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1

A practical application of kernel-based fuzzy discriminant analysis

Gao J. Q., Fan L. Y., Li L., Xu L. Z.

International Journal of Applied Mathematics and Computer Science

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2013

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Vol. 23, no. 4

887--903

EN

A novel method for feature extraction and recognition called Kernel Fuzzy Discriminant Analysis (KFDA) is proposed in this paper to deal with recognition problems, e.g., for images. The KFDA method is obtained by combining the advantages of fuzzy methods and a kernel trick. Based on the orthogonal-triangular decomposition of a matrix and Singular Value Decomposition (SVD), two different variants, KFDA/QR and KFDA/SVD, of KFDA are obtained. In the proposed method, the membership degree is incorporated into the definition of between-class and within-class scatter matrices to get fuzzy between-class and within-class scatter matrices. The membership degree is obtained by combining the measures of features of samples data. In addition, the effects of employing different measures is investigated from a pure mathematical point of view, and the t-test statistical method is used for comparing the robustness of the learning algorithm. Experimental results on ORL and FERET face databases show that KFDA/QR and KFDA/SVD are more effective and feasible than Fuzzy Discriminant Analysis (FDA) and Kernel Discriminant Analysis (KDA) in terms of the mean correct recognition rate.

2

The investigation of the technical condition of railway systems

Żółtowski B.

Journal of KONES

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2012

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Vol. 19, No. 2

591-600

EN

The multidimensional monitoring of symptoms applied to railway systems allow to detect and locate the sections of the track (straight and curved) that generate the decrement of the safety and comfort of the passengers. It also evaluates the technical state of the rail-vehicle interface. In addition, it allows observing, evaluating, and controlling the reliability and availability of the system. The objective of the study is to propose an alternative to evaluate the condition of the technical state of railway systems from a dynamical point of view that guarantees the safety and comfort of the passengers. One looks for diminishing the operative costs of maintenance, improving the use of equipment for tasks of maintenance for the track, vehicle and auxiliary equipment, optimizing the time of the maintenance personal, the maintenance frequencies (corrective, preventive, etc.). It also aims to identify the variables related to maintenance actions that have a high influence on the technical state of the system. This paper presents the results obtained when applying a modelling of this type to a railway system, being cantered mainly in the application of SVD theory to the technical diagnosis of systems.

3

Singular Vectors in Acoustic Simulation Tests of St. Paul the Apostle Church in Bochnia

Kosała K.

Archives of Acoustics

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2012

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Vol. 37, No. 1

23-30

EN

A new approach to acoustic quality assessment of churches during simulation tests is proposed in the article. The numerical global index, based on four partial indices: reverberation, speech intelligibility, music sound index and a proposed new one – sound strength index, assesses the acoustic parameters of the model of the tested church in a complex manner. The global single number index was obtained from 17 simulations of acoustic adaptation options of the investigated church’s interior. The equation of the approximate global index has been obtained by means of singular vectors, obtained from Singular Value Decomposition (SVD) of the Index Observation Matrix of Simulation Variants (IOMSV). The weights of four partial indices and a universal equation of the global index have been calculated using the SVD technique to solve the problem of correlated acoustical parameters. The global index may be a helpful tool during simulation tests of acoustic quality assessment of churches. The proposed final equation of the global index does not require knowledge of the SVD technique and the values of acoustic parameters preferred for churches. Therefore the methodology proposed is easily applicable.

4

A Single Number Index to Assess Selected Acoustic Parameters in Churches with Redundant Information

Kosała K.

Archives of Acoustics

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2011

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Vol. 36, No. 3

545-560

EN

The paper presents an innovative approach for the index assessment of the acous- tic properties of churches. A new formula for an approximate single number index to assess selected acoustic parameters of church interiors, such as reverberation time (RT), speech intelligibility index (RASTI) and music clarity index (C80), is presented in the paper. The formula is created by means of the Singular Value Decomposition (SVD) method. An innovative approach for calculating the weights of partial in- dices is shown by solving the problem of redundant information, i.e., the system of overdetermined linear equations, using a computed pseudoinverse matrix. The new procedures for calculating the values of three partial indices and the single number index to assess selected acoustic parameters are presented. The proposed method was verified by measurements in several selected churches.

