Signed Digraph Research Articles

Fully Distributed Event-Triggered Bipartite Formation Tracking Control for Heterogeneous Multi-Agent Systems on Signed Digraph

Considering that communication between neighboring agents may be cooperative or antagonistic, this study is concerned with the bipartite time-varying output formation tracking (BTVOFT) problem for heterogeneous multi-agent systems (MASs) with multiple leaders on signed digraph. A fully distributed event-triggered output feedback formation tracking (FDETOFFT) control scheme is constructed to address this problem. It is noteworthy that the control scheme does not involve any global information, which enables it to be implemented in a fully distributed fashion. The biggest contribution of this study is to extend event-triggered techniques to the formation tracking control scheme. Compared with previous related works, continuous communication between neighboring agents is avoided. Moreover, it is further proved that no agents exhibit the Zeno behavior.

Collective Behaviors of Discrete-Time Multi-Agent Systems Over Signed Digraphs

This article is concerned with the collective behaviors of discrete-time multi-agent systems with single-integrator dynamics under general signed digraphs, in which each agent iteratively updates its own state based upon the current relative states between itself and its neighbors. By using graph-theoretic, matrix-theoretic, and control-theoretic tools, it is shown that with the step-size suitably selected, the states of all agents always converge. More specifically, all agents reach: 1) bipartite consensus (trivial consensus, respectively) if and only if they are related to a strongly connected signed digraph which is structurally balanced (unbalanced, respectively); 2) interval bipartite consensus (trivial consensus, respectively) if and only if their related signed digraph is quasi-strongly connected and contains a structurally balanced (unbalanced, respectively) rooted subdigraph; and 3) bipartite containment (trivial consensus, respectively) if the signed digraph relevant to them is weakly connected and has at least one structurally balanced vertex (has no structurally balanced vertices, respectively). Numerical examples are finally provided to verify the theoretical findings.

Observer-Based Bipartite Containment Control for Singular Multi-Agent Systems Over Signed Digraphs

This paper aims at solving the bipartite containment problem for linear singular multi-agent systems (MASs) with multiple dynamic leaders over general signed digraphs, where each leader can be autonomous or dynamically evolving via interactions with its neighboring leaders. To this end, we first establish some properties for the Laplacian matrices of signed digraphs. Then, three distributed observer-based bipartite containment protocols are proposed using different local output information. Multi-step algorithms for constructing the corresponding proposed protocols are also given. It is shown that under the proposed control protocols, bipartite containment can be achieved for any admissible initial states provided that the underlying signed digraph is weakly connected. Compared to the existing related works, the major contribution of present work is that the developed results are applicable for arbitrary weakly connected signed digraphs, no matter whether they are sign-symmetric or sign-asymmetric and whether they are structurally balanced or unbalanced. Two numerical examples are finally given to demonstrate the validity of our results.

On Single Valued Neutrosophic Signed Digraph and its Applications

The development of the theory of the single valued neutrosophic (SVN) digraph is done in this paper. Also this paper introduces the conceptof SVN signed digraph. Some basic terminologies and operations of SVN digraphs and SVN signed digraphs have been defined. Finally classificationproblem in a signed network system is solved with the help of SVN signed digraphs.

A Fault Magnitude-Based Strategy for Effective Fault Diagnosis and Isolation

Various multivariate statistical methods based on pattern recognitions for the Tennessee Eastman (TE) process have been developed to identify and diagnose the root cause of assumed faults. However, even if the same fault occurs, its patterns or traces generated from such conventional approaches can be different according to fault magnitudes. Thus, the fault magnitude should be considered. In this study, a signed digraph (SDG) based on process knowledge is used to identify the relationships between process variables and conceivable faults. A support vector regression (SVR) and dynamic independent component analysis (DICA) are then applied to construct empirical models as a function of process variables associated with assumed faults and their fault magnitudes for isolating a fault and handling non-Gaussian information. In addition, empirical models for predicting fault magnitudes are constructed. The efficacy of the proposed approach is illustrated by comparing it with the previous studies applied for the benchmark process.

A Balanced Signed Digraph

We extend a balanced signed graph to a digraph, and present a necessary and sufficient condition for a signed digraph to be balanced. Moreover, we give another necessary and sufficient condition fo...

