Two-stage fuzzy-stochastic robust programming: a hybrid model for regional air quality management

In this study, a hybrid two-stage fuzzy-stochastic robust programming (TFSRP) model is developed and applied to the planning of an air-quality management system. As an extension of existing fuzzy-robust programming and two-stage stochastic programming methods, the TFSRP can explicitly address complexities and uncertainties of the study system without unrealistic simplifications. Uncertain parameters can be expressed as probability density and/or fuzzy membership functions, such that robustness of the optimization efforts can be enhanced. Moreover, economic penalties as corrective measures against any infeasibilities arising from the uncertainties are taken into account. This method can, thus, provide a linkage to predefined policies determined by authorities that have to be respected when a modeling effort is undertaken. In its solution algorithm, the fuzzy decision space can be delimited through specification of the uncertainties using dimensional enlargement of the original fuzzy constraints. The developed model is applied to a case study of regional air quality management. The results indicate that reasonable solutions have been obtained. The solutions can be used for further generating pollution-mitigation alternatives with minimized system costs and for providing a more solid support for sound environmental decisions.     

Two-Stage Fuzzy-Stochastic Robust Programming: A Hybrid Model for Regional Air Quality Management

Abstract

In this study, a hybrid two-stage fuzzy-stochastic robust programming (TFSRP) model is developed and applied to the planning of an air-quality management system. As an extension of existing fuzzy-robust programming and two-stage stochastic programming methods, the TFSRP can explicitly address complexities and uncertainties of the study system without unrealistic simplifications. Uncertain parameters can be expressed as probability density and/or fuzzy membership functions, such that robustness of the optimization efforts can be enhanced. Moreover, economic penalties as corrective measures against any infeasibilities arising from the uncertainties are taken into account. This method can, thus, provide a linkage to predefined policies determined by authorities that have to be respected when a modeling effort is undertaken. In its solution algorithm, the fuzzy decision space can be delimited through specification of the uncertainties using dimensional enlargement of the original fuzzy constraints. The developed model is applied to a case study of regional air quality management. The results indicate that reasonable solutions have been obtained. The solutions can be used for further generating pollution-mitigation alternatives with minimized system costs and for providing a more solid support for sound environmental decisions.     

A two-stage interval-stochastic programming model for waste management under uncertainty

This study introduces a two-stage interval-stochastic programming (TISP) model for the planning of solid-waste management systems under uncertainty. The model is derived by incorporating the concept of two-stage stochastic programming within an interval-parameter optimization framework. The approach has the advantage that policy determined by the authorities, and uncertain information expressed as intervals and probability distributions, can be effectively communicated into the optimization processes and resulting solutions. In the modeling formulation, penalties are imposed when policies expressed as allowable waste-loading levels are violated. In its solution algorithm, the TISP model is converted into two deterministic submodels, which correspond to the lower and upper bounds for the desired objective-function value. Interval solutions, which are stable in the given decision space with associated levels of system-failure risk, can then be obtained by solving the two submodels sequentially. Two special characteristics of the proposed approach make it unique compared with other optimization techniques that deal with uncertainties. First, the TISP model provides a linkage to predefined policies determined by authorities that have to be respected when a modeling effort is undertaken; second, it furnishes the reflection of uncertainties presented as both probabilities and intervals. The developed model is applied to a hypothetical case study of regional solid-waste management. The results indicate that reasonable solutions have been generated. They provide desired waste-flow patterns with minimized system costs and maximized system feasibility. The solutions present as stable interval solutions with different risk levels in violating the waste-loading criterion and can be used for generating decision alternatives.     

81st APCA Annual Meeting & Exhibition

Abstract

This study introduces a two-stage interval-stochastic programming (TISP) model for the planning of solid-waste management systems under uncertainty. The model is derived by incorporating the concept of two-stage stochastic programming within an interval-parameter optimization framework. The approach has the advantage that policy determined by the authorities, and uncertain information expressed as intervals and probability distributions, can be effectively communicated into the optimization processes and resulting solutions. In the modeling formulation, penalties are imposed when policies expressed as allowable waste-loading levels are violated. In its solution algorithm, the TISP model is converted into two deterministic submodels, which correspond to the lower and upper bounds for the desired objective-function value. Interval solutions, which are stable in the given decision space with associated levels of system-failure risk, can then be obtained by solving the two submodels sequentially. Two special characteristics of the proposed approach make it unique compared with other optimization techniques that deal with uncertainties. First, the TISP model provides a linkage to prede?ned policies determined by authorities that have to be respected when a modeling effort is undertaken; second, it furnishes the reflection of uncertainties presented as both probabilities and intervals. The developed model is applied to a hypothetical case study of regional solid-waste management. The results indicate that reasonable solutions have been generated. They provide desired waste-flow patterns with minimized system costs and maximized system feasibility. The solutions present as stable interval solutions with different risk levels in violating the waste-loading criterion and can be used for generating decision alternatives.     

