values were calculated for R, G and B channels, difference channels R-G, R-B and G- B and for mean values from R, G and B channels. The analysis was performed for pinewood. Error escape rate and false alarm rates were used as evaluation criteria. In this paper, R and G channel thresholding methods were the best ones.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The use of a TDI camera is restricted to cases of viewing from the direction of the surface normal. Our previous work indicated that a TDI camera can be used with viewing angles up to 30° from the surface normal which extends the usability of TDI for visual inspection applications. The objective of this paper is to examine the use of a TDI camera at a non-zero viewing angle under vibration conditions. The effects caused by vibration of the surface to be viewed become critical when using a TDI camera at non-zero viewing angles. A method of approximating the TDI performance under vibration conditions was determined and evaluated experimentally. The resulting measurements support the approximating method developed here.

A variety of time delay and integration (TDI) arrays have been developed. The TDI image sensor offers significant improvement in performance over a linear CCD-sensor with respect to sensitivity. This is particularly significant in low light level operation since the effective exposure time is increased by a factor which is equal to the number of the TDI stages in the sensor. Our previous work has indicated that the TDI camera can be used with viewing angles up to 30 degrees from the surface normal. The effects caused by vibration of the viewed surface become critical when using a TDI camera at non-zero viewing angles.FOr this reason, a study was made on the vibration effects. This paper reports this study, concentrating ont he relation between the vibration of the inspected surface and the sharpness of the image. The contrast perceived by the TDI camera as a function of the vibration amplitude and frequency is measured. The measurements are performed using a special test pattern in a dynamic situation. The results based on the contrast modulation function (CMF) in the vertical and horizontal directions are reported. A hypothesis of the effect of vibration on the CMF was formulated as a rule, which was then tested with measured data. Tentative result support the hypothesis.

A variety of time delay and integration (TDI) arrays have been developed. The TDI image sensor offers significant improvement in performance over a linear CCD-sensor with respect to sensitivity. This is particularly significant in low level operations since the exposure time is increased by a factor which is equal to the number of the TDI stages in the sensor. Typically, the use of a TDI camera is restricted to cases where the surface is viewed from the direction of the surface normal. This is because the TDI-camera sensor has to be parallel to the viewed surface plane, in order to avoid a decrease of image quality due to varying magnification. However, in certain visual inspection applications it would be advantageous to use non-zero viewing angles. Three different solutions were tested and analyzes: a commercial shifting lens, standard lenses with an extension structure to support the lens in the shifting position and a commercial shifting and tilting lens. The results indicate that the TDI-camera can be used with viewing angles up to 30 degrees from the surface normal,which has been found to be the optimal viewing angle in some visual inspection applications.

Since the design of an inspection system typically requires a lot of application-dependent work, the provision of systematic methods and tools to assist in the design process could significantly reduce the system development and installation time. With this in view, a step-by-step design procedure for image acquisition systems is suggested, consisting of measurements of certain important optical parameters for the surfaces to be inspected, modelling of the measurements and arrangement of the imaging in a form that a computer can understand, simulation of the imaging process in a computer using optical analysis tools, and verification of the results through a pilot system. The procedure is exemplified by describing its application to the design of a steel sheet inspection system and its capacity for optimising the detection of various defects is demonstrated. For comparison, measurements made on some other materials are shown and the implications discussed. The results of the simulation and the pilot system for steel are compared and the usefulness of the computer-based design method is evaluated.