Curvilinear Regression Equations Research Articles

Weld Quality Prediction Using Artificial Intelligence Technique

Decision-making process in manufacturing environment is increasingly difficult due to the rapid changes in design and demand of quality products. To make decision making process online, effective and efficient artificial intelligent tools like neural networks are being attempted. Usually, the desired welding parameters are determined using traditional methods like welder’s experiences, charts and handbooks (preferred values) which are simple and inexpensive. But this does not ensure that the selected welding parameters result in satisfactory welding and this method is not applicable to new welding process. To overcome this problem, various methods of obtaining the desired output variables through models to correlate input variables with output variables have been developed. Fractional factorial techniques, Mathematical modeling, curvilinear regression equations, linear regression equations, response surface methodology, finite element modeling, grey-based Taguchi method and sensitivity analysis were used to model SAW process. These methods are limited in application due to difficulties in modeling, time consuming and cumbersome. Due to the inadequacy and inefficiency of the mathematical models to explain the nonlinear properties existing between the input and output parameters of welding lead to the development of intelligent modeling techniques. Precise simulation and analysis of the process needs attention which helps to predict the wide variety of process parameters to set the factory floor in real time. The type of artificial intelligence capable of responding to changes in the automated manufacturing environment, and having the ability to capture vast manufacturing knowledge isAdaptive Neuro Fuzzy Inference System (ANFIS). It is becoming widely used in all aspects of manufacturing process to assist humans. Realizing that matter, ANFIS a state of the art artificial intelligent method, has the possibility to enhance the prediction of weld quality to find the best combination of independent variables which is welding current (I), speed (S) and welding voltage (V) as the input variables in order to achieve desired weld quality. Thus, the main objectives of this project is to develop ANFIS model to predict weld quality.

Risk to Onion (Allium cepa L.) Field Cultivation in Poland from Precipitation Deficiency

The onion is the most common vegetable cultivated in Poland and yield is marked by high year to year variability. The yield quantity is predominantly affected by variable meteorological conditions, especially by precipitation deficiency. Data were collected from the Research Centre for Cultivar Testing and the Institute of Meteorology and Water Management for the period 1966-2005 to evaluate the effect of precipitation conditions on the yield of onions (Allium cepa L.) cultivated in Poland using multiple regression analysis. Verification of the curvilinear regression equation was conducted on the basis of relative forecast error and average relative forecast error. For this equation the ARFE amounted to 9.6%. The threshold precipitation value, i.e. the value at which reduction by at least 5% of the total yield occurs, was determined by curvilinear regression. Reduction of potential yield caused by precipitation deficiency and the frequency of precipitation deficiency were determined. Reductions of at least 5% in the average domestic onion yield in Poland occurred when atmospheric precipitation was ? 183 mm. This level of precipitation constituted 87% of the norm and took place in the period between the end of emergence to the beginning of leaf bending. Potential reduction in onion yield in Poland caused by precipitation deficiency in this period varied between 9 and 18%. In Poland, the frequency of atmospheric precipitation deficiency between 1966 to 2005 varied from 10% in the south-east to 50% in the central west and north west. The average frequency of atmospheric precipitation deficiency amounted to about 37%.

Predicting germination in semi-arid wildland seedbeds. I. Thermal germination models

The key to stopping high-frequency or catastrophic wildfires in the western U.S.A. is the successful restoration of burned lands to functional plant communities. Developing models of seedling establishment for invasive and native species will help in the selection of species for restoration projects that are able to establish and compete with invasive species given the abiotic conditions of specific sites. Modeling germination is the first step in modeling seedling establishment. We developed thermal germination models and compared predicted and measured germination timing in incubators as a precursor to testing germination model prediction in field seedbeds. We incubated 11 revegetation species and three weed ( Bromus tectorum L.) seedlots at constant temperatures to develop linear and curvilinear regression equations to estimate days to 10, 25, and 50% germination for each seedlot. We compared actual time to germination with predicted time for three field-simulated diurnal temperature regimes representing March, mid-March to mid-April, and May temperatures in a big sagebrush ( Artemisia tridentata Nutt. ssp. wyomingensis Beetle & Young) plant community. Bromus tectorum seedlots germinated faster than perennial grasses and forbs, especially at cooler temperatures. However, most of the revegetation species had high and fast germination for a wide range of temperatures. Germination time generally fit constant temperatures well with R 2 values ≥ 0.85 for 33 of 40 linear equations and ≥0.80 for 40 of 48 curvilinear equations. Models overestimated germination time for field-simulated diurnal temperatures by 1–4 days for most seedlots. Model accuracy was sufficient for most seedlots to encourage subsequent testing of model accuracy under field conditions.