5

Multidimensional Monitoring Of Condition – Mmc - Based On The Single Value Decomposition – Svd - Case Study: Railway System

Żółtowski B., Castaneda Heredia L., Betancur Giraldo G.

Journal of Polish CIMAC

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2009

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Vol. 4, no 1

177-187

EN

The multidimensional monitoring of symptoms applied to railway systems allow to detect and locate the sections of the track (straight and curved) that generate the decrement of the safety and comfort of the passengers. It also evaluates the technical state of the rail-vehicle interface. In addition, it allows observing, evaluating, and controlling the reliability and availability of the system. The objective of the study is to propose an alternative to evaluate the condition of the technical state of railway systems from a dynamical point of view which guarantees safety and comfort of the passengers. One looks for diminishing operative costs of maintenance, improving the use of equipment for maintenance tasks of the track, vehicle and auxiliary equipment, optimizing the time of the maintenance personal, the maintenance frequencies (corrective, preventive, etc.). It also aims to identify the variables related to maintenance actions that have a high influence on the technical state of the system. This paper presents the results obtained when applying a modeling of this type to a railway system, being centered mainly in the application of SVD theory to the technical diagnosis of systems.

6

Calculation models for acoustic analysis of sacral objects

Kosała K.

Archives of Acoustics

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2009

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Vol. 34, No. 1

3-11

EN

Application of the technique of singular value decomposition (SVD) for analysis of acoustic properties of sacral objects has been presented in the paper. Previous researches by means of the SVD technique were related to the simplified calculation model basing on a three-index observation matrix. The next stage of researches presented in the paper is an attempt of decomposition of the observation matrix containing five partial indices of the index acoustic assessment of sacral objects. The matrices obtained through the SVD decomposition have been used for calculation of weights of partial indices applied for the global assessment of acoustic quality of the sanctuaries. The comparison of acoustic assessments of the sanctuaries by the global indices containing traditional weights and the weights obtained by means of the SVD technique has been performed.

7

The multidimensional diesel engine diagnosis based on the vibroacoustic signal spectrum analysis

Boruta G., Jasiński M.

Journal of KONES

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2008

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Vol. 15, No. 4

63-71

EN

Higher and higher exploitation demands given to the equipment and machines from reasons of safety and minimalization of exploitation costs, cause the necessity of the search for the new methods of the damages detection in the diagnosed objects, for example on the base of the vibroacoustics signals analysis. The natural feature of vibroacoustics diagnostics is the possibility for an easy and fast recording of a high figure of strongly redundant vibroacoustics signals and related with this the large surplus of information, which is not utilized in great part, but simultaneously the necessity for the usage of the multidimensional diagnostic vector steps out most often. This causes the necessity diminution of utilized information to the level permitting on design of adequate diagnostic model. One of methods of machines defects diagnose is the correlation of the objective technical condition with diagnostic parameters received from the vibroacoustic signal. Principal Components Analysis (PCA) offers an approach for a linear transformation of those parameters. The redundant information included into those parameters is reduced and the obtained diagnostic model is more reliable. The product chosen for the investigation presented in this paper is a Diesel engine. The application of the presented method eliminates the necessity of the performing analytical model which are time consuming and costly. It is possible to diagnose of the engine from objective parameters of the specially prepared vibroacoustic signal without performing simulation models.

