Estimating the loading condition of a diesel engine using instantaneous angular speed analysis

Continuing monitoring of diesel engine performance is critical for early detection of fault developments in the engine before they materialize and become a functional failure. Instantaneous crank angular speed (IAS) analysis is one of a few non intrusive condition monitoring techniques that can be utilized for such tasks. In this experimental study, IAS analysis was employed to estimate the loading condition of a 4-stroke 4-cylinder diesel engine in a laboratory condition. It was shown that IAS analysis can provide useful information about engine speed variation caused by the changing piston momentum and crankshaft acceleration during the engine combustion process. It was also found that the major order component of the IAS spectrum directly associated with the engine firing frequency (at twice the mean shaft revolution speed) can be utilized to estimate the engine loading condition regardless of whether the engine is operating at normal running conditions or in a simulated faulty injector case. The amplitude of this order component follows a clear exponential curve as the loading condition changes. A mathematical relationship was established for the estimation of the engine power output based on the amplitude of the major order component of the measured IAS spectrum.

Estimating the loading condition of a diesel engine using instantaneous angular speed analysis

Continuing monitoring of diesel engine performance is critical for early detection of fault developments in the engine before they materialize and become a functional failure. Instantaneous crank angular speed (IAS) analysis is one of a few non intrusive condition monitoring techniques that can be utilized for such tasks. In this experimental study, IAS analysis was employed to estimate the loading condition of a 4-stroke 4-cylinder diesel engine in a laboratory condition. It was shown that IAS analysis can provide useful information about engine speed variation caused by the changing piston momentum and crankshaft acceleration during the engine combustion process. It was also found that the major order component of the IAS spectrum directly associated with the engine firing frequency (at twice the mean shaft revolution speed) can be utilized to estimate the engine loading condition regardless of whether the engine is operating at normal running conditions or in a simulated faulty injector case. The amplitude of this order component follows a clear exponential curve as the loading condition changes. A mathematical relationship was established for the estimation of the engine power output based on the amplitude of the major order component of the measured IAS spectrum.

An improved genetic algorithm and graph theory based method for optimal sectionalizer switch placement in distribution networks with DG

In this paper a new graph-theory and improved genetic algorithm based practical method is employed to solve the optimal sectionalizer switch placement problem. The proposed method determines the best locations of sectionalizer switching devices in distribution networks considering the effects of presence of distributed generation (DG) in fitness functions and other optimization constraints, providing the maximum number of costumers to be supplied by distributed generation sources in islanded distribution systems after possible faults. The proposed method is simulated and tested on several distribution test systems in both cases of with DG and non DG situations. The results of the simulations validate the proposed method for switch placement of the distribution network in the presence of distributed generation.

The impact of taxes on optimal portfolio choice : an Australian study

Taxes are an important component of investing that is commonly overlooked in both the literature and in practice. For example, many understand that taxes will reduce an investment’s return, but less understood is the risk-sharing nature of taxes that also reduces the investment’s risk. This thesis examines how taxes affect the optimal asset allocation and asset location decision in an Australian environment. It advances the model of Horan & Al Zaman (2008), improving the method by which the present value of tax liabilities are calculated, by using an after-tax risk-free discount rate, and incorporating any new or reduced tax liabilities generated into its expected risk and return estimates. The asset allocation problem is examined for a range of different scenarios using Australian parameters, including different risk aversion levels, personal marginal tax rates, investment horizons, borrowing premiums, high or low inflation environments, and different starting cost bases. The findings support the Horan & Al Zaman (2008) conclusion that equities should be held in the taxable account. In fact, these findings are strengthened with most of the efficient frontier maximising equity holdings in the taxable account instead of only half. Furthermore, these findings transfer to the Australian case, where it is found that taxed Australian investors should always invest into equities first through the taxable account before investing in super. However, untaxed Australian investors should invest their equity first through superannuation. With borrowings allowed in the taxable account (no borrowing premium), Australian taxed investors should hold 100% of the superannuation account in the risk-free asset, while undertaking leverage in the taxable account to achieve the desired risk-return. Introducing a borrowing premium decreases the likelihood of holding 100% of super in the risk-free asset for taxable investors. The findings also suggest that the higher the marginal tax rate, the higher the borrowing premium in order to overcome this effect. Finally, as the investor’s marginal tax rate increases, the overall allocation to equities should increase due to the increased risk and return sharing caused by taxation, and in order to achieve the same risk/return level as the lower taxation level, the investor must take on more equity exposure. The investment horizon has a minimal impact on the optimal allocation decision in the absence of factors such as mean reversion and human capital.