Applying a computer program, based on a developed mathematical model, to protect cereal crops from leaf beetles (Oulema spp.)

In many countries, including Poland, one of the most economically significant pests on cereal crops are leaf beetles (Oulema spp.). Determining the optimum time for chemical control of Oulema spp. is not easy due to extended duration of egg laying and larval development of the species. For this reason, cereal crops producers are not always able to determine correctly proper timing for a chemical treatment. Research conducted in the years 2006–2009 in the conditions of Wielkopolska province regarded short-term forecasting of leaf beetles on cereal crops using a computer program. The program is based on a mathematical model of multiple curvilinear regression equation. The computer program is of assistance when making a decision to set an optimum date for Oulema spp. control. The differences between the date set by the computer program and the date set using signalling oscillated between + 2 and −2 days.

Using a Tree Ring δ 13C Annual Series to Reconstruct Atmospheric CO 2 Concentration over the Past 300 Years

The annual series of δ^13C were measured in tree rings of three Cryptomeria fortunei disks (CF-1, CF-2, and CF3) collected from West Tianmu Mountain, Zhejiang Province, China, according to cross-dating tree ring ages. There was no obvious decreasing trend of the δ^13C annual time series of CF-2 before 1835. However, from 1835 to 1982 the three tree ring δ^13C annual series exhibited similar decreasing trends that were significantly (P≤0.001) correlated. The distribution characteristics of a scatter diagram between estimated δ^13C series of CF-2 from modeling and the atmospheric CO2 concentration extracted from the Law Dome ice core from 1840 to 1978 were analyzed and a curvilinear regression equation for reconstructing atmospheric CO2 concentration was established with R^2=0.98. Also, a test of independent samples indicated that between 1685 and 1839 the reconstructed atmospheric CO2 concentration using the δ^13C series of CF-2 had a close relationship with the Law Dome and Siple ice cores, with a standard deviation of 1.98. The general increasing trend of the reconstructed atmospheric CO2 concentration closely reflected the long-term variation of atmospheric CO2 concentration recorded both before and after the Industrial Revolution. Between 1685 and 1840 the evaluated atmospheric CO2 concentration was stable, but after 1840 it exhibited a rapid increase. Given a longer δ^13C annual time series of tree rings, it was feasible to rebuild a representative time series to describe the atmospheric CO2 concentration for an earlier period and for years that were not in the ice core record.

Effect of temperature on intrinsic rates of natural increase (rm) of a coccinellid and its spider mite prey

The intrinsic rate of natural increase(rm) is useful to estimate the populationgrowth potential of insects and mites, whichmay help predict the outcome of pest-naturalenemy interactions. This study was conductedto determine how 12 constant temperatureregimes between 10–38 °C (± 0.5 °C) may differentially affect therm of the McDaniel spider mite, Tetranychus mcdanieli McGregor (Acarina: Tetranychidea), a common pest of raspberry, andits coccinellid predator, Stethoruspunctillum Weise (Coleoptera: Coccinellidae). Tetranychus mcdanieli survived tomaturity in the 14–36 °C range, comparedto the 14–32 °C range for S.punctillum. Survival above 24 °Cremained high for the spider mite, butdecreased markedly for the coccinellid. Tetranychus mcdanieli's range forreproduction was similar to its survival range,but S. punctillum failed to reproduce at14 °C and reproduced only poorlyat 16 °C. Offspring production peakedat 24 °C for both T. mcdanieli(average 152 eggs per female), and S.punctillum (280 eggs per female). At alltemperatures suitable for reproduction, femalelongevity of the coccinellid was greater thanthe spider mite, which was characterized byearlier/faster reproduction than thecoccinellid. As temperature increased, therm followed a typical asymmetricaldome-shape pattern, with maximum values of0.196 d−1 and 0.385 d−1at 30 °C and 34 °C, for S.punctillum and T. mcdanieli,respectively. For each species, therm-temperature relation was successfullymodelled using a curvilinear regressionequation previously shown to predictdevelopment rate. In both species, thedevelopment rate response to temperature has amajor influence on the temperature-rmrelationship. In the 16–32 °C rangesuitable for population growth of both species,the rm of T. mcdanieliwas 1.9 (30 °C) to 8 (16 °C) times greaterthan S. punctillum. These growthpotential ratios are consistently in favor ofthe prey, suggesting a limitation of thecoccinellid with respect to its capacity totrack T. mcdanieli populations. However,under short season conditions, the inferiorreproductive dynamics of S. punctillum'svs. spider mite prey should not have aprevailing influence in determining impact, andmay be compensated by high voracity incombination with a strong aggregativeresponse.