PL

Coraz wyższe wymagania eksploatacyjne stawiane urządzeniom i maszynom ze względów bezpieczeństwa oraz minimalizacji kosztów eksploatacji, powodują konieczność poszukiwania nowych metod wykrywania uszkodzeń w diagnozowanych obiektach np. na podstawie analizy sygnałów wibroakustycznych. Naturalną cechą diagnostyki wibroakustycznej jest możliwość łatwej i szybkiej rejestracji dużej liczby silnie redundantnych sygnałów wibroakustycznych i związanego z tym dużego nadmiaru informacji, która w znacznej części nie jest wykorzystywana, a równocześnie najczęściej występuje konieczność wykorzystania wielowymiarowego wektora diagnostycznego. Powoduje to konieczność zredukowania wykorzystywanej informacji do poziomu pozwalającego na zbudowanie adekwatnego modelu diagnostycznego. Jedną z metod diagnozowania maszyn jest korelacja obiektywnego stanu technicznego z parametrami diagnostycznymi uzyskanym z sygnału wibroakustycznego. Korzystając z metody składowych głównych (PCA) istnieje możliwość uzyskania liniowego przekształcenia tych parametrów. Pozwala to zredukować redundantną informację zawartą w tych parametrach i uzyskać bardziej wiarygodny model diagnostyczny. Obiektem wybranym do badań zaprezentowanych w pracy był silnik o zapłonie samoczynnym. Stosowanie przedstawionej metody eliminuje konieczność wykonywania czasochłonnych i kosztownych modeli analitycznych. Możliwe jest diagnozowanie silnika na podstawie odpowiednio przygotowanego, wymiarowo zredukowanego sygnału wibroakustycznego, bez wykonywania modeli symulacyjnych.

8

Global index of the acoustic quality of sacral buildings at incomplete information

Kosała K.

Archives of Acoustics

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2008

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Vol. 33, No. 2

165-183

EN

The global assessment of acoustic quality of sacral building was, up to the present, performed when the full information about the object - determined by partial indices calculated from the measurements of acoustic parameters - was known. The formula for calculating the global index of acoustic quality at incomplete information by means of the Singular Value Decomposition (SVD) is given in the paper. Having only one of the indices - the reverberation index - it is possible to approximately assess the acoustic quality of the church. Application of the SVD method required certain modifications of the previously proposed index method. The technique of decomposition into singular values enabled the transformation of initial variables being in the form of correlated indices - into mutually orthogonal new variables. The decomposition versus singular values was done on the previously built empirical model of the index observation matrix of sacral objects. Due to this operation the weight values, which were applied in the global assessment of acoustic quality of sacral objects, were obtained. The approximate theoretical models containing information on interdependency of partial indices - were developed. The developed formula for the global assessment of acoustic quality - at incomplete information on the sacral object - was applied for comparing acoustic qualities of ten churches.

9

Latent semantic indexing for patent documents

Moldovan A., Boţ R. I., Wanka G.

International Journal of Applied Mathematics and Computer Science

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2005

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Vol. 15, no 4

551-560

EN

Since the huge database of patent documents is continuously increasing, the issue of classifying, updating and retrieving patent documents turned into an acute necessity. Therefore, we investigate the efficiency of applying Latent Semantic Indexing, an automatic indexing method of information retrieval, to some classes of patent documents from the United States Patent Classification System. We present some experiments that provide the optimal number of dimensions for the Latent Semantic Space and we compare the performance of Latent Semantic Indexing (LSI) to the Vector Space Model (VSM) technique applied to real life text documents, namely, patent documents. However, we do not strongly recommend the LSI as an improved alternative method to the VSM, since the results are not significantly better.

10

Wykorzystanie analizy składowych głównych w diagnostyce silników o zapłonie samoczynnym

Boruta G., Jasiński M.

Diagnostyka

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2005

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Vol. 34

43--50

PL

Jedną z metod diagnozowania i prognozowania wczesnych faz rozwoju uszkodzeń, jest korelacja obiektywnego stanu technicznego z diagnostycznym parametrem uzyskanym z sygnału wibroakustycznego. Korzystając z metody składowych głównych (PCA) mamy możliwość uzyskania liniowego przekształcenia zmiennych, w związku z czym redundantna informacja jest redukowana, co pozwala uzyskać bardziej wiarygodny model diagnostyczny. Obiektem wybranym do badań, prezentowanym w naszym referacie, jest silnik o zapłonie samoczynnym. Konkludując, metoda przedstawiona w tym referacie unika potrzeby wykonywania czasochłonnych i kosztownych modeli analitycznych. Możliwe jest diagnozowanie silnika na podstawie odpowiednio przygotowanego, wymiarowo zredukowanego sygnału wibroakustycznego, bez wykonywania modeli symulacyjnych.

