Conventional Deterministic Methods Research Articles

A Novel Combinatorial Approach to Discrete Fracture Network Modeling in Heterogeneous Media

Fractured reservoirs contain about 85 and 90 percent of oil and gas resources respectively in Iran. A comprehensive study and investigation of fractures as the main factor affecting fluid flow or perhaps barrier seems necessary for reservoir development studies. High degrees of heterogeneity and sparseness of data have incapacitated conventional deterministic methods in fracture network modeling. Recently, simulated annealing (SA) has been applied to generate stochastic realizations of spatially correlated fracture networks by assuming that the elastic energy of fractures follows Boltzmann distribution. Although SA honors local variability, the objective function of geometrical fracture modeling is defined for homogeneous conditions. In this study, after the introduction of SA and the derivation of the energy function, a novel technique is presented to adjust the model with highly heterogeneous data for a fractured field from the southwest of Iran. To this end, the regular object-based model is combined with a grid-based technique to cover the heterogeneity of reservoir properties. The original SA algorithm is also modified by being constrained in different directions and weighting the energy function to make it appropriate for heterogeneous conditions. The simulation results of the presented approach are in good agreement with the observed field data.

Coordinated Damping Control Design for DFIG-Based Wind Generation Considering Power Output Variation

To alleviate the impacts of stochastic wind generation on stability performance, this paper proposes a novel control design method for coordination and synthesis of damping controllers for conventional synchronous generators (SG) and double fed induction generators (DFIG)-based wind generation in multi-machine power systems. A probabilistic model of wind generation under Weibull distribution of wind speed is first introduced. Based on this model, an extended probabilistic small signal stability analysis (SSSA) incorporating wind power generation is proposed for handling probability density function (PDF) of its power output. The optimization problem for tuning of damping controllers is then formulated, considering the cumulative distribution function (CDF) of the real part and damping ratio of eigenvalues obtained by the proposed probabilistic SSSA as stability constraints. Particle swarm optimization (PSO) is used to solve the optimization problem and to determine parameters of damping controllers. The effectiveness of the proposed method is demonstrated on the modified New England power system with multi-wind farms through probabilistic SSSA and transient stability analysis, and it is compared with conventional deterministic methods. Accuracy of the proposed probabilistic SSSA is also validated by Monte Carlo simulations (MCS).

Effect of Climate Change on Performance-Based Design of Caisson Breakwaters

This paper presents a method to incorporate the effect of climate change on the performance-based design of a caisson breakwater and its application to the East Breakwater of the Port of Hitachinaka in Honshu, Japan. The up-to-date projection estimated a future sea-level rise of 0.25–0.6 m and a wave-height increase of 1.7 m (from 8.3 to 10 m) during the 21st century in this area. The influence of a sea-level rise on caisson sliding was minimal; the sea-level rise was much smaller than the water depth at the breakwater site. When the effects of climate change were not included, the performance-based design method calculated the same caisson width as that of the constructed breakwater, partly validating the consistency between conventional deterministic methods and performance-based design methods. The effects of climate change dictate an increase in caisson width of approximately 1.5 and 0.5 m for linear and parabolic increases of wave height, respectively, which are approximately 6.8 and 2.3% of the present caisson width of 22 m. Finally, it is recommended that the caisson breakwater be designed using the projected wave height and water level in 30 years from construction, if the deterministic design method is used and the effects of climate change are to be taken into account.

Analysis of the particle swarm algorithm in the optimization of a three-phase slurry catalytic reactor

The Particle Swarm Optimization (PSO) method was employed to optimize an industrial chemical process characterized by being difficult to be optimized by conventional deterministic methods. The chemical process is a three phase catalytic slurry reactor (tubular geometry) in which the reaction of the hydrogenation of o-cresol producing 2-methyl-cyclohexanol is carried out. The optimization problem was formulated considering as input variables the operating conditions of the reactor and as objective function the maximization of productivity, subject to the environmental constraint of conversion. The process was represented by a multivariable non-linear rigorous mathematical model and in order to solve the optimization problem, the performance of the PSO algorithm was evaluated considering four sets of parameters values suggested by the literature. PSO demonstrated to be efficient and robust to solve the constrained optimization problem, independently of the values of the PSO parameters. The solution of the rigorous mathematical model of the reactor was associated with a high computational burden, and although the PSO algorithm presented high rate of convergence, the attempt to make possible the optimization in a timeframe suitable to real time applications failed because the algorithm lost robustness (fraction of the number of runs the algorithm reached the optimization goal) when run with a reduced number of function evaluations. Therefore, if this type of application is desired, simplified mathematical models with fast and simple numerical methods must be preferred.