Critical periods of weed competition in cotton in Greece

Four experiments were conducted in central Greece during 1997 and 1998 to determine the late-season presence of weeds in cotton (Gossypium hirsutum L.) and the critical times for removing weeds. Experiments were conducted in natural, heavily infested cropland. The presence of weeds for more than 3 weeks after crop emergence caused significant reductions in crop growth and lint yields. However, weeds that emerged 11 weeks or more after crop emergence did not adversely impact yields. Total weed biomass increased with increasing time prior to weed removal. A weed-free period of 11 weeks after crop emergence was needed to prevent significant reductions in cotton height, biomass, number of squares, and yield. These results indicated that postemergence herbicides or other control measures should be initiated within 2 weeks after crop emergence to avoid significant yield reduction. For greater efficiency, soil-applied herbicides in cotton should provide effective weed control for at least 11 weeks. Curvilinear regression equations were derived to describe the relationship between critical periods of weed presence and cotton growth and fruit development.

Peak expiratory flow in normal healthy Japanese adults: Comparisons with values reported in other races

We investigated the relationship between peak expiratory flow (PEF), age and standing height in 2785 Japanese volunteers (1047 males), aged 15–84 years, who had never smoked and who satisfied other strict criteria of normality. Many reports of regression equations for PEF by country and ethnicity are prepared using Wright or mini-Wright PEF meters, which have been calibrated by human subjects. Yet, no study has been performed in any country to determine the reference values of PEF on the American Thoracic Society (ATS) scale, which is calibrated by a computerdriven mechanical pump. Peak expiratory flow was measured with mini-Wright meters calibrated on the Wright scale. All subjects were taught how to perform a forced expiratory maneuver: the highest of three PEF values was recorded and standing height was measured. The Miles equation was used to convert mini-Wright PEF values (traditional scale) to values using the new ‘mechanical’ PEF, which the ATS has recommended (ATS scale). In the analysis of the data, a model based on age, age squared and age cubed was used to derive curvilinear regression equations for PEF on age and standing height for each sex. There was adequate representation of subjects of each sex at all ages to 74 years. Curves plotted from the regression equations rose during adolescence and early adulthood, reached maximum values at 35 years in males and 40 years in females and then declined in an approximately linear manner. For both sexes, standing height fell progressively with increasing age. From the regression equations, predicted values of PEF can be derived for any Japanese adult aged 15–74 years. We were able to obtain predicted equations for PEF in normal Japanese adults using both the Wright and ATS scales. Direct comparison of our regressions with those reported in other populations was limited by differences in methodology and analysis. In comparable studies of Chinese and Indian populations, the PEF values in those studies were appreciably lower than ours. Our regressions were remarkably similar to those reported in a study of British subjects that used virtually identical entry criteria and methods.

Heart Rate and Oxygen Consumption of Exercising Gentoo Penguins

Heart rate () and oxygen consumption () were recorded from gentoo penguins walking on a variable-speed treadmill. After an initial increase, and increased linearly with walking speed. A curvilinear regression equation best described the relationship between and . Over a 3-d period, and were recorded continuously from six gentoo penguins that had been injected with doubly labeled water (DLW). When was used to predict over the 3 d, the estimate uwas not significantly different from the measured with an error (-1.0%) that was less than that produced by the DLW method (+ 1.6%). The estimate produced by the technique was also accurate when applied both to shorter periods (30 min) and to periods of activity and inactivity. Seven gentoo penguins were also swum in a water channel, and and were again recorded. The relationship between and determined from the birds in the water channel was not significantly different from that obtained from the walking birds. It is seems reasonable that, since the relationship of most behaviors of the penguin have been determined while the animal is walking and swimming, can be used to predict the metabolic rate of free-ranging animals.