EN

One of method of defects evolution early stages diagnostic and prediction, is the correlation of the objective technical condition with the diagnostic parameter received from the vibroacoustic signal. Principal Components Analysis (PCA) offers an approach for linear transformation of the problem variables so that the redundant information is reduced and the diagnostic model is more easily extracted. The product chosen for the investigation presented in this paper is a diesel. To conclude, the method presented here avoids the need for performing analytical model which are time consuming and costly. It is possible to diagnose of engine from the objective parameters of the specially prepared vibroacoustic signal without performing simulation models.

11

Zastosowanie składowych głównych w diagnozowaniu maszyn

Jasiński M., Radkowski S.

Diagnostyka

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2004

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Vol. 30, T. 1

207--210

PL

Jedną z metod diagnozowania i prognozowania wczesnych faz rozwoju uszkodzeń, jest korelacja obiektywnego stanu technicznego z diagnostycznym parametrem uzyskanym z sygnału wibroakustycznego. Korzystając z metody składowych głównych (PCA) mamy możliwość uzyskania liniowego przekształcenia zmiennych, w związku z czym redundantna informacja jest redukowana, co poz.wala uzyskać bardziej wiarygodny model diagnostyczny. Obiektem wybranym do badań, prezentowanym w naszym referacie, jest przekładnia zębata. Konkludując, metoda przedstawiona w tym referacie unika potrzeby wykonywania czasochłonnych i kosztownych modeli analitycznych. Możliwe jest oszacowanie typu i stopnia uszkodzenia przekładni zębatej na podstawie odpowiednio przygotowanego, wymiarowo zredukowanego sygnału wibroakustycznego, bez wykonywania modeli symulacyjnych.

EN

One of method of defects evolution early stages diagnostic and prediction, is the correlation of the objective technical condition with the diagnostic parameter received from the vibroacoustic signal. Principal Components Analysis (PCA) offers an approach for linear transformation of the problem variables so that the redundant information is reduced and the diagnostic model is more easily extracted. The product chosen for the investigation presented in this paper is a gear. To conclude, the method presented here avoids the need for performing analytical model which are time consuming and costly. It is possible to estimate the type and stage of defect to any gear vibroacoustic signal from the objective parameters of the specially prepared signal without performing simulation models.

12

Pewność diagnozy stanu maszyn w podejściu jedno i wielowymiarowym

Krakowiak M., Cempel C.

Diagnostyka

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2004

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Vol. 32

125--134

PL

W pracy przedstawiono problematykę związaną z badaniami możliwości wielowymiarowej diagnostyki stanu maszyn. Zaprezentowano przejście od macierzy obserwacji diagnostycznej obiektu i wykorzystanie dostępnych narzędzi wnioskowania diagnostycznego w środowisku Matlak. Pokazano między innymi wyznaczenie wartości granicznych symptomu i prognozy. W pracy porównano rezultaty uzyskane po zastosowaniu prognozy najpierw jedno a następnie wielowymiarowej, aby w końcowej fazie ocenić zysk wielowymiarowości w diagnostyce wybranych obiektów.

EN

The paper presents introductory consideration of the reliability of condition assessment, when using one symptom approach against the symptom observation matrix in the multidimensional condition monitoring. The comparison was made by using some software for condition assessment and forecasting prepared in the MATLAB environment, and basing on real symptoms used in vibration condition monitoring of the railroad diesel engines. The residual system life time was used as the quantity of comparison in a single and multi dimensional case. It was found in a given case, that multidimensionality can give us more reliability of assessment of the engine residual life.

13

Reduction of Redundancy of Symptom Observation Space in Systems Condition Monitoring

Cempel C.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2001

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vol. 49, nr 2

267-284

EN

It was shown in this paper that classical approach to the assessment of systems condition evolution can be much improved by special processing of observed symptoms of condition. When we have a large symptom data base, we can apply singular value decomposition (SVD) as the newest data mining procedure, to obtain a symptom and condition evolution model. By using SVD it is possible to have two additional independent fault discriminants: named here SD and SG, with high dynamics of evolution during system life. Moreover, we can add an additional column of system life count, as the first approximation of a logistic vector describing the unit life history. It is also possible to use the value of a pseudo - determinant of a symptom observation matrix, and correlation between this new discriminant and the symptom observation matrix to minimize the redundancy of symptom measuring space, and choose the best symptom for condition observation.