Adaptive and optimal under frequency load shedding

Power systems in many countries are stressed towards their stability limit. If these stable systems experience any unexpected serious contingencies, or disturbances, there is a significant risk of instability, which may lead to wide-spread blackout. Frequency is a reliable indicator for such instability condition exists on the power system; therefore under-frequency load shedding technique is used to stable the power system by curtail some load. In this paper, the SFR-UFLS model redeveloped to generate optimal load shedding method is that optimally shed load following one single particular contingency event. The proposed optimal load shedding scheme is then tested on the 39-bus New England test system to show the performance against random load shedding scheme.

An approximate Bayesian computation approach for estimating parameters of complex environmental processes in a cellular automata

Modelling an environmental process involves creating a model structure and parameterising the model with appropriate values to accurately represent the process. Determining accurate parameter values for environmental systems can be challenging. Existing methods for parameter estimation typically make assumptions regarding the form of the Likelihood, and will often ignore any uncertainty around estimated values. This can be problematic, however, particularly in complex problems where Likelihoods may be intractable. In this paper we demonstrate an Approximate Bayesian Computational method for the estimation of parameters of a stochastic CA. We use as an example a CA constructed to simulate a range expansion such as might occur after a biological invasion, making parameter estimates using only count data such as could be gathered from field observations. We demonstrate ABC is a highly useful method for parameter estimation, with accurate estimates of parameters that are important for the management of invasive species such as the intrinsic rate of increase and the point in a landscape where a species has invaded. We also show that the method is capable of estimating the probability of long distance dispersal, a characteristic of biological invasions that is very influential in determining spread rates but has until now proved difficult to estimate accurately.

Body composition and its relationship to metabolic risk factors in Asian children

