Influence of Hankel matrix dimension on system identification of structures using stochastic subspace algorithms

We have endeavored in the preceding chapters to draw attention to the richness and flexibility of canonical analysis. The flexibility of the underlying model, in particular, is expressed in part by the number of apparently distinct methods which prove on examination to be special cases of canonical correlation analysis. Canonical variate analysis and dual scaling were both shown abstractly to be equivalent to canonical correlation analysis. The model’s flexibility is complemented by a correspondingly diverse range of application. While, in relation to the worked examples of Chaps. 6–12, it may be that the ability of canonical analysis to have parsimoniously summarized the dependence structures in question is to be attributed to the small scale of these investigations, within the class of small-scale investigations the applicability of canonical analysis was shown to be very wide. Altogether, it seems justifiable to conclude that canonical analysis offers an unusually versatile structure by means of which statistical theory, ecological theory and empirical data can be harnessed to provide insight into the organization of ecological systems.

Canonical Variate Analysis (CVA) has two major problems: sampling error and accumulated rounding error. This paper describes a method designed to minimize these problems. The combined effect of the two problems was assessed for CVA and the new technique in an empirical study. The new technique appears to be superior to CVA when the ratio of variables to sampling units is greater than 1/10.

This paper deals with the fault detection of a pneumatic control valve using canonical variate analysis (CVA). CVA can find the optimal linear combinations of p-window and f-window data, so that the correlation between these combinations can be maximized. Based on CVA, the p-window data is considered by traditional hotelling T <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> statistic and squared prediction error (SPE) indicators, the corresponding fault detection rates (FDR) are low. In order to improve the FDR, a detection indicator based on SMD (square of the Mahalanobis distance) of the residual is proposed in this paper. The proposed indicator considers not only the information in the p-window data, but also that of the f-window data, which can improve the FDRs. The proposed techniques have been validated using a Development and Application of Methods for Actuator Diagnosis in Industrial Control Systems (DAMADICS) benchmark. It concludes that 14 out of the 19 faults can be successfully detected using the proposed method (CVA-SMD). Simulation results have shown that the CVA-SMD can improve the FDR compared with existing CVA-T <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and CVA-SPE methods. Experiments based on real-world data have also demonstrated that the CVA-SMD has better performance than existing PCA-T <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , PCA-SPE, PCA-SMD, CVA-T <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and CVA-SPE methods.

Owing to the importance of rolling bearings in mechanical systems, many meaningful works have been presented for bearing degradation assessment. However, most of contributions fail to take into account the influence of input features on the performance of a degradation model. As a potential multivariable process control method considering serial correlations, canonical variate analysis (CVA) is introduced to detect abnormal behaviours of rolling bearings. This study combines the CVA and support vector data description (SVDD) to develop a robust approach to weaken or remove the negative impact of input data on bearing degradation estimation. First, the time‐domain features extracted from healthy vibration signals are fused by CVA to generate projection data for SVDD training. Second, the distance of new variables to the centre of the hypersphere is calculated as an indicator to describe the degradation of rolling bearings. To demonstrate the effectiveness and robustness of the proposed method, two different experiments on bearing run‐to‐failure tests are conducted. Experimental results validate that the proposed work is capable of detecting bearing failure under various working conditions. Besides, comparison of the proposed work with the original CVA is implemented. The robustness of the proposed work is enhanced obviously compared with the original CVA.

Comparison between five pattern-based approaches for automated diagnostic classification of mature/peripheral B-cell neoplasms based on standardized EuroFlow flow cytometry immunophenotypic data.

Financial liquidity and profitability are two critical phenomena present in the financial economy of a company, whose relations depend on each other and may course in different directions. At the same time, they are an example of the complexity of the problem, which demands a proper approach, allowing one to reconcile two opposing objectives of any enterprise, i.e., maximizing the benefits for the owners and minimizing the risk of losing financial liquidity. Until now, the relationship between liquidity and profitability has not been examined explicitly, using multidimensional methods in particular. Nevertheless, the links between profitability and financial liquidity maintenance ensure the sustainable development of enterprises in different branches. This paper formulates two aims: scientific and practical. The scientific one concerns adopting the canonical variate analysis method to visualize the differences and relationships between food industry companies regarding financial liquidity and profitability. The practical one relates to indicating the relationship between financial liquidity and profitability in different groups of food industry companies. To study the relationships between the selected groups of enterprises and describe them, the liquidity and profitability ratios were utilized, involving canonical variate analysis based on transformation by linear combination and singular value decomposition. The analysis found that the most important feature highlighting the group of the examined entities regarding financial liquidity was the cash conversion cycle. The research results showed the existence of multidirectional relationships between liquidity and profitability. The research indicates that they depend on indicators describing financial dependencies and the industries in which they operate. This led to a much deeper and broader interpretation of the assessment of the financial situation of companies to support their sustainable development.

