Efficient Linear Method Research Articles

Data-Driven Chance-Constrained Schedule Optimization of Cascaded Hydropower and Photovoltaic Complementary Generation Systems for Shaving Peak Loads

The coordinated scheduling of cascade hydropower with photovoltaic (PV) power stations can significantly improve the utilization rate of delivery transmission lines. However, the inherent uncertainty associated with photovoltaic (PV) forecasts challenges the reliable and economic operation of the complementary energy system. Against this background, in this paper, a day-ahead, chance-constrained scheduling for cascaded hydro–photovoltaic complementary generation systems (CHPSs) considering the transmission capacity is proposed. Firstly, the uncertainty of PV forecast errors is simulated by a probability density function fitted using kernel density estimation with historical sampling data. Then, a chance-constrained optimization model considering peak-shaving demands of the receiving-end power grid is developed to determine the day-ahead optimal schedules of CHPSs. Also, complex hydraulic coupling and unit operation constraints of cascade hydropower are considered in the proposed model. To deal with the nonlinear and stochastic constraints, an efficient linearization method is adopted to transform the proposed model into a mixed-integer linear programming (MILP) problem. Finally, the effectiveness and feasibility are verified by case studies. The results show that the day-ahead schedule optimized by the proposed method can fully balance peak-shaving and photovoltaic accommodation while considering photovoltaic output uncertainty.

Analyzing the backbone curve of piecewise-linear non-smooth systems using a generalized bilinear frequency approximation method

Estimating the resonant frequency of non-smooth systems with contacting elements is critical for the design, control, and health monitoring of various mechanical and aerospace structures. The nonlinearity caused by the intermittent contact excludes the use of efficient linear methods; hence, predicting vibration characteristics of these systems becomes computationally challenging. Furthermore, several numerical and analytical approaches that have been developed for analyzing smooth nonlinear systems cannot be applied to analyze non-smooth oscillators. To understand the dynamic properties of non-smooth dynamical systems, the bilinear frequency approximation (BFA) method, a classical analytical tool, was developed to estimate the nonlinear natural frequency of bilinear oscillators by using the linear characteristics of underlying linear subsystems to construct a closed-form analytical solution. However, the traditional BFA method is only applicable to systems in which the gap size between the contacting element is zero, which limits the capability of this efficient analytical technique. In this paper, a generalized BFA method is proposed to extend the capability of the method to capture the nonlinear natural frequency of high-dimensional non-smooth systems where either gaps or prestress exist. The generalized BFA method employs the natural frequencies, mode shapes, and modal amplitudes of the linear subsystems as well as the gap size at the contacting degrees of freedom (DOF) to estimate the nonlinear natural frequencies at different amplitude levels. The backbone curve of non-smooth oscillators can be efficiently constructed using the proposed analytical method. The generalized BFA method is demonstrated on a single-DOF system, a three-DOF system, and a finite element model (FEM) of a cantilever plate with contacting elements. The results show that the proposed method provides an accurate approximation of the backbone curve for the first resonance, which has the most dominant vibration response, with very low computational effort, but a rather poor approximation for higher resonances. The proposed technique can be integrated with high-dimensional FEMs to analyze the nonlinear resonance of complex structures. The performance of the method is validated both numerically and experimentally in this work.

Guest Editorial: Situational awareness of integrated energy systems

Guest Editorial: Situational awareness of integrated energy systems

On stress in abdominal aortic aneurysm: Linear versus non-linear analysis and aneurysm rupture risk.

