Application of local coordinates rectification in linearization of selected parameters of dynamic nonlinear systems

2014 ◽  
Vol 33 (5) ◽  
pp. 1819-1830 ◽  
Author(s):  
Andrzej Zawadzki
Keyword(s):  
Nonlinear System ◽  
Coordinate System ◽  
State Space ◽  
State Equation ◽  
The State ◽  
Content Type ◽  
Electric Circuits ◽  
First Order ◽  
State Space Transformation ◽  
Nonlinear State

Purpose – The purpose of this paper is to aim to an application of element of the theory of differential geometry for building the state space transformation, linearizing nonlinear dynamic system into a linear form. Design/methodology/approach – It is assumed that the description of nonlinear electric circuits with concentrated parameters or electromechanical systems is given by nonlinear system of differential equations of first order (state equations). The goal is to find transformation which leads nonlinear state equation (written in one coordinate system) to the linear in the other – sought coordinate system. Findings – The necessary conditions fulfilled by nonlinear system undergoing linearization process are presented. Numerical solutions of the nonlinear equations of state together with linearized system obtained from direct transformation of the state space are included (transformation input – the state of the nonlinear system). Originality/value – Application of first order exact differential forms for determining the transformation linearizing the nonlinear state equation. Simple linear models obtained with the use of the linearizing transformation are very useful (mainly because of the known and well-mastered theory of linear systems) in solving of various practical technical problems.

Optimal control method on assembly precision for a remanufactured car engine based on state space model

2016 ◽  
Vol 36 (4) ◽  
pp. 460-472 ◽  
Author(s):  
Jing Hu ◽  
Yuan Zhang ◽  
Maogen GE ◽  
Mingzhou Liu ◽  
Liu Conghu ◽  
...  
Keyword(s):  
Optimal Control ◽  
State Space ◽  
Control Method ◽  
State Space Model ◽  
The State ◽  
Content Type ◽  
Space Model ◽  
Optimal Control Method ◽  
Assembly Error ◽  
Assembly Precision

Purpose The optimal control on reassembly (remanufacturing assembly) error is one of the key technologies to guarantee the assembly precision of remanufactured product. However, because of the uncertainty existing in remanufactured parts, it is difficult to control assembly error during reassembly process. Based on the state space model, this paper aims to propose the optimal control method on reassembly precision to solve this problem. Design/methodology/approach Initially, to ensure the assembly precision of a remanufactured car engine, this paper puts forward an optimal control method on assembly precision for a remanufactured car engine based on the state space model. This method takes assembly workstation operation and remanufactured part attribute as the input vector reassembly status as the state vector and assembly precision as the output vector. Then, the compensation function of reassembly workstation operation input vector is calculated to direct the optimization of the reassembly process. Finally, a case study of a certain remanufactured car engine crankshaft is constructed to verify the feasibility and effectiveness of the method proposed. Findings The optimal control method on reassembly precision is an effective technology in improving the quality of the remanufactured crankshaft. The average qualified rate of the remanufactured crankshaft increased from 83.05 to 90.97 per cent as shown in the case study. Originality/value The optimal control method on the reassembly precision based on the state space model is available to control the assembly precision, thus enhancing the core competitiveness of the remanufacturing enterprises.

scholarly journals Parameter and State Estimator for State Space Models

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ruifeng Ding ◽  
Linfan Zhuang
Keyword(s):  
State Space ◽  
State Equation ◽  
The State ◽  
Parameter Estimates ◽  
Identification Algorithm ◽  
State Variables ◽  
Input Output ◽  
State Estimator ◽  
Output Data ◽  
Canonical State

This paper proposes a parameter and state estimator for canonical state space systems from measured input-output data. The key is to solve the system state from the state equation and to substitute it into the output equation, eliminating the state variables, and the resulting equation contains only the system inputs and outputs, and to derive a least squares parameter identification algorithm. Furthermore, the system states are computed from the estimated parameters and the input-output data. Convergence analysis using the martingale convergence theorem indicates that the parameter estimates converge to their true values. Finally, an illustrative example is provided to show that the proposed algorithm is effective.