Fuzzy programming method for multi-objective optimal allocation of sediment resources and the cooperative bargaining: a case study in Weishan irrigation area,China

The optimal allocation of sediment resources needs to balance three objectives including ecological, economic, and social benefits so as to realize sustainable development of sediment resources. This study aims to apply fuzzy programming and bargaining approaches to solve the problem of optimal allocation of sediment resources. Firstly, Pareto-optimal solutions of multi-objective optimization were introduced, and the multi-objective optimal allocation model of sediment resources and fuzzy programming model was constructed. Then, from the perspective of multiplayer cooperation, the optimal allocation model of sediment resources was transformed into a game model by using Nash bargaining, and Nash bargaining solution was obtained as the optimal equilibrium strategy. Finally, the influence of different disagreement utility points and bargaining weights on the results was discussed, and the results of Nash bargaining and fuzzy programming methods were compared and analyzed. Results corroborate that Nash bargaining can achieve the cooperative optimization of multiple objectives with competitive relationship and obtain satisfactory scheme. Disagreement utility points and bargaining weights have a certain impact on the optimization results. The solution of fuzzy programming is close to that of Nash bargaining, which provides different ideas for multi-objective optimization problem.

     

Simulating uncertainty in climate-pest models with fuzzy numbers

Inputs in climate-pest models are commonly expressed as point estimates ('crisp' numbers), which implies perfect knowledge of the system in study. In reality, however, all model inputs harbor some level of uncertainty. This is particularly true for climate change impact assessments where the inputs (i.e., climate projections) are highly uncertain. In this study, uncertainties in climate projections were expressed as 'fuzzy' numbers; these are uncertain numbers for which one knows that there is a range of possible values and that some values are 'more possible' than others. A generic pest risk model incorporating the combined effects of temperature, soil moisture, and cold stress was implemented in a fuzzy spreadsheet environment and run with three climate scenarios: (1) present climate (control run); (2) crisp climate change; and (3) fuzzy climate change. Under the crisp climate change scenario, winter and summer temperatures and precipitation were altered using best estimates (averaged predictions from the 1995 assessment report of the Intergovernmental Panel on Climate Change [IPCC]). Under the fuzzy scenario, climate changes were expressed as triangular fuzzy numbers, utilizing the extremes (lowest and highest predictions from the IPCC report) in addition to the best estimates. Under each scenario, environmental favorability was calculated for six locations in two geographical regions (Central North America and Southern Europe) with two hypothetical pest species having temperate or mediterranean climate requirements. Simulations with the crisp climate change scenario suggested only minor changes in overall environmental favorability compared with the control run. When simulations were conducted with the fuzzy climate change scenario, however, important changes in environmental favorability emerged, particularly in Southern Europe. In that region, the possibility of considerably increased winter precipitation led to increased values of environmental favorability. However, the simulations also showed that this result harbored a very broad range of possible outcomes. The results support the notion that uncertainty in climate change projections must be reduced before reliable impact assessments can be achieved.     

Toxicological response of a bioluminescent microbial assay to Zn, Pb and Cu in an artificial soil solution: relationship with total metal concentrations and free ion activities.

The relationship between toxicological response and both total concentrations and free ion activities of Pb, Cu and Zn in an artificial soil solution has been investigated using lux-marked Escherichia coli HB101 (pUCD607) as a bioassay. SO4(2-) (as K2SO4) was added as an inorganic complexing agent up to 0.01 M representing the range of ionic strengths found in soil solutions and giving a wide range of free metal ion activities. EC50 values expressed in terms of concentration, varied significantly with K2SO4 molarity for all metals. However, when EC50 values were expressed in terms of free ion activity they were not significantly different for Pb and Zn, supporting the free ion activity model. Conversely, EC50 values expressed as free Cu activity did vary significantly with K2SO4 molarity, possibly due to a greater degree of adsorption of Cu onto inactive sites on the cell surfaces than for Zn and Pb. Linear regression analysis of bioluminescence on free ion activity revealed significant correlations for each metal above the toxicity threshold. In conclusion, lux-marked E. coli is suitable for investigating the toxicity of metal ions and complexes in non saline systems although cell surface adsorption effects could be important for some metals, e.g. Cu.     