Lessons from stochastic small-area population projections: the case of Waikato subregions in New Zealand

Subnational population projections in New Zealand by means of the conventional deterministic cohort-component method have had a tendency to be conservative: underprojecting fast-growing populations and overprojecting slow-growing ones. In this paper we use a stochastic population projection method as an alternative. We generate population projections for five demographically distinct administrative areas within the Waikato region of New Zealand: Hamilton City, Franklin District, Thames-Coromandel District, Otorohanga District and South Waikato District. The results are compared to official subnational deterministic projections. The accuracy of subnational population projections in New Zealand is strongly affected by the instability of migration as a component of population change. Differently from the standard cohort-component method, in which net migration levels are projected, the key parameters of our method are age-gender-area specific probabilistic net migration rates. Generally, the identified and modelled uncertainty makes the traditional ‘mid-range’ scenario of subnational deterministic projections of limited use for policy analysis or planning beyond a relatively short projection horizon. We find that the projected range of rates of population growth is wider for smaller regions and/or regions more strongly affected by net migration. Directions for further development of the methodology are suggested.

Design of Intergreen Times Based on Safety Reliability

This study proposes a stochastic approach for the design of intergreen times, that is, signal change and clearance intervals, at signalized intersections based on safety reliability. Unlike the conventional deterministic methods, the proposed method accounts for the uncertainty of input variables deriving intergreen times as well as driver decision randomness at the onset of yellow. The probability of risky behavior, including abrupt stop and red light running, was selected as the safety reliability measure for determining yellow time, and the probability of the occurrence of clearance failure was used as the measure for determining all-red time. A theoretical model of estimating safety reliability and deriving intergreen times was developed and was validated by the use of the Monte Carlo simulation technique. Comparisons with the current methods used in Japan, the United States, and Germany indicated that the proposed method captured the probabilistic nature of traffic and driving decision and thus provided a more rational design of intergreen times.

An Evolutionary Approach to Allocate Frequency in Cellular Telephone System

This paper presents an evolutionary approach (genetic algorithm) to allocate frequencies in the cells of cellular network. In cellular telephone system, each cellular area is divided into small regions called cells. Each cell uses a unique set of frequencies. There is limited frequency so the frequency needs to be reuse. The Frequency allocation problem states that given any area separated into cells are allocated frequencies in such a way that no neighbor cells could have the same frequency... Since the problem looks very simple but as the number of cells is increased it becomes very complex and becomes NP-Complete problem. To find the solution of this problem, we have explored the use of genetic algorithm where possible solutions are improved generation by generation and there is more probability to find the exact solution. . Fitness function is developed which is the backbone of the concept of genetic algorithm and directly affects the performance; since this is NP problem and traditional heuristics have had only limited success in solving small to mid size problems. In this paper we have tried to show that genetic algorithm is an alternative solution for this NP problem where conventional deterministic methods are not able to provide the optimal solution.

Non-binary functional synthesis using ACO-based heuristic

Multiple-valued logic (MVL) synthesis is a problem that has attracted increased interest in recent years. The MVL synthesis problem is more involved compared to its binary counterpart. The search space for finding optimal MVL functional synthesis is enormous. Conventional deterministic methods for MVL functional synthesis are prohibitively expensive, indicating an eminent need for the use of iterative heuristic-based synthesis techniques. In this paper, an ant colony optimization (ACO) based heuristic algorithm for synthesis of MVL functions is proposed. The algorithm mimics the ants' behaviour in the real world. Real ants are found to be able to select the shortest path between their nest and food sources in the existence of alternate paths, or even hurdles between the two. The proposed ACO algorithm uses some of the known real ant techniques in finding the shortest paths to the (near) optimal number of product terms that can cover the minterms of a given MVL function. The proposed algorithm is tested using 50 000 randomly generated 2-variable 4-valued functions. The results obtained using the proposed approach show that the proposed approach outperforms existing direct cover (DC) techniques in terms of the average number of product terms (implicants) required to synthesize a given MVL function.