A synthesis of canonical variate analysis, generalised canonical correlation and Procrustes analysis

Pneumatic control valves are the most frequently used actuators in industrial processes. Its property definitely affects the performance of processes and therefore process monitoring of the pneumatic control valve is of great importance. Canonical Variate Analysis (CVA) is a multivariate data-driven method which considers time correlations and has been demonstrated to be superior to some methods in certain benchmark case studies. Inspired by the successful application of the CVA technique in process industry, we firstly monitor the pneumatic control valve using CVA and demonstrate its effectiveness and practicability on the DAMADICS benchmark.

Quality-related fault detection is an effective way to ensure the stability of product quality and the safety of industrial processes. Quality abnormality is often caused by incipient faults, which propagate through the connectivity path among the equipment and subsystems, and eventually become significant faults that affect product quality and production efficiency. In this paper, a quality-related incipient fault detection method for large-scale industrial process is proposed. Firstly, a fault-relevant variable selection strategy based on Kullback-Leibler divergence (KLD) is proposed to obtain the optimal variable subsets of quality-related and quality-unrelated faults. Secondly, canonical variate analysis is applied to estimate the canonical variables from the collected processes data. Thirdly, considering that KLD has a high sensitivity to incipient faults, it is used to quantify the dissimilarity between the distributions of canonical vectors before and after fault occurs. Finally, Bayesian inference is employed to fuse the detection results of all sub-blocks to get an intuitive global detection result. The advantages and validity of the proposed scheme are verified based on the Tennessee Eastman process.

Modern industrial processes are characterized by increasing complexity, often exhibiting pronounced dynamic behaviors and significant nonlinearity. Addressing these dynamic and nonlinear characteristics is essential for effective process monitoring. However, many existing methods for process monitoring and fault diagnosis are insufficient in handling these challenges. In this article, we present a novel process monitoring approach, CVA-DisDAE, which integrates an improved Denoising Autoencoder (DAE) with Canonical Variate Analysis (CVA) to address the challenges posed by dynamic behaviors and nonlinear relationships in industrial processes. First, CVA is employed to reduce data dimensionality and minimize information redundancy by maximizing correlations between past and future observations, thereby effectively capturing process dynamics. Following this, we introduce a discriminative DAE model (DisDAE) designed to serve as a semi-supervised denoising autoencoder for precise feature extraction. This is achieved by incorporating both between-class separability and within-class variability into the traditional DAE framework. The key distinction between the proposed DisDAE and the conventional DAE lies in the integration of a linear discriminant analysis (LDA) penalty into the DAE’s loss function, resulting in extracted features that are more conducive to fault classification. Finally, we validate the effectiveness of the proposed semi-supervised dynamic process monitoring approach through its application to the Tennessee Eastman benchmark process, demonstrating its superior performance.

Effect of sampling procedure and strain variation in Listeria monocytogenes on the discrimination of species in the genus Listeria by Fourier transform infrared spectroscopy and canonical variates analysis

In this paper an online identification and control strategy is developed for chemical processes. The procedure used for system identification is canonical variate analysis, a method that operates on input-output data sequences batch-wise to provide an optimized state-space model; the resulting models are then used in a multivariable predictive control procedure to yield excellent overall closed-loop results. The resulting adaptive control procedure is demonstrated to have excellent properties for control of a continuous stirred tank reactor with inverse dynamics, delays and nonlinearities.

Model Algorithmic Control (MAC) is a relatively new control technique which has been applied to many industrial processes during the last few years. Simplified analysis of the technique has shown that MAC, as an output based controller, has excellent robustness properties. It uses a model of the actual plant to compute an optimal control sequence by using an on-line optimization scheme. When the model is not known apriori, a relatively new technique based on Canonical Variate Analysis (CVA) can be used to identify the plant on-line. CVA, using Akaike Information Criteria (AIC), can determine the state-order and can identify a plant or a part of it in a closed loop configuration. It does not need any initialization and yet performs near maximum likelihood. In this paper, MAC and CVA has been integrated together to form an excellent robust adaptive controller known as AMAC (Adaptive MAC). The performance of AMAC has been demonstrated on an air-to-air missile model with asymmetric aerodynamic properties.

The 10 species of Galaxias in Tasmania, G. olidus from mainland Australia and the four species of Paragalaxias were studied using principal co‐ordinates analysis (PCOA) and cluster analysis of a standardized Euclidean distance matrix based upon variate means, and by canonical variate analysis (CVA) conducted as a stepwise multiple discriminant analysis. Thirty‐five variables comprising 30 morphometric and five meristic characters were analysed. The meristic characters were not included in the CVA. Excellent separation of the two genera was achieved in all analyses. The multivariate analyses were repeated on each genus separately to see if relationships suggested by the overall analysis remain stable. When the resultant groupings of species are compared for the different analyses, no consistent, distinct groupings of species within each genus are apparent. Despite the absence of distinct groupings, some trends in the affinities of some species are evident. In particular, species affinities as indicated by the CVA are more consistent with established opinions of species relationships. From the results of the study it is suggested that caution be exercised in the application of multivariate statistical analyses of morphological data to ichthyological systematics and phylogeny.

Canonical variable analysis and long short-term memory for fault diagnosis and performance estimation of a centrifugal compressor