State Space Reduction Methods Research Articles

An efficient physics-dimension-based reduction method for computing frequency response functions of viscoelastically damped systems

The frequency response functions (FRFs) are of critical interest to dynamic problems, however, they suffer from computational challenges for viscoelastically damped systems. In this paper, a physics-space-based reduction method is proposed for predicting the FRFs of large-scale viscoelastically damped systems involving the standard linear solid model. A physics-dimension subspace is constructed based on original system matrices and viscoelastic parameters, which can be easily generated by using a recursive manner. A projection basis generation algorithm is then developed to generate a standard orthonormal basis within the physics-dimension subspace. With the help of the standard orthonormal basis and the moment-matching-based reduction method, a physics-space-based reduction method is proposed for efficiently predicting the FRFs of large-scale viscoelastically damped systems. Unlike the widely used state-space reduction method, the reduced system of the proposed method can preserve system’s physical structure so that the physical meaning can be captured. Using both theoretical and numerical analyses, the proposed physics-space-based method is more accurate and efficient than the state-space-based reduction method.

Hybrid Deep Modeling of a GS115 (Mut+) Pichia pastoris Culture with State–Space Reduction

Hybrid modeling workflows combining machine learning with mechanistic process descriptions are becoming essential tools for bioprocess digitalization. In this study, a hybrid deep modeling method with state–space reduction was developed and showcased with a P. pastoris GS115 Mut+ strain expressing a single-chain antibody fragment (scFv). Deep feedforward neural networks (FFNN) with varying depths were connected in series with bioreactor macroscopic material balance equations. The hybrid model structure was trained with a deep learning technique based on the adaptive moment estimation method (ADAM), semidirect sensitivity equations and stochastic regularization. A state–space reduction method was investigated based on a principal component analysis (PCA) of the cumulative reacted amount. Data of nine fed-batch P. pastoris 50 L cultivations served to validate the method. Hybrid deep models were developed describing process dynamics as a function of critical process parameters (CPPs). The state–space reduction method succeeded to decrease the hybrid model complexity by 60% and to improve the predictive power by 18.5% in relation to the nonreduced version. An exploratory design space analysis showed that the optimization of the feed of methanol and of inorganic elements has the potential to increase the scFv endpoint titer by 30% and 80%, respectively, in relation to the reference condition.

A model-based safety analysis approach for airborne systems using state traversals

Safety analysis is an important task in both the development and certification of civil aircraft. The traditional safety analysis is significantly dependent on the skills and experiences of analysts. A model-based safety analysis approach is proposed for airborne systems based on the model built with Simulink. This study builds Simulink models of typical failure modes as well as the fault injection methods. The responses of system performances are monitored by traversing all failure combinations based on a state space reduction method. The system will be in an unsafe condition when the responses exceed their thresholds. The minimal cut sets of the system are obtained automatically by recording the failure combinations leading to the unsafe condition. Finally, a lateral-directional flight control system is taken as a practical example to illustrate the application and effectiveness of our proposed method. The result shows that our method has higher accuracy and the causes of the unsafe conditions can be determined by the automatic generation of the minimal cut sets. Additionally, the cumbersome work of building a traditional safety analysis model such as the fault tree, the Markov model, or the dependence diagram can be avoided.

Modelling different aspects of final exam scheduling problems for a graph-based state space reduction method

Final exam scheduling is a subtopic of scheduling where various special requirements with different levels of strictness should be managed. The formalisation of these requirements can be a challenge in itself. The number of possible schedules that should be examined is usually large, so the state space is vast. However, many of these schedules can be excluded completely at an early stage based on their inconsistency with the hard requirements, thus reducing the state space. The modelling approach for different aspects of final exam scheduling problems is presented in this paper through the modelling of an actual, complex problem. The created model was used as the basis for a state space reduction method. The results show that the method could handle all the hard and soft constraints of the problem and reduce the state space significantly based on them. The modelling approach can be used for formalising the requirements of various final exam scheduling and similar problems.

