Remaining useful life (RUL) prediction plays a significant role in the health prognostic of lithium‐ion batteries (LIBs). The capacity or internal resistance is commonly used to quantify degradation process and predict RUL of LIB, but those two indicators are difficult to be obtained due to complex operational conditions and high costs, respectively. To address this issue, we extract a novel health indicator (HI) from the battery current profiles that can be directly measured online. Furthermore, the indicator is optimized by Box‐Cox transformation and evaluated by correlation analysis for degradation modeling accurately. Finally, relevance vector machine (RVM) algorithm is utilized to make a probabilistic prediction for battery RUL based on the extracted HI. The correlation analysis verifies the effectiveness of the novel HI, and comparative experiments demonstrate the proposed method can predict RUL of LIB more accurately.

Remaining useful life (RUL) prediction plays an important role in the prognosis and health management of lithium-ion batteries (LIBs). This paper proposes a new method based on the Wiener process for the RUL prediction of LIBs. Firstly, a state-space model based on the Wiener process is constructed to describe the LIBs degradation process, which considers the four variability sources of the degradation process simultaneously. Then, the model parameters are initialized using maximum likelihood estimation (MLE) and dynamically estimated by an unscented particle filter (UPF) algorithm. Finally, through comparison with other models, the proposed method shows its effectiveness and superiority in describing the degradation process and RUL prediction of LIBs.

The average bit error rate (ABER) and capacity of multiuser diversity freespace optical (FSO) systems with Nth best user selection scheme are investigated by considering atmospheric turbulence-induced fading. The atmospheric turbulence channel is modeled by the exponentiated Weibull distribution, and it can accurately predict the probability density function of the irradiance fluctuations in weak-to-strong turbulence regimes under all aperture averaging conditions. With the help of the Gauss-Laguerre quadrature rule, the analytical expression of ABER is derived and studied with different receiver aperture sizes, turbulence strength values, user numbers K, and orders N. Results show that, under moderate turbulence condition, the mitigation effect of aperture averaging for ABER degradation by decreasing K or increasing N is more significant than that of weak turbulence condition. The average capacity is then achieved on the basis of the second kind Stirling number and Meijer's G-function. The investigation on the average capacity shows that a higher capacity can be obtained in the strong turbulence regime than that in the weak turbulence regime, and this improvement is more significant with large receiver aperture size. Monte Carlo simulation and Romberg integration are first provided to verify the proposed analytical ABER and average capacity expressions, respectively. This paper benefits the design and development of multiuser FSO systems.

The average bit error rate (ABER) and outage performances of decode-and-forward (DF) based multi-hop parallel free-space optical (FSO) communication system with the combined effects of path loss, pointing errors (i.e., misalignment fading), and atmospheric turbulence-induced fading modeled by M distribution have been investigated in detail. Particularly, the end-to-end probability density function (PDF) and cumulative distribution function (CDF) over the aggregated fading channel are derived for the first time. Based on the binary phase-shift keying (BPSK) subcarrier intensity modulation scheme, the analytical expressions for the end-to-end ABER and outage probability are obtained, respectively. The ABER and outage performances of the present FSO system are then analyzed systematically with the effects of turbulence strengths, weather conditions, pointing errors, and structure parameters (M and N) taken into account. This study shows that the turbulent atmosphere, weather conditions and pointing errors can be mitigated by increasing the number of cooperative path (N) over M fading channels. For the fixed hop length, the FSO system performance will be degraded with the increasing hop numbers (M). But the performance will be improved with the increasing hop numbers (M) when the total distance from the source to destination is fixed. Monte Carlo simulation is also provided to verify the correctness of the proposed ABER expression.

The impact of nonzero boresight pointing errors on the system performance of decode-and-forward protocol-based multihop parallel optical wireless communication systems is studied. For the aggregated fading channel, the atmospheric turbulence is simulated by an exponentiated Weibull model, and pointing errors are described by one recently proposed statistical model including both boresight and jitter. The binary phase-shift keying subcarrier intensity modulation-based analytical average bit error rate (ABER) and outage probability expressions are achieved for a nonidentically and independently distributed system. The ABER and outage probability are then analyzed with different turbulence strengths, receiving aperture sizes, structure parameters (P and Q), jitter variances, and boresight displacements. The results show that aperture averaging offers almost the same system performance improvement with boresight included or not, despite the values of P and Q. The performance enhancement owing to the increase of cooperative path (P) is more evident with nonzero boresight than that with zero boresight (jitter only), whereas the performance deterioration because of the increasing hops (Q) with nonzero boresight is almost the same as that with zero boresight. Monte Carlo simulation is offered to verify the validity of ABER and outage probability expressions.