Linear regression equations for modeling the submerged-arc welding process

Traditionally, curvilinear regression equations have been used for modeling the geometrical features of the submerged-arc welding process. However, recent investigation has shown that, due to low tolerance in some cases, it is not possible to include all variables in the regression analysis. This investigation was therefore carried out to study the feasibility of using linear regression equations instead of curvilinear techniques to model the weld features. The linear regression equations are found to give correlation coefficients similar to those obtainable from curvilinear regression equations. The average mean, standard deviation, minimum value and maximum value of the deviations between the measured features and those computed by use of the linear regression equations are only slightly (1.38–5.40%) higher. Linear regression equations are equally suitable, therefore, for modeling the sub-merged-arc welding process.

Estimating seasonal herbage production of a semi‐arid grassland based on veld condition, rainfall, and evapotranspiration

Abstract The relation between above‐ground phytomass production and three independent variables, namely, seasonal rainfall, evapotranspiration (E t ) and veld condition, were investigated using fourteen years’ data (1977–1991) from the dry Themeda‐Cymbopogon grassveld of the central Orange Free State. The data showed that rainfall and E t have equivalent estimation value. The multiple curvilinear regression equation (r = 0.88) that was established, with seasonal rainfall and veld condition score as the independent variables, can be used with great success in this veld type to estimate seasonal production potential. In terms of the above‐ground phytomass production, it would appear that veld in good condition responds more efficiently to rainfall than veld in poor condition. Basal cover decreased linearly with a deterioration in veld condition.

An analysis of curvilinear regression equations for modeling the submerged-arc welding process

Curvilinear regression equations have traditionally been used for modeling the weld bead geometrical features of the submerged-arc welding process, but, however, only the correlation coefficients have been reported. This investigation was carried out to study the relationship, if any, between the correlation coefficient and the standard deviation of the deviations between the predicted and measured values, with respect to melting rate, total fusion area, penetration, deposit area, bead height and bead width. It is found that there is no strong relationship between the correlation coefficient of a correlation equation and the standard deviation of the deviations between the predicted and measured values. A low correlation coefficient does not necessarily mean that there are standard-deviation consequences for weld-bead features. The statistical analysis has provided other useful information also. It is found that the mean deposit area obtained directly from the melting rate is higher, since it is assumed that all the melted metal goes into the weld deposit without any losses. It is estimated that the metal loss through vaporization is about 4% and 8% for positive electrode polarity and negative electrode polarity, respectively.

The Basingstoke Canal — Britain's richest waterway under threat: A. Byfield, British Wildlife, 2(1), 1990, pp 13–21

The key to stopping high-frequency or catastrophic wildfires in the western U.S.A. is the successful restoration of burned lands to functional plant communities. Developing models of seedling establishment for invasive and native species will help in the selection of species for restoration projects that are able to establish and compete with invasive species given the abiotic conditions of specific sites. Modeling germination is the first step in modeling seedling establishment. We developed thermal germination models and compared predicted and measured germination timing in incubators as a precursor to testing germination model prediction in field seedbeds. We incubated 11 revegetation species and three weed (Bromus tectorum L.) seedlots at constant temperatures to develop linear and curvilinear regression equations to estimate days to 10, 25, and 50% germination for each seedlot. We compared actual time to germination with predicted time for three field-simulated diurnal temperature regimes representing March, mid-March to mid-April, and May temperatures in a big sagebrush (Artemisia tridentata Nutt. ssp. wyomingensis Beetle & Young) plant community. Bromus tectorum seedlots germinated faster than perennial grasses and forbs, especially at cooler temperatures. However, most of the revegetation species had high and fast germination for a wide range of temperatures. Germination time generally fit constant temperatures well with R2 values ≥ 0.85 for 33 of 40 linear equations and ≥0.80 for 40 of 48 curvilinear equations. Models overestimated germination time for field-simulated diurnal temperatures by 1–4 days for most seedlots. Model accuracy was sufficient for most seedlots to encourage subsequent testing of model accuracy under field conditions.