We present comprehensive biomechanical analyses of abdominal aortic aneurysms (AAA) for 43 patients. We compare stress magnitudes and stress distributions within arterial walls of abdominal aortic aneurysms (AAA) obtained using two simulation and modelling methods: (a) Fully automated and computationally very efficient linear method embedded in the software platform Biomechanics based Prediction of Aneurysm Rupture Risk (BioPARR), freely available from https://bioparr.mech.uwa.edu.au/; (b) More complex and much more computationally demanding Non-Linear Iterative Stress Analysis (Non-LISA) that uses a non-linear inverse iterative approach and strongly non-linear material model. Both methods predicted localised high stress zones with over 90% of AAA model volume fraction subjected to stress below 20% of the 99th percentile maximum principal stress. However, for the non-linear iterative method, the peak maximum principal stress (and 99th percentile maximum principal stress) was higher and the stress magnitude in the low stress area lower than for the automated linear method embedded in BioPARR. Differences between the stress distributions obtained using the two methods tended to be particularly pronounced in the areas where the AAA curvature was large. Performance of the selected characteristic features of the stress fields (we used 99th percentile maximum principal stress) obtained using BioPARR and Non-LISA in distinguishing between the AAAs that would rupture and remain intact was for practical purposes the same for both methods.

Modeling and dispatch of advanced adiabatic compressed air energy storage under wide operating range in distribution systems with renewable generation

Abstract Advanced adiabatic compressed air energy storage (AA-CAES) is a scalable physical energy storage technology with great potential in peak regulation and renewables accommodation. Due to load fluctuation and limited volume of air tank and heat reservoir, the operating status of AA-CAES often varies in a wide range, which is called off-design or part load status, and thus the charging/discharging efficiency and generation capacity tightly correlate with the power level and storage states. This paper proposes a tri-state model of AA-CAES which meets the computational requirements of power system dispatch. Thermodynamics at the compression and expansion side can be characterized via either theoretical analysis or experiments, and the three storage states that impact charging/discharging power is calibrated by piecewise linear functions. By above construction, AA-CAES resembles a traditional battery storage except for the three correlated storage states and state-dependent charging/discharging efficiencies, while the thermodynamics related information is encapsulated in the piecewise linear approximation. As a result, the power system dispatch problem gives rise to a mixed-integer nonlinear program. An efficient linearization method is proposed, in which the number of binary variables involved is a logarithmic function in the number of breakpoints. IEEE 33-bus system is used to validate the proposed model.

A model-based prognostics method for fatigue crack growth in fuselage panels

This paper proposes a model-based prognostics method that couples the Extended Kalman Filter (EKF) and a new developed linearization method. The proposed prognostics method is developed in the context of fatigue crack propagation in fuselage panels where the model parameters are unknown and the crack propagation is affected by different types of uncertainties. The coupled method is composed of two steps. The first step employs EKF to estimate the unknown model parameters and the current damage state. In the second step, the proposed efficient linearization method is applied to compute analytically the statistical distribution of the damage evolution path in some future time. A numerical case study is implemented to evaluate the performance of the proposed method. The results show that the coupled EKF-linearization method provides satisfactory results: the EKF algorithm well identifies the model parameters, and the linearization method gives comparable prediction results to Monte Carlo (MC) method while leading to very significant computational cost saving. The proposed prognostics method for fatigue crack growth can be used for developing predictive maintenance strategy for an aircraft fleet, in which case, the computational cost saving is significantly meaningful.

An Efficient Linearization Method for Long-Term Operation of Cascaded Hydropower Reservoirs

The hydropower reservoir operation is a challenging optimization problem due to the nonlinear factors, where the water head, reservoir storage, release, generating capacity, and water rate are interconnected. To solve such a difficult problem in an efficient and stable way based on mathematical programming, efficient linearization method with high accuracy is of vital importance. This paper simplifies the hydropower output as the function of average reservoir storage and release, and presents an efficient piecewise linearization method that concaves the hydropower output function with a series of planes, which transforms the original nonlinear problem into a linear programming one without introducing any integer variables. The presented method is applied to a long-term hydropower scheduling (LHS) problem with 7 cascaded reservoirs, and a nonlinear direct search procedure is then employed to search further. The performance is compared with that of another linearization method that uses special ordered sets of type two, case study shows that LHS using the presented linearization method runs much faster and obtains results very close to that of the latter one. The presented method, as a high performance exact algorithm, should be very promising in solving the real-world hydropower operation problems.

Prediction of aromatase inhibitory activity using the efficient linear method (ELM).