The end-to-end (EE) average bit error rate (ABER) performance of a decode-and-forward-based multihop free-space optical communication system is investigated over composite exponentiated Weibull fading channels with nonzero boresight pointing errors considered. In particular, the cumulative distribution function of the aggregated fading channel for non-identically and independently distributed multihop system is derived. Then, the analytical expression of EE ABER with $M$ -ary phase shift keying subcarrier intensity modulation is achieved in terms of Gauss–Laguerre quadrature rule considering aperture averaging effect. The results show that the ABER performance is mainly limited by nonzero boresight pointing errors for larger receiver aperture size. The comparison with Monte Carlo simulation verifies the validity of the proposed ABER model.

The average bit error rate(ABER) performance of a decode-and-forward(DF) based relay-assisted free-space optical(FSO) communication system over gamma-gamma distribution channels considering the pointing errors is studied. With the help of Meijer’s G-function, the probability density function(PDF) and cumulative distribution function(CDF) of the aggregated channel model are derived on the basis of the best path selection scheme. The analytical ABER expression is achieved and the system performance is then investigated with the influence of pointing errors, turbulence strengths and structure parameters. Monte Carlo(MC) simulation is also provided to confirm the analytical ABER expression.

The performances of multihop parallel free-space optical (FSO) cooperative communication systems with decode-and-forward protocol under exponentiated Weibull (EW) fading channels have been investigated systematically. With the max-min criterion as the best path selection scheme, the probability density function and the cumulative distribution function of the max-min EW random variable are derived. The analytical expressions for the average bit error rate (ABER) and outage probability with identically and independently distributed (i.i.d.) links are then obtained, respectively. Based on it, the ABER for a non-identically and independently distributed (non-i.i.d.) FSO system is also deduced with the help of the Gauss-Laguerre quadrature rule. The ABER performance of the considered system are further analyzed, in detail, under different turbulence conditions, receiver aperture sizes, and structure parameters (R and C). The comparison between i.i.d. and non-i.i.d. FSO systems over EW fading channels shows that the performances of both systems could be improved with large aperture diameters adopted for the structure parameters R and C selected. Monte Carlo simulation is also provided to confirm the correctness of the analytical ABER expressions. This work presents a generalized system model, and it can be used to analyze and design FSO communication systems.

The performances of the decode-and-forward (DF) multihop free-space optical communication system with exponentiated Weibull distribution considering the fading induced by pointing error have been studied. With Meijer's G-function, the probability density function (PDF) of the aggregated channel model and the closed-form expression for the average bit error rate (ABER) of binary pulse position modulation are derived. The average bit-error-rate performance is then investigated with different hop numbers $H$ , turbulence strength values, receiver aperture sizes, beamwidths, and jitter variances. Compared with the case without pointing error, the mitigation effect of aperture averaging for fading is more significant over the aggregated channel, regardless of the selected $H$ , and it is less effective for the degradation induced by the increase in $H$ , which can be restrained by larger beamwidth and lower jitter. The outage probability is also investigated, and the results show that aperture averaging has less of an effect on the outage probability under moderate turbulence than that under the weak turbulence condition at a given value of $H$ , which is different from the scenario without pointing error. After this, the end-to-end average capacity is analyzed. Monte Carlo simulation is provided to confirm the validity of the proposed ABER expression.

Based on the space diversity reception, the binary phase-shift keying (BPSK) modulated free space optical (FSO) system over Málaga (M) fading channels is investigated in detail. Under independently and identically distributed and independently and non-identically distributed dual branches, the analytical average bit error rate (ABER) expressions in terms of H-Fox function for maximal ratio combining (MRC) and equal gain combining (EGC) diversity techniques are derived, respectively, by transforming the modified Bessel function of the second kind into the integral form of Meijer G-function. Monte Carlo (MC) simulation is also provided to verify the accuracy of the presented models.

The average bit error rate (BER) for binary phase-shift keying (BPSK) modulation in free-space optical (FSO) links over turbulence atmosphere modeled by the exponentiated Weibull (EW) distribution is investigated in detail. The effects of aperture averaging on the average BERs for BPSK modulation under weak-to-strong turbulence conditions are studied. The average BERs of EW distribution are compared with Lognormal (LN) and Gamma-Gamma (GG) distributions in weak and strong turbulence atmosphere, respectively. The outage probability is also obtained for different turbulence strengths and receiver aperture sizes. The analytical results deduced by the generalized Gauss-Laguerre quadrature rule are verified by the Monte Carlo simulation. This work is helpful for the design of receivers for FSO communication systems.