Comprehensive Weighting Method Research Articles

Evaluation of Integrated Energy System in Airports Based on Comprehensive Weighting Method

Airport is a typical integrated energy system in a park with various energy requirements. In this paper, a multi-dimensional quantitative analysis of system performance indicators was conducted by using a comprehensive weighting method based on the analytic hierarchy process (AHP) and anti-entropy weight method. A distributed energy system evaluation matrix model was used to evaluate and compare different integrated energy designs. The results showed that electric boilers would increase the primary energy ratio and primary energy consumption than the ones caused by gas boilers. Also, energy storage devices could significantly decrease pollutant emissions of integrated energy systems but would increase investment costs and reduce the economic indicators of system solutions. In a word, the configuration with ice storage, combined cooling, heating and power (CCHP), gas boiler, ground source heat pump (GSHP), air source heat pump (ASHP), and absorption chiller had the best evaluation indicators.

俄罗斯东部城镇化与生态环境协调发展的时空演变特征

以俄罗斯东部地区为对象，结合PES和PSR模型分别构建其城镇化和生态环境的评价指标体系，结合熵值赋权、变异系数赋权的综合确权法测算城镇化和生态环境的发展水平，利用耦合协调度模型探讨二者协调发展程度，划分其阶段类型。研究表明：2005-2018年，（1）俄东部城镇化发展水平呈上升趋势，经济城镇化的贡献份额最大；生态环境发展水平呈小幅下降态势，生态环境压力的影响作用最大；二者的耦合协调度呈增长趋势，但整体处于基本不协调阶段，其内部由城镇化滞后转变为系统均衡发展。（2）西伯利亚联邦区的城镇化发展水平高于远东联邦区，二联邦区生态环境发展水平差距较小，西伯利亚区协调发展程度略强于远东区；西伯利亚区内部由城镇化滞后→系统均衡发展，远东区内部始终为城镇化滞后。多数联邦主体处于基本不协调阶段、高级协调的数量最少。（3）空间上，城镇化、生态环境、二者协调发展度均呈"西高东低"的格局特征，核心高值区分布在新西伯利亚州-阿尔泰边疆区-克麦罗沃州-克拉斯诺亚尔斯克边疆区-伊尔库茨克州的串联区，边缘低值区位于阿尔泰共和国和楚科奇自治区。最后探讨了促进俄东部城镇化和生态环境协调发展的具体对策。;Under the background of the Belt and Road and the economic corridor of China, Mongolia and Russia initiatives, this paper studied the urbanization development level, eco-environment development level, the coupling coordinated development degree between urbanization and eco-environment, and their spatial differentiation of the eastern Russia. Combining with the Population-Economic-Sociology model and Pressure-State-Response model, the paper first built two index systems of urbanization and eco-environment. Then based on the comprehensive weighting method of entropy weight and variation coefficient weight, we calculated the urbanization development level with regard to the population urbanization, economic urbanization and social urbanization, and the eco-environment development level with regard to the eco-environment pressure, eco-environment state, eco-environment response during 2005-2018. Next, the coupling coordinated development degree of the urbanization and eco-environment development level was measured by the coupling coordination degree model during 2005-2018. Finally, the spatial differentiation of the urbanization development levels, the eco-environment development levels, and their coupling coordinated development degree were performed respectively by using ArcGIS. The results were as follows. (1) The economic urbanization and eco-environment pressure were the main factors that affected the urbanization development and eco-environment development, respectively. The comprehensive urbanization development level, the coupling coordination degree between urbanization and eco-environment of eastern Russia had increased from 2005 to 2018. The comprehensive eco-environment development level had decreased from 2005 to 2018. However, they were still in the uncoordinated stage, and their internal development showed the changes from the urbanization lagging to the balanced development. (2) From 2005 to 2018, the urbanization development level, the coupling coordination degree between urbanization and eco-environment of the Siberian Federal District were higher than that of the Far East Federal District. The eco-environment development level in Siberian Federal District was roughly balanced to that in the Far East Federal District. Most of the federal subjects were in the uncoordinated stage. (3) The urbanization development level, the eco-environment development level, and their coupling coordinated development degree were all spatially imbalanced in the eastern Russia. They showed the High in West, Low in East spatial pattern, which in generally displayed the tendency of space attenuation from the west to east. The areas with high levels were concentrated in the Novosibirsk Region, Altay Territory, Kemerovo Region, Krasnoyarsk Territory, and Irkutsk Region. The areas with low ones were mostly in the Republic of Altay and Chukotka Autonomous Area. Finally, we suggested policies and strategies that could boost the coordinated development of urbanization and ecological environment in eastern Russia.