Sensor configuration and test for fault diagnoses of subway braking system based on signed digraph method

Fault diagnosis of various systems on rolling stock has drawn the attention of many researchers. However, obtaining an optimized sensor set of these systems, which is a prerequisite for fault diagnosis, remains a major challenge. Available literature suggests that the configuration of sensors in these systems is presently dependent on the knowledge and engineering experiences of designers, which may lead to insufficient or redundant development of various sensors. In this paper, the optimization of sensor sets is addressed by using the signed digraph (SDG) method. The method is modified for use in braking systems by the introduction of an effect-function method to replace the traditional quantitative methods. Two criteria are adopted to evaluate the capability of the sensor sets, namely, observability and resolution. The sensors configuration method of braking system is proposed. It consists of generating bipartite graphs from SDG models and then solving the set cover problem using a greedy algorithm. To demonstrate the improvement, the sensor configuration of the HP2008 braking system is investigated and fault diagnosis on a test bench is performed. The test results show that SDG algorithm can improve single-fault resolution from 6 faults to 10 faults, and with additional four brake cylinder pressure (BCP) sensors it can cover up to 67 double faults which were not considered by traditional fault diagnosis system. SDG methods are suitable for reducing redundant sensors and that the sensor sets thereby obtained are capable of detecting typical faults, such as the failure of a release valve. This study investigates the formal extension of the SDG method to the sensor configuration of braking system, as well as the adaptation supported by the effect-function method.

Sensor Network Design for Efficient Fault Diagnosis and Signed Digraph Update

An optimally designed sensor network is essential to ensure optimal and safe process operation. Several approaches for designing sensor networks for efficient fault diagnosis have been presented in the literature. Most of these utilize signed digraph (SDG) based process representation and assume that the SDG is accurately known. For a nonlinear system, the signs on the edges in a SDG depend on the operating conditions and can thus change with time or operating mode and hence may not be accurately known. However, such uncertainties in SDG modeling have been largely ignored in sensor network design literature. In this work, we propose a design approach that considers such uncertainties while selecting optimal sensor networks. The resulting network is optimal in the sense that it results in the lowest number (or lowest cost) of sensors that can ensure observability and resolution of faults while simultaneously identifying the signs on the uncertain edges. Similar to faults, the concepts of observability and resolution are defined for such uncertain edges as well and used in the design procedure. The utility of the proposed approach is demonstrated by applying it on a five tank system.

Fault Diagnosis Based on Signed Digraph Combined with Dynamic Kernel PLS and SVR

The signed digraph (SDG) method for fault diagnosis, which is one of the model-based methods, has been widely applied in the chemical industry in recent years. However, how to elicit appropriate th...

SDG-based HAZOP analysis of operating mistakes for PVC process

As modern chemical plants are becoming more complex and bigger in scale, the associated chance of things going wrong is also increasing rapidly. Due to the flammable, explosive, toxic and corrosive nature of chemical process, any single accident may trigger a major catastrophe that brings tremendous environmental, social and economical loss. In order to prevent any accident from happening, hazard and operability (HAZOP) analysis has been brought in to monitor chemical process and provide early warning for signs of accident. However, most existing HAZOP is carried out manually, and there are always obstacles in terms of cost overrun and incompleteness of the analysis. To address the difficulties in current HAZOP method, this paper proposes a signed digraph (SDG)-based HAZOP analysis method. It is used to identify the most likely operating mistakes that may cause certain process variable deviating from its normal value, which is the main source of safety concern. A case study on polyvinyl chloride (PVC) plant is presented to demonstrate the effectiveness of SDG-based HAZOP analysis method in providing complete analysis result.

Layered digraph model for HAZOP analysis of chemical processes

AbstractProcess modeling has remained challenging in the area of automating hazard and operability (HAZOP) analysis of complex chemical processes. Even though signed digraph(SDG) model has been proposed and widely applied in various HAZOP expert systems in the past one decade, the limitations of SDG have not been recognized and discussed in literature. The drawbacks of SDG models have caused incompleteness of HAZOP analysis results, which poses a significant limitation on wide acceptance of HAZOP expert systems in industrial practices. In this work, layered digraph (LDG) model extended from SDG is introduced to overcome the drawbacks of SDG models. Knowledge storage and management of LDG models are discussed in detail. Industrial case studies are used to illustrate the effectiveness of this new modeling methodology. Since process variables, process deviations, and interactions of deviations are explicitly decoupled in three dimensions, LDG model has shown to provide a much more flexible and comprehensive mechanism for HAZOP analysis. © 2008 American Institute of Chemical Engineers Process Saf Prog, 2008