Obesity is a major public health problem in both developed and developing countries. The body mass index (BMI) is the most common index used to define obesity. The universal application of the same BMI classification across different ethnic groups is being challenged due to the inability of the index to differentiate fat mass (FM) and fat�]free mass (FFM) and the recognized ethnic differences in body composition. A better understanding of the body composition of Asian children from different backgrounds would help to better understand the obesity�]related health risks of people in this region. Moreover, the limitations of the BMI underscore the necessity to use where possible, more accurate measures of body fat assessment in research and clinical settings in addition to BMI, particularly in relation to the monitoring of prevention and treatment efforts. The aim of the first study was to determine the ethnic difference in the relationship between BMI and percent body fat (%BF) in pre�]pubertal Asian children from China, Lebanon, Malaysia, the Philippines, and Thailand. A total of 1039 children aged 8�]10 y were recruited using a non�]random purposive sampling approach aiming to encompass a wide BMI range from the five countries. Percent body fat (%BF) was determined using the deuterium dilution technique to quantify total body water (TBW) and subsequently derive proportions of FM and FFM. The study highlighted the sex and ethnic differences between BMI and %BF in Asian children from different countries. Girls had approximately 4.0% higher %BF compared with boys at a given BMI. Filipino boys tended to have a lower %BF than their Chinese, Lebanese, Malay and Thai counterparts at the same age and BMI level (corrected mean %BF was 25.7�}0.8%, 27.4�}0.4%, 27.1�}0.6%, 27.7�}0.5%, 28.1�}0.5% for Filipino, Chinese, Lebanese, Malay and Thai boys, respectively), although they differed significantly from Thai and Malay boys. Thai girls had approximately 2.0% higher %BF values than Chinese, Lebanese, Filipino and Malay counterparts (however no significant difference was seen among the four ethnic groups) at a given BMI (corrected mean %BF was 31.1�}0.5%, 28.6�}0.4%, 29.2�}0.6%, 29.5�}0.6%, 29.5�}0.5% for Thai, Chinese, Lebanese, Malay and Filipino girls, respectively). However, the ethnic difference in BMI�]%BF relationship varied by BMI. Compared with Caucasians, Asian children had a BMI 3�]6 units lower for a given %BF. More than one third of obese Asian children in the study were not identified using the WHO classification and more than half were not identified using the International Obesity Task Force (IOTF) classification. However, use of the Chinese classification increased the sensitivity by 19.7%, 18.1%, 2.3%, 2.3%, and 11.3% for Chinese, Lebanese, Malay, Filipino and Thai girls, respectively. A further aim of the first study was to determine the ethnic difference in body fat distribution in pre�]pubertal Asian children from China, Lebanon, Malaysia, and Thailand. The skin fold thicknesses, height, weight, waist circumference (WC) and total adiposity (as determined by deuterium dilution technique) of 922 children from the four countries was assessed. Chinese boys and girls had a similar trunk�]to�]extremity skin fold thickness ratio to Thai counterparts and both groups had higher ratios than the Malays and Lebanese at a given total FM. At a given BMI, both Chinese and Thai boys and girls had a higher WC than Malays and Lebanese (corrected mean WC was 68.1�}0.2 cm, 67.8�}0.3 cm, 65.8�}0.4 cm, 64.1�}0.3 cm for Chinese, Thai, Lebanese and Malay boys, respectively; 64.2�}0.2 cm, 65.0�}0.3 cm, 62.9�}0.4 cm, 60.6�}0.3 cm for Chinese, Thai, Lebanese and Malay girls, respectively). Chinese boys and girls had lower trunk fat adjusted subscapular/suprailiac skinfold ratio compared with Lebanese and Malay counterparts. The second study aimed to develop and cross�]validate bioelectrical impedance analysis (BIA) prediction equations of TBW and FFM for Asian pre�]pubertal children from China, Lebanon, Malaysia, the Philippines, and Thailand. Data on height, weight, age, gender, resistance and reactance measured by BIA were collected from 948 Asian children (492 boys and 456 girls) aged 8�]10 y from the five countries. The deuterium dilution technique was used as the criterion method for the estimation of TBW and FFM. The BIA equations were developed from the validation group (630 children randomly selected from the total sample) using stepwise multiple regression analysis and cross�]validated in a separate group (318 children) using the Bland�]Altman approach. Age, gender and ethnicity influenced the relationship between the resistance index (RI = height2/resistance), TBW and FFM. The BIA prediction equation for the estimation of TBW was: TBW (kg) = 0.231�~Height2 (cm)/resistance (ƒ¶) + 0.066�~Height (cm) + 0.188�~Weight (kg) + 0.128�~Age (yr) + 0.500�~Sex (male=1, female=0) . 