Are songbirds at risk from lead at small arms ranges? An application of the spatially explicit exposure model

Use of small arms during training is an important activity associated with the development and proficiency of soldiers. These weapons traditionally have used copper-jacketed lead projectiles; the copper facilitates the oxidation of the metallic lead resulting in more mobile oxides and carbonates. Consequently, many ranges at installations have high soil concentrations of lead. Many of these ranges are no longer used and have become habitat for wildlife. To address the potential for adverse effects from lead exposure in songbirds, we compared the outputs of traditional deterministic exposure models with a spatial model and compared the results of both with blood-lead levels from songbird species at two small arms range complexes. An integrative data collection procedure was used and incorporated into the spatially explicit exposure model (SEEM) for two small arms range sites. Site-specific data were used to refine model input parameters. These data included lead soil concentrations, analysis of lead concentrations in nestling food items, acid-insoluble ash content of feces (to estimate soil ingestion), location and mapping of singing males, and nest site location and characteristics. Territorial males also were spot-mapped to determine likelihood of breeding activity. Modeled estimates of risk were compared with blood and feather lead levels of adults and nestlings. Overall, edge species had higher blood-lead concentrations; however, most had concentrations below subclinical effect levels. Conventional deterministic methods produced risk estimates exceeding 10-fold the highest SEEM estimates. The spatially explicit exposure model provided good agreement with field observations and therefore produced more accurate risk estimates. The present study provides support for the application of spatial methods over conventional deterministic methods.

Applying fuzzy goal programming to production/transportation planning decisions in a supply chain

In real-world production/transportation planning decision (PTPD) problems in a supply chain, because of the conflicting nature of the multiple objectives and the vagueness in information regarding the environmental coefficients and related parameters, conventional deterministic methods are unsuitable for yielding an effective solution. This study presents a fuzzy goal programming approach for solving the integrated PTPD problems with fuzzy multiple goals in uncertain environments. The proposed model aims to simultaneously minimize the total distribution and production costs, the total number of rejected items, and the total delivery time with reference to available capacity, labor level and quota flexibility constraints at each source, as well as forecasting demand and warehouse space at each destination. The proposed approach adopts the piecewise linear membership functions to represent the fuzzy goals of the decision maker for the integrated PTPD problems in a supply chain, and achieves more flexible doctrines via an interactive decision-making process. The analytical results obtained by implementing an industrial case indicate that the proposed approach is practically applicable for the solving the integrated multi-objective PTPD problems in uncertain environments, and can effectively improve producer/distributor relationships in a supply chain.

現行の原子炉圧力容器の健全性評価手法に対するＰＡＳＣＡＬ ｖｅｒ．２を用いた確率論的検討

Fifty-five nuclear power plants of light water reactors (LWRs) in Japan including seven plants which have already reached a 30-year operation have been operated as of September 2006. The probabilistic fracture mechanics (PFM) method has been recently highlighted to rationally incorporate the uncertainties arising from the material properties, defect distribution, inspection quality and so on, unlike the conventional deterministic method. As a part of the materials aging degradation and structural integrity research for LWR components, the PFM analysis code PASCAL has been developed in JAEA. This code evaluates the conditional probabilities of crack initiation and fracture of a reactor pressure vessel (RPV) under transient conditions such as pressurized thermal shock (PTS). Sensitivity analyses for pre-service and in-service inspections have been performed according to JSME S NA1-2004 and the correlation between the results by deterministic analysis according to the JEAC 4206-2004 and probabilistic analysis based on PFM for the integrity of RPV under PTS has also been described.

