A method of resume-training of discontinuous wear state trackers for composing boosting high-accurate ensembles needed to regard ... Проблеми трибології (Problems of Tribology) 2015, № 3 19 Romanuke V.V. Khmelnitskiy National University, Khmelnitskiy, Ukraine E-mail: romanukevadimv@gmail.com A METHOD OF RESUME-TRAINING OF DISCONTINUOUS WEAR STATE TRACKERS FOR COMPOSING BOOSTING HIGH-ACCURATE ENSEMBLES NEEDED TO REGARD STATISTICAL DATA INACCURACIES AND SHIFTS UDC 539.375.6+539.538+519.237.8 For tracking metal wear states at bad statistical data inaccuracies and shifts, there is a method of resume-training of discontinuous wear state trackers for boosting them within high-accurate ensembles. These trackers are Gaussian-noised- data-trained two-layer perceptrons. An ordinary tracker is selected and, if its performance is satisfactory, it is resumed-trained cyclically. Number of additional passes of training sets is limited. The resume-training procedure wholly can be cycled. Key words: metal wear, wear state tracker, statistical data inaccuracies and shifts, boosting high-accurate ensemble. Use of discontinuous wear state trackers Particularly, discontinuous wear state trackers (DWST) allow to watch and control metal wear states (MWS), whose range is sampled into a scale starting from the initial wears and ending up to the ultimate wears. DWST get a set of wear influencing factors (WIF), including direct (speed, pressure, temperature, etc.) and indi- rect (time duration) ones, and return the wear state number (WSN). According to WSN, the controller assigns an operating mode, load, pressure, torque, cooldown, if any. If WSN is returned inaccurate, its aftermath influences badly on both the processed metal billets and metal tools. In their compositions, DWST are boosted up [1, 2] to a high-accurate DWST ensemble (HADWSTE) capable to track MWS at bad statistical data inaccuracies and shifts (SDIS). Any other compositions of wear predictors issuing from stochastic differential equations track worse as wear increases. For composing HADWSTE, however, DWST of perfected accuracy are required as well. Composing HADWSTE for tracking MWS at higher intensities of SDIS Two-layer perceptron with nonlinear transfer functions (2LPNLTF) is a universal statistical approxima- tor, fitting to track MWS [1]. For its identification, it requires finite statistical data set (FSDS)   1 , L L jj j F w   X including each of  \ 1N  wear states by  \ 1, 1L N  and the j -th WSN  1,jw N for Q  WIF within the point 1 j j i Q x X     X . FSDS is accumulated via assigning the fixed original groups of WIF to WSN. These groups should be quite different. And if L N then there are similar WIF groups, among which unique groups are selected and assigned to their corresponding classes. Non-assigned groups are to be sent into training sets. These sets are   : sjis isQ N iy y x Y and     11 10, 1, , , 0, , 0, 1 , 0, , 1, :HR h h h is is is is sHR h hr hY h H h H H                          Y Y Y Ξ Θ Ξ ΘY         01, 1, , , 0, , 0, 1 , 0, , 10,R h h h is is is is sQ N Q NY h H h H H                           Ξ Θ Ξ Θ   (1) for WIF original groups and SDIS correspondingly, where    1 0; 1s Qj i i x   and  0R  , and  0, 1 is the infinite set of standard normal variate’s values. In statement (1), the term h Ξ models jitter inaccuracies and omissions in statistical data or measurements, and the term h Θ models WIF shifts in every state. Co- efficient 0 characterizes ultimate jitters and  is ratio between WIF shifts and the suspected jitters [2]. For tracking MWS at higher intensities of SDIS, HADWSTE is composed whose output is * 1, arg max s N ss m    by     * * * 1 B s sm m       at  * 0   * 1, B   and   * * 1 1 B      (2) by the * -th 2LPNLTF [2], giving the value  *sm  in its s -th output neuron weighted with  *  ,  \ 1B  . However, only high-accurate 2LPNLTF (HA2LPNLTF) are required for that. For example, for a problem of tracking 24 MWS with 16 WIF in [2], it had taken 17818 ordinary Gaussian-noised-data-trained A method of resume-training of discontinuous wear state trackers for composing boosting