Sophistication of mathematical models in the pharmacological context reflects the progress being made in understanding physiological, pharmacological, and disease relationships. This progress has ...illustrated once more the need for advanced quantitative tools able to efficiently extract information from these models. While dynamical systems theory has a long history in the analysis of systems biology models, as emphasized under the dynamical disease concept by Mackey and Glass Science 197, 287-289 (1977), its adoption in pharmacometrics is only at the beginning Chae, Transl. Clin. Pharmacol. 28, 109 (2020). Using a quantitative systems pharmacology model of tumor immune dynamics as a case study Kosinsky et al., J. Immunother. Cancer 6, 17 (2018), we here adopt a dynamical systems analysis to describe, in an exhaustive way, six different statuses that refer to the response of the system to therapy, in the presence or absence of a tumor-free attractor. To evaluate the therapy success, we introduce the concept of TBA, related to the Time to enter the tumor-free Basin of Attraction, and corresponding to the earliest time at which the therapy can be stopped without jeopardizing its efficacy. TBA can determine the optimal time to stop drug administration and consequently quantify the reduction in drug exposure.
Neither the existence nor the nonexistence of a liveness enforcing supervisory policy (LESP) for an arbitrary Petri net (PN) is semidecidable. In an attempt to identify decidable instances, we ...explore the decidability of certain properties of the set of initial markings for which an LESP exists, and the decidability of the existence of a specific class of LESPs. We first prove that for an arbitrary PN structure, determining if there is an initial marking, or there are no initial markings, for which there is an LESP, is not semidecidable. Then, we characterize the class of PN structures for which the set of all initial markings for which an LESP exists is right-closed. We show that testing membership, or nonmembership, of an arbitrary PN in this class of PNs is not semidecidable. We then consider a restricted class of LESPs, called marking monotone LESPs (MM-LESPs). We show that the existence of an MM-LESP for an arbitrary PN is decidable.
Abstract
The problem of orbit flips caused by eccentric von Zeipel–Lidov–Kozai effects is systematically investigated by means of three approaches, including Poincaré sections, dynamical system ...theory (periodic orbits and invariant manifolds), and perturbation treatments. Poincaré sections show that orbit flips are due to the existence of islands of libration centered at inclination of 90°, dynamical system theory shows that orbit flips are due to the existence of polar periodic orbits and invariant manifolds, and perturbative treatments indicate that orbit flips are due to the libration of a certain critical argument. Using these approaches, the boundaries of flipping regions in the entire parameter space are produced, and they are in excellent agreement with one another. Through analysis, the essence of flipping orbits is reached: (a) flipping orbits are a kind of quasiperiodic trajectory around polar periodic orbits and invariant manifolds at the same level of Hamiltonian provide boundaries of flipping regions, and (b) flipping orbits are a kind of resonant trajectory, and resonant width measures the size of flipping regions.
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•Surrogate models for dynamic systems in chemical engineering.•Evaluation of recursive neural network designs.•First ever surrogate model for a batch distillation from start-up to ...shut down.•Hyperparameter tuning by Bayesian and Bandit optimization.
Surrogate models for dynamic systems in chemical engineering are increasingly of interest. Neural networks have already been applied in research, but it remains unclear which types of neural network architectures are actually required for practical systems. The focus here lies on recurrent neural networks of type Jordan, Elman, and LSTM layers. These are investigated for different types of data sets as training basis: batch trajectories, data of a proper excitation of a continuous process, and a typical operation trajectory of a large chemical plant. To ensure a rigorous investigation, hyperparameter tuning by Bayesian and Bandit optimization is included. As a first, a dynamic surrogate model using LSTM layers for a batch distillation system is presented, which is valid from start-up until shutdown. The evaluation shows further need for adjustments in data preparation and objective/loss function compared to the state of the art.
The trend towards lightweight in the automotive industry give rise to new challenges when assessing the influence of material replacements on stick–slip effects. These effects may lead to new ...acoustic phenomena when aluminium is applied, e.g. coming from the interfaces of the wheel assembly between the rim, brake disk hat and the wheel carrier. Detecting the key influencing parameters is an important task to avoid undesired noises or wear. Whereas self-excited oscillators were intensively discussed in the last decades, much fewer studies about harmonically excited systems were published. The goal of this study is to investigate the effect of different parameters on the stick–slip behaviour of a harmonically excited oscillator exposed to friction. Based on a statistical evaluation of huge experimental data sets with stick–slip effects, a two-degree-of-freedom model for the frictional testing machine is proposed and implemented with several friction models. These models are compared with respect to their ability to fit the measurement data and their computational effort. Numerical parameter studies including a huge amount of different parameter sets are performed to determine the effect of several parameters on the limit cycle of the dynamic system, quantified by the number of stops per cycle. The influence of more complex friction laws on the parameter maps are discussed in relation to the published results by Hong and Liu as well as Papangelo and Ciavarella.
•Statistical evaluation of huge experimental data sets of stick slip probability.•Benefit of complex friction models regarding their ability to fit experimental data.•Friction law approach combining a bristle-based model with velocity dependency.•Dimensionless parameter maps with number of stops for complex friction laws.
•A single-degree-of-freedom spring-mass-damper model is used to represent a human performing rhythmic jumping.•This is a non-smooth piece-wise linear problem defined by contact and flight phases of ...the jumper.•A parametric exploration is employed to evaluate the steady-state jumping behaviour of a human.•The influence of a structure’s oscillating amplitude and frequency on a human jumper are investigated.