Efficient Component Reductions in a Large-Scale Flexible Multibody Model

To make better use of simulations in the automotive driveline design process there is a need for both improved predictive capabilities of typical system models and increased number of variant evaluations carried out during system concept design phase. A previously developed large-scale multibody rotor dynamical powertrain model that combines detailed linear-elastic finite element components and nonlinear joints is used to more accurately simulate system response modes and their variations across the operating-range. However, the total simulation time is too long to include extensive parameter evaluations during the rapid design iterations, which will have a negative influence on the total understanding of the designed system's behaviour. Therefore this paper is about reducing such a large-scale model to one that runs faster, but without losing the ability to predict the most fundamental system characteristics. Reduction methods considering defined stimuli-response relations are well established and used within the field of control systems, to balance prediction accuracy and evaluation effort, but are not yet commonly applied to large-scaled structural models and analysis of vibrations in continuous and lightly damped structures. Here, an implementation of two such state-space reduction methods into a common computational software workflow is described and their overall efficiency is compared to standard methods. Reductions are applied to two major structural components of the powertrain model. Steady-state simulations are performed for multiple engine speeds and responses related to vehicle noise and vibrations are compared using a quantitative error metric. The prediction accuracy, reduction and response simulation times of different model orders are evaluated, as well as the corresponding mode frequency spectra.

An M/PH/K queue with constant impatient time

This paper is concerned with an M/PH/K queue with customer abandonment, constant impatient time, and many servers. By combining the method developed in Choi et al. (Math Oper Res 29:309–325, 2004) and Kim and Kim (Perform Eval 83–84:1–15, 2015) and the state space reduction method introduced in Ramaswami (Stoch Models 1:393–417, 1985), the paper develops an efficient algorithm for computing performance measures for the queueing system of interest. The paper shows a number of properties associated with matrices used in the development of the algorithm, which make it possible for the algorithm, under certain conditions, to handle systems with up to one hundred servers. The paper also obtains analytical properties of performance measures that are useful in gaining insight into the queueing system of interest.

공간의존 파론도 게임의 재분배 모형

N명의 게임자들이 둥글게 둘러앉아 공간의존 파론도 게임 B를 실시한다. 게임 B는 여러 명의 게임자들 중에서 한 명을 임의로 선택하고, 선택된 게임자는 양 옆에 있는 두 명의 게임자들의 상태에 따라 앞면이 나올 확률이 달라지는 동전을 던져서 앞면이 나오면 1원을 얻고 뒷면이 나오면 1원을 잃는다. 게임 A'은 임의로 선택된 게임자가 나머지 N - 1명의 게임자들 중에서 한 명을 임의로 선택하여 본인의 상금 1원을 전달하는 게임으로 전체 게임자들의 총 상금에는 변함이 없으므로 전체 게임자들에게는 항상 공정한 게임이다. 만약 게임 B가 지는 게임인 반면에 두 게임 A'와 B를 결합한 혼합게임 C는 이기는 게임이 되면 파론도 효과가 존재하고, 게임 B가 이기는 게임이고 혼합게임 C는 지는 게임이면 역파론도 효과가 존재한다고 한다. 먼저 마코프 체인의 상태공간의 축소를 위한 lumpability 조건이 게임 A', B 그리고 혼합게임 C에 대해 만족함을 보이고, 축소된 상태공간에서 게임 B와 C의 기대상금을 계산한다. 이를 이용하여 파론도 효과와 역파론도 효과의 존재를 확인하고, 특별히 <TEX>$3{\leq}N{\leq}6$</TEX>의 경우에는 파론도 효과와 역파론도 효과가 존재하는 확률 모수의 영역을 도식화 한다. An ansemble of N players arranged in a circle play a spatially dependent Parrondo game B. One player is randomly selected to play game B, which is based on the toss of a biased coin, with the amount of the bias depending on states of the selected player's two nearest neighbors. The player wins one unit with heads and loses one unit with tails. In game A' the randomly chosen player transfers one unit of capital to another player who is randomly chosen among N - 1 players. Game A' is fair with respect to the ensemble's total profit. The games are said to exhibit the Parrondo effect if game B is losing and the random mixture game C is winning and the reverse-Parrondo effect if game B is winning and the random mixture game C is losing. We compute the exact mean profits for games B and C by applying a state space reduction method with lumped Markov chains and we sketch the Parrondo and reverse-Parrondo regions for <TEX>$3{\leq}N{\leq}6$</TEX>.

Parrondo Games with Spatial Dependence, III

We study Toral’s Parrondo games with [Formula: see text] players and one-dimensional spatial dependence as modified by Xie et al. Specifically, we use computer graphics to sketch the Parrondo and anti-Parrondo regions for [Formula: see text]. Our work was motivated by a recent paper of Li et al., who applied a state space reduction method to this model, reducing the number of states from [Formula: see text] to [Formula: see text]. We show that their reduced Markov chains are inconsistent with the model of Xie et al.