high-accurate ensembles needed to regard ... Проблеми трибології (Problems of Tribology) 2015, № 3 20 (GND-trained) 2LPNLTF by (1) with 70 hidden layer neurons by 1R  and 18H  for getting 60 HA2LPNLTF. Those 60 HA2LPNLTF were subsequently resume-trained (optimized) for making a better HADWSTE. The goal of making a set of HA2LPNLTF into HADWSTE for tracking MWS at bad SDIS As tracking MWS at bad SDIS is possible only under boosting HADWSTE of a set of HA2LPNLTF, a method of DWST resume-training shall be stated. It implies performance optimization of every HA2LPNLTF. After the optimization, HADWSTE shall perform closely to its best. Selection of HA2LPNLTF out of a set of ordinary GND-trained 2LPNLTF Suppose there is an aggregate of ordinary GND-trained 2LPNLTF, any of which cannot cope singly with tracking MWS at bad SDIS. Denote by    the averaged tracking error rate (TER) of the  -th 2LPNLTF along with its TER  ;H   at SDIS maximum. Selection of HA2LPNLTF out of the aggregate lies in accumulating such 2LPNLTF whose performance (in percentage) is either   max    or   max; H H    for some defined max or max H (Fig. 1). The selected 2LPNLTF is resume-trained until its performance is bettered enough. Total aggregate of ordinary GND-trained 2LPNLTF Selecting a 2LPNLTF Resume-train the selected 2LPNLTF   max    or   max; H H    Is performance bettered enough? Yes (True) No (False) Fig. 1 – Selection of an HA2LPNLTF out of the aggregate of ordinary GND-trained 2LPNLTF, and resume-training it subsequently Note that it is hard to know whether the performance could be bettered further. Therefore, the number of cycles of the resume-training will be limited. It is adjusted for each problem of tracking MWS at bad SDIS specifically. The same concerns those limits max and max H to sort out 2LPNLTF into HA2LPNLTF and others. Cyclic resume-training of the selected HA2LPNLTF Before boosting B HA2LPNLTF, they are resume-trained cyclically under the following parameters.  outer \ 1c  is number of outer cycles of repeating the resume-training over all B HA2LPNLTF, and an HA2LPNLTF is resume-trained for  inner \ 1c  inner cycles. The resume-training implies passing additional training sets HRY in (1) through HA2LPNLTF for A times. While passing, if the HA2LPNLTF perform- ance is not bettered for  0D  times by D A then the inner cycle is broken, HA2LPNLTF is not up- dated, and the next inner cycle begins. It runs while    * * *     by the current TER  * *  of the * -th HA2LPNLTF, but no longer than for innerc cycles. An outer cycle is ended with saving the set of the optimized HA2LPNLTF. The saved set HA2LPNLTFC is re-run within the inner cycles for outerc times (Fig. 2). Fig. 2 – MATLAB code of a script for cyclic resume-training of the selected HA2LPNLTF within the set HA2LPNLTFC A method of resume-training of discontinuous wear state trackers for composing boosting high-accurate ensembles needed to regard ... Проблеми трибології (Problems of Tribology) 2015, № 3 21 The code in Fig. 2 is adjusted for a problem of tracking at 0 0,12  and 1,5  by 1R  and 10H  . These magnitudes nonetheless can be changed easily in lines 1 and 2. The parameters of cyclic resume- training innerc , outerc , A , D are changed in line 6 as well. The exampled problem is of tracking 20 MWS by 10 WIF. Note that generalized regression neural network (GRNN) as a kind of radial basis network (RBF, often used for function approximation) solves it at poor TER (which, on average, is 3,92 % at least). Probabilistic neu- ral network (PNN) as a kind of RBF suitable for classification problems, tracks unstably and poorer. RBF itself, in different configurations, doesn’t track 20 MWS by 10 WIF at 0 0,12  and 1,5  appropriately. For the exampled problem, a 2LPNLTF tracker performs at    2, 9; 4,1   by 60 neurons in hidden layer and passing the training set 101Y in (1) through 2LPNLTF for 16 times. This is near-optimal 2LPNLTF configuration for that problem. Setting max 3  over 2000 ordinary GND-trained 2LPNLTF, we got 97 HA2LPNLTF performing at  * 3   * 1, 97   . Figure 3 shows results of running the code in Fig. 