Estimation of cable safety factors of suspension bridges using artificial neural network‐based inverse reliability method

AbstractThe design of the main cables of suspension bridges is based on the verification of the rules defined by standard specifications, where cable safety factors are introduced to ensure safety. However, the current bridge design standards have been developed to ensure structural safety by defining a target reliability index. In other words, the structural reliability level is specified as a target to be satisfied by the designer. Thus, calibration of cable safety factors is needed to guarantee the specified reliability of main cables. This study proposes an efficient and accurate algorithm to solve the calibration problem of cable safety factors of suspension bridges. Uncertainties of the structure and load parameters are incorporated in the calculation model. The proposed algorithm integrates the concepts of the inverse reliability method, non‐linear finite element method, and artificial neural networks method. The accuracy and efficiency of this method with reference to an example long‐span suspension bridge are studied and numerical results have validated its superiority over the conventional deterministic method or inverse reliability method with Gimsing's simplified approach. Finally, some important parameters in the proposed method are also discussed. Copyright © 2006 John Wiley & Sons, Ltd.

Estimation of settlements due to shallow tunnels and their effects

In this paper an empirical function for estimating settlements due to tunnels advancing in clayey soils is described. From the synthesis of the experience of many authors, a profile function was found and its validity was proved through some real cases described in the bibliography. After this, two possible ways of using the function are described and it is illustrated with a real case. One of them is the conventional deterministic method: introducing the ground parameters and the tunnel design parameters, the settlements trough and the horizontal strains are calculated. The other way is to do a probabilistic analysis helped by the calculation speed of the computers nowadays: assuming a variation in the characteristic parameters of the ground (that always have uncertainty) all possible settlements troughs and associated horizontal strains are estimated and then, the probability of the appearance of strains over a limit at the surface is calculated. (A) This paper was presented at Safety in the underground space - Proceedings of the ITA-AITES 2006 World Tunnel Congress and the 32nd ITA General Assembly, Seoul, Korea, 22-27 April 2006. For the covering abstract see ITRD E129148. Reprinted with permission from Elsevier.

Adequacy Assessment of Small Isolated Power Systems Using a Well-Being Approach

In spite of the widespread applications of probabilistic criteria in large systems there is considerable reluctance to apply probabilistic techniques in small isolated power systems. This reluctance dictates a need to create a bridge between the conventional deterministic methods and the prevalent probabilistic teclmiques. This paper presents a well-being approach to illustrate the adequacy assessment of small isolated power systems. A well-being index designated as LOHE and the conventional LOLE index are utilized to determine the maximum load carrying capability in two isolated systems.

Role of slope reliability analysis in landslide risk management

Progress in the use of qualitative and quantitative methods of landslide risk assessment is briefly reviewed. The use of a hazard-consequence matrix approach is highlighted and attention is then restricted to aspects of hazard assessment in which formal reliability concepts can be used. Widely accepted geotechnical and geological models must form the basis of credible hazard assessments under different environmental conditions. However, conventional deterministic methods of geotechnical analysis need to be supplemented by studies within a probabilistic framework which takes into consideration parameter variability and other uncertainties. Suggestions are made for using the "reliability index" in preference to the "factor of safety" in comprehensive procedures for landslide risk management.

Fuzzy variational principle and its applications

Linear and non-linear peaky fuzzy numbers and their arithmetic operations are constructed for the analysis of engineering structures with fuzzy characteristic quantities. Fuzziness of the corresponding quantities is consistently incorporated into the functional of the total potential energy. A set of deterministic recursive equations is obtained as the alternative expressions of the fuzzy variational principle by means of the second-order perturbation technique. The fuzzy Ritz method and the fuzzy finite element method are presented as the applications of the fuzzy variational principle. Accordingly, the roundabout procedures frequently used in the formulations of the fuzzy finite element method are avoided. A benchmark problem of a bending beam with fuzzy Young's modulus under fuzzy external loading is solved by the developed fuzzy numerical methods. Numerical examples show that results determined by these two fuzzy methods are both little conservative, and are in good agreement with those obtained by the analytical method. Moreover, the fuzzy Ritz method or the fuzzy finite element method can provide more valuable information than the conventional deterministic methods.