Identification of nonlinear state-space time-delay system

2019 ◽  
Vol 40 (1) ◽  
pp. 22-30
Author(s):  
Xin Liu ◽  
Hang Zhang ◽  
Pengbo Zhu ◽  
Xianqiang Yang ◽  
Zhiwei Du
Keyword(s):  
Time Delay ◽  
Em Algorithm ◽  
State Space ◽  
Latent Variable ◽  
Industrial Process ◽  
Delay System ◽  
Model Parameters ◽  
Content Type ◽  
Output Time ◽  
Nonlinear State

Purpose This paper aims to investigate an identification strategy for the nonlinear state-space model (SSM) in the presence of an unknown output time-delay. The equations to estimate the unknown model parameters and output time-delay are derived simultaneously in the proposed strategy. Design/methodology/approach The unknown integer-valued time-delay is processed as a latent variable which is uniformly distributed in a priori known range. The estimations of the unknown time-delay and model parameters are both realized using the Expectation-Maximization (EM) algorithm, which has a good performance in dealing with latent variable issues. Moreover, the particle filter (PF) with an unknown time-delay is introduced to calculated the Q-function of the EM algorithm. Findings Although amounts of effective approaches for nonlinear SSM identification have been developed in the literature, the problem of time-delay is not considered in most of them. The time-delay is commonly existed in industrial scenario and it could cause extra difficulties for industrial process modeling. The problem of unknown output time-delay is considered in this paper, and the validity of the proposed approach is demonstrated through the numerical example and a two-link manipulator system. Originality/value The novel approach to identify the nonlinear SSM in the presence of an unknown output time-delay with EM algorithm is put forward in this work.

Hydraulic-seasonal-time-based state space model for displacement monitoring of high concrete dams

2021 ◽  
pp. 014233122110183
Author(s):  
Shaowei Wang ◽  
Cong Xu ◽  
Chongshi Gu ◽  
Huaizhi Su ◽  
Bangbin Wu
Keyword(s):  
State Space ◽  
Elastic Deformation ◽  
State Space Model ◽  
State Equation ◽  
Time Effect ◽  
The State ◽  
Arch Dam ◽  
Model Parameters ◽  
Concrete Dams ◽  
Space Model

Displacement is the most intuitive reflection of the comprehensive behavior of concrete dams, especially the time effect displacement, which is a key index for the evaluation of the structural behavior and health status of a dam in long-term service. The main purpose of this paper is to establish a state space model for separating causal components from the measured dam displacement. This approach is conducted by initially proposing two equations, which are the state and observation equations, and model parameters are then optimized by the Kalman filter algorithm. The state equation is derived according to the creep deformation of dam concrete and foundation rock and is used to preliminarily predict the dam time effect displacement. Considering the generally recognized three components of dam displacement, the hydraulic-seasonal-time (HST) model is used to establish the observation equation, which is used to update the time effect displacement. The efficiency and rationality of the established state space model is verified by an engineering example. The results show that the hydraulic component separated by the state space model only contains the instantaneous elastic hydraulic deformation, while the hysteretic elastic hydraulic deformation is divided into the time effect component. The inverted elastic modulus of dam body concrete is an instantaneous value for the state space model but a comprehensive reflection of the instantaneous and hysteretic elastic deformation ability for the HST model, where the hysteretic elastic deformation is a part of the hydraulic component. For the Xiaowan arch dam, the inverted values are 42.9 and 36.7 GPa for the state space model and HST model, respectively. The proposed state space model is useful to improve the interpretation ability of the separated displacement components of concrete dams.

scholarly journals Learning First-Order Representations for Planning from Black Box States: New Results

2021 ◽  
Author(s):  
Ivan D. Rodriguez ◽  
Blai Bonet ◽  
Javier Romero ◽  
Hector Geffner
Keyword(s):  
State Space ◽  
Partial Information ◽  
Large Family ◽  
The State ◽  
Initial State ◽  
New Approach ◽  
First Order ◽  
Sat Solver ◽  
State Graphs ◽  
Domain Description