Identification of water quality management policy of watershed system with multiple uncertain interactions using a multi-level-factorial risk-inference-based possibilistic-probabilistic programming approach

In this study, a multi-level-factorial risk-inference-based possibilistic-probabilistic programming (MRPP) method is proposed for supporting water quality management under multiple uncertainties. The MRPP method can handle uncertainties expressed as fuzzy-random-boundary intervals, probability distributions, and interval numbers, and analyze the effects of uncertainties as well as their interactions on modeling outputs. It is applied to plan water quality management in the Xiangxihe watershed. Results reveal that a lower probability of satisfying the objective function (θ) as well as a higher probability of violating environmental constraints (q _i ) would correspond to a higher system benefit with an increased risk of violating system feasibility. Chemical plants are the major contributors to biological oxygen demand (BOD) and total phosphorus (TP) discharges; total nitrogen (TN) would be mainly discharged by crop farming. It is also discovered that optimistic decision makers should pay more attention to the interactions between chemical plant and water supply, while decision makers who possess a risk-averse attitude would focus on the interactive effect of q _i and benefit of water supply. The findings can help enhance the model’s applicability and identify a suitable water quality management policy for environmental sustainability according to the practical situations.

     

Multi-stage optimal design for groundwater remediation: A hybrid bi-level programming approach

This paper presents the development of a hybrid bi-level programming approach for supporting multi-stage groundwater remediation design. To investigate remediation performances, a subsurface model was employed to simulate contaminant transport. A mixed-integer nonlinear optimization model was formulated in order to evaluate different remediation strategies. Multivariate relationships based on a filtered stepwise clustering analysis were developed to facilitate the incorporation of a simulation model within a nonlinear optimization framework. By using the developed statistical relationships, predictions needed for calculating the objective function value can be quickly obtained during the search process. The main advantage of the developed approach is that the remediation strategy can be adjusted from stage to stage, which makes the optimization more realistic. The proposed approach was examined through its application to a real-world aquifer remediation case in western Canada. The optimization results based on this application can help the decision makers to comprehensively evaluate remediation performance.     

Greenhouse Gas Mitigation-Induced Rough-Interval Programming for Municipal Solid Waste Management

Abstract

A greenhouse gas (GHG) mitigation-induced rough-interval programming model is proposed in this study. Components of GHG emission and environmental pollution control are incorporated into the objective function and a series of relevant constraints. To explicitly examine more complexities existing in many parameters, rough intervals are also communicated into the modeling framework. The proposed model presents satisfactory capabilities in analyzing complicated interrelationships among municipal solid waste (MSW) management, climate-change impact, and environmental pollution control. It can also provide optimal allocation schemes and facilitate decision-makers regulating environmentally sustainable strategies. The developed model is then applied to a case study for demonstrating its applicability. Two representative scenarios (relatively representing two potential management policies that may be implemented in the future years) are considered. The results indicate that the developed model presents advantages in mitigating GHG emissions and the associated climate-change impact. The comparison between the GHG mitigation-induced model with and without rough-interval parameters is also investigated. Completely different solutions of the two models imply the significant impact of dual-uncertain information on the system, which can hardly be addressed through the existing optimization approaches.     

Minimax regret analysis for municipal solid waste management: an interval-stochastic programming approach

In this study, an interval minimax regret programming (IMMRP) method is developed for the planning of municipal solid waste (MSW) management under uncertainty. It improves on the existing interval programming and minimax regret analysis methods by allowing uncertainties presented as both intervals and random variables to be effectively communicated into the optimization process. The IMMRP can account for economic consequences under all possible scenarios without any assumption on their probabilities. The developed method is applied to a case study of long-term MSW management planning under uncertainty. Multiple scenarios associated with different cost and risk levels are analyzed. Reasonable solutions are generated, demonstrating complex tradeoffs among system cost, regret level, and system-failure risk. The method can also facilitate examination of the difference between the cost incurred with identified strategy and the least cost under an ideal condition. The results can help determine desired plans and policies for waste management under a variety of uncertainties.     

An efficient method for deriving mass-consistent flow fields from wind observations in rough terrain

Mass-consistent wind fields can be generated for observed wind data. The usual process involves the minimal adjustment of a trial wind field by relaxation techniques to achieve nondivergent flow. This paper describes how linear combinations of a limited number of solutions obtained by the conventional iterative relaxation methods can be used to achieve the same results with greatly reduced computational requirements. The solutions must only be obtained for linearly independent data sets. The application described uses eigenvectors of the covariance matrix of the input wind component data as the linearly-independent data sets. The model with which this technique is applied uses a relaxation scheme to achieve mass-conservative flow with minimum difference between the initial trial wind field obtained by interpolation and the resulting mass-conserving flow.     