Effects of tidal stage and sun angles on intertidal benthic microalgal productivity

Motile benthic diatoms exhibit rhythmlc vertical migrations that are influenced by tidal and llght cycles. As a consequence of these periodlc migrations, corresponding periodicities in benthic microalgal production should occur. Using oxygen microelectrodes, hourly measurements of microalgal production were obtained from subaerially exposed cores collected from low-intertidal muddy sediments in North Inlet estuary, South Carolina, USA Microalgal productivity at low tide was twce that at high tlde (mean difference 52 %) and was significantly correlated with diurnal and tidal periodicities (r2 = 0.41; p < 0.0001). Production values ranged from 28.0 to 460.5 pm01 O2 mg chl a-' h' and maximum rates were achieved during mid-afternoon low tides. A curvilinear regression equation was constructed to simulate daily and monthly benthic microalgal production based on tidal and light cycles. Comparisons between predictions of the curvilinear equation and published data sets showed a reasonable agreement (r2 = 0.77), suggesting similar phenomena in other estuaries. Current benthic microalgal production models do not account for hourly variability in productivity, leading to potentially large errors when measurements are extrapolated over monthly and annual time scales. Although other physiological and abiotic factors also influence benthic microalgal productivity, much of the short-term variability in production rates may be simply attributed to migratory rhythms within estuarine sediments.

Citrus Root Growth as Affected by Soil Aluminum Level under Field Conditions

AbstractMost research on the effects of Al on citrus rootstocks has been limited to nutrient‐solution studies. This study employed an implanted soil‐mass technique to determine the effects of Al level in soils on growth and mineral content of fibrous citrus roots under field conditions. The implanted soil, E horizon material from an Immokalee fine sand (sandy, siliceous, hyperthermic Arenic Haplaquod), had a pH of 4.2 and a very low exchangeable‐Al content. It was either limed, unamended, or amended with three levels of Al using AlCl3. Each of the five treatments was replicated 15 times. Mesh bags containing the treated soil were placed in holes at the drip line of mature trees (Citrus aurantium L. sour orange rootstock) in a producing citrus grove. The bags were removed after 46 d. Results showed that, at a concentration of 9.14 mg Al L−1 of soil saturation extract, root density was twice that of the unamended treatment (0.13 mg Al L−1) and equaled that of the lime treatment (0.03 mg Al L−1). More roots grew into the bag, and they produced more lateral roots. Aluminum concentrations in roots were lower than those in the unamended treatment, however. Root‐length density decreased to about 60% of the value for the unamended treatment when Al concentration increased to 34.60 mg L−1. The optimum Al concentration for root growth appears to be 10 mg L−1 calculated by a curvilinear regression equation. In general, the concentrations of Zn, Fe, and Mn in roots decreased with increased Al application to the soil, while concentrations of Ca, Mg, K, P, and B were unchanged.

World patterns and amounts of detrital soil carbon

AbstractSoil carbon data were collected from published sources for 50 measurement sites spanning the globe's major climate and vegetation types. For each site, climate, vegetation, and land‐use variables were determined and entered into a multiple curvilinear regression program to predict soil carbon. The best model incorporates an estimate of site disturbance, annual actual evapotranspiration, and annual soil moisture deficit, and yields an R = 0‐803. The curvilinear regression equation was coupled with a large climatic database and computer cartography programs to produce first‐generation maps of estimated soil carbon. These maps correctly portray soil carbon as high in boreal and cool temperate zones and low in deserts and tropical zones.Computer planimetry of maps of soil carbon for an ‘undisturbed’ world and for a ‘disturbed’ world resulted in estimates of 1457 × 109 mtC and 504 × 109 mtC respectively. These estimates compare favourably with recent estimates using other approaches. Clearly, the disturbance factor is critical to future refinements in estimates, suggesting the need for detailed studies of the relationship between land‐use history and the creation and destruction of this important carbon pool.

Fiber Size Distribution, Bulk Density, and Ash Content of Peats in Minnesota, Wisconsin, and Michigan