State estimation using multibody models and non-linear Kalman filters

The aim of this work is to provide a thorough research on the implementation of some non-linear Kalman filters (KF) using multibody (MB) models and to compare their performances in terms of accuracy and computational cost. The filters considered in this study are the extended KF (EKF) in its continuous form, the unscented KF (UKF) and the spherical simplex unscented KF (SSUKF). The MB formulation taken into consideration to convert the differential algebraic equations (DAE) of the MB model into the ordinary differential equations (ODE) required by the filters is a state-space reduction method known as projection matrix-R method. Additionally, both implicit and explicit integration schemes are used to evaluate the impact of explicit integrators over implicit integrators in terms of accuracy, stability and computational cost. However, state estimation through KFs is a closed-loop estimation correcting the model drift according to the difference between the predicted measurement and the actual measurement, what limits the interest in using implicit integrators despite being commonly employed in MB simulations. Performance comparisons of all the aforementioned non-linear observers have been carried out in simulation on a 5-bar linkage. The mechanism parameters have been obtained from an experimental 5-bar linkage and the sensor characteristics from off-the-shelf sensors to reproduce a realistic simulation. The results should highlight useful clues for the choice of the most suitable filters and integration schemes for the aforementioned MB formulation.

Acceleration Strategies in Generalized Belief Propagation

Generalized belief propagation is a popular algorithm to perform inference on large-scale Markov random fields (MRFs) networks. This paper proposes the method of accelerated generalized belief propagation with three strategies to reduce the computational effort. First, a min-sum messaging scheme and a caching technique are used to improve the accessibility. Second, a direction set method is used to reduce the complexity of computing clique messages from quartic to cubic. Finally, a coarse-to-fine hierarchical state-space reduction method is presented to decrease redundant states. The results show that a combination of these strategies can greatly accelerate the inference process in large-scale MRFs. For common stereo matching, it results in a speed-up of about 200 times.

Automotive observers based on multibody models and the extended Kalman filter

This work is part of a project aimed to develop automotive real-time observers based on detailed nonlinear multibody models and the extended Kalman filter (EKF). In previous works, a four-bar mechanism was studied to get insight into the problem. Regarding the formulation of the equations of motion, it was concluded that the state-space reduction method known as matrix-R is the most suitable one for this application. Regarding the sensors, it was shown that better stability, accuracy and efficiency are obtained as the sensored magnitude is a lower derivative and when it is a generalized coordinate of the problem. In the present work, the automotive problem has been addressed, through the selection of a Volkswagen Passat as a case-study. A model of the car containing fifteen degrees of freedom has been developed. The observer algorithm that combines the equations of motion and the integrator has been reformulated so that duplication of the problem size is avoided, in order to improve efficiency. A maneuver of acceleration from rest and double lane change has been defined, and tests have been run for the “prototype,” the “model” and the “observer,” all the three computational, with the model having 100 kg more than the prototype. Results have shown that good convergence is obtained for position level sensors, but the computational cost is high, still far from real-time performance.

Model checking of emergent behaviour properties of robot swarms

This paper presents a case study on scalability of explicit state model checking. Three state space reduction methods - state vector compression, bit state hashing, and symmetry reduction - were applied on an exercise with the objective of verifying a distributed coordination algorithm for robot swarms. Based on the analysis results, the feasibility of using explicit state model checking to prove properties of large multi-agent systems is questioned and the limitations faced in verifying a dynamic cleaning algorithm are outlined.

Guaranteeing Weak Termination in Service Discovery

A big issue in the paradigm of Service Oriented Architectures (SOA) is service discovery. Organizations publish their services via the Internet. These published services can then be automatically found and accessed by other services, meaning, the services are composed. A fundamental property of a service composition is weak termination, which guarantees the absence of deadlocks and livelocks. In principle, weak termination can be verified by inspecting the state space of the composition of (public views of) the involved services. We propose a methodology to build that state space from precomputed fragments, which are computed upon publishing a service. That way, we shift computation effort from the resource critical “find” phase to the less critical “publish” phase. Interestingly, our setting enables state space reduction methods that are intrinsically different from traditional state space reductions. We further show the positive impact of our approach to the computational effort of service discovery.

Real-time state observers based on multibody models and the extended Kalman filter

This work is a preliminary study on the use of the extended Kalman filter (EKF) for the state estimation of multibody systems. The observers based on the EKF are described by first-order differential equations, with independent, non-constrained coordinates. Therefore, it should be investigated how to formulate the equations of motion of the multibody systems so that efficient, robust and accurate observers can be derived, which can serve to develop advanced real-time applications. In the paper, two options are considered: a state-space reduction method and the penalty method. Both methods are tested on a four-bar mechanism with a linear spring-damper. The results enable us to analyze the pros and cons of each method and provide clues for future research.

