AI-Enhanced Performance Evaluation of Python, MATLAB, and Scilab for Solving Nonlinear Systems of Equations: A Comparative Study Using the Broyden Method

This research extensively evaluates three leading mathematical software packages: Python, MATLAB, and Scilab, in the context of solving nonlinear systems of equations with five unknown variables. The study’s core objectives include comparing software performance using standardized benchmarks, employing key performance metrics for quantitative assessment, and examining the influence of varying hardware specifications on software efficiency across HP ProBook, HP EliteBook, Dell Inspiron, and Dell Latitude laptops. Results from this investigation reveal insights into the capabilities of these software tools in diverse computing environments. On the HP ProBook, Python consistently outperforms MATLAB in terms of computational time. Python also exhibits a lower robustness index for problems 3 and 5 but matches or surpasses MATLAB for problem 1, for some initial guess values. In contrast, on the HP EliteBook, MATLAB consistently exhibits shorter computational times than Python across all benchmark problems. However, Python maintains a lower robustness index for most problems, except for problem 3, where MATLAB performs better. A notable challenge is Python’s failure to converge for problem 4 with certain initial guess values, while MATLAB succeeds in producing results. Analysis on the Dell Inspiron reveals a split in strengths. Python demonstrates superior computational efficiency for some problems, while MATLAB excels in handling others. This pattern extends to the robustness index, with Python showing lower values for some problems, and MATLAB achieving the lowest indices for other problems. In conclusion, this research offers valuable insights into the comparative performance of Python, MATLAB, and Scilab in solving nonlinear systems of equations. It underscores the importance of considering both software and hardware specifications in real-world applications. The choice between Python and MATLAB can yield distinct advantages depending on the specific problem and computational environment, providing guidance for researchers and practitioners in selecting tools for their unique challenges.

STUDY ON CONTROLLABILITY AND OBSERVABILITY FOR THIN PLATE SYSTEM WITH PARAMETER UNCERTAINTY

The controllability and observability analysis of thin plate system with parameter uncertainty is presented using the degree of controllability/observability and the robustness index. It provides a guidance to the design of robust active vibration control for thin plate system.

Resilience indices from a family of recovery functions

Defining and measuring resilience using a unified framework has been a topic of intense research.This article presents a perspective on how resilience could be quantitatively assessed through a set of indices.It starts with a brief explanation of resilience in the context of supply chain and a quick summary of existing quantitative measures of resilience.It then discusses how resilience could be quantified in a constructive manner so that the resulting metrics are representative of the performance throughout the system's life cycle.In particular,it is proposed that resilience should be evaluated according to different time periods,i.e.before,during and after a disruption has occurred.Four dimensions of resilience,namely reliability,robustness,recovery and reconfigurability,can then be used to make up a set of indices for resilience.For numerical illustration,these indices are computed based on recovery data arising from Hurricane Sandy in October 2012.Finally,it is postulated that resilience will be the performance metric that complements productivity and sustainability as the third pillar for measuring success of organizations,and in turn,that of sovereign countries in their quests for developing smart cities.

Multi-stage Coordinated Robust Optimization for Soft Open Point Allocation in Active Distribution Networks with PV

To optimize the placement of soft open points(SOPs)in active distribution networks(ADNs),many aspects should be considered,including the adjustment of transmission power,integration of distributed generations(DGs),coordination with conventional control methods,and maintenance of economic costs.To address this multi-objective planning problem,this study proposes a multi-stage coordinated robust optimization model for the SOP allocation in ADNs with photovoltaic(PV).First,two robust technical indices based on a robustness index are proposed to evaluate the operation conditions and robust optimality of the solutions.Second,the proposed coordinated allocation model aims to optimize the total cost,robust voltage offset index,robust utilization index,and voltage collapse proximity index.Third,the optimization methods of the multiand single-objective models are coordinated to solve the proposed multi-stage problem.Finally,the proposed model is implemented on an IEEE 33-node distribution system to verify its effectiveness.Numerical results show that the proposed index can better reveal voltage offset conditions as well as the SOP utilization,and the proposed model outperforms conventional ones in terms of robustness of placement plans and total cost.