The problem of local fault (unknown input) reconstruction for interconnected systems is addressed in this paper. This contribution consists of a geometric method which solves the fault reconstruction (FR) problem via observer based and a differential algebraic concept. The fault diagnosis (FD) problem is tackled using the concept of the differential transcendence degree of a differential field extension and the algebraic observability. The goal is to examine whether the fault occurring in the low-level subsystem can be reconstructed correctly by the output at the high-level subsystem under given initial states. By introducing the fault as an additional state of the low subsystem, an observer based approached is proposed to estimate this new state. Particularly, the output of the lower subsystem is assumed unknown, and is considered as auxiliary outputs. Then, the auxiliary outputs are estimated by a sliding mode observer which is generated by using global outputs and inverse techniques. After this, the estimated auxiliary outputs are employed as virtual sensors of the system to generate a reduced-order observer, which is caplable of estimating the fault variable asymptotically. Thus, the purpose of multi-level fault reconstruction is achieved. Numerical simulations on an intensified heat exchanger are presented to illustrate the effectiveness of the proposed approach.

In this paper, the invertibility of an interconnected system that consists of two dynamic subsystems was studied. It can be viewed as the distinguishability of the impacts of local input on the final global output, that is to say, whether the input at the local level can be recovered uniquely under a given output at the global level and initial state. The interconnected system constitutes two dynamic subsystems connected in a cascade manner. In order to guarantee the invertibility of the studied system, a necessary and sufficient condition was established. On the condition that both individual subsystems are invertible, the invertibility of the global system can be guaranteed. In order to recover the local input which generates a given global output, an algorithm was proposed for the studied interconnected system. Numerical examples were considered to confirm the effectiveness and robustness of the proposed algorithm.

Incipient fault diagnosis is particularly important in process industrial systems, as its early detection helps to prevent major accidents. Against this background, this study proposes a combined method of mixed kernel principal components analysis and dynamic canonical correlation analysis (MK-DCCA). The robust generalization performance of this approach is demonstrated through experimental validation on a randomly generated dataset. Furthermore, comparative experiments were conducted on a CSTR Simulink model, comparing the MK-DCCA method with DCCA and DCVA methods, demonstrating its excellent detection performance for incipient faults in nonlinear and dynamic systems. Meanwhile, fault identification experiments were conducted, validating the high accuracy of the fault identification method based on contribution. The experimental findings demonstrate that the method possesses a certain industrial significance and academic relevance.

This paper emphasizes the importance of the influences of local dynamics on the global dynamics of a control system. By considering an actuator as an individual, nonlinear subsystem connected with a nonlinear process subsystem in cascade, a structure of interconnected nonlinear systems is proposed which allows for global and local supervision properties of the interconnected systems. To achieve this purpose, a kind of interconnected observer design method is investigated, and the convergence is studied. One major difficulty is that a state observation can only rely on the global system output at the terminal boundary. This is because the connection point between the two subsystems is considered unable to be measured, due to physical or economic reasons. Therefore, the aim of the interconnected observer is to estimate the state vector of each subsystem and the unmeasurable connection point. Specifically, the output used in the observer of the actuator subsystem is replaced by the estimation of the process subsystem observer, while the estimation of this interconnection is treated like an additional state in the observer design of the process subsystem. Expression for this new state is achieved by calculating the derivatives of the output equation of the actuator subsystem. Numerical simulations confirm the effectiveness and robustness of the proposed observer, which highlight the significance of the work compared with state-of-the-art methods.

Incipient fault diagnosis is particularly important in process industrial systems, as its early detection helps to prevent major accidents. Against this background, this study proposes a combined method of Mixed Kernel Principal Components Analysis and Dynamic Canonical Correlation Analysis (MK-DCCA). The robust generalization performance of this approach is demonstrated through experimental validation on a randomly generated dataset. Furthermore, Comparative experiments were conducted on a CSTR Simulink model, comparing the MK-DCCA method with DCCA and DCVA methods, demonstrating its excellent detection performance for incipient fault in nonlinear and dynamic system. Meanwhile, fault identification experiments were conducted, validating the high accuracy of fault identification method based on contribution. The experimental findings demonstrate that the method possesses a certain industrial significance and academic relevance.

Multi-material structures such as carbon fiber reinforced polymer (CFRP) and epoxy resin are increasingly used in modern power equipment. However, significant differences in their thermophysical properties result in distinct defect thermal responses, which can reduce the reliability of infrared thermography inspections. To address this issue, this study investigates the thermal response mechanisms and quantitative characterization of defects in multi-material power equipment through finite element simulation and experimental validation. Three-dimensional transient heat transfer models containing air-void and heterogeneous insert defects were established using COMSOL Multiphysics for both CFRP and epoxy resin matrices. Pulsed infrared thermography experiments were subsequently conducted to verify the simulation results. The effects of material properties, defect geometry, and cover-layer thickness on thermal response characteristics were systematically analyzed. The results show that thermal diffusivity is the key factor governing defect signal evolution. CFRP exhibits rapid thermal propagation and early transient responses, whereas epoxy resin produces delayed and slowly increasing thermal signals. Greater defect depth weakens thermal contrast and delays peak response time, while larger defect diameters enhance defect detectability. In-creasing cover-layer thickness significantly attenuates defect signals and reduces imaging contrast. Experimental results are in good agreement with simulation predictions, confirming the validity of the proposed models. This work provides a quantitative understanding of defect thermal behavior in multi-material systems and offers a theoretical basis for adaptive infrared thermography inspection and condition assessment of power equipment.