Formal specification and state space analysis of an operational planning process

Formal models of business processes support performance and behavioural analysis of the processes for continuous improvement. Formal models are also useful in guiding the development of software tools to support the processes. This paper presents a formal model of the operational planning process used in an operational headquarters of the Australian Defence Force. The formal process model was developed using coloured petri nets (CPN or CP-nets). The constructed CPN model has allowed the planning process to be validated and analysed using simulation and state spaces. State space analysis was conducted using full state spaces and the sweep-line state space reduction method.

Exploiting Equivalence Reduction and the Sweep-Line Method for Detecting Terminal States

State-space exploration is one of the main approaches to computer-aided verification and analysis of finite-state systems. It is used to reason about a wide range of properties during the design phase of a system, including system deadlocks. Unfortunately, state-space exploration needs to handle huge state spaces for most practical systems. Several state-space reduction methods have been developed to tackle this problem. In this paper, we develop algorithms for combining two of these methods: state equivalence class reduction and the sweep-line. The algorithms allow deadlocks to be detected by recording terminal states of the system on-the-fly during state-space exploration. We derive expressions for the complexity of the algorithms and demonstrate their usefulness with an industrial case study. Our results show that the combined method achieves at least a six-fold reduction of the state space for interesting parameter values compared with either method used in isolation while still proving the desired system property of the terminal states. The runtime performance of the combined method is almost the same as that of the equivalence class method over the chosen parameter range. Moreover, the improvement in space reduction increases with increased parameter values.

Verification by State Spaces with Equivalence Classes

&lt;p&gt;This paper demonstrates the pontential of verification based on state spaces reduced by equivalence relations. The basic observation is that quite often, some states of a system are similar, i.e., they induce similar behaviours. Similarity can be formally expressed by defining equivalence relations on the set of states and the set of actions of a system under consideration. A state space can be constructed, in which the nodes correspond to equivalence classes of states and the arcs correspond to equivalence classes of actions. Such a state space is often much smaller than the ordinary full state space, but does allow derivation of many verification results.&lt;/p&gt;&lt;p&gt;Other researches have taken advantage of the symmetries of systems, which induce a certain kind of equivalence. The contribution fo this paper is to show that a more general notion of equivalence is useful. As example, a communication protocol modelled in the formalism of Coloured Petri Nets is verified. Aided by a computer tool supporting state spaces with equivalence classes, significant reduction of state spaces are exhibited.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Topics&lt;/strong&gt;. State space reduction methods, equivalence vs. symmetry, High-level Petri Nets, communication protocols.&lt;/p&gt;

Application of the correlation integral to respiratory data of infants during REM sleep.

Non-linear time sequence analysis has been performed on infant sleep measurement data in order to obtain more information about the respiratory processes. As a first step, respiration data during REM sleep were analysed with methods from non-linear dynamics, especially, the correlation integral and the slope of its log-log plot, representing the correlation dimension. Before calculation of the correlation integral, a special kind of filtering has to be applied to the data. This filtering algorithm is a state space and singular value decomposition-based noise reduction method, and it is used to separate the noise and signal subspaces. The dynamics of a signal (in our case data from the respiratory process) and its degrees of freedom can be characterised by the correlation integral and by the correlation dimension, respectively. The main result of this study is that the highly irregular-looking breathing patterns during REM sleep could be described by a deterministic system, and finally the physiological significance of this finding is discussed.

Application and experimental evaluation of state space reduction methods for deadlock analysis in Ada

An emerging challenge for software engineering is the development of the methods and tools to aid design and analysis of concurrent and distributed software. Over the past few years, a number of analysis methods that focus on Ada tasking have been developed. Many of these methods are based on some form of reachability analysis, which has the advantage of being conceptually simple, but the disadvantage of being computationally expensive. We explore the effectiveness of various Petri net-based techniques for the automated deadlock analysis of Ada programs. Our experiments consider a variety of state space reduction methods both individually and in various combinations. The experiments are applied to a number of classical concurrent programs as well as a set of “real-world” programs. The results indicate that Petri net reduction and reduced state space generation are mutually beneficial techniques, and that combined approaches based on Petri net models are quite effective, compared to alternative analysis approaches.

Using state space reduction methods for deadlock analysis in Ada tasking

Over the past few years, a number of research investigations have been initiated for static analysis of concurrent and distributed software. In this paper we report on experiments with various optimization techniques for reachability-based deadlock detection in Ada programs using Petri net models. Our experimental results show that various optimization techniques are mutually beneficial with respect to the effectiveness of the analysis.