Application of first-order reliability method to modelling the fate and transport of benzene in groundwater

Parameter uncertainty plays a significant role in decision making regarding groundwater contamination and remediation, especially for non-conservative chemicals. This paper presents a probabilistic screening model to accommodate parameter uncertainty in the aquifer media, and physical–chemical parameters, using the first-order reliability method (FORM). The application of the developed model is illustrated on transport of benzene in groundwater. The results matched those obtained using the Monte Carlo simulation method, with a smaller number of functional evaluations. Parametric studies were conducted to estimate the effect of various parameters on the results.     

Minimax Regret Analysis for Municipal Solid Waste Management: An Interval-Stochastic Programming Approach

Abstract

In this study, an interval minimax regret programming (IMMRP) method is developed for the planning of municipal solid waste (MSW) management under uncertainty. It improves on the existing interval programming and minimax regret analysis methods by allowing uncertainties presented as both intervals and random variables to be effectively communicated into the optimization process. The IMMRP can account for economic consequences under all possible scenarios without any assumption on their probabilities. The developed method is applied to a case study of long-term MSW management planning under uncertainty. Multiple scenarios associated with different cost and risk levels are analyzed. Reasonable solutions are generated, demonstrating complex tradeoffs among system cost, regret level, and system-failure risk. The method can also facilitate examination of the difference between the cost incurred with identified strategy and the least cost under an ideal condition. The results can help determine desired plans and policies for waste management under a variety of uncertainties.     

ANFIS在混凝投药前馈控制器中应用的仿真研究

在水处理中混凝投药前馈控制器的应用效果好坏关键在于控制器是否对混凝投药过程具有良好的模型辨识能力,传统的控制器效果都不太理想,而且存在沉淀池出水浊度波动大,药剂浪费严重等问题。为了解决该问题,介绍了一种用多层前馈神经网络优化模糊逻辑系统的自适应模糊推理系统——ANFIS。它具有良好的非线性函数逼近能力,在ANFIS投药前馈控制器的设计中,运用减法聚类对样本数据进行空间划分,获取初始模糊隶属函数和模糊规则,得到ANFIS模型的初始结构。用烧杯试验历史数据进行了仿真验证,并与传统的回归模型前馈投药控制仿真比较,结果表明ANFIS投药前馈控制模型明显优于回归模型,它能够根据原水水质适时有效预测混凝投药量。     

A fuzzy composting process model

Composting processes are normally complicated with a variety of uncertainties arising from incomplete or imprecise information obtained in real-world systems. Previously, there has been a lack of studies that focused on developing effective approaches to incorporate such uncertainties within composting process models. To fill this gap, a fuzzy composting process model (FCPM) for simulating composting process under uncertainty was developed. This model was mainly based on integration of a fractional fuzzy vertex method and a comprehensive composting model. Degrees of influence by projected uncertain factors were also examined. Two scenarios were investigated in applying the FCPM method. In the first scenario, model simulation under deterministic conditions was conducted. A pilot-scale experiment was provided for verifications. The result indicated that the proposed composting model could provide an excellent vehicle for demonstrating the complex interactions that occurred in the composting process. In the second scenario, application of the proposed FCPM was conducted under uncertainties. Six input parameters were considered to be of uncertain features that were reflected as fuzzy membership functions. The results indicated that the uncertainties projected in input parameters will result in significant derivations on system predictions; the proposed FCPM can generate satisfactory system outputs, with less computational efforts being required. Analyses on degree of influence of system inputs were also provided to describe the impacts of uncertainties on system responses. Thus, suitable measures can be adopted either to reduce system uncertainty by well-directed reduction of uncertainties of those high-influencing parameters or to reduce the computational requirement by neglecting those negligible factors.     