Fault diagnosis of the multi-stage flash desalination process based on signed digraph and dynamic partial least square

Multi-stage flash (MSF) desalination is a process used to produce distilled water from brine. MSF desalination can reduce the amount of energy consumption by utilizing the condensation heat of steam to boil incoming seawater. This study made a fault diagnosis of a MSF desalination process using a hybrid method of signed digraph (SDG) and dynamic partial least squares (DPLS). Among many methodologies used in fault diagnosis, SDG offers a simple and graphical representation of the relationship between various process variables and has been widely used. Using the system decomposition based on an SDG, the local models of each measured variable were constructed using DPLS, which has been shown to be a powerful regression technique for problems associated with using chemical process data. The values estimated by the models were compared with the measured values to diagnose the faults. The performance of the proposed model was verified by examining and comparing the results from case studies. The proposed method demonstrated a good diagnostic capability compared with previous methods.

Fault Diagnosis Using the Hybrid Method of Signed Digraph and Partial Least Squares with Time Delay: The Pulp Mill Process

Although the existence of a time delay worsens the diagnosis accuracy, most research efforts on fault diagnosis have not considered the time delay. The hybrid fault diagnosis method that is based on the signed digraph (SDG) and the partial least-squares (PLS) has the advantage of improving diagnosis resolution and accuracy, compared to those of previous qualitative methods, and is capable of enhancing the ability to diagnose multiple-fault [Lee et al., Ind. Eng. Chem. Res. 2003, 42, 6145−6154]. The current research modified this method to include the information of the time delay between process variables, and the time delay can be obtained through the open-loop responses of set-point changes. The modified method is applied for the fault diagnosis of the pulp mill process, which produces pulp from wood chips. It is one of the biggest processes in the fault diagnosis area, and it will be a new benchmark process to evaluate the fault diagnosis method. Also, its units, such as the storage tank and the bleaching tower, have a very large time delay. Dynamic principal component analysis (DPCA)-based fault diagnosis was used to get a reference of the diagnosis performance comparison. Although fault detection of the proposed method is frequently slower than DPCA, it gives more accurate results. Also, it demonstrates much-better diagnosis capabilities, compared to the original hybrid method.

A Hybrid Model for Fault Diagnosis Using Model Based Approaches and Support Vector Machine

The procedure followed in chemical processes can be expressed in simple terms such as the flow of events from the raw materials to the product. To obtain the best final product, chemical engineers have to consider many factors including environmental effects, stability, economic considerations, and so on. In particular, when considering the stability if the process and the purity of the product, it is very important to detect any faults in the chemical process immediately.In this paper, a hybrid fault diagnosis model based on the signed digraph (SDG) and support vector machine (SVM) is proposed. By means of the system decomposition based on SDG, the local models of each measured variable are constructed and more accurate and fast models are using an SVM, which has no loss of information and shows good performance, in order to obtain the estimated value of the variable, which is then compared with the measured value in order to diagnose the fault. To verify the performance of the proposed model, the Tennessee Eastman (TE) Process was studied and the proposed method was found to demonstrate a good diagnosis capability compared with previous statistical methods.

Lexicographic Optimization Based Sensor Network Design for Robust Fault Diagnosis

An appropriately designed sensor network is crucial for the success of any fault diagnostic strategy. In previous works (Bhushan and Rengaswamy, 2002a,b) strategies for optimally locating sensors based on criteria of reliability maximization and cost minimization have been devised. These opposing objectives were treated in a lexicographic (a special type of multiobjective optimization) manner. Signed digraph (SDG) based process models were used to generate the cause-effect information and fault occurrence and sensor failure probabilities were used to calculate a measure of reliability of a sensor network. While reliability and cost were considered in selecting the optimal sensor network, the robustness of the selected network with respect to uncertainties/errors in the underlying signed directed graph models and the available probability data was not considered explicitly. In this article, lexicographic formulations which incorporate some robustness enhancing criteria while designing cost-optimal sensor network for reliable fault diagnosis are presented. Some robustness to modeling errors in the SDG can be incorporated by choosing a distributed sensor network. Robustness to available probability data can be incorporated by maximizing reliability of the faults involving uncertain probability data. Integer linear programming (ILP) formulations incorporating these criteria in a lexicographic manner along with overall reliability-maximization and cost-minimization objectives are presented. The utility of the proposed approach is demonstrated through application to the Tennessee Eastman case study.