Aromatase inhibition is an effective treatment strategy for breast cancer. Currently, several in silico methods have been developed for the prediction of aromatase inhibitors (AIs) using artificial neural network (ANN) or support vector machine (SVM). In spite of this, there are ample opportunities for further improvements by developing a simple and interpretable quantitative structure-activity relationship (QSAR) method. Herein, an efficient linear method (ELM) is proposed for constructing a highly predictive QSAR model containing a spontaneous feature importance estimator. Briefly, ELM is a linear-based model with optimal parameters derived from genetic algorithm. Results showed that the simple ELM method displayed robust performance with 10-fold cross-validation MCC values of 0.64 and 0.56 for steroidal and non-steroidal AIs, respectively. Comparative analyses with other machine learning methods (i.e. ANN, SVM and decision tree) were also performed. A thorough analysis of informative molecular descriptors for both steroidal and non-steroidal AIs provided insights into the mechanism of action of compounds. Our findings suggest that the shape and polarizability of compounds may govern the inhibitory activity of both steroidal and non-steroidal types whereas the terminal primary C(sp3) functional group and electronegativity may be required for non-steroidal AIs. The R code of the ELM method is available at http://dx.doi.org/10.6084/m9.figshare.1274030.

Anti-optimisation for modelling the vibration of locally nonlinear structures: An exploratory study

Modelling the vibration of complex structures with uncertain nonlinearities is a significant challenge. However, nonlinearities are often spatially localised: this enables efficient linear methods to describe the behaviour of the majority of the structure and reduces the size of the nonlinear problem. This paper explores anti-optimisation as an approach to modelling uncertain nonlinearities for this class of system. The ‘worst-case’ output metric is sought by considering nonlinear forces as an external input subject to constraints that capture what is known about the nonlinearity. A systematic sequence of tests is carried out using a mass on spring system within a pair of end-stops: the results show how the anti-optimised solutions become less conservative as the constraints are increasingly restrictive. The method is applied to bending vibration of a beam within a pair of local end-stops. Anti-optimised solutions are found as a function of frequency and are compared with a Monte Carlo set of benchmark simulations. Almost all anti-optimised solutions over-predict the simulations and the overall trend of the simulations is also clearly captured. The method shows significant potential and motivates further research.

Human Pose Estimation Using Consistent Max Covering

A novel consistent max-covering method is proposed for human pose estimation. We focus on problems in which a rough foreground estimation is available. Pose estimation is formulated as a jigsaw puzzle problem in which the body part tiles maximally cover the foreground region, match local image features, and satisfy body plan and color constraints. This method explicitly imposes a global shape constraint on the body part assembly. It anchors multiple body parts simultaneously and introduces hyperedges in the part relation graph, which is essential for detecting complex poses. Using multiple cues in pose estimation, our method is resistant to cluttered foregrounds. We propose an efficient linear method to solve the consistent max-covering problem. A two-stage relaxation finds the solution in polynomial time. Our experiments on a variety of images and videos show that the proposed method is more robust than previous locally constrained methods.

Identifying Important Observations Using Cross Validation and Computationally Frugal Sensitivity Analysis Methods

Sensitivity analysis methods are used to identify measurements most likely to provide important information for model development and predictions. Methods range from computationally demanding Monte Carlo and cross-validation methods that require thousands to millions of model runs, to very computationally efficient linear methods able to account for interrelations between parameters that involve tens to hundreds of runs. Some argue that because linear methods neglect the effects of model nonlinearity, they are not worth considering. However, when faced with computationally demanding models needed to simulate, for example, climate change, the chance of obtaining insights with so few model runs is tempting. This work compares results for a nonlinear groundwater model using computationally demanding cross-validation and computationally efficient local sensitivity analysis methods.

Improving efficiency of linear techniques to estimate epipolar geometry

Important analytical aspects of efficient linear methods to estimate the epipolar geometry are studied. Based on the obtained results a novel low cost and accurate linear algorithm is introduced. Owing to low complexity and accuracy the proposed approach appears to be suitable for real-time stereo vision applications.