Relation between estimated dry deposition and throughfall in a coniferous forest exposed to controlled levels of SO2 and NO2

Throughfall was collected in a Scots pine forest exposed to about 14 microg m(-3) of both SO2 and NO2, and in a control forest with 1 microg m(-3) SO2 and < 1 microg m(-3) NO2. Precipitation was collected in a nearby open field. Collection was performed on an event basis during the whole vegetation period. Exposure was made by an open-air release system during the vegetation period, except during rain and at night. Additional sulfate deposition in the exposed forest (compared to control forest) was nearly equal to dry deposition of sulfur dioxide, as estimated with a stomatal conductance model adapted for the particular forest. It is thus concluded that essentially all of the dry deposited sulfur dioxide is eventually extracted and appears in throughfall-including the fraction that has been deposited through stomata. Attempts to relate net throughfall deposition to dry deposition of sulfate in the control forest were inconclusive, since a minor (10%) uncertainty in the water balance had a major influence on calculated deposition velocity for particulate sulfate. Nitrate throughfall deposition is about half of the open field wet deposition, both for the exposed and control forest. Thus, a long-term exposure with about 14 microg m(-3) NO2 decreased nitrate throughfall deposition.     

Improving nitrogen removal using a fuzzy neural network-based control system in the anoxic/oxic process

Due to the inherent complexity, uncertainty, and posterity in operating a biological wastewater treatment process, it is difficult to control nitrogen removal in the biological wastewater treatment process. In order to cope with this problem and perform a cost-effective operation, an integrated neural-fuzzy control system including a fuzzy neural network (FNN) predicted model for forecasting the nitrate concentration of the last anoxic zone and a FNN controller were developed to control the nitrate recirculation flow and realize nitrogen removal in an anoxic/oxic (A/O) process. In order to improve the network performance, a self-learning ability embedded in the FNN model was emphasized for improving the rule extraction performance. The results indicate that reasonable forecasting and control performances had been achieved through the developed control system. The effluent COD, TN, and the operation cost were reduced by about 14, 10.5, and 17 %, respectively.     

Identification of sources of Phoenix aerosol by positive matrix factorization

Chemical composition data for fine and coarse particles collected in Phoenix, AZ, were analyzed using positive matrix factorization (PMF). The objective was to identify the possible aerosol sources at the sampling site. PMF uses estimates of the error in the data to provide optimum data point scaling and permits a better treatment of missing and below-detection-limit values. It also applies nonnegativity constraints to the factors. Two sets of fine particle samples were collected by different samplers. Each of the resulting fine particle data sets was analyzed separately. For each fine particle data set, eight factors were obtained, identified as (1) biomass burning characterized by high concentrations of organic carbon (OC), elemental carbon (EC), and K; (2) wood burning with high concentrations of Na, K, OC, and EC; (3) motor vehicles with high concentrations of OC and EC; (4) nonferrous smelting process characterized by Cu, Zn, As, and Pb; (5) heavy-duty diesel characterized by high EC, OC, and Mn; (6) sea-salt factor dominated by Na and Cl; (7) soil with high values for Al, Si, Ca, Ti, and Fe; and (8) secondary aerosol with SO4(-2) and OC that may represent coal-fired power plant emissions. For the coarse particle samples, a five-factor model gave source profiles that are attributed to be (1) sea salt, (2) soil, (3) Fe source/motor vehicle, (4) construction (high Ca), and (5) coal-fired power plant. Regression of the PM mass against the factor scores was performed to estimate the mass contributions of the resolved sources. The major sources for the fine particles were motor vehicles, vegetation burning factors (biomass and wood burning), and coal-fired power plants. These sources contributed most of the fine aerosol mass by emitting carbonaceous particles, and they have higher contributions in winter. For the coarse particles, the major source contributions were soil and construction (high Ca). These sources also peaked in winter.     

The impact of SO2 and SO2 + ascorbic acid treatments on growth and partitioning of dry matter in Trigonella foenum-graecum L

To study the impact of SO(2) and SO(2) + ascorbic acid on growth and partitioning of dry matter in Trigonella foenum-graecum L., two-week-old plants were exposed to SO(2) for 2 h daily over a 42 day period. One of the exposed sets was treated with ascorbic acid. Plants were grown in a wire house and unexposed plants were used as controls for comparison. The parameters measured, such as dry weights of leaf, stem and root per plant, were found to be lower in the exposed sets than in the controls. The reductions were greater in dry weights of stem and root as compared with weights of leaves, indicating that the partitioning of the dry matter was altered. Greater amounts of soluble sugars and starch in the leaves of exposed plants, compared with the stem, also revealed that translocation was hampered. Reductions were greater in fruiting than in flowering, suggesting that fruit abortion was high. Although ascorbic acid treatment could mitigate the effect of SO(2), the differences were not found to be statistically significant. Significant changes were seen in fruit yield, suggesting that the effect of ascorbic acid is cumulative. The impact of SO(2) and SO(2) + ascorbic acid on partitioning of dry matter to different 'sinks' is discussed.