A Systematic Framework for the Development and Analysis of Signed Digraphs for Chemical Processes. 2. Control Loops and Flowsheet Analysis

The objectives of this part of the two part paper are (i) development of signed digraph (SDG) models for control loops and (ii) discussion of a framework for application of graph-based approaches at a flowsheet level. Further, two case studies are used to explain the methods developed in part 11 (Ind. Eng. Chem. Res. 2003, 42, in press) and this paper. The first case study (continuous stirred tank reactor case study) explains the basic concepts of the generate and test method for SDG analysis, generation of redundant equations using algebraic manipulation, and analysis of systems with a single control loop. Case study 2 (flash vaporizer case study) deals with different methods of generating redundant equations and the analysis of systems with multiple interacting control loops.

Systematic Development and Application of Digraphs for Process Diagnosis and Hazards Analysis

Many researchers have proposed digraph (DG) based techniques for safety analysis and fault diagnosis in the recent past. There are two main drawbacks in the applications of DG to large flowsheets. First, digraph generation is error prone, time consuming and second, a large number of spurious solutions are generated due to the qualitative nature of the analysis. Though Mylaraswamy et al. (1994) have proposed an algorithm for automatic generation of digraphs, little attention has been given to designing correct methodologies for DG analysis and their application to large problems. The multiple objectives of this paper are- (i) discussion on algorithms for DG generation, (ii) design of suitable methodologies for DG analysis and demonstration of their correctness, (iii) development of guidelines for eliminating spurious solutions, (iv) discussion on incipient fault detection and diagnosis through signed digraph (SDG) and (v) demonstration of SDG results on a CSTR case study.

A formulation of the collaboration mechanism for integrated abnormal situation management

To better support computer integrated abnormal situation management (ASM), a multiagent system architecture is proposed within which user and functional agents cooperate based on a collaboration mechanism. Each agent participating in the collaboration is composed of a local module and a collaboration module. Different types of collaboration are systematically analyzed. In particular, interactions among functional agents are represented by an ASM activity diagram and an extended signed digraph (SDG). A prototype operation support system for the simulated Tennessee Eastman process is used to illustrate the application of the framework and the collaboration mechanism.

Multiple-Fault Diagnosis under Uncertain Conditions by the Quantification of Qualitative Relations

Among many fault diagnosis methodologies for chemical processes, the signed digraph (SDG) offers a simple and graphical representation of the causal relationship between process variables and has been widely used. The assumptions of SDG such as single-fault assumption and consistent path assumption, however, have limited its applications to real processes. This paper presents a multiple-fault diagnosis methodology utilizing many advantages of SDG. The diagnosis model is organized by carefully modifying SDG and searching the fault propagation path. The on-line diagnosis is performed through quantifying the qualitative relation of the fault propagation path, and this quantification enables the diagnosis to overcome the weakness of SDG under uncertainty and to diagnose multiple faults. Also, this work suggests how modified-CUSUM (cumulative sum) can be used to handle compensatory or inverse response. The proposed methodology is illustrated with a case study of a continuously stirred tank reactor (CSTR) with ...

Causal Graphs and Rule Generation: Application to Fault Diagnosis of Dynamic Processes

This paper describes a systematic off-line algorithm for constructing a rule-based fault diagnostic system using the signed digraph (SDG) model. In order to overcome certain limitations related to the SDG (Iri and al. 1979), (Kramer and Palowitch 1987) and (Oyeleye and Kramer 1988), we have developped an alternative strategy for elimining spurious interpretations attributed to system compensations and inverse responses from backward loops and forward paths in the process when fault exist. Moreover, this method apply fuzzy logic to represent the rule base, in order to explain fault propagation and to ascertain fault origins. The algorithm was then successfully applied to a level controlled tank process to extract rules and these rules were evaluated using on-line data to discover the fault origins in an early stage and perform the diagnosis.