0.316�~Ethnicity (Thai ethnicity=1, others=0) �] 4.574, and for the estimation of FFM: FFM (kg) = 0.299�~Height2 (cm)/resistance (ƒ¶) + 0.086�~Height (cm) + 0.245�~Weight (kg) + 0.260�~Age (yr) + 0.901�~Sex (male=1, female=0) �] 0.415�~Ethnicity (Thai ethnicity=1, others=0) �] 6.952. The R2 was 88.0% (root mean square error, RSME = 1.3 kg), 88.3% (RSME = 1.7 kg) for TBW and FFM equation, respectively. No significant difference between measured and predicted TBW and between measured and predicted FFM for the whole cross�]validation sample was found (bias = �]0.1�}1.4 kg, pure error = 1.4�}2.0 kg for TBW and bias = �]0.2�}1.9 kg, pure error = 1.8�}2.6 kg for FFM). However, the prediction equation for estimation of TBW/FFM tended to overestimate TBW/FFM at lower levels while underestimate at higher levels of TBW/FFM. Accuracy of the general equation for TBW and FFM compared favorably with both BMI�]specific and ethnic�]specific equations. There were significant differences between predicted TBW and FFM from external BIA equations derived from Caucasian populations and measured values in Asian children. There were three specific aims of the third study. The first was to explore the relationship between obesity and metabolic syndrome and abnormalities in Chinese children. A total of 608 boys and 800 girls aged 6�]12 y were recruited from four cities in China. Three definitions of pediatric metabolic syndrome and abnormalities were used, including the International Diabetes Federation (IDF) and National Cholesterol Education Program (NCEP) definition for adults modified by Cook et al. and de Ferranti et al. The prevalence of metabolic syndrome varied with different definitions, was highest using the de Ferranti definition (5.4%, 24.6% and 42.0%, respectively for normal�]weight, overweight and obese children), followed by the Cook definition (1.5%, 8.1%, and 25.1%, respectively), and the IDF definition (0.5%, 1.8% and 8.3%, respectively). Overweight and obese children had a higher risk of developing the metabolic syndrome compared to normal�]weight children (odds ratio varied with different definitions from 3.958 to 6.866 for overweight children, and 12.640�]26.007 for obese children). Overweight and obesity also increased the risk of developing metabolic abnormalities. Central obesity and high triglycerides (TG) were the most common while hyperglycemia was the least frequent in Chinese children regardless of different definitions. The second purpose was to determine the best obesity index for the prediction of cardiovascular (CV) risk factor clustering across a 2�]y follow�]up among BMI, %BF, WC and waist�]to�]height ratio (WHtR) in Chinese children. Height, weight, WC, %BF as determined by BIA, blood pressure, TG, high�]density lipoprotein cholesterol (HDL�]C), and fasting glucose were collected at baseline and 2 years later in 292 boys and 277 girls aged 8�]10 y. The results showed the percentage of children who remained overweight/obese defined on the basis of BMI, WC, WHtR and %BF was 89.7%, 93.5%, 84.5%, and 80.4%, respectively after 2 years. Obesity indices at baseline significantly correlated with TG, HDL�]C, and blood pressure at both baseline and 2 years later with a similar strength of correlations. BMI at baseline explained the greatest variance of later blood pressure. WC at baseline explained the greatest variance of later HDL�]C and glucose, while WHtR at baseline was the main predictor of later TG. Receiver�]operating characteristic (ROC) analysis explored the ability of the four indices to identify the later presence of CV risk. The overweight/obese children defined on the basis of BMI, WC, WHtR or %BF were more likely to develop CV risk 2 years later with relative risk (RR) scores of 3.670, 3.762, 2.767, and 2.804, respectively. The final purpose of the third study was to develop age�] and gender�]specific percentiles of WC and WHtR and cut�]off points of WC and WHtR for the prediction of CV risk in Chinese children. Smoothed percentile curves of WC and WHtR were produced in 2830 boys and 2699 girls aged 6�]12 y randomly selected from southern and northern China using the LMS method. The optimal age�] and gender�]specific thresholds of WC and WHtR for the prediction of cardiovascular risk factors clustering were derived in a sub�]sample (n=1845) by ROC analysis. Age�] and gender�]specific WC and WHtR percentiles were constructed. The WC thresholds were at the 90th and 84th percentiles for Chinese boys and girls, respectively, with sensitivity and specificity ranging from 67.2% to 83.3%. The WHtR thresholds were at the 91st and 94th percentiles for Chinese boys and girls, respectively, with sensitivity and specificity ranging from 78.6% to 88.9%. The cut�]offs of both WC and WHtR were age�] and gender�]dependent. In conclusion, the current thesis quantifies the ethnic differences in the BMI�]%BF relationship and body fat distribution between Asian children from different origins and confirms the necessity to consider ethnic differences in body composition when developing BMI and other obesity index criteria for obesity in Asian children. Moreover, ethnicity is also important in BIA prediction equations. In addition, WC and WHtR percentiles and thresholds for the prediction of CV risk in Chinese children differ from other populations. Although there was no advantage of WC or WHtR over BMI or %BF in the prediction of CV risk, obese children had a higher risk of developing the metabolic syndrome and abnormalities than normal�]weight children regardless of the obesity index used.