Lightweight and long-span civil structures, such as grandstand tiers, are susceptible to vertical vibrations due to jumping or bobbing of human spectators. After a careful review of experimental evidence, including new data, a simple mathematical model is investigated in order to characterise human-structure interactions observed during human rhythmic jumping on a perceptibly moving surface. A passive mass-spring-damper is used to model a human jumper whilst subjected to an input structural oscillation. The coupled system is modelled as a piecewise-smooth contact dynamics problem allowing for the loss of contact during rhythmic jumping. Parametric sweeps are interpreted using methods from non-linear dynamical systems theory, including bifurcation analysis and the use of Poincaré maps. Hysteresis and coexistence of qualitatively different stable periodic motions over a broad range of parameter values of the system are observed. The presence of such coexisting non-intuitive motions is verified by preliminary experimental results that indicate period-doubled jumping behaviour (a repeating sequence of large-jump-small-jump) of test subjects both above and below a structure’s natural frequency. At large amplitudes of structural motion, the model shows that the behaviour can become chaotic. This provides an explanation for experimental findings that it is difficult to jump periodically around the natural frequency of a supporting structure. The simple model provides a detailed map of where different motions occur in parameter space, which should be amenable to further experimental validation.
•The failure correlation with time progressing is illustrated and quantified.•The time-variant reliability estimation method is presented based on the time-varying copula function and subset ...simulation.•The time-variant reliability prediction framework with partial information is proposed.•The time-variant reliability prediction method is provided.
Efficient time-variant reliability prediction for dynamic systems is a challenging problem to reduce the risk because large amounts of information is needed for the prediction. In this paper, a physics-based reliability prediction method is presented with partial information. The cumulative probabilities of failure are first estimated for the given time intervals with complete information based on the subset simulation with splitting and time-variant copula function. An appropriate probability distribution is then selected for fitting the estimated cumulative probabilities of failure. The partial information, which can be collected from mathematical models or the physical experiments during the later time intervals, is used to effectively update the distribution parameters to improve the prediction accuracy. A case study of a vibratory system representing the quarter car model is employed to testify the proposed method.
Unknown nonstationary processes require modeling and control design to be done in real time using streams of data collected from the process. The purpose is to stabilize the closed-loop system under ...changes of the operating conditions and process parameters. This paper introduces a model-based evolving granular fuzzy control approach as a step toward the development of a general framework for online modeling and control of unknown nonstationary processes with no human intervention. An incremental learning algorithm is introduced to develop and adapt the structure and parameters of the process model and controller based on information extracted from uncertain data streams. State feedback control laws and closed-loop stability are obtained from the solution of relaxed linear matrix inequalities derived from a fuzzy Lyapunov function. Bounded control inputs are also taken into account in the control system design. We explain the role of fuzzy granular data and the use of parallel distributed compensation. Fuzzy granular computation provides a way to handle data uncertainty and facilitates incorporation of domain knowledge. Although the evolving granular approach is oriented to control systems whose dynamics is complex and unknown, for expositional clarity, we consider online modeling and stabilization of the well-known Lorenz chaos as an illustrative example.
•New hybrid model is proposed by combining probabilistic/non-probabilistic exponential models.•A new hybrid exponential probability integral method is developed for reliability analysis.•Lower and ...upper bounds of failure probability of static and dynamic systems are computed.•Examples verify the generality, accuracy and efficiency of proposed model and methods.
Uncertainty propagation and reliability evaluation, being the crucial parts of engineering system analysis, play vital roles in safety assessment. How to reasonably consider the complex multisource uncertainty behavior in both static and dynamic systems is paramount to ensuring their safe operation. However, there is a significant lack of research on aleatory and epistemic uncertainties for both static and dynamic systems. To this end, a new hybrid exponential model is proposed by combining probabilistic and non-probabilistic exponential models, which aims to accurately measure the uncertainty propagation and reliability evaluation problem with aleatory and epistemic uncertainties for static and dynamic systems. The proposed hybrid exponential model consists of nested double optimization loops. The outer loop performs a probabilistic analysis based on the direct probability integral method, and the inner loop performs a non-probabilistic computation. Then, a new hybrid exponential probability integral method is developed to effectively perform uncertainty propagation and reliability analysis. Finally, four examples, including two static and two dynamic examples with complex performance functions, are tested. The results indicate that the proposed hybrid exponential model offers a universal tool for uncertainty quantification in static and dynamic systems. Moreover, the hybrid exponential probability integral method can accurately and efficiently obtain the upper and lower bounds of the probability density function and cumulative distribution function.
M-Shadowing and Transitivity for Flows Wang, Jianjun; Lu, Tianxiu
Journal of dynamical and control systems,
06/2023, Letnik:
29, Številka:
2
Journal Article
Recenzirano
Smale pointed out a very important problem in dynamical systems theory is to find the minimal set. In this paper, we show that if a flow on compact metric space has the
M
0
-shadowing property or the
...M
1
2
-shadowing property, then it is chain transitive. In addition, we prove that a Lyapunov stable flow with the
M
0
-shadowing or the
M
1
2
-shadowing is topologically transitive. Furthermore, it also is a minimal flow. As an application, we obtain that a
C
1
generic vector field
X
^
of a closed smooth 3-dimensional manifold with
Sing
(
X
^
)
=
∅
is Anosov provided that it has the
M
0
-shadowing property or the
M
1
2
-shadowing property.
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