AbstractBoelter (1969) described the physical characteristics of some undrained organic soils in northern Minnesota. This paper expands upon Boelter's work. Bulk density, ash content, and percent (dry weight basis) of rubbed and unrubbed fiber &gt; 2.0 mm, 1.0 – 2.0 mm, 0.5 – 1.0 mm, 0.25 – 0.5 mm, and 0.1 – 0.25 mm were determined for 176 peat samples from 38 peatlands in northern Minnesota, Wisconsin, and the Upper Peninsula of Michigan. When the distribution of various sizes of plant fibers in the peat is used as an index of the stage of peat decomposition, the increase in bulk density that accompanies increasing decomposition is easily seen. Fibers &gt; 0.5 mm predominate in low bulk density peats, but are quickly lost as decomposition proceeds and bulk density increases. Curvilinear regression equations between bulk density and rubbed and unrubbed fiber &gt;0.5, &gt;0.25 and 0.1 mm were developed that represent improvements over such equations previously calculated for northern Minnesota peats only. At the same bulk density, moss peats contained larger amounts of fiber than herbaceous peats; the unrubbed fiber content of the woody peats studied was higher than that of moss peats, but fell to an intermediate level between moss and herbaceous peats when subjected to rubbing. When a dispersing agent such as sodium metaphosphate (NaPO3) is used before sieving and percent fiber is calculated on a dry weight basis, the traditional rubbed fiber content appears to have little advantage over unrubbed fiber content as a descriptive criterion for characterizing organic soil.

Cotton Allelochemics and Growth of Tobacco Budworm Larvae1

Eight alleged allelochemics that naturally occur in cotton, Gossypium hirsutum L., or as a constituent part, were added to a commercial wheat‐germ diet at various concentrations. Neonate larvae of tobacco budworm [Heliothis virescens (F.)] were allowed to feed for 5 days and then weighed to determine the effects of allelochemics on larval growth. Regression equations were fitted to the data. A linear regression in the form Y = a + bX described the relationship for cyanidin, delphinidin, and gossypol up to 0.20% in the diet. A curvilinear regression equation in the general form of Y = aXb described the relationships for catechin, condensed tannin, chrysanthemin (cyanidin ‐3‐β‐glucoside), isoquercitrin, and quercetin. These were fed at higher levels (up to 1%) than the three allelochemics fitted with the linear regression equation. The level of each allelochemic in cotton required to reduce larval weight 90% is within the range of the amounts found in various cotton strains and primitive accessions. All except gossypol are found in several plant families and may thus be useful in developing plant resistance to tobacco budworm in several plant families. Several species of Heliothis are pests of economic importance worldwide.

Associations of cadmium with zinc and copper in cancer cases and controls

This study was performed in order to search for possible associations between cadmium (Cd) and other metals~ Cd, zinc (Zn), and copper (Cu) levels of renal cortex and liver samples obtained from 196 cancer cases and 198 noncancer controls were analyzed in eight regional institutes in Japan. Cd, Zn, and Cu concentrations in liver and renal cortex of the selected cancer cases were compared to the controls whose localities, age, and sex were matched with the cancer cases. The cancer cases clearly showed higher accumulations of Zn in liver and renal cortex than the noncancer group. Cd showed a similar tendency, but there was no statistical significance between case and control subjects. There was no marked difference in Cu accumulation between the pairs.The best fit regression curve of Zn to Cd on a molar basis in renal cortex was obtained. Curvilinear regression equations of Zn to Cd for both cancer and noncancer groups were drawn. From these two equations, the Zn level of the cancer cases was found to reach a maximum when the Cd level showed 1.4 mmol/kg (157 pxg/g), whereas Zn in the noncancer group peaked at 1.6 mmol/kg (180 Ixg/g) of Cd in renal cortex. This may suggest that excessive Cd accumulation deprives binding sites of Zn in renal cortex when both metals are saturated.

Effect of surface hardness on the wear resistance of steel 40Kh under hydroabrasive wear

This article presents equations which can be used in the selection of optimal correlations of the hardness of the surface layer of steel 40Kh and the abrasive filler in the design and manufacture of components of oil-well equipment operating under conditions of hydroabrasive wear. An experiment was conducted to determine the relation of the surface hardness of steel 40Kh to wear resistance under hydroabrasive wear in a slurry stream. The test conditions were: velocity of the hydroabrasive stream of 15 m/sec, abrasive concentration in the slurry of 50 g/liter, quartz abrasive sand from the Karadag sand pit with a grain size of 0.2-0.315 mm and microhardness of 11,000 N/mm/sup 2/, medium of technical water, and test duration of 5 h. It is determined that the approximation of the relation of the amount of wear of steel 40Kh to the surface hardness by means of a curvilinearregression equation makes it possible to determine more accurately the nature and amount of wear of steel 40Kh under hydorabrasive wear in a slurry stream.