New percentage body fat prediction equations for Japanese females

Anthropometry is a simple and cost-efficient method for the assessment of body composition. However prediction equations to estimate body composition using anthropometry should be ‘population-specific’. Most popular body composition prediction equations for Japanese females were proposed more than 40 years ago and there is some concern regarding their usefulness in Japanese females living today. The aim of this study was to compare percentage body fat (%BF) estimated from anthropometry and dual energy x-ray absorptiometry (DXA) to examine the applicability of commonly used prediction equations in young Japanese females. Body composition of 139 Japanese females aged between 18 and 27 years of age (BMI range: 15.1–29.1 kg/m2) was measured using whole-body DXA (Lunar DPX-LIQ) scans. From anthropometric measurements %BF was estimated using four equations developed from Japanese females. The results showed that the traditionally employed prediction equations for anthropometry significantly (p<0.01) underestimate %BF of young Japanese females and therefore are not valid for the precise estimation of body composition. New %BF prediction equations were proposed from the DXA and anthropometry results. Application of the proposed equations may assist in more accurate assessment of body fatness in Japanese females living today.

Optimal allocation of water in village irrigation systems of Sri Lanka

This PhD study examines whether water allocation becomes more productive when it is re-allocated from 'low' to 'high' efficient alternative uses in village irrigation systems (VISs) in Sri Lanka. Reservoir-based agriculture is a collective farming economic activity, which inter-sectoral allocation of water is assumed to be inefficient due to market imperfections and weak user rights. Furthermore, the available literature shows that a „head-tail syndrome. is the most common issue for intra-sectoral water management in „irrigation. agriculture. This research analyses the issue of water allocation by using primary data collected from two surveys of 460 rice farmers and 325 fish farming groups in two administrative districts in Sri Lanka. Technical efficiency estimates are undertaken for both rice farming and culture-based fisheries (CBF) production. The equi-marginal principle is applied for inter and intra-sectoral allocation of water. Welfare benefits of water re-allocation are measured through consumer surplus estimation. Based on these analyses, the overall findings of the thesis can be summarised as follows. The estimated mean technical efficiency (MTE) for rice farming is 73%. For CBF production, the estimated MTE is 33%. The technical efficiency distribution is skewed to the left for rice farming, while it skewed to the right for CBF production. The results show that technical efficiency of rice farming can be improved by formalising transferability of land ownership and, therefore, water user rights by enhancing the institutional capacity of Farmer Organisations (FOs). Other effective tools for improving technical efficiency of CBF production are strengthening group stability of CBF farmers, improving the accessibility of official consultation, and attracting independent investments. Inter-sectoral optimal allocation shows that the estimated inefficient volume of water in rice farming, which can be re-allocated for CBF production, is 32%. With the application of successive policy instruments (e.g., a community transferable quota system and promoting CBF activities), there is potential for a threefold increase in marginal value product (MVP) of total reservoir water in VISs. The existing intra-sectoral inefficient volume of water use in tail-end fields and head-end fields can potentially be removed by reducing water use by 10% and 23% respectively and re-allocating this to middle fields. This re-allocation may enable a twofold increase in MVP of water used in rice farming without reducing the existing rice output, but will require developing irrigation practices to facilitate this re-allocation. Finally, the total productivity of reservoir water can be increased by responsible village level institutions and primary level stakeholders (i.e., co-management) sharing responsibility of water management, while allowing market forces to guide the efficient re-allocation decisions. This PhD has demonstrated that instead of farmers allocating water between uses haphazardly, they can now base their decisions on efficient water use with a view to increasing water productivity. Such an approach, no doubt will enhance farmer incomes and community welfare.

A Bayesian approach for estimating detection times in horses : exploring the pharmacokinetics of a urinary acepromazine metabolite

We describe the population pharmacokinetics of an acepromazine (ACP) metabolite (2-(1-hydroxyethyl)promazine) (HEPS) in horses for the estimation of likely detection times in plasma and urine. Acepromazine (30 mg) was administered to 12 horses, and blood and urine samples were taken at frequent intervals for chemical analysis. A Bayesian hierarchical model was fitted to describe concentration-time data and cumulative urine amounts for HEPS. The metabolite HEPS was modelled separately from the parent ACP as the half-life of the parent was considerably less than that of the metabolite. The clearance ($Cl/F_{PM}$) and volume of distribution ($V/F_{PM}$), scaled by the fraction of parent converted to metabolite, were estimated as 769 L/h and 6874 L, respectively. For a typical horse in the study, after receiving 30 mg of ACP, the upper limit of the detection time was 35 hours in plasma and 100 hours in urine, assuming an arbitrary limit of detection of 1 $\mu$g/L, and a small ($\approx 0.01$) probability of detection. The model derived allowed the probability of detection to be estimated at the population level. This analysis was conducted on data collected from only 12 horses, but we assume that this is representative of the wider population.

Optimal coordination of overcurrent relays in distribution systems with distributed generators based on differential evolution algorithm

Distributed generators (DGs) are defined as generators that are connected to a distribution network. The direction of the power flow and short-circuit current in a network could be changed compared with one without DGs. The conventional protective relay scheme does not meet the requirement in this emerging situation. As the number and capacity of DGs in the distribution network increase, the problem of coordinating protective relays becomes more challenging. Given this background, the protective relay coordination problem in distribution systems is investigated, with directional overcurrent relays taken as an example, and formulated as a mixed integer nonlinear programming problem. A mathematical model describing this problem is first developed, and the well-developed differential evolution algorithm is then used to solve it. Finally, a sample system is used to demonstrate the feasiblity and efficiency of the developed method.