Recently Bonet and Geffner have shown that first-order representations for planning domains can be learned from the structure of the state space without any prior knowledge about the action schemas or domain predicates. For this, the learning problem is formulated as the search for a simplest first-order domain description D that along with information about instances I_i (number of objects and initial state) determine state space graphs G(P_i) that match the observed state graphs G_i where P_i = (D, I_i). The search is cast and solved approximately by means of a SAT solver that is called over a large family of propositional theories that differ just in the parameters encoding the possible number of action schemas and domain predicates, their arities, and the number of objects. In this work, we push the limits of these learners by moving to an answer set programming (ASP) encoding using the CLINGO system. The new encodings are more transparent and concise, extending the range of possible models while facilitating their exploration. We show that the domains introduced by Bonet and Geffner can be solved more efficiently in the new approach, often optimally, and furthermore, that the approach can be easily extended to handle partial information about the state graphs as well as noise that prevents some states from being distinguished.

scholarly journals LP Heuristics over Conjunctions: Compilation, Convergence, Nogood Learning

2018 ◽  
Author(s):  
Marcel Steinmetz ◽  
Joerg Hoffmann
Keyword(s):  
State Space ◽  
State Equation ◽  
The State ◽  
Convergence Properties ◽  
Performance Improvements ◽  
State Space Search ◽  
Refinement Method ◽  
Significant Performance

Two strands of research in classical planning are LP heuristics and conjunctions to improve approximations. Combinations of the two have also been explored. Here, we focus on convergence properties, forcing the LP heuristic to equal the perfect heuristic h* in the limit. We show that, under reasonable assumptions, partial variable merges are strictly dominated by the compilation Pi^C of explicit conjunctions, and that both render the state equation heuristic equal to h* for a suitable set C of conjunctions. We show that consistent potential heuristics can be computed from a variant of Pi^C, and that such heuristics can represent h* for suitable C. As an application of these convergence properties, we consider sound nogood learning in state space search, via refining the set C. We design a suitable refinement method to this end. Experiments on IPC benchmarks show significant performance improvements in several domains.

Bayesian monthly index for building activity based on mixed frequencies: the case of Chile

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Byron J. Idrovo-Aguirre ◽  
Javier E. Contreras-Reyes
Keyword(s):  
Kalman Filter ◽  
Bayesian Inference ◽  
State Space ◽  
State Space Model ◽  
Natural Extension ◽  
The State ◽  
Likelihood Method ◽  
Content Type ◽  
Space Model ◽  
Construction Activity

PurposeThis paper combines the objective information of six mixed-frequency partial-activity indicators with assumptions or beliefs (called priors) regarding the distribution of the parameters that approximate the state of the construction activity cycle. Thus, this paper uses Bayesian inference with Gibbs simulations and the Kalman filter to estimate the parameters of the state-space model, used to design the Imacon.Design/methodology/approachUnlike other economic sectors of similar importance in aggregate gross domestic product, such as mining and industry, the construction sector lacked a short-term measure that helps to identify its most recent performance.FindingsIndeed, because these priors are susceptible to changes, they provide flexibility to the original Imacon model, allowing for the assessment of risk scenarios and adaption to the greater relative volatility that characterizes the sector's activity.Originality/valueThe classic maximum likelihood method of estimating the monthly construction activity index (Imacon) is rigid to the incorporation of new measures of uncertainty, expectations or different volatility (risks) levels in the state of construction activity. In this context, this paper uses Bayesian inference with 10,000 Gibbs simulations and the Kalman filter to estimate the parameters of the state-space model, used to design the Imacon, inspired by the original works of Mariano and Murasawa (2003) and Kim and Nelson (1998). Thus, this paper consists of a natural extension of the classic method used by Tejada (2006) in the estimation of the old Imacon.

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