Stability Assessment of Ground Surface along Tunnels in Karst Terrain Using Improved Fuzzy Comprehensive Evaluation

The stability of ground surface along tunnels in karst terrain is influenced by complex factors, among which the karst features are the significant ones. Under the influence of karst, the ground surface along tunnels is very easy to collapse, thus causing great casualties and economic losses. To provide guidance for maintaining the stability of ground surface along tunnels, an analysis system is proposed for assessing the stability of ground surface along tunnels in karst terrain based on an improved fuzzy comprehensive evaluation. Based on the case analysis of ground collapse along tunnels in karst terrain and the review of the related researches, the evaluation index system for ground surface stability assessment was established. The ridge‐shaped membership functions were constructed to calculate the membership degree for the evaluation indices. The comprehensive weighting method combining the Fuzzy Analytical Hierarchy Process and correlation analysis was applied to determine weights for evaluation indices. And the ground surface stability level was recognized based on the maximum membership principle. The proposed assessment system was applied to assess the ground surface stability along the tunnels of Guiyang Metro Line 1, and the assessment results agreed well with the regional ground collapse history, verifying the effectiveness and reliability of the assessment system. Combining with the assessment results, a series of measures were conducted to promote the ground surface stability before tunnel excavation. This system provides a valuable tool for assessing and guiding to improve stability of the ground surface along tunnels in karst terrain.

Graph classification based on structural features of significant nodes and spatial convolutional neural networks

Many real-world problems can be abstracted into graph classification problems. Recently, graph convolutional networks have achieved great success in the task of node classification and link prediction. However, when using graph convolution network to process the task of graph classification, either global topology information or local information is ignored. Therefore, designing graph convolutional networks to improve the accuracy of graph classification has attracted more and more attention. Inspired by the use of convolutional neural networks to process graph-structured data, we put forward a new spatial convolutional neural network architecture for graph classification. To be specific, we first design a comprehensive weighting method to measure the significance of vertices in the graph based on multiple indicators to choose the central node sequence. Then, the normalization process of the graph is realized by constructing the same size neighborhood graphs for the central vertices. After that, the structural characteristics of the graph are extracted from both local and global aspects. Finally, the tensors obtained after the above steps are respectively input into the following two spatial convolutional neural network architectures to perform classification, one is a simple CNN structure, which has only two convolution layers, one dense layer and one softmax layer. The other is to modify the architecture of CNN, and the channel concatenation layer is introduced to determine the classification result of the entire graph according to the category of the neighborhood graphs. Experimental results on two kinds of real-world datasets, bioinformatics and social network datasets, indicate that our approach obtains competitive results and is superior to some classic kernels and similar deep learning-based algorithms on 6 out of 8 benchmark data sets.

Comprehensive weight method based on game theory for identify critical transmission lines in power system

Identify critical transmission lines is significant for power system to prevent large-scale blackouts. To address this concern, based on topological structure and power flow distribution, a topological model is constructed to simply the power system. Subsequently, three indexes are derived to assess the importance of transmission line from three different aspects: global topological structure, line operation parameters and local line connection. Furthermore, in order to assess the line importance more comprehensively, the three indexes are integrated to a line comprehensive index by adopting comprehensive weight method based on game theory. Simulation results show that the method can identify the critical transmission lines in power system, and verify the correctness and effectiveness though network transmission efficiency.