Optimal sitting and sizing of distributed generators considering plug-in electric vehicles

Some uncertainties such as the stochastic input/output power of a plug-in electric vehicle due to its stochastic charging and discharging schedule, that of a wind unit and that of a photovoltaic generation source, volatile fuel prices and future uncertain load growth, all together could lead to some risks in determining the optimal siting and sizing of distributed generators (DGs) in distributed systems. Given this background, under the chance constrained programming (CCP) framework, a new method is presented to handle these uncertainties in the optimal sitting and sizing problem of DGs. First, a mathematical model of CCP is developed with the minimization of DGs investment cost, operational cost and maintenance cost as well as the network loss cost as the objective, security limitations as constraints, the sitting and sizing of DGs as optimization variables. Then, a Monte Carolo simulation embedded genetic algorithm approach is developed to solve the developed CCP model. Finally, the IEEE 37-node test feeder is employed to verify the feasibility and effectiveness of the developed model and method. This work is supported by an Australian Commonwealth Scientific and Industrial Research Organisation (CSIRO) Project on Intelligent Grids Under the Energy Transformed Flagship, and Project from Jiangxi Power Company.

The accuracy of a new system for estimating organ volume using ultrasound

A new system is described for estimating volume from a series of multiplanar 2D ultrasound images. Ultrasound images are captured using a personal computer video digitizing card and an electromagnetic localization system is used to record the pose of the ultrasound images. The accuracy of the system was assessed by scanning four groups of ten cadaveric kidneys on four different ultrasound machines. Scan image planes were oriented either radially, in parallel or slanted at 30 C to the vertical. The cross-sectional images of the kidneys were traced using a mouse and the outline points transformed to 3D space using the Fastrak position and orientation data. Points on adjacent region of interest outlines were connected to form a triangle mesh and the volume of the kidneys estimated using the ellipsoid, planimetry, tetrahedral and ray tracing methods. There was little difference between the results for the different scan techniques or volume estimation algorithms, although, perhaps as expected, the ellipsoid results were the least precise. For radial scanning and ray tracing, the mean and standard deviation of the percentage errors for the four different machines were as follows: Hitachi EUB-240, −3.0 ± 2.7%; Tosbee RM3, −0.1 ± 2.3%; Hitachi EUB-415, 0.2 ± 2.3%; Acuson, 2.7 ± 2.3%.

On selecting an optimal wavelet for detecting singularities in traffic and vehicular data

Serving as a powerful tool for extracting localized variations in non-stationary signals, applications of wavelet transforms (WTs) in traffic engineering have been introduced; however, lacking in some important theoretical fundamentals. In particular, there is little guidance provided on selecting an appropriate WT across potential transport applications. This research described in this paper contributes uniquely to the literature by first describing a numerical experiment to demonstrate the shortcomings of commonly-used data processing techniques in traffic engineering (i.e., averaging, moving averaging, second-order difference, oblique cumulative curve, and short-time Fourier transform). It then mathematically describes WT’s ability to detect singularities in traffic data. Next, selecting a suitable WT for a particular research topic in traffic engineering is discussed in detail by objectively and quantitatively comparing candidate wavelets’ performances using a numerical experiment. Finally, based on several case studies using both loop detector data and vehicle trajectories, it is shown that selecting a suitable wavelet largely depends on the specific research topic, and that the Mexican hat wavelet generally gives a satisfactory performance in detecting singularities in traffic and vehicular data.

Efficient preconditioning of the method of lines for solving nonlinear two-sided space-fractional diffusion equations

A standard method for the numerical solution of partial differential equations (PDEs) is the method of lines. In this approach the PDE is discretised in space using �finite di�fferences or similar techniques, and the resulting semidiscrete problem in time is integrated using an initial value problem solver. A significant challenge when applying the method of lines to fractional PDEs is that the non-local nature of the fractional derivatives results in a discretised system where each equation involves contributions from many (possibly every) spatial node(s). This has important consequences for the effi�ciency of the numerical solver. First, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. Second, since the Jacobian matrix of the system is dense (partially or fully), methods that avoid the need to form and factorise this matrix are preferred. In this paper, we consider a nonlinear two-sided space-fractional di�ffusion equation in one spatial dimension. A key contribution of this paper is to demonstrate how an eff�ective preconditioner is crucial for improving the effi�ciency of the method of lines for solving this equation. In particular, we show how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.