How the variability issue was uncovered: the history of the UK residue variability findings

As a result of routine monitoring data on carrots generated in the 1990s indicating MRL exceedances, further studies showed that residues of organophosphorus compounds in individual roots could vary up to 25 times the levels found in composite samples. Additional work found that this phenomenon also extended to other crops including apples, peaches and celery. Variability (defined as the highest residue level found in any one crop item divided by the level found in a composite sample from the same batch) of up to 34 times mean values was found in one batch of plums. Conventional deterministic methods used in consumer assessments were likely to give gross overestimates of short-term exposure because of the assumptions employed. This led to the development of probabilistic models which made the best use of all available information and was capable of indicating percentages of consumers that could exceed relevant toxicological end points. This indicated that there was unlikely to be serious health effects as a result of ingesting these residues and has subsequently proved to be a useful aid to regulatory decision making.

Determination of the Optimum Partial Factors in Structural Reliability Analysis

In this paper, an optimization method is used to determine the values of partial factors in structural reliability analysis. Once the proper objective function is defined, a group of optimum partial factors, which enable the objective function to take its minimum value, will need to be determined. In the present study, two kinds of objective function are considered. The conditions that have to be satisfied for optimum partial factors of these two kinds of objective function are then derived. In both cases, the result shows that the partial factors of both dead and live loads should satisfy the same proportional expression and should be inversely proportional to the partial factor of resistance force. A simple beam is used as an example to illustrate the computations involved. It is found that the design concept proposed in this paper leads to a design criterion similar to that which applies to the conventional deterministic method. Thus, this concept can be easily used in practice. The illustrative example shows that the values of the dead load and live load have a significant effect on the reliability design criteria.

Risk assessment through probabilistic structural analysis

The increase in computer power over the last twenty to thirty years has resulted in the availability of a wide range of programs for structural analysis. Best-known among these are finite element programs which can solve many problems involving static and dynamic loading, heat transfer and fluid dynamics. Most of these programs are deterministic in that users specify “constant” values for the model parameters. In many instances this is sufficient: in the design or analysis of non-critical components, or ones for which all parameters are well-known, a deterministic analysis can provide adequate solutions. In the design of critical components the conventional approach is to perform a deterministic analysis and to build in reliability through suitably chosen safety factors. In problems where the risk associated with a component needs to be assessed conventional deterministic analysis methods are insufficient and methods which incorporate the probabilistic aspects of loads and material properties need to be used, especially if material degradation with time is a factor. Although the randomness of the problem parameters can be simulated through, for instance, Monte Carlo methods, these methods are computationally expensive. This paper discusses computationally efficient, fast probability integration methods where conventional deterministic programs can be adapted to calculate the reliability of a component using mean value-based perturbation methods. This adaptation has been performed for the general purpose finite element program ABAQUS and the general purpose fracture mechanics program NASCRAC. The methods are illustrated in a case study involving the fracture mechanics analysis of a turbine shaft: it is suspected that cracks have been present since commissioning at a shoulder in the shaft. The likely failure time and the probability of catastrophic failure prior to the first scheduled shutdown is calculated.

First-order reliability application and verification methods for semistatic structures

Escalating risks of aerostructures stimulated by increasing size, complexity, and cost should no longer be ignored by conventional deterministic safety design methods. The deterministic pass-fail concept is incompatible with probability and risk assessments, its stress audits are shown to be arbitrary and incomplete, and it compromises high strength materials performance. A reliability method is proposed which combines first order reliability principles with deterministic design variables and conventional test technique to surmount current deterministic stress design and audit deficiencies. Accumulative and propagation design uncertainty errors are defined and appropriately implemented into the classical safety index expression. The application is reduced to solving for a factor that satisfies the specified reliability and compensates for uncertainty errors, and then using this factor as, and instead of, the conventional safety factor in stress analyses. The resulting method is consistent with current analytical skills and verification practices, the culture of most designers, and with the pace of semistatic structural designs.