System Reliability Evaluation of a Bridge Structure Based on Multivariate Copulas and the AHP–EW Method That Considers Multiple Failure Criteria

The system reliability evaluation of a bridge structure is a complicated problem. Previous studies have commonly used approximate estimation methods, such as the wide bounds method and the narrow bounds method, but neither could obtain an accurate result. In recent years, the copula theory has been introduced into the system reliability evaluation, which can obtain more accurate results than the approximate methods. However, most studies simply construct binary copula functions to consider the joint failure of two failure modes. For a complex bridge structure composed of multiple components and failure modes, the joint failure of multiple failure modes needs to be considered. Before evaluating the system reliability, it is necessary to determine the failure criteria of the system. Different failure criteria for simply supported beam bridges have been proposed. However, there is no standard available to determine which failure criterion to choose, and the selection of failure criteria is ambiguous. In this paper, a novel method is proposed to evaluate the system reliability of a simply supported beam bridge by considering multiple failure criteria based on multivariate copulas and the analytic hierarchy process entropy weight (AHP–EW) method. The method first considers multiple failure criteria comprehensively and constructs multivariate copulas for the joint failure of multiple components in a bridge system reliability evaluation. The AHP–EW method is a comprehensive weighting method combining the analytic hierarchy process and entropy weight methods, which is used to establish the hierarchical analysis model between system reliability and multiple failure criteria. By considering the joint failure of multiple failure modes in the system reliability evaluation under a single failure criterion, multivariate copula functions were constructed. In order to verify the applicability of the proposed bridge system reliability method, a simply supported reinforced concrete (RC) hollow slab bridge composed of nine slab segments was selected as the numerical example. The results indicate that the method proposed in this paper could evaluate the bridge system reliability more comprehensively and reasonably.

Safety Evaluation Method of Antifloating Anchor System Based on Comprehensive Weighting Method and Gray-Fuzzy Theory

The risk factors in the safety evaluation of antifloating anchor system of underground structure have the characteristics of complexity, grey, and fuzziness. Based on the Delphi method, analytic hierarchy process (AHP), and entropy weight method, this paper establishes a three-level evaluation index system based on four main risk factors and calculates the subjective and objective comprehensive weights of the index according to the comprehensive weighting method. It not only takes into account the valuable experience of the expert group but also reflects the objective impact of the subjective score on the system. On the basis of the above research, the grey-fuzzy safety evaluation method of antifloating anchor system is established by using the grey theory and the relevant theory of fuzzy mathematics. The reliability of the method is verified by an example, which has certain theoretical significance and application value.

Evaluation on the Stability of Vertical Mine Shafts below Thick Loose Strata Based on the Comprehensive Weight Method and a Fuzzy Matter-Element Analysis Model

Damage to mine shafts located below thick loose aquifers, caused by coal seam mining, can seriously affect the operational safety of mines. In view of such a problem, the comprehensive weight method and the fuzzy matter-element analysis method were used to analyze and evaluate the stability of mine shafts below thick, loose aquifers. Based on data relating to shaft structure parameters collected from fifteen damaged shafts in coal mines in East China, a comprehensive analysis was performed. The results showed that (1) the two indexes of surface subsidence velocity and water level drop value at the bottom of a loose aquifer have a large influence on the stability of shafts below thick loose aquifers, and (2) the predicted results of thirteen sets of samples were the same as the results measured during actual production; the accuracy of the model was 86.67%. The comprehensive weight method and the fuzzy matter-element analysis model both show good reliability for evaluating the stability of mine shafts below thick loose aquifers and can provide a scientific reference for the analysis of the stability of mine shafts in areas with thick loose strata, as well as for the design of comprehensive control plans that could subsequently be implemented.

Network Selection Algorithm Based on Chi-Square Distance in Heterogeneous Wireless Networks

This paper proposes an access network selection algorithm based on a cooperative strategy with Chi square distance, subjective weights for traffic classes and objective attributes of network. The algorithm gets the subjective weights of attribute in four traffic classes using AHP at first, then calculates objective weights using a cooperative method of entropy weight and criteria importance though intercriteria correlation. The final weights are obtained by a comprehensive weighting method based on minimizing the deviation between weights. Finally we measure the Chi square distance between every candidate network and the ideal network and choose the one which has the minimum Chi square distance to the idea network as the best access network. Simulation results show that the proposed algorithm can select the most suitable access network to meet the requirements of current traffic and observably extend the discernibility between candidate networks. The ratio between the best and the second-best network in this algorithm is 8 or 9 times bigger than that in technique for order preference by similarity to ideal solutions, simple additive weighting and grey relational analysis. Furthermore, it can avoid falling into local optimal situation, choose the correct optimal access network when some network attributes appear extreme data, and has good algorithm robustness.

A Novel Method in Surface Water Quality Assessment Based on Improved Variable Fuzzy Set Pair Analysis.

