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In this study, the effects of residual stress induced by three different cooling methods during heat treatment on the crack propagation behaviour of the GH4169 disc were investigated. Different levels of stress fields were induced to the specially designed discs by using air cooling (AC), air jetting cooling (AJC) and water quenching (WQ) methods and were quantitated by numerical simulation. These discs were then subjected to prefabricated cracking, and crack propagation tests were conducted on a spin tester with two load spectrums. Crack growth behaviour was depicted via the surface replica technique and fracture morphology. Regarding the linear superposition of residual stress and centrifugal force, the crack propagation behaviour of different discs was simulated using the FRANC3D software. AJC and WQ introduced compressive residual stress (-259 MPa and -109 MPa, respectively) into the disc compared with the AC method (about -1.5 MPa). The AJC method increases the crack propagation life of the disc by introducing residual compressive stress into the area near the surface of the central hole to inhibit the opening of the crack surface. When the fatigue load was low, this inhibition effect was more significant.

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Labyrinth-honeycomb seals are a state-of-the-art sealing technology commonly used in aero-engine interstage seal. The undesirable severe rub between the seal fins and the honeycomb due to the clearance change may induce the cracking of the seal fins. A pervious study investigated the wear of the seal fins at different radial incursion rates. However, due to the axial thrust and mounting clearance, the axial rub between the seal fins and the honeycomb may occur. Hence, this paper focuses on the influence of the axial rub added in the radial rub on the wear of the seal fins. The rub tests results, including rubbing forces and temperature, wear rate, worn morphology, cross-sectional morphology and energy dispersive spectroscopy results, are presented and discussed. Overall, the participation of the axial rub leads to higher rubbing forces, temperature, and wear rate. The tribo-layer on the seal fin is thicker and the cracks are more obvious at high axial incursion rate. These phenomena indicate the axial rub has a negative influence on the wear of the seal fins and should be avoided.

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Labyrinth seals as a noncontact sealing technology are widely used in aero-engine. To improve the efficiency of the aero-engine, the clearance between the rotor and stator must be as small as possible. However, the change of the clearance between the rotor and stator because of thermal expansion, vibration, mechanical loading may lead to undesirable high-speed rub, which will lead to the cracking of the seal fins. This paper focuses on the wear of the seal fin after the rub and presents the rubbing tests between seal fins and the metal honeycomb under rubbing speed of 380 m/s and incursion rates between 20 and 180 µm/s, with an incursion depth of 1500 µm and a temperature of 350 °C. The rubbing force and temperature were recorded, and the seal fins were checked by SEM and EDS. The results show that the wear mechanism of seal fins changed from oxidation wear and adhesive wear to delamination wear and then to metal wear with the increasing incursion rate. The axial cracks appeared on the worn surface of the seal fins due to the cracking of tribo-layers under periodic thermomechanical stress. The wear mechanism of the seal fin also has a great influence on the rubbing force and temperature.

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Periodic rhythms are ubiquitous phenomena that illuminate the underlying mechanism of cyclic activities in biological systems, which can be represented by cyclic attractors of the related biological network. Disorders of periodic rhythms are detrimental to the natural behaviours of living organisms. Previous studies have shown that the state transition from one to another attractor can be accomplished by regulating external signals. However, most of these studies until now have mainly focused on point attractors while ignoring cyclic ones. The aim of this study is to investigate an approach for reconciling abnormal periodic rhythms, such as diminished circadian amplitude and phase delay, to the regular rhythms of complex biological networks. For this purpose, we formulate and solve a mixed-integer nonlinear dynamic optimization problem simultaneously to identify regulation variables and to determine optimal control strategies for state transition and adjustment of periodic rhythms. Numerical experiments are implemented in three examples including a chaotic system, a mammalian circadian rhythm system and a gastric cancer gene regulatory network. The results show that regulating a small number of biochemical molecules in the network is sufficient to successfully drive the system to the target cyclic attractor by implementing an optimal control strategy.

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Recent studies showed that certain drugs can change regulatory reaction parameters in gene regulatory networks (GRNs) and therefore restore pathological cells to a normal state. A state control framework for regulating biological networks has been built based on attractors and bifurcation theory to analyze this phenomenon. However, the control signal is self-developed in this framework, of which the parameter perturbation method can only calculate the state transition time of cells with single control variable. Therefore, an optimal control method based on the dynamic optimization algorithms is proposed for complex biological networks modeled by nonlinear ordinary differential equations (ODEs). In this approach, dynamic optimization problems are constructed based on basic characteristics of the biological networks. Furthermore, using an example of a simple low-dimensional three-node GRN and a complex high-dimensional cancer GRN, MATLAB is utilized to calculate optimal control strategies with either single or multiple control variables. This method aims to achieve accurate and rapid state regulation for biological networks, which can provide a reference for experimental researches and medical treatment.

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RESUMEN

Attractors represent steady states of biological networks. Recent studies have shown that regulatory variables can be used to steer a network state transition from an undesired attractor, such as a cancerous state, to a desired healthy one. Therefore, it is important to identify the regulatory variables and determine their time-dependent profile for state transition of a given network. However, this is a challenging task since regulatory variables have to be identified among numerous candidates in a large-scale biological network. In this study, we developed a new method for identifying regulatory variables in large-scale biological networks for the purpose of state transition. As a result, a set of optimal regulatory variables can be determined based on formulating and solving a mixed-integer nonlinear dynamic optimization problem. A relaxation scheme is used to overcome the difficulties in solving this complex problem containing a large number of binary variables. The solution to this problem simultaneously identifies the optimal regulatory variables, provides strength of regulatory interactions, and obtains the minimal control time to realize the required state transition. In addition, by adjusting the objective function, various combinations of the strength of regulatory interactions and the transition time can be achieved according to the requirement for disease therapy. Results of three case studies (a myeloid differentiation regulatory network, a cancer gene regulatory network, and a T-LGL signaling network) demonstrate the efficacy of the proposed approach. Therefore, this study establishes an appropriate framework for identifying the regulatory variables for state transition of complex biological networks.

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RESUMEN

Complex biological networks typically contain numerous parameters, and determining feasible strategies for state transition by parameter perturbation is not a trivial task. In the present study, based on dynamical and structural analyses of the biological network, we optimized strategies for controlling variables in a two-node gene regulatory network and a T-cell large granular lymphocyte signaling network associated with blood cancer by using an efficient dynamic optimization method. Optimization revealed the critical value for each decision variable to steer the system from an undesired state into a desired attractor. In addition, the minimum time for the state transition was determined by defining and solving a time-optimal control problem. Moreover, time-dependent variable profiles for state transitions were achieved rather than constant values commonly adopted in previous studies. Furthermore, the optimization method allows multiple controls to be simultaneously adjusted to drive the system out of an undesired attractor. Optimization improved the results of the parameter perturbation method, thus providing a valuable guidance for experimental design.