2. Fig. 3 – Six polylines whose vertices are the decreasing averaged TER, starting from the initial set HA2LPNLTFC (dots) and descending down through five successively optimized sets of HA2LPNLTF (circles, stars, squares, diamonds, and the best is thicker hexagrams) For severer selection with TER at 2,9 %, TER decreases tighter (Fig. 4). Predictably, at both Fig. 3 and 4 some points remain unmoved. Alto- gether there are three such points, where the single unmoved point occurred for severer selection. Discussion and conclusive remarks The resume-training method optimizes HA2LPNLTF performance, adjusting heuristically the number of passes of the training set in (1) through HA2LPNLTF. After the optimization, HADWSTE performs closely to its best, even under equally-weighted compositions [2]. Thus the inner cycles’ limit should be extended if selection be- comes severer. For a problem of tracking 20 MWS by 10 WIF, 97 HA2LPNLTF are selected, whose averaged TER is decreased off 2,92 % down to 2,7 % owing to five cycles of the resume-training. TER of 32 HA2LPNLTF selected by severer condi- tions, is decreased off 2,83 % down to 2,69 %. Fig. 4 – Descending TER of 32 HA2LPNLTF for severer selection For tracking MWS at bad SDIS, boosting by HADWSTE is far beyond better than RBF, GRNN, PNN, or their combinations. But boosting has its own limit [1, 2]. This limit may be revealed nearly by sufficiently great numbers of outer and inner cycles, and number of passes of the training set in (1) through HA2LPNLTF. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 2.57 2.58 2.59 2.6 2.61 2.62 2.63 2.64 2.65 2.66 2.67 2.68 2.69 2.7 2.71 2.72 2.73 2.74 2.75 2.76 2.77 2.78 2.79 2.8 2.81 2.82 2.83 2.84 2.85 2.86 2.87 2.88 2.89 2.9 2.91 8 9 10 11 12 13 14 15 16 17 18 2.64 2.652.66 2.672.68 2.69 2.7 2.71 2.72 2.73 2.74 2.75 2.76 2.77 2.78 2.79 2.8 2.81 2.82 2.83 2.84 2.85 2.86 2.87 2.882.89 2.9 1 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 97 2.42 2.47 2.52 2.57 2.62 2.67 2.72 2.77 2.82 2.87 2.92 2.97 3 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 2.67 2.72 2.77 2.82 2.87 2.92 2.97 3 12 13 14 15 2.67 2.72 2.77 2.82 2.87 2.92 2.97 3 80 81 82 83 84 85 2.42 2.47 2.52 2.57 2.62 2.67 2.72 2.77 2.82 2.87 2.92 2.97 A method of resume-training of discontinuous wear state trackers for composing boosting high-accurate ensembles needed to regard ... Проблеми трибології (Problems of Tribology) 2015, № 3 22 Like boosting, resume-training has its own limit also. Nonetheless the limit, the severer selection of HA2LPNLTF isn’t necessarily followed by greater number of TER points remaining unmoved. Here decrement of the averaged TER just grows down. References 1. Romanuke V.V. Optimizing parameters of the two-layer perceptrons’ boosting ensemble training for accuracy improvement in wear state discontinuous tracking model regarding statistical data inaccuracies and shifts / V.V. Romanuke // Problems of tribology. – 2015. – N. 1. – P. 65 – 68. 2. Romanuke V.V. Equally-weighted compositions of Gaussian-noised-data-trained two-layer percep- trons in boosting ensembles for high-accurate discontinuous tracking of wear states regarding statistical data in- accuracies and shifts / V.V. Romanuke // Problems of tribology. – 2015. – N. 2. – P. 53 - 56. Поступила в редакцію 02.07.2015 Романюк В. В. Метод донавчання відслідковувачів дискретного стану зносу для складання бустинго- вих високоточних комітетів, необхідних для урахування похибок і зсувів у статистичних даних. Для відслідковування станів зносу металу за значних похибок і зсувів у статистичних даних пропонується метод донавчання відслідковувачів дискретного стану зносу з метою їх підсилення у високоточних комітетах. Цими відслідковувачами є двошарові персептрони, навчені на даних з гаусовими шумами. Відбирається звичайний відслідковувач і, якщо його продуктивність задовільна, він циклічно донавчається. Кількість додаткових подач нав- чальних множин обмежується. Повна процедура донавчання може бути зациклена. Ключові слова: знос металу, відслідковувач стану зносу, похибки і зсуви у статистичних даних, високоточний комітет бустингу.