In the case of surface water pollution, it is important and necessary to accurately assess the level of contaminated water and ensure the safety of drinking water for people in disaster areas during floods. However, for the assessment of the strict requirements of drinking water, traditional assessment methods still have some limitations, such as low precision and rationality. In order to overcome these limitations, in the light of the theory of set pair analysis and variable fuzzy set, we propose an improved variable fuzzy set pair analysis method (IVFSPA), which combines the analysis framework of variable fuzzy set and set pair analysis, and has made some improvements to the fusion architecture. Firstly, we present a novel game theory comprehensive weighting method, in which the objective entropy method and the subjective analytic hierarchy process(AHP) method employed to obtain the reasonable weight. Then, based on the Nemerow index method, we improve the arithmetic form of “” (Equation P) to replace the fuzzy comprehensive evaluation method. Furthermore, we design a double judgment mode of combining the principle of maximum membership degree with the positive and negative relationship between the standard value and the measured value, which can accurately judge the evaluation level of surface water quality. Finally, to validate and verify the effectiveness of the proposed method, experiments was conducted at the representative river collection sections of Nanking, China, employing water quality data of 14 sampling sections in their rivers in Nanking during the 2017 flood. In terms of performance metcrics of precision and rationality, based on the values of “TP”, “NH3-N”, “Pb”, “AS” and “KMnO4” of “Ch-lh section/Chuhe gate” are 0.415, 3.77, 0.07, 0.23 and 7.12, respectively, the level of Ch-lh section/Chuhe gate is that the IVFSPA is Class V and the rest are class IV. Results of experiments show that our IVFSPA method can achieve a good performance, compared with other traditional methods.

Index Empowerment Based on comprehensive Entropy Weight Method—Taking Chinese Residents' Consumption Structure as an Example

In order to improve the scientific and comprehensive nature of the index evaluation system, this paper takes the Chinese residents' consumption structure as an example, and uses the index weighting method combined with the entropy weight method and the correlation analysis, that is, the comprehensive entropy weight method to determine the weight value of each index of the Chinese residents' consumption structure. By calculating the method of comprehensive weight, it overcomes the shortcomings of using a single weighting method, makes the calculation of weight more scientific and reasonable, and through case analysis, the evaluation result obtained by this method is more objective and reasonable, practical and feasible.

Risk assessment index system for equipment maintenance project of civil military integration

In view of the risks of equipment maintenance in the military and civilian integration, by analyzing the experience of foreign military and civilian integration, the relevant cases are analyzed, combined with modern management theory of agency theory, entrustment theory, risk management theory, and virtual organization theory. This paper constructs the risk assessment index system of the military and civilian integration equipment maintenance project on the basis of fully considering the particularity of the service and uses the factor clustering, the comprehensive weighting method, and the double base point evaluation method to carry out the evaluation. The validity and practicability of the evaluation are verified by examples, which can provide some reference for the risk assessment of equipment maintenance project in the integration of military and civilian.

Site selection of LNG terminal based on cloud matter element model and principal component analysis

With the development of liquefied natural gas(LNG) port, as one of the crucial LNG port sitting process, the LNG terminal site’s condition assessment method has always received attention from experts, scholars concern more and more about the method’s practicality and reliability. In the traditional condition assessment method, due to the characteristics of the complex and extensive factors in the comprehensive assessment of the LNG terminal site, the assessment system is not comprehensive enough, or the assessment is too complex, the indexes are not easy to quantify, such problems are emerging. In view of the above reasons, the principal component analysis(PCA) method is used to transform the multi-indicators that affect the comparison of terminal sites into a few comprehensive indicators. A comprehensive evaluation model of the LNG terminal site based on cloud matter element theory and subjective and objective comprehensive weighting method was constructed. By the subjective and objective comprehensive weighting method, the comprehensive weight of each index is determined and the LNG terminal site comprehensive assessment standard cloud element model is constructed with the combination of cloud model and matter-element theory. The cloud matter-element correlation function is established to determine the degree of association between the matter element to be evaluated and the standard cloud matter element model. In order to eliminate random errors and improve the credibility of the results, the algorithm is used for multiple calculations and analysis to achieve the purpose of simultaneously giving the evaluation results and coefficients of credible degree. Finally, the reliability and rationality of the method are verified by an example.

A Novel Approach for Green Supplier Selection under a q-Rung Orthopair Fuzzy Environment

With environmental issues becoming increasingly important worldwide, plenty of enterprises have applied the green supply chain management (GSCM) mode to achieve economic benefits while ensuring environmental sustainable development. As an important part of GSCM, green supplier selection has been researched in many literatures, which is regarded as a multiple criteria group decision making (MCGDM) problem. However, these existing approaches present several shortcomings, including determining the weights of decision makers subjectively, ignoring the consensus level of decision makers, and that the complexity and uncertainty of evaluation information cannot be adequately expressed. To overcome these drawbacks, a new method for green supplier selection based on the q-rung orthopair fuzzy set is proposed, in which the evaluation information of decision makers is represented by the q-rung orthopair fuzzy numbers. Combined with an iteration-based consensus model and the q-rung orthopair fuzzy power weighted average (q-ROFPWA) operator, an evaluation matrix that is accepted by decision makers or an enterprise is obtained. Then, a comprehensive weighting method can be developed to compute the weights of criteria, which is composed of the subjective weighting method and a deviation maximization model. Finally, the TODIM (TOmada de Decisao Interativa e Multicritevio) method, based on the prospect theory, can be extended into the q-rung orthopair fuzzy environment to obtain the ranking result. A numerical example of green supplier selection in an electric automobile company was implemented to illustrate the practicability and advantages of the proposed approach.

Extension Model for Safety Appraisal of Existing Concrete Members Based on an Improved Comprehensive Weighting Method

An effective evaluation model for safety appraisal of existing concrete members plays a significant role in promoting the management of an existing building. This study aims to introduce extension theory into the safety appraisal of existing concrete members based on five indices (bearing capacity, deflection-to-span ratio, cracks, reinforcement corrosion, and concrete carbonation depth) and inspection data. A matter-element model is established for the safety appraisal of existing concrete members based on matter-element theory. The safety appraisal rating is identified by the comprehensive correlation degrees, which can be calculated by the weights and single-index correlation degrees of the five indices. Owing to the one-sidedness in the single-weighting method, a comprehensive weighting method integrating the merits of subjective weight and objective weight is adopted based on game theory. The interval analytic hierarchy process (IAHP) and entropy weight method are, respectively, used to determine the subjective and objective weight of each index. It was found that the subjective weight vector calculated by IAHP consists of interval numbers. Therefore, the traditional comprehensive weighting method based on game theory needs to be improved by the interval number theory. A comparison analysis between the results generated by the proposed model and an analytic hierarchy process-fuzzy comprehensive evaluation model is conducted. The results show that the matter-element extension model based on comprehensive weight is more accurate and rational. The proposed model makes full use of inspection data and gives a clear safety level to decision makers avoiding disorganized data of a single index. Hence, it can serve as guidance for safety appraisal of existing concrete members in the future. Furthermore, the improved comprehensive weighting method has practical merits and high scientific value in terms of safety evaluation and other applications in different research fields.

Research of Ambiguity checking by NLP in EIA Report

The environment impact assessment(EIA) report is an important reference measure for measuring the overall environmental status of the region. Both the data and the text description in the report are intuitive manifestations of the environmental status. Therefore, the consistency of the text description and data is very important in the EIA report. This paper focus on text description and data ambiguity detection of atmospheric indices by using natural language processing(NLP) techniques in EIA report. The key issue of detection is matching. In the process, firstly taking the EIA of a project in Haidian District of Beijing as an example source data and establishing a corpus of atmospheric EIA. The corpus contains atmospheric environmental indicators, the degree of description of these indices, values, etc. Secondly, comparing the subjective and objective weighting method and choose a comprehensive weight method to match target for ambiguity detection. Finally, using regular expression to match the text description and data of atmospheric indices in EIA report. This method of matching can reduce the complexity compared with traditional matching method.

Selection of optimal access point for offshore wind farm based on multi-objective decision making

This paper analyzes the problem of selecting the optimal access point in power grid for the offshore wind farm (OWF), which is increasingly integrated into the onshore power system by use of voltage-source converter based high voltage direct current (VSC-HVDC) transmission. The development of the selecting method includes three steps. First, three major factors, which have significant impacts on deciding the optimal location of the onshore VSC, are introduced, i.e., voltage support from onshore VSCs, voltage fluctuation caused by the change of wind power and construction costs of the VSC-HVDC transmission system. Secondly, three evaluation indexes that are corresponding to the three factors are put forward. Thirdly, in the face of this multi-objective programming problem, a linear weighted model is proposed in this paper and the comprehensive weight method based on the theory of information entropy and the analytic hierarchy process (AHP) method is adopted to get the weight coefficients. The method is carried out in a practical power system in China. The results demonstrate that the proposed methodology is an effective way for selecting the optimal access point of the OWF.

Effects of different components of Mao Dongqing's total flavonoids and total saponins on transient ischemic attack (TIA) model of rats.

Objective: To study the effects of the different components of the total flavonoids and total saponins from Mao Dongqing's active site on the rats of TIA model, determine the optimal reactive components ratio of Mao Dongqing on the rats of TIA. Methods: TIA rat model was induced by tail vein injection of tert butyl alcohol, the blank group was injected with the same amount of physiological saline, then behavioral score wasevaluated.Determination the level of glutamic acid in serum, the activity of Na+-K+-ATP enzyme, CA++-ATP enzyme and Mg++-ATP enzyme in Brain tissue, observe the changes of hippocampus in brain tissue, the comprehensive weight method was used to evaluate the efficacy of each component finally. Results: The contents of total flavonoids and total saponins in the active part of Mao Dongqing can significantly improve the pathological changes of brain tissue in rats, improve the activity of Na+-K+-ATP enzyme, Ca++-ATP enzyme and Mg++-ATP enzyme in the brain of rats, and reduce the level of glutamic acid in serum. The most significant of the contents was the ratio of 10:6. Conclusion: The different proportions of total flavonoids and total saponins in the active part of Mao Dongqing all has a better effect on the rats with TIA, and the ratio of 10:6 is the best active component for preventing and controlling TIA.

Roof aquifer water abundance evaluation: a case study in Taigemiao, China

To ensure safe mining of the Taigemiao no. 3 mine field in Inner Mongolia, China, it is very important to make clear the roof aquifer water abundance distribution feature. On the basis of collecting the main controlling factors of aquifer water abundance from the geological and hydrogeological prospecting data of the study area, the no. 2 coal seam roof aquifer water abundance of Taigemiao no. 3 mine field was analyzed and evaluated using three methods. The first method is analytic hierarchy process (AHP)-type water-richness index method (AHP-type WIM) which is commonly used. But AHP is relatively subjective, so we trying to use a more objective method which is weighed gray relational degree method (WGRDM); this method mainly used pure data analyzing, it is better than AHP-type WIM but still not perfect, so the comprehensive weighted method (CWM) is put forward by adopting the advantage of the former two methods. In order to assess the accuracy rate of the three methods quantificationally, the evaluation results of the three methods are compared respectively with the measured unit water inflow which can directly reflect the aquifer water abundance, which shows that the WGRDM is more accurate than AHP-type WIM, and the CWM is more scientific and accurate in both weight calculation and water abundance grading. The superiority of CWM is more obvious when there are too many evaluation factors.

Effect of different component ratio of Astragalus total saponins and Verbena total glycosides on the cerebral infarction area and serum biochemical indicators in the focal cerebral ischemia-reperfusion rat model

Our purpose is to study the effect of different component ratio of Astragalus Total Saponins (ATS) and Verbena Total Glycosides (VTG) on the cerebral infarction area and the serum biochemical indicators in the focal cerebral ischemia-reperfusion rat model. Compared with the model group, different component ratio of ATS and VTG could significantly improve the neurological deficit scores to the focal cerebral ischemia-reperfusion rat model, and the group of 7:3, 6:4, 5:5 got the best results; it could reduce the mortality of rat model to a certain extent, and the group of 5:5 group got the best results; it can significantly reduce the cerebral infarction area, and the group of 7:3, 5:5, 4:6 got the best results; it could significantly reduce the content of TNF-α, and the group of 8:2, 6:4 got the best results; it could significantly reduce the content of NO, and the group of 7:3, 5:5 got the best results; it could significantly increase the content of SOD, and the group of 6:4, 5:5 got the best results. This indicates that different component ratio of ATS and VTG may protect the damage of focal cerebral ischemia-reperfusion rat model to a certain extent, which are compared using the comprehensive weight method and the ratio of 5:5